Electroacoustics: The Analysis of Transduction, and its Historical Background [Reprint 2014 ed.] 9780674183582, 9780674334861

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ELECTROAGOUSTICS

HARVARD MONOGRAPHS IN APPLIED SCIENCE These monographs are devoted primarily to reports of University research in the applied physical sciences, with especial emphasis on topics that involve intellectual borrowing among the academic disciplines. 1. M A T R I X ANALYSIS OF ELECTRIC NETWORKS,

2.

EARTH WAVES,

P. Le Corbeiller

L. Don Leet

3 . T H E O R Y OF ELASTICITY AND PLASTICITY,

4 . MAGNETIC COOLING, C. G. B.

Η. M.

Westergaard

Garrett

Editorial Committee

F. V. Hunt, Chairman Howard W. Emmons L. Don Leet P. Le Corbeiller E. Bright Wilson Clifford Frondel Arthur Casagrande I Bernard Cohen

HARVARD

MONOGRAPHS

APPLIED

IN

SCIENCE

NUMBER

5

ELECTROACOUSTICS The Analysis of Transduction, and Its Historical Background

FREDERICK V. H U N T Rumford Professor of Physics and Gordon McKay Professor of Applied Physics, Harvard University

1954

Cambridge, Massachusetts HARVARD UNIVERSITY PRESS New York: JOHN WILEY & SONS, INC.

COPYRIGHT

PRINTED

1954 BY T H E P R E S I D E N T AND OF H A R V A R D COLLEGE IN

LIBRARY

THE

UNITED

OF

CONGRESS NUMBER

STATES

OF

CATALOG

54-8874

FELLOWS

AMERICA CARD

PREFACE

This monograph is concerned with three topics selected from the wide range of subject matter embraced by the general field of electroacoustics. The first of these is a long introduction devoted to the placement of electroacoustical transduction in its proper historical setting relative to the allied arts and to the basic sciences from which it derives. This is followed by three chapters that include the description of a new scheme for the analysis of both electrostatic and electromagnetic systems of electromechanical coupling in a single homogeneous frame of reference. This method of analysis is then illustrated in the succeeding chapters by examples of its application to three representative transducer systems. Electric-circuit analogs have been widely exploited as a tool for the study of acoustical and mechanical systems. They have been less widely used, however, for the representation of electromechanical transducers owing to the disparity in the symmetry conditions pertaining to electromagnetic and electrostatic coupling. I t has been standard practice to say that one type of analog recommends itself for use with one type of coupling, and that the "other" type must be used with the other — but never the twain could be connected back to back! I had been experimenting pedagogically since about 1937 with a method for resolving this dilemma by using a space operator to import analytical symmetry into the electromechanical-coupling equations for the antireciprocal cases involving magnetic fields. After the war, when there was an opportunity to reöxamine the question, it became possible to resolve the basic issues more clearly and to establish, on sound physical grounds, the validity of using such a space operator to restore symmetry in the analysis of electromagnetic coupling. As a consequence, it now becomes possible to give a unified discussion of all types of electromechanical coupling, including magnetic, electric, and mixed transduction fields. I hope that the novelty of this unified approach will justify in part the publication of this material in advance of the completion of the textbook in whose context it was first drafted. The ability to represent all transducer types with a single form of equivalent circuit makes it relatively more useful to invoke the methods of electric-impedance analysis for the study of transducer performance.

vi

PREFACE

These methods, like the use of equivalent circuits, had already been widely exploited but they were still further developed during the war period. The account of this subject appearing in Chapter 4 leans heavily on the work carried out under NDRC auspices at the Harvard Underwater Sound Laboratory during the period 1941-1945. Although the relevant results of these studies are no longer classified, in the military sense, the research reports have not been generally available and their only summary was incorporated in another document that could receive only limited distribution. Most of the novel features of this work originated with Malcolm H. Hebb and Harvey Brooks, but Francis P. Bundy and many other members of the HUSL staff contributed significantly, and the cogency of the summary report owed much to Paul E. Sabine. In marshaling this material, I have attempted to act as spokesman for this group of wartime colleagues. None of them can be held responsible, however, for the form of presentation I have adopted, since substantial changes from the original have been introduced in order to adapt the procedures to the broadened frame of reference. The primary generic types of electromechanical coupling include two that make use of a magnetic field and one that uses an electric field. These are exemplified by movable conductors in a fixed magnetic field, by fixed conductors linking a variable magnetic field, and by movable conductors bearing fixed or variable electric charges. The last two categories embrace both lumped-constant systems, such as the movingarmature earphone and the electrostatic loudspeaker, and distributedconstant systems, such as magnetostriction and piezoelectric transducers. Although the methods of analysis presented here are equally applicable to all these transducer types, the gamut of analytical procedures can be illustrated adequately, and a good bit more succinctly, in terms of the lumped-constant systems. This is fortunate, since an adequate discussion of magnetostriction and piezoelectric transducers could not have been included in any case without far exceeding the dimensional limitations of the monograph format. As a consequence, the consideration of these distributed systems, in which electromechanical coupling is effected through body forces, is perforce relegated to a later monograph or other publication. In the original form of these notes, a few "firsts" had been mentioned casually as an introduction to the various sections devoted to specific mechanisms of transduction. The process of recasting the material in the form of a monograph provided an opportunity to broaden the scope of

PREFACE

vii

these historical allusions and to draw them together into a coherent introduction designed to exhibit electroacoustical transduction in its relevant historical context. There is a close parallelism between electroacoustics and the science of electrical communication, and the mushroom expansion of the latter industry has provided incentive for the publication of many accounts dealing with the history of its growth. Some of these accounts contain useful material bearing on electroacoustics, but I had been well coached about not relying on such secondary sources except as an auxiliary guide in prospecting for original source material. For better or worse, these historical notes are based on the cited primary sources, and while it may not be fluent history, I can at least guarantee that every bibliographical reference has been verified at first hand. Fortunately, most of the needed source material was available in the rich collections of the Harvard College Library, but a few items (identified by LC) had to be run to ground in the Library of Congress, a few in the Engineering Societies Library (New York) NNE , and a few in the Vail Library of the Massachusetts Institute of Technology MCM. I am also indebted to Mr. David P. Wheatland for graciously making available from his private collection the choice items listed in notes 10, 20, 21, and 68 to Chapter 1. The almost complete files of United States, British, and German patents maintained by the Boston Public Library were also invaluable. Some readers may be surprised by the prominent role played by patent references in the documentation of a history of transduction. However one may feel about the probity of scientists applying for letters patent, if one wishes to be realistic it is necessary to recognize that electroacoustical transduction is an applied science that presents both electricity and acoustics in their working clothes. It follows that many of the most significant gaitis in know-how, as well as in basic understanding, have made their earliest public appearance — and some, their only appearance — as publications of the Patent Office. On the basis of my experience in assembling the material for Chapter 1, I am persuaded that a good many scientists and most of the science historians have paid too little attention to this class of source material. I feel overwhelmed by the inadequacy of any acknowledgment I can record here of my indebtedness to others. Since this material has been accumulating throughout most of my adult life, the list needs to start with Professors G. W. Pierce and E. L. Chaffee, who initiated me into these mysteries a good many years ago. The history chapter presented

viii

PREFACE

many problems that were novel, at least to me, but generous help came from many quarters. Professor I Bernard Cohen was always ready with wise guidance, kindly criticism, and warm encouragement. Mr. David Rines, patent expert extraordinary, deepened my long-standing obligation to him by making available documents, briefs, his collection of patents, and much good advice. I am also indebted to several makers of this history who were kind enough to read and criticize relevant portions of the manuscript. Among these were Robert W. Boyle, Willoughby G. Cady, Edward W. Kellogg, Edward C. Wente, Raymond L. Wegel, Hugh S. Knowles, and Harry F. Olson. I owe special thanks to Mr. Fred J. Harbaugh for comments and many helpful leads to the patent literature on dynamic loudspeakers. To the students of many classes, and to my colleagues in our Acoustics Research Laboratory, I am deeply grateful for their patient forebearance through many long discussions of points and viewpoints. Professor Philippe Le Corbeiller has been a gracious tutor and a stout foil, and his careful reading and criticism of this manuscript now puts me further in his debt. I am in no position to deny that completing a first book has its painful moments, alike for the author and for his wife and son. Without their unfailing devotion and indulgence this book probably never would have been finished. F . V . HUNT

Belmont, Massachusetts December 1958

CONTENTS 1. Introduction — Historical Context 2. Electromechanical Coupling — General

1 92

3. Reciprocity and Symmetry Considerations in Electromechanical Coupling 4. Electrical-Impedance Analysis of Transducer Performance

103 117

5. Moving-Conductor (Dynamic) Transducer Systems

143

6. Electrostatic Transducer Systems

168

7. Moving-Armature (Magnetic) Transducer Systems

213

Appendix A. Dimensions and Units

236

Appendix B. Conversion Charts

238

Index of Names

247

Index of Subjects

255

CHAPTER

1

Introduction — Historical Context Electroacoustics is as old and as familiar as thunder and lightning, but the knowledge that is the power to control such modes of energy conversion is still a fresh conquest of science not yet fully consolidated. Like many other frontiers of acoustics, this one could only be attacked by flanking movements. Acoustical manifestations of electricity were in the forefront of notice throughout the shocking and crackling adolescence of static electricity during the 18th century, yet before a satisfying measure of control of these effects could be achieved, there had to be sought first an understanding of the underlying electrical phenomena. This was not to be the only course of evolution, however, for human needs sometimes assert themselves with irresistible insistence without waiting for calm scientific inquiry to run its own well-ordered course. Throughout man's history, his progress as a social being has been marked by ceaseless efforts to improve the means for moving about from place to place and for satisfying the universal urge to communicate. Common speech and the written word are still the staunchest bulwarks against isolation, but to extend the one and speed the other is a goal that challenges perpetually man's best creative effort. Since ancient times, men of practical science have sought to nourish this basic need for the sharing of perception by making available ever more useful instrumentalities for communication. Signal fires and smoke, the gleam of reflected sunlight, the beat of drums and flight of pigeons — every means for producing observable effects at a distance was bent in its own time and within its limitations to the task of serving man, as Hermes, the messenger and bearer of tidings, had served the gods. The momentous discovery,1 in 1729, that some substances "would 1 Stephen Gray, "A Letter to Cromwell Mortimer, M. D., Seer. R. S. containing several Experiments concerning Electricity," PAi/.[osopMcaQ Tra«i.[actions of the] Koy.Hal] Soe.pety] {London) 37, 1S-44 (1731-1732).

2

ELECTROACOUSTICS

carry the electrical vertue" while others would not, established almost at once the unique fitness of electricity as an agency for signal transmission. Few discoveries can be said to have had more profound influence on the course of history than this one, which established that electric energy could be transmitted from a point of origin to some other place where "the vertue" could be utilized. The subsequent history of discovery in electricity revealed many examples of electrical action — audible, visible, tactile, mechanical, and electrochemical, to mention only the simple ones. Patient study of such effects provided objectives for a century-long pursuit of theoretical understanding; but each novel effect was also greeted eagerly by those — and there were always some — who saw in each a new vehicle for the transmission of intelligence. The story of this dual search for utility and understanding, and of the proposals both fanciful and practical for exploiting one within the limitations of the other —• this is the transducer story. The word transducer is now used as a generic term denoting, in its broadest sense, any device or agency that serves the function of converting one form of energy into some other form. The nature of the energy exchange is often indicated by prefixing to the generic term a selfdefining compound modifier, as may be illustrated by defining an electroacoustic transducer as a device for converting electric energy into acoustic energy, or vice versa. The generality of this definition is greater than might be required if such devices had no other function than to serve as "terminal transducers" for communication systems, but such a limitation is implicitly denied. It is indeed to be acknowledged — proudly claimed, in fact — that the historical origins of electroacoustical transduction are inseparably linked with the early history of electrical communication. This close relationship continues to account for most, by far, of the transducers now in service throughout the world. The breadth and vigor of this market, awesome as it is in point of numbers, 2 should not, however, divert attention from the vital role played by a smaller class of specialized transducers that allow sound energy to serve directly in physical research and for the needs of industry. 2 The Radio-Television Manufacturers Association estimates that more than 206 million receivers have been made and sold by manufacturers in the United States alone during the thirty years 1922-1952, and that 130 million of these are currently in use. To these must be added the 168 million transducers accounted for by the 84 million telephones estimated by the American Telephone and Telegraph Company to be in public service throughout the world by the end of 1952. These figures do not include the transducers that have been required for military and miscellaneous end use.

HISTORICAL CONTEXT

3

Exciting new frontiers have been opened up for exploration by the 20th-century renaissance of physical acoustics. In the area of fundamental research, these frontiers often lie in zones of overlap with other disciplines, as illustrated by the use of sound in studies of such diverse topics as the behavior of viscous polymers, the structure of liquids and of metals, the distribution of temperature in the upper atmosphere or of fish in the sea, and the topography of ocean bottoms. The frontiers of applied acoustics are just as widely diversified. Modest beginnings have been made in exploring the use of sound waves, at both low and ultrasonic frequencies, for such operations as nondestructive testing, emulsification, flocculation, cleaning, and process control; and in the area of medical therapy. An even wider field for exploitation is suggested by the use of sound-wave agitation as a more effective agency than stirring for promotion of chemical reactions. One common feature of this catalog commands attention. I t is that every novel application requires a source of sound especially adapted to the circumstances of use. The pioneer is thus confronted at the outset, and at every reappearance of a speculative gleam in his eye, with a novel problem of transducer design. The moral is obvious, though hardly new. Professor Joseph Henry pointed it out to Alexander Graham Bell, who had consulted him in connection with his telephone experiments in 1875 and had lamented his "lack of electrical knowledge". Henry's advice 3 was sympathetic but brief; he said, "Get it." Terminology

Before coming to grips with the detailed analysis of mechanisms of transduction, it may be useful, or at least diverting, to extend these introductory remarks by surveying briefly the historical background of electroacoustical transduction. The kinship between the old and the new can be made more pointed, however, if the present nomenclature is first established. It is a secondary consequence of choosing a broad definition of electroacoustic transducers that a few acoustical orphans are accidentally included in the family, such as domestic or industrial machinery that produces sound or noise only as a by-product of normal operation. These can easily be excluded, however, by defining and applying additional criteria of electroacoustical performance, such as linearity, passivity,

and

reversibility.

• Incident related by Thomas Coulson in Joseph Henry, His Life and Work, p. 314 (Princeton, Princeton University Press, 1950). See also 126 U. S. 297 (cf. note 56 below).

4

ELECTROACOUSTICS

Transducers are linear if the principal variables describing their output, such as sound pressure and particle velocity (or electromotive force and current), are substantially linear functions of the related quantities describing the transducer input. The qualifying term "substantially" suggests that minor departures from linearity will not alter the classification, and that it is both proper and desirable to speak of evaluating the nonlinear (harmonic) distortion occurring in a transducer otherwise described as "linear." Transducers are passive if all the energy delivered to the electric (or acoustic) load is obtained from the energy accepted by the transducer from the acoustic (or electric) source. The term reversible indicates primarily the ability of a transducer to convert energy in either direction between the acoustic and electric forms, but the concept of reversibility is also used frequently in a more specialized sense to imply that energy conversion in either direction takes place with equal efficiency. Transducers used primarily to receive sound energy and deliver electric signals were, for a long time, referred to as transmitters in the specialized jargon of telephony, and their companion instruments for the converse transformation were called receivers. These designations are often ambiguous, however, and the ambiguity is enhanced when one or both instruments are inherently reversible; hence, such usage is now deprecated, except where it may be required for maintaining contact with previous literature. Transducers that function as sources or sinks for sound in air are now designated, in general conformity with American Standard Terminology,4 as earphones, loudspeakers, or microphones; and their companion instruments for use in water or liquids are called projectors or hydrophones. A good many sound generators, such as bells, automobile horns, and sirens, are not reversible; and although these sources are usually driven electrically and have a sound output that is roughly proportional to the electric input, they are not linear in the sense intended here since there is no correspondence of wave form between the electric input and the acoustic output. The carbon microphone, which has the distinction of being the only "bad connection" tolerated in the telephone system, is neither passive nor reversible, but prolonged development effort has endowed it with a relatively high degree of linearity, and it is still uni4

American Standard Acoustical Terminology, ZS4.1-1951, sponsored by the Acoustical Society of America and the Institute of Radio Engineers, and published by the American Standards Association, New York.

HISTORICAL CONTEXT

5

versally used throughout the telephone system. The thermophone, the hot-wire microphone, and the ionization microphone are examples of another class of transducers to which only a limited kind of reversibility can be ascribed. While the principles on which these devices operate can indeed be adapted for energy conversion or the control of energy flow in either direction, the design requirements for serving one function usually preclude the use of the same instrument for the converse function. Of course, the oldest of all the mechanisms of electroacoustics is one that generates impulsive sound by the sudden expansion of air heated by the energy released in an electric discharge — in short, the thunder and lightning referred to in the opening line. This one can certainly not be classed as reversible, although one might claim for it a distant-cousin relationship to the ionization microphone and the "ionic" loudspeaker. Another novel transducer that is not linear, not very reversible, and most certainly not passive, is the one based on the discovery that a musical note can be perceived when the ear is placed close to the arm or chest of a person through whose body is passing the intermittent current from a Ruhmkorff induction coil. One can surmise that there was little contest of the monopoly duly granted for the use of this transducer mechanism by a British patent 5 issued as recently as 1874! It is an almost universal feature of the conversion of electric energy into acoustic energy that the electric energy is first converted into the mechanical motion of a surface in contact with the acoustic medium. The "unconventional" transducers mentioned above are obvious exceptions, and the ingenious can undoubtedly (and did) invent others; but this author is not familiar with any exceptions that satisfy the joint conditions of passivity, linearity, and reversibility. Energy conversion in the reverse direction similarly involves the mechanical motion of a surface that is coupled to the electrical system and is driven by the forces arising in the acoustic medium. It is convenient, therefore, to assume that the transducer problem can be divided so that the electromechanical coupling and the coupling between the mechanical system and the sound radiation field can each be considered separately. In dealing only with the first of these problems, it will be presumed that a solution of the second is available,® so that the radiation loading of the mechanical system can 5

Elisha Gray, represented by John Henry Johnson, in whose name British Pat. No. 2646 was issued 23 October 1874 (complete specification filed 29 July 1874). • See, for example, L. L. Beranek, Acoustics (New York, McGraw-Hill, 1954); or H. F. Olson, Elements of Acoustical Engineering, 2nd ed. (New York, D. Van Nostrand, 1947).

6

ELECTROACOUSTICS

be adequately represented by a generalized mechanical radiation impedance connected, in effect, at the output terminals of the electromechanical system. Classification of the Mechanisms of Transduction The electromechanical coupling problem is the venerable one of the electric motor or the electric generator, here specialized to the case of linear vibration rather than rotation. Methods of coupling can be broadly classified according to whether the mechanical forces are produced by the action of electric fields on electric charges, or by the interaction of magnetic fields and electric currents. Each of these classes may be further subdivided, and in this way the five most important motor mechanisms involved in linear electroacoustic transducers can be characterized as follows. (a) Electrodynamic (dynamic): Motor and generator action are produced by the current in, or the motion of, an electric conductor located in a fixed transverse magnetic field. (b) Electrostatic: Motor action is produced by variations of the mechanical stress established by maintaining a potential difference between two or more electrodes, one of which is movable and usually comprises a very light, conducting diaphragm from which sound is radiated directly. The electric output of a condenser microphone comprises the variable charging current arising when the capacitance between a fixed electrode and the diaphragm changes as the diaphragm moves under the influence of a sound wave. (c) Magnetic: Motor action is produced by variations of the tractive force tending to close the air gap in a ferromagnetic circuit. Generated voltages appear in fixed coils linked with the magnetic circuit when the flux is changed by variations in the reluctance of the magnetic circuit. (id) Magnetostriction: Motor and generator action are derived from the direct and converse magnetostriction effect — an effect arising in a variety of ferromagnetic materials whereby magnetic polarization gives rise to elastic strain, and vice versa. (e) Piezoelectric (crystal): Motor and generator action are derived from the direct and converse piezoelectric effect — an effect arising in a variety of nonconducting crystals whereby dielectric polarization gives rise to elastic strain, and vice versa. The ingenuity of designers has led to the production of each of these transducer types in a wide variety of modifications, many of which have

HISTORICAL CONTEXT

7

been given descriptive designations. For example, electrostatic transducers are available in "push-pull" or "single-sided" versions; magnetic transducers in "balanced-armature" and "ring-armature" types, as well as in the form of the familiar bipolar earphone or "telephone receiver." Piezoelectric transducers may use various crystal " c u t s " that can operate in longitudinal, thickness, or shear vibration; or they may use composite "bimorphs" operating as "benders" or "twisters." Magnetostriction vibrators may occur as rods, tubes, scrolls, rings, or laminated stacks, and may use longitudinal, flexural, or radial vibrations. Electrodynamic coupling may involve "moving coil" or "ribbon" conductors which may be either conductively or inductively connected in external circuits. i8th-Century

Electrostatic

Transduction

The electric machines of the 18th century, with their whirling globes of glass or brimstone, provided experimenters with ample opportunity to become familiar with the loud impulsive sounds that accompany spark discharges in air. Accumulating the charge on a condenser or Leyden jar still further enhanced these noisy discharges. When the main spark could be caused to occur at some remote point, however, thus removing the primary acoustical distraction, it was usually possible to observe a faint clicking sound that seemed to emanate from the Leyden jar itself at the moment of discharge. This effect can now be identified as a shock excitation of compressional waves in the material of the jar, produced by the sudden release of electrostrictive stresses established by the electric charge. A ringing musical tone corresponding to the frequencies of mechanical resonance of the Leyden jar might have been expected to be elicited by this type of excitation, but the resonance vibrations died out so quickly, presumably as a result of the damping introduced by the foil electrodes, that only the click remained. Owing to a lack of the kind of incentive that would have been provided by identifying the source of these clicks, little further attention was devoted to the phenomenon. A similar clicking sound issuing at the discharge of a flat-plate condenser was observed much later, in 1863, by Lord Kelvin,7 who correctly inferred 7

Sir William Thomson (Lord Kelvin), in a letter to Professor P. G. Tait, dated 10 October 1863; reprinted in Kelvin's Papers on Electrostatics and Magnetism, §§ 302-304 (London, Macmillan & Co., 1872, 1884). [Can any reader supply an 18th-century reference to this phenomenon? I feel sure I have seen one and several of my friends think they have too, but 1 have not been able to relocate it. As for the phenomenon, I'm sure it exists, because I have heard the clicks myself, F.V.H.]

8

ELECTROACOUSTICS

that the cause of the effect must be closely related to the electrostatic stresses about which Faraday had speculated. Not long after the Leyden jar itself had been invented, Benjamin Franklin used one for an experiment that provides the first exemplar of controlled electromechanical transduction. When a terminal connected to the outer coating of the jar is brought near the central terminal, a light cork ball suspended between them will be attracted to one, will share its charge on impact, and will then be repelled from it and attracted toward the other terminal. Thus, as Franklin described the action, the ball "will play incessantly from one to the other, 'till the bottle is no longer electrised; that is, it fetches and carries fire from the top to the bottom [that is, from the inside to the outside coating] of the bottle, 'till the equilibrium is restored." 8a Franklin was primarily concerned with the demonstration this afforded of the equality of the charges on the inner and outer coatings of the Leyden jar. With characteristic promptness, however, the ingenious Mr. Franklin soon found an application for the motive principle in a multipole arrangement adapted for producing continuous rotation of a wheel. He called this an "electrical jack," and suggested that "if a large fowl were spitted on the upright shaft, it would be carried round before a fire with a motion fit for roasting." 8b Once the principle of this relaxation-type oscillator had been made known, Franklin regarded its electro acoustical modification as " a contrivance obvious to every electrician," 8c since it involved no more than mounting a bell on each terminal and substituting a light metal striker for the cork ball. When one bell is grounded and the other connected to an electrical machine, they would continue to sound as long as the potential difference was maintained. De Laborde proposed to use this striking mechanism as the basis for an "electrical piano" 8d in 1761, and similar "electrical chimes" were enjoyed as an electroacoustical toy throughout the following half century of waiting for electromagnetism to be discovered. Franklin had already made better use of the effect by 8b Benjamin Franklin, Experiments and Observations on Electricity, edited, with a critical and historical introduction, by I Bernard Cohen, p. 183 [in Letter III of 28 July 1747] and p. 189 (Cambridge, Harvard University Press, 1941). 8b Ibid., pp. 194-197. 80 Ibid., p. 268. 8d R. P. [Jean Baptiste] D e Laborde, Le clavessin electrique; avec une nouvelle tMorie du mechanisme et des phenomhnes de l'eleciricite (Paris, H. L. Guerin & L. F. deLatour, 1761).

HISTORICAL CONTEXT

9

arranging for such a pair of bells to signal the appearance of high potentials on the otherwise-ungrounded lightning rod he had installed on his house for experimental purposes in 1752.8e When his family finally tired of hearing the portentous ringing of these bells during Franklin's absences abroad, he sent to them from London a suggestion 8f that still retains its effectiveness as a means of evading electroacoustical insult — that a short piece of wire be firmly connected across the electrical terminals of the transducer! The Sympathetic

Telegraph

The earliest proposals for harnessing electricity in man's service took the form of primitive schemes that were suggested for realizing an electric telegraph. The basic concept of the telegraph itself is a very old one that sprang up long before science had made available the instrumentalities for realizing it in practice. The primitive notion usually took the form of a "sympathetic-needle" telegraph, and Fahie 9 has found references to the idea dating as far back as the 4th century. The first clear allusion to it, however, is probably that given in several places by Porta, 10 who simply stated with disarming presumption, "And to a friend that is at a far distance . . . we may relate our minds; which I doubt not may be done by two Mariners Compasses, having the Alphabet writ about them." A fuller description of this bit of science fancy, and one that came to be widely copied, was given a little later by Famianus Strada, who wrote in 1617 of two friends who maintained rapport by carrying 80 A full account in I B. Cohen, "The Two Hundredth Anniversary of Benjamin Franklin's Two Lightning Experiments and the Introduction of the Lightning Rod," Proceedings of the American Philosophical Society 96, 331-366 (June 1952), p. 352. 8f Albert Henry Smyth, The writings of Benjamin Franklin, vol. 3, pp. 438-443 (in 10 vols., New York, Macmillan, 1907). 9 J. J. Fahie, A History of Electric Telegraphy to the year 1837, pp. 20-25 (London, E. & F. N. Spon, 1884). For a tolerably complete summary of references, early and late, to the "sympathetic telegraph" idea, see also the Appendix, pp. 409-418 of vol. II, of Catalogue of the Wheeler Gift of Books, Pamphlets and. Periodicals [the Latimer Clark collection] in the Library of the American Institute of Electrical Engineers [New York], edited by Wm. D. Weaver (in 2 vols., New York, American Institute of Electrical Engineers, 1909). 10 Giambattista della Porta, Magiae Naturalis, sive de miraculis rerum naturalium, Libri IUI, in Lib. II, Cap. XXI, p. 89 (1st ed., small folio, Neapoli, Matthiam Cancer, 1558); also in Magiae Naturalis, Libri XX, in preface to Lib. VII (1st ed., small folio, Neapoli, Horatium Saluianum, D.D.LXXXVIIII. [recte 1589]); among the many later editions was one in English, Natural Magick: in twenty books (small folio, London, Thomas Young and Samuel Speed, 1658).

ELECTROACOUSTICS

10

"sympathetic loadstones" having dial plates inscribed with the letters of the alphabet. 11 When one friend turned the point of his compass needle to a selected letter, the other's instrument responded, as with . . . fond spontaneous sympathy; While his own steel in like rotation flies, And bids the gradual syllables arise: Each word he marks to full perfection brought, And eyes th' expressive point, interpreter of thought. No respecter of distance, this mode of communication! As Strada puts it, in the lyrical "Student" translation, Thus, if at Rome thy hand the steel applies, Tho' seas may roll between, or mountains rise, To this some sister needle will incline, Such nature's mystic pow'r, and dark design! Addison brought forward his translation of Strada's proposal as a suggested remedy for the plight of a wife who felt herself widowed by a husband's absence. Apparently he could not resist adding the suggestion that a good bit of time might be saved by including on the dial plate "several entire words which have always a place in passionate epistles" — a suggestion that has been not only accepted but extended by modern telegraph companies who offer reduced rates for the transmission of stylized greetings. The Electrostatic

Telegraph

More realistic proposals for communication by means of signals transmitted over wires began to appear during the middle of the 18th century, not long after Stephen Gray 1 had discovered that some materials would conduct electricity, and that the electricity could be confined to these pathways by isolating or supporting the conductors with other substances which were nonconductors. Most of these proposals involved as many wires between the terminals as there were different letters or symbols to be transmitted; and each wire was to be terminated by some form of electromechanical transducer — usually a modification of the suspendedpith-ball electrometer — for indicating which symbol was being trans11

Famianus Strada, Prolusiones academicae oratoriae, historicae, poeticae, etc., pp. 351-352 (8°, Coloniae Agrippinae, 1617). The quoted passages are taken from the lyrical translation titled "The Sympathetic Loadstones" in The Student, or, the Oxford and Cambridge Monthly Miscellany, vol. 1, pp. 354-356 (Oxford, 1750); also freely translated by Jos. Addison in The Spectator, No. 241, December 6, 1711.

HISTORICAL

CONTEXT

11

mitted. The first system of this kind to be constructively reduced to practice appears to be the one proposed, and said to have been set up at Geneva in 1774, by Georges-Louis Lesage.12 Others followed, and before the turn of the century transmission was reported for distances as great as 26 miles.13 The curious fixation on the notion that a separate wire must be provided for each transmitted character adhered to most of the telegraph proposals made before 1830, although single-channel systems began to make their appearance as early as 1795. In that year, Tiberius Cavallo 14 experimented with such a system, and there is a prophecy of modern pulse-time modulation in his suggestion that "by sending a number of sparks at different intervals of time according to a settled plan, any sort of intelligence might be conveyed instantaneously". Another scheme involving use of the time interval between pulses for encoding the transmitted information was proposed by Harrison Gray Dyar 1 6 in 1828. This system was operated over a single-wire line a few miles long (strung around a racetrack on Long Island, in fact), and employed an electrochemical process (spark discoloration of moist litmus paper) as the receiving transducer. It thus became the first recording telegraph system. The ancestry of the modern "ticker" telegraph can be traced back in a similar way to an experimental telegraph constructed by Sir Francis Ronalds 16 in 1816. In this system, rotating lettered dials at each end of the 8-mile line were kept in synchronism by mounting each one on the seconds shaft of a carefully regulated clock. The symbol to be transmitted was indicated by the response of an electrometer when a static charge was placed on the single-wire line just as the desired symbol passed the reference mark at each station. 12 Lesage's telegraph is described in a letter of 22 June 1782, quoted by M. 1'АЬЬё Moigno in Traiti de TeUgraphie Electrique, 2nd ed., part ii, p. 59 (Paris, A. Franck, 1852); Fahie (see note 9) questions whether this telegraph was actually built and his skepticism seems to be supported by the brief contemporary notice in Journal des Siavans, pp. 637-638 (1782). 1! This evidence is also questionable: see the discussion in Laurence Turnbull, The Electro-Magnetic Telegraph, 2nd ed., pp. 21-22 (Philadelphia, A. Hart, 1853). 14 Tiberius Cavallo, A Complete Treatise on Electricity, vol. 3, p. 295 (London, C. Dilly, 3d ed. in 2 vols., 1786; vol. 3 added 1795). 15 Harrison Gray Dyar, quoted in G. B. Prescott, History of the Electric Telegraph, pp. 427-428 (Boston, Ticknor and Fields, 1860). 16 (Sir) Francis Ronalds, Descriptions of an electrical telegraph, and of some other electrical apparatus, pp. 1-24 (8°, London, R. Hunter, 1823).

12

ELECTROACOUSTICS

The electrostatic transducers that had been universal in the telegraph art began to disappear soon after the announcement in 1800 of Volta's 17 discovery of the battery or "voltaic pile," which made current electricity available for study and experiment and which was to open the door for the exploitation of electromagnetism. Volta's battery was used first, however, as the basis for several proposals for telegraphs involving electrochemical transducers. Of these, the one taken most seriously was advanced in 1809 by S. T. von Soemmerring 18 of Munich. The receiving transducer for this system comprised a series of 35 inverted test tubes in which electrolytic decomposition of water was to take place, the symbol transmitted being indicated by the test tube in which a bubble of hydrogen was observed. One may wonder how such a system of signaling could ever have been regarded as practical, but retrospective judgments should probably be rendered with caution and charity; a good many of today's proudest technical achievements may appear just as impractical as soon as someone finds a better way to get the same results. The Discovery of

Electromagnetism

The discovery of electromagnetism and the first observation of electromagnetic transduction are perhaps to be credited to Gian Domenico Romagnosi,19 an Italian jurist and journalist, who is said to have observed in 1802 the deflection of a magnetic needle by the action of a galvanic current. The only publication of this momentous discovery by its maker was contained in an article on galvanism appearing in a local 17 Alessandro Volta described his battery in a letter dated 20 March 1800, addressed to Sir Joseph Banks, and published in Phil. Trans. Roy. Soc. (London) 90, 403-431 (1800). An English translation appeared during the same year in [The] PAi/.[osophical] Mag.[azine] 7, 289-311 (1800), and it has been reprinted many times since, most recently in American Journal of Physics 13, 398-406 (December 1945). 18 Samuel Thomas von Soemmerring, "Ueber einen elektrischen Telegraphen," Denkschriften der Königlichen Akademie der Wissenschaften zu München, Math. u. Phys. Classe II, pp. 401-414 (1809, 1810); see also a three-part presentation and discussion "Ueber Sömmerring's elektrischen Telegraphen," (Schweigger's) Journal für Chemie und Physik 2, Part 2, pp. 217-247 (1811), containing (α) [von Soemmerring], "Darstellung der Sache mit den Worten ihres Erfinders," pp. 217-231; (δ) comments by J. W. Ritter, pp. 231-237; (c) comments by Schweigger, pp. 238-247. 19 Gian Domenico Romagnosi, "Articolo sul Galvanismo," Gazzetta di Trentino (3 August 1802); reprinted, with interpolated commentary, by Gilberto Govi in his paper "Romagnosi e l'elettro-magnetismo," Atti della Reale Accademia della Scienze di Torino 4, 426-439 (1869), and translated by J. J. Fahie at pp. 259-260 of his History of the Electric Telegraph . . . (see note 9); see also the discussion by William B. Taylor in Eenry and the Telegraph, pp. 73-76, separately printed as an extract "from the Smithsonian Report for 1878" (Washington, Govt. Printing Office, 1879).

HISTORICAL CONTEXT

13

newspaper published at Trent. Slightly wider notice was given to the discovery by passing references to Romagnosi's work in popular treatises on "Galvanism" published at Paris in 1804 by Giovanni Aldini,20 a nephew of Galvani, and by Joseph Izarn; 21 but it is still difficult to understand how this discovery could have attracted so little attention among scientists prior to 1820. To be sure, Napoleon was providing a generous measure of distraction on the Continent. What had been the French Academy of Sciences until its suppression in 1793 was still functioning as the Premiere Classe of the Institut National, but its members were under some pressure to concern themselves with what would now be called applied science — a situation that prevailed until the reöstablishment of the Academie des Sciences in 1816 after Napoleon's second exile. It also seems reasonable to infer that the Aldini and Izarn treatises were probably not widely circulated in England. Even so, these treatises may have been more widely noticed than highly regarded, since " therapeutic " galvanism, not to mention Aldini's showmanship, was suspect even then in the eyes of serious scientists. Late 19th-century historians differ as to whether Romagnosi actually observed the magnetic effect of a current or whether the effect he noticed was an electrostatic phenomenon. Fahie's translation would support the latter interpretation, but he translates from a secondary source consisting of a reprint of the Romagnosi article contained in a paper devoted to an expose of Romagnosi's claims. On the other hand, Taylor's Smithsonian report, written a few years before the appearance of Fahie's History . . , assigns the discovery to Romagnosi without reservation. Whether it was a discovery or a rediscovery, the announcement of the magnetic effect of a current by Hans Christian Oersted22 in 1820 arrested the attention of scientists everywhere. Reprints or notices of Oersted's discovery appeared within a year in almost every scientific 20 Jean (Giovanni) Aldini, Essai Theorique et Expirimental sur le Galvanisme, p. 191 of the quarto edition or p. 340 of Tome 1 of the octavo edition (Paris, Fournier Fils, 1804). 21 Joseph Izarn, Manuel du Galvanisme, p. 120 of 1st ed. (8°, Paris, J. F. Barru, 1804) or of the edition usually cited, which seems to have come from the same plates a year later with a new title page inserted (Paris, Levrault, Schoell, et О 1 ", 1805); or at pp. 7879 of the Italian translation, Manuale del Galvanismo (8°, Florence, Guglielmo Piatti, 1805). 22 Hans Christian Oersted, Experimenta circa eßectum conflictus electrici injacum magneticam (Copenhagen, Hafniae, 1820); appeared also within the same year in five other languages, the English version being "Experiments on the Effect of a Current of Electricity on the Magnetic Needle," Annals of Philosophy 16, 273-276 (London, 1820).

14

ELECTROACOUSTICS

journal of the world and they can be said to have triggered off a flurry of scientific research whose fruitfulness has not yet been exhausted. Almost immediately after the announcement of Oersted's discovery, Arago23 and Davy 24 independently discovered that magnetism could be induced in a piece of iron by the action of an electric current. Within the same year, Ampere26 and Biot and Savart 26 began their definitive experiments that were to provide a mathematical basis for "current" electricity; and J. S. C. Schweigger27 and J. C. Poggendorff,28 independently and in that order, devised a current-indicating instrument comprising a coil of wire for "multiplying" the effect of the current on a magnetic needle suspended within the coil. Especial interest attaches to Ampere's papers of this period, since they served to establish much of the terminology that is still in common use; for example, the terms electrostatic, electromagnetic, electrodynamic, electric current, electric tension, galvanometer, and solenoid, not to mention

his unfortunate arbitrary choice of the direction of the current to be designated as positive. Ampere included also in his famous paper of 1820 some comments on a suggestion Laplace had made for using the deflection of the magnetic needle as a telegraph. Apparently neither had been following the telegraph literature very closely, since "as many conducting wires and magnetized needles as there are letters" were to be employed; but no harm was done since they made no serious attempt to follow up the proposal. The Early Electromagnetic

Telegraph 29

A few years later, in 1824, Peter Barlow undertook to explore the practicability of Ampere's proposal; but he found the mechanical force 23

[Dominique Francois Jean Arago], "Expiriences relatives ä. l'aimantation du fer et de l'acier par l'action du courant voltaique," Л яге.[ales de] Chim.\_ie] et [de] Phys.[ique] [ 2 ] 16, 93-102 (1820). 24 Sir Humphry Davy, "On the magnetic phenomena produced by Electricity," Phil. Trans. Roy. Soc. (London) 111, 7-19 (1821). "Andre Marie Атрёге, "De l'Action mutuelle de deux courans 61ectriques," Ann. Chim. et Phys. [ 2 ] 16, 59-76, 170-218 (1820). 25 Jean Baptiste Biot and Fdlix Savart, "Note sur le Magn6tisme de la pile de Volta," Ann. Chim. et Phys. [ 2 ] 16, 222-223 (1820). 27 Johann Salomo Christoph Schweigger, "Zusätze zu Oersteds elektromagnetischen Versuchen," (Schweigger's) Journal für Chemie und Physik 31, 1-17 (1821). 28 [Johann Christian Poggendorff], "Account [by the editor, Dr. Brewster] of the New Galvano-Magnetic Condenser invented by M. Poggendorff of Berlin," Edinburgh Philosophical Journal 6, 112-113 (1821). 28 Peter Barlow, "On the Laws of Electro-Magnetic Action," Edinburgh Philosophial Journal 12, 105-114 (1825).

HISTORICAL CONTEXT

15

on the magnetic needle so much diminished after transmission of the current through a few hundred feet of wire that he expressed grave doubts about the possibility of ever transmitting telegraph signals over a long distance. This disappointment persuaded Barlow to launch an inquiry into the laws governing the diminution of the magnetic influence, and these studies led him independently to several of the conclusions embodied in the " l a w " announced by G. S. Ohm 3 0 in 1826. Similar restrained skepticism about the telegraph's future was expressed publicly by William Ritchie 31 when he demonstrated a model telegraph based on Ampere's "ingenious project" at the conclusion of an evening lecture to the Royal Institution in February 1830. Later in the same year, however, Ritchie conducted a series of experiments directed toward a test of Ohm's law and recanted his skepticism by declaring that "we need scarcely despair of seeing the Electro-Magnetic Telegraph established for regular communication from one town to another, at a great distance." An electromagnetic telegraph of this type, but using the SchweiggerPoggendorff "multiplier," was put in operation at Saint Petersburg by Baron Schilling,32 probably as early as 1823. Descriptions of Schilling's instruments indicate that he made various improvements from time to time over a period of several years, but his efforts are chiefly distinguished for his introduction of a telegraphic code for signaling with right-left movements of a single needle. Schilling's later apparatus had much in common with the experimental telegraph constructed at Göttingen in 1833 by Gauss and Weber.33 The latter used for their receiving trans80 Georg Simon Ohm, [experimental] "Bestimmung des Gesetzes, nach welchem Metalle die Contaktelektricität leiten, nebst einem Entwürfe zu einer Theorie des Voltaischen Apparates und des SchweiggerschenMultiplicators," (Schiveigger's) Journal für Chemie und Physik 46, 137-166 (1826); [theoretical] Die Galvanische Kette mathematisch bearbeitet (Berlin, Т. H. Riemann, 1827). 31 William Ritchie, [Secretary's account of an evening lecture, 12 February 1830] Quarterly Journal of Science, Literature, and Art (London) 29, 183-185 (1830): but see also, "Description and Application of a Torsion Galvanometer," Journal of the Royal Institution of Great Britain 1, 29-38 (1830). 3S Baron Paul Ludovitsch Schilling does not himself appear to have published any description of his telegraph. J. Hamel was personally acquainted with Soemmerring, Schilling, Gauss, Weber, and other telegraphic pioneers, and he was able, as a result, to speak with eye-witness authority in his " Historical account of the introduction of the galvanic and electro-magnetic telegraph," Journal of the Society of Arts {London) 7, 595-599, 605-610 (1859); see also, pp. 235 and 453. 33 The Gauss and Weber telegraph is briefly noticed at the conclusion of a report from Göttingen on measurements of the earth's magnetic field, Göltingische Gelehrte Anzeigen, Part ii, No. 128, pp. 1272-1273 (9 August 1834); mentioned also at pp. 39-40 of an article by Gauss, "Erdmagnetismus und Erdmagnetometer," pp. 1-47 of Jahrbuch für 1836 edited by Η. С. Schumacher (Stuttgart und Tubingen, 1836). N N E

16

ELECTROACOUSTICS

ducer a reflecting galvanometer made by mounting a small mirror on the deflecting needle of a "multiplier." They also incorporated a signaling device, as Schilling had done, perhaps earlier. There is some question whether Gauss or Schilling was first to use a telegraphic code, but the one devised by Gauss had features of superiority. In spite of the merit of the Schweigger-Poggendorff "multiplier," the mechanical forces that could be aroused magnetically were still quite feeble. William Sturgeon 34 took in 1824 what now seems to have been an obvious step in the direction of improving this situation by winding a multiturn spiral of wire around a bent piece of soft iron, thus creating the first electromagnet. At about the same time, Joseph Henry was qualifying himself for the post of Professor of Mathematics and Natural Philosophy in the Albany Academy of New York, to which he was appointed in 1826. Soon thereafter he began the series of classic experiments that were to transform Sturgeon's toy electromagnet into a staunch servant, and in a series of communications presented to the Albany Institute, Henry 3 5 described electromagnets that far exceeded the lifting power of Sturgeon's. During successive summers devoted to research between academic terms, he continued to improve both his magnets and his understanding. His most important contribution to the magnet art during this period was to sectionalize the winding into "spools" which could be connected either in parallel, to constitute what Henry called a "quantity" magnet, or in series, to form an "intensity" magnet. His so-called quantity magnet would correspond in modern terminology to a low-impedance or current-controlled magnet, and his intensity magnet to a high-impedance or voltage-controlled magnet. Henry and the Electromagnetic Telegraph As early as 1830, Henry realized that his "intensity" magnet held the key to the success of the electric telegraph, and he demonstrated by a 34 William Sturgeon, "Improved Electro-Magnetic Apparatus," Transactions of the Society for the Encouragement of Arts, Manufactures, and Commerce (London) 43, 38-52 (1825). 35 Joseph Henry: A few brief notices of his magnetic researches appeared in the Transactions of the Albany Institute, the first in 1, 22-24 (1828); his "quantity" and "intensity" electromagnets are described in (Silliman's) American Journal of Science 19, 400-408 (1831). For his novel reciprocating electromechanical transducer, see ibid. 20, 340-343 (1831), and for his celebrated discovery of mutual and self-induction, ibid. 22, 403-408 (1832). For accounts of Henry's demonstration telegraph and his relay, see the memoir by W. B. Taylor, Henry and the Telegraph, (note 19), or Coulson's new biography of Henry (note 3).

HISTORICAL

CONTEXT

17

series of methodical experiments that the activity of such a magnet was not seriously diminished even when it was operated at the end of very long connecting wires. As an experimental demonstration of this performance, Henry exhibited to his classes a t the Albany Academy in 1831 a telegraph using an " i n t e n s i t y " magnet operated by an "intensity" (that is, a series-connected) battery a t the end of a mile of wire strung around the walls of one of his classrooms. Of special significance in the present context, this demonstration telegraph was the first to make use of the linear attraction of an armature by an intermittent electromagnet (in contrast with the deflection of a magnetic needle), and the first to use electromagnetism to actuate an electroacousiic transducer. Henry's receiving transducer operated as a polarized "sounder"; the position of an armature would reverse when the current was reversed and make evident the transmitted signal by the sound produced by the impact of the armature against its stops. Henry accepted an appointment as Professor of Natural Philosophy a t the College of New Jersey, a t Princeton, in 1832 and there rounded out his contributions to the telegraph by including in his demonstration equipment the first " r e l a y " or "repeater." This took the form of an intensity magnet arranged with contacts on its armature for opening the local battery circuit of a high-current quantity magnet of great lifting power. Henry's demonstration telegraph embodied substantially all that the early telegraph art had to contribute to electroacoustics, but this phase of the history can hardly be terminated without mention of S. F. B. Morse's 3 6 invention of the printing telegraph in 1837. Morse soon became involved in bitter controversy over priority claims, his contests eventually spreading to include nearly all the people who had collabo36 Samuel Finley Breese Morse. A caveat announcing his invention of a printing telegraph was filed in the U. S. Patent Office, October 1837, and was followed up by a formal application filed 7 April 1838 and then later withdrawn to allow exploitation (abortive) in Europe; application reinstated and first Patent No. 1647 issued 20 June 1840; subsequently reissued 15 January 1846 (as Reissue No. 79) on amended specification dated 27 December 1845; reissued again 13 June 1848 (as Reissue No. 117) with further amendment extending claims (e.g., No. 8, " . . . motive power . . . of electromagnetism . . . however developed . . ."); after disallowance of Claim 8, the required Disclaimer was filed 17 March and entered on 19 June 1854, and the remainder of the patent was extended for 7 years from 20 June 1854. A second patent (including the relay and local-battery circuit), No. 4453, was issued 11 April 1846 and reissued 13 June 1848 (as Reissue No. 118), but its claims were subsequently reduced by a Disclaimer filed 20 April and entered on 20 June 1854. A third patent directed to an electrochemical telegraph issued routinely as No. 6420 in May 1849.

18

E L E C T R O ACOUSTICS

rated with or assisted him during the development of his system of telegraphy. When the facts are reviewed at this much later date, it appears that Morse was actually anticipated by others in regard to almost every individual feature of his system, as might be illustrated by citing the Henry "intensity" magnet and relay, the Gauss-Schilling code, the earth return of Steinheil, and several earlier but less practical methods of recording. Nevertheless, Morse's imaginative combination of these features into a workable system suitable for commercial telegraphy did represent invention of the highest type. Enough credit, not to mention reward, would have accrued from this to have satisfied most, but Morse wanted more. His original patent was reissued twice, and each time his claims were further extended in the direction of embracing the fundamental concepts on which he had built. Eventually, a Supreme Court decision 37 invalidated the most ambitious of these — Morse's muchcontested Claim 8 — by which he would otherwise have gained a monopoly for any method of using the motive power of an electric current to print intelligible characters at a distance. The bitterness with which Morse subsequently attacked those whose expert testimony he regarded as adverse, and especially his unprincipled attack on the integrity of Joseph Henry, could not fail to diminish the honor, although not the credit, due him for an outstanding invention of major social and economic significance. Early Experiments with Magnetostriction Another of the basic mechanisms of electroacoustical transduction may have made its appearance in 1837 when Charles G. Page,38 a physician of Salem, Massachusetts, discovered that musical sounds could be produced by interrupting the current in a coil placed between or in front of the poles of a horseshoe magnet. The doubt reflected by the use of the word " m a y " bespeaks the uncertainty left by Page's report as to whether the musical sounds he heard were generated by the release of a magnetostrictive stress or by a change in the magnetomechanical force acting externally on the poles of his bent magnet. Of course, Page was not concerned with this question at the time, since several years were to pass before the fundamental nature of magnetostriction was identified. To Page, this was "galvanic music." In a subsequent variaw O'Reilly v. Morse, 15 Howard 62 [December 1853]. This decision was often cited as a precedent in later patent cases involving functional claims. 38 Charles Grafton Page, "The Production of Galvanic Music," (Silliman's) American Journal of Science 32, 396-397 (1837); "Experiments in Electro-Magnetism," ibid. 33, 118-120 (1837).

HISTORICAL CONTEXT

19

tion of his experiment that greatly enhanced the tone, Page rotated a soft-iron armature rapidly in front of the pole pieces. Delezenne39 repeated this test and confirmed the enhancement, but not enough quantitative detail was furnished in the description of either experiment to allow the mechanism of tone production to be identified unambiguously. There can be no doubt, however, that Marrian 40 did observe the magnetostrictive excitation of vibration in a soft-iron bar in the experiments he described in 1844. He found, as Page had, that the sound was produced either "at the instant that the magnetism is imparted", or when the electric circuit was broken. Marrian used bars from 6 inches to 20 feet in length, but found always that the " sound produced was the tonic of each bar"; and that the tone could be imitated by striking the end of the bar, but that no sounds resembling it could be produced by a lateral blow. As to the cause of this effect, Marrian could only say that "particles of a bar of iron, when changing its electrical state, have a tendency decidedly motive, and that too along the bar in the direction of its axes." He was also alert to the possibility of a converse effect, although he was "unable to prove that any excitation in the same direction will induce an electric current (which I think is highly probable)". After Marrian's report had appeared, both Beatson 41 and La Rive 42 published accounts of their observations of similar effects, Beatson remarking that he had observed these phenomena as early as 1843. Still further confirmation was soon forthcoming from Matteucci 43 at Pisa in Italy, from Wartmann 44 at Lausanne in Switzerland, and from Wertheim48 in Paris. 8 ' Charles Edouard Joseph Delezenne, "Note sur de nouvelles experiences sur la production de sons musicaux" [Communique par M. E.-F. Wartmann], Bibliotheque Universelle {de Geneve), Nouvelle [2»] serie 16, 406-407 (1838). 40 J. P. Marrian, "On Sonorous Phaenomena in Electro-Magnets," Phil. Mag. [3] 26, 382-384 (1844). 41 W. Beatson, "On Electro-Magnetic and other Vibrations," The Electrical Magazine 1, 555-559 (April, 1845) LC ; reprinted in Archives de VElectriciU Б, 197-199 (1845). 42 Auguste Arthur de La Rive, " Sur les mouvements vibratoires que d6terminent dans les corps, soit la transmission des courants 61ectriques, soit leur influence extirieure," Compt.[zs] Rend.[us des Seances de l'Academie des Sciences] 20, 1287-1291 (1845). 43 Carlo Matteucci, " Sur le son que rend une barre de fer en tour ёе d'une spirale au moment oü l'on ouvre ou ferme le circuit," L'Institut 13, 315-316 (No. 609, 3 September 1845); reprinted in Archives de l'Electricite 6, 389-394 (1845). 44 Elie-Franrois Wartmann, "On the Causes to which Musical Sounds produced in Metals by discontinuous Electric Currents are attributable," Phil. Mag. [3] 28, 544546 (Supplement, 1846). 45 Wilhelm Wertheim, "Note sur les vibrations qu'un courant galvanique fait naltre dans le fer doux," Compt. Rend. 22, 336-339, 544^547 (1846); "Memoire sur les sons produits par le courant 61ectrique," ibid. 26, 505-506 (1848).

20

ELECTROACOUSTICS

All of these thoughtful experimenters tried to express, each in his own way, an intuitive understanding of the nature of magnetostriction, as these extracts will illustrate: "The alternate separation and attraction of the particles or certain particles composing the material acted upon" (Marrian); "The molecular vibration that determines the magnetization" (La Rive); "This internal vibration . . . made periodical by the discontinuity of current" (Wartmann); "An expansion followed by a contraction . . . quite distinct from that due to h e a t " (Beatson). There was nothing vague, however, about Joule's approach to this question. One of his friends had heard of Page's experiments and had suggested to Joule that the effect might be utilized as the transducer mechanism for an electric motor. Joule 46 was already concerned with the economy of energy conversion, so he proceeded to explore his friend's suggestion, contriving in 1842 a compound-lever system that enabled him to determine by direct measurement that the fractional change in the length of an iron bar on being magnetized was about 1 part in 720,000. Five years later, in 1847, Joule carried out a more extensive and more accurate series of observations on the change of length associated with magnetization, and it is this work that is usually cited as marking the "discovery" of magnetostriction. If it is just to concede to Joule the credit for "discovering" magnetostriction — and it probably is — then it can be said that this is one effect whose manifestations had been studied extensively for several years prior to its discovery. As is usually the case, Joule's definitive work increased rather than terminated the interest in further study of magnetomechanical effects. Both Guillemin 47 and Wertheim 45 had observed that a bent rod would tend to straighten when magnetized, and each had searched specifically for the effect of magnetization on the modulus of elasticity. Wiedemann's 48 name appears along with those of Wertheim 49 and Mat45 James Prescott Joule, "On a New Class of Magnetic Forces," (Sturgeon's) Annals of Electricity, Magnetism, and Chemistry 8, 219-224 (1842); also "On the Effects of Magnetism upon the Dimensions of Iron and Steel bars," Phil. Mag. [3] 30, 76-87, 225-241 (February, April 1847). 47 Amedee Victor Guillemin, " Observations relatives au changement qui se produit dans l'61asticit6 d'un barreau de fer doux sous l'influence de Pelectricite," Compt. Rend. 22, 264-265, 432-433 (1846). 48 Gustav Heinrich Wiedemann, "Ueber die Beziehungen zwischen Magnetismus, Wärme und Torsion," (Poggendorß's) Anneden der Physik und Chemie 103, 563-577 (1858). 49 W. Wertheim, "Note sur des courants d'induction produits par la torsion du fer," Compt. Rend. 36, 702-704 (1852): "Memoire sur la torsion: 2е Partie, Sur les effets magnetiques de la torsion," Ann. Chim. et Phys. [3] 60, 385-432 (1857).

HISTORICAL CONTEXT

21

teucci50 in connection with studies of the relation between torsional strains and the associated tangential and longitudinal magnetic fields. Still later, the volumetric strain produced by a magnetic field, which had been looked for in vain by Joule, was detected by Barrett,61 and in due course its converse effect was exhibited and studied by Nagaoka and Honda.62 The discovery of the primary converse effect in magnetostriction — a change in magnetization produced by longitudinal strain in a ferromagnetic rod — is usually credited to Villari,63 although the qualitative nature of a good many converse effects had been revealed in the various studies already alluded to. It would probably be more just to identify as the "Villari effect" the reversal of magnetostrictive strain that sometimes occurs with increasing magnetic field, since Villari's careful quantitative measurements were the first to show that this reversal could occur. The consistency of the appearance of a converse effect for every direct effect might well have been remarked sooner, but the universality of this relation does not seem to have been pointed out explicitly until J. J. Thomson 64 took up the question in 1886. Mid-Century

Retrospect and Prospect

The modern reader who goes back to consult the original papers appearing during this period can hardly fail to be impressed by two things. The language seems, first of all, to be quaint and circumlocutory, and to suggest a scientific naivete not unlike that of modern children who use novel figures of speech to describe relationships that involve concepts they do not understand. To judge how apt this comparison is, it is only necessary to scan the general state of knowledge prevailing in related 60 C. Matteucci, "Sui fenomeni elettro-magnetici sviluppati dalla torsione: ricerche sperimentali: Parte I, Di un nuovo caso d'induzione elettro-magnetica," II Nuovo Cimenlo [ 1 ] 7, 66-97 (January-February 1858); French translation in Ann. Chim. et Phys. [ 3 ] 63, 385-417 (1858). S1 William Fletscher Barrett, "On the Alterations in the Dimensions of the Magnetic Metals by the Act of Magnetization," Nature 26, 585-586 (12 October 1882). 62 H. Nagaoka and K. Honda, "On Magnetostriction," Phil. Mag. [ 5 ] 46, 261-290 (1898). 63 Emilio Villari, "Intorno alle modificazioni del momento magnetico di una verga di ferro e di acciaio, prodotte par la trazione della medesima e pel passaggio di una corrente attraverso la stessa," II Nuovo Cimento 20, 317-362 (1864); a free (German) translation by the author also in (Poggendorß's) Annalen der Physik und Chemie 126, 87-122 (1865). 64 (Sir) Joseph John Thomson, "On some Applications of Dynamical Principles to Physical Phenomena," Phil. Trans. Roy. Soc. (London) 176, 307-342 (1886); also, Applications of Dynamics to Physics and Chemistry, Chaps. 4-5, pp. 31-88 (London, Macmillan & Co., 1888).

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fields during the decade between Page's first notice of galvanic music and Joule's second paper on the magnetostriction effect. Although the electric telegraph was being put into successful commercial operation both in America and in England (1843-1844), the fundamental law of the conservation of energy had not yet been broadened in scope to embrace electric and thermal energy as well as mechanical (R. Mayer, 1842; Joule and Helmholtz, 1847); no basis had yet been established for an absolute scale of temperature (Kelvin, 1848), and there was no second law of thermodynamics (Clausius, 1850; Kelvin, 1851); there were no motors or dynamos yet worthy to be regarded as more than toys (W. Siemens, and many others, from 1856) nor had it yet been recognized that any electric motor could be operated reversibly as a dynamo (Μ. H. Jacobi, 1850). Wheatstone had reinvented S. Hunter Christie's bridge for measuring resistance (1843), Kirchhoff's laws for d.c. circuits had just appeared (1847), and the use of absolute units as a basis for measurements of electrical quantities had been suggested (W. Weber, 1846) — yet it was to be a precious long time before there was either a named unit or an accepted standard of resistance (British committee led by Lord Kelvin, 1861), let alone methods of measurement, standards, or even names for the volt, ampere, coulomb, or farad (International Congress, Paris, 1881) or for the joule, watt, or henry (Chicago Congress, 1892). The desperate need for measuring instruments was felt most keenly of all, and in this respect the growing pains of the burgeoning science of electricity were much like those that had long afflicted the science of acoustics. For acoustics, these pains of want had been dulled by long bearing, but the lusty infant, electricity, was clearly possessed of no such patience. The second impression that rewards a sympathetic encounter with the early 19th-century scientific literature is one of thrusting impatience, a feeling of incipience, of great things about to happen. And happen they did! So far as electroacoustics was concerned, this expectancy reached a climax of fulfillment during the vintage years between 1873 and 1880. The early boundary is the publication date of Maxwell's classic treatise on Electricity and Magnetism; the later one marks the prediction and discovery of piezoelectricity by the Curie brothers. The one event above all others, however, that made this period a momentous interval of time for all of mankind was the invention of the telephone. Alexander Graham Bell had devoted his youth to teaching the deaf to speak and the mute to understand visible speech, but his greatest triumph of all was to endow the stuttering telegraph with the power of articulate speech.

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Invention and the Telephone

I t is often suggested that great inventions and great ideas, such as the telephone, the steam engine, the telegraph, or the infinitesimal calculus, do not come into being as the result of an isolated act of creative imagination on the part of a single individual. I t is more often the case that such ideas are latent in the prevailing state of scientific consciousness, and that when the time is ripe the great idea is bound to come forth at the hands of one man or another. There is a good bit of evidence to support this point of view, for in the shadow of every man whose name becomes associated with major innovation there seems to stand a host of others who "almost had it." When only glory is at stake, as was the case with Newton and Leibniz when the calculus was young, it is not necessary to assign credit on an all-or-none basis. Instead, praise for novelty can be apportioned with due regard for fractional contribution to a nonstatic whole as well as for priority of conception. On the other hand, when objective rewards and substantial economic consequences hinge on priority, such questions demand a firm yes-or-no answer that carries the authority of a legal court decision beyond appeal. There can be no grays — only blacks or whites — when it comes down to the final question of determining at law who was the one first inventor. This is a race in which there is no prize and no reward for coming in second. With ample justification, therefore, the primary telephone patent, for which Alexander Graham Bell {S filed his application on the stormy morning of 14 February 1876, became the focal point of a prolonged series of legal actions without parallel in the history of patent law. That Bell did invent the telephone was ultimately, and decisively, established by a decision66 handed down in 1887 by the United States Supreme Court. I t takes more than just the act of imagining a new and useful result 66

Alexander Graham Bell, U. S. Pat. No. 174,465 (filed 14 February 1876) issued 7 March 1876 [probably the most valuable single patent ever issued]. See also "Researches in Telephony," Proceedings of the American Academy of Arts and Sciences 12, 1 - 1 0 (1877); and a lecture delivered before the Society of Telegraph Engineers (London), 31 October 1877, reprinted in G. B. Prescott, The Speaking Telephone, pp. 5 0 - 8 2 ( N e w York, D . Appleton and Co., 1878). 56 The Telephone Cases, 126 U. S. 531. [Scientists may well envy the efficiency of this compact method of citing references to legal reports, made feasible by the fmiteness of the Court system. As a typical translation, 126 U. S. 531 = United States [Supreme Court] Reports, vol. 126, pp. 531 ff. (October Term, 1887). This is, incidentally, the only case on record to which an entire volume of the U. S. Reports is devoted.]

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to constitute a patentable invention. The would-be inventor must also have in hand means of accomplishing the new result, means that have the element of novelty and that reveal enough of the "flash of genius" to define a level of accomplishment that clearly goes beyond what would be expected of one normally skilled in the particular art in question. In short, there must be invention as well as novelty and utility. There must also be a constructive reduction to practice or its equivalent, a specific claim to the thing invented, and the disclosure of a detailed specification of the invention sufficiently clear and complete to teach others how to practice the invention. This disclosure of the method of practicing the invention is, in fact, the quid pro quo exacted by the government in exchange for the granting of a temporary monopoly. Honor and credit may be due and can be properly accorded to the authors of innovation who achieve some, but not all, of these attributes of invention; but the true, sole, and first inventor must qualify on all the counts. Each of Bell's many counterclaimants for the invention of the telephone acquired champions and supporters among reputable scientists and science historians, both in Bell's time and later. Some of the writings of these scientific advocates seem on review to reveal so much bias as to constitute a reportorial phenomenon worthy of investigation in its own right. It seems most charitable to suggest that if these authors could be submitted to cross-examination, they would probably be found to differ less in their interpretation of the physical facts concerning the origin of telephony than in their understanding and appreciation of the relative importance of the various constituents of patentable invention. If novelty of result and means, without the support of a rounded conception reducible to practice, were enough to constitute invention, the telephone would belong to Charles Bourseul. This young French electrician had barely launched himself on a career in telegraphy in 1854 when he essayed a venture in scientific romance that was prophetic enough to set a pattern for Jules Verne to follow a decade later. Bourseul 67 told his story this way: The electric telegraph is based on the following principle: an electric current, passing through a metallic wire, circulates through a coil around a piece of soft iron which it converts into a magnet. The moment the current stops, the piece of iron ceases to be a magnet. This magnet, which takes the name of electro87 Charles Bourseul, "Transmission electrique de la parole," L'Illustration {Paris) 24, 139 (26 August 1854). [Translations of portions of this article are quoted in most histories of telephony, and the entire article is cited in 126 U. S. 30 (see preceding note) from which this quotation is taken.]

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magnet, can thus in turn attract and then release a movable plate . . . [Bourseul goes on to describe the use of this effect for telegraphy, ending with a reference to what must have been a primitive form of telautograph.] I t would seem impossible to go beyond this in the region of the marvelous. Let us try, nevertheless, to go a few steps further. I have asked myself, for example, if the spoken word itself could not be transmitted by electricity; in a word, if what was spoken in Vienna may not be heard in Paris? The thing is practicable in this way: We know that sounds are made by vibrations, and are made sensible to the ear by the same vibrations, which are reproduced by the intervening medium. But the intensity of the vibrations diminishes very rapidly with the distance; so that even with the aid of speaking tubes and trumpets, it is impossible to exceed somewhat narrow limits. Suppose that a man speaks near a movable disk, sufficiently flexible to lose none of the vibrations of the voice; that this disk alternately makes and breaks the connection with a battery; you may have at a distance another disk which will simultaneously execute the same vibrations. It is true that the intensity of the sounds produced will be variable at the point of departure, at which the disk vibrates by means of the voice, and constant at the point of arrival, where it vibrates by means of electricity; but it has been shown that this does not change the sounds. [? Q I t is, moreover, evident that the sounds will be reproduced at the same pitch. The present state of acoustic science does not permit us to declare a priori if this will be precisely the case with syllables uttered by the human voice . . . However this may be, observe that the syllables can only reproduce upon the sense of hearing the vibrations of the intervening medium. Reproduce precisely these vibrations, and you will reproduce precisely these syllables. I t is, at all events, impossible, in the present condition of science, to prove the impossibility of transmitting sound by electricity. Everything tends to show, on the contrary, that there is such a possibility. When the application of electromagnetism to the transmission of messages was first discussed, a man of great scientific attainments treated the idea as Utopian, and yet there is now direct communication between London and Vienna by means of a simple wire. Men declared it to be impossible, but it is done. I t need not be said that numerous applications of the highest importance will immediately arise from the transmission of speech by electricity. Any one who is not deaf and dumb may use this mode of transmission, which would require no apparatus except an electric battery, two vibrating disks and a wire . . . However this may be, it is certain that in a more or less distant future, speech will be transmitted by electricity. I have made some experiments in this direction. They are delicate, and demand time and patience; but the approximations obtained promise a favorable result. T h e Vicomte d u Moncel, 58 a 19th-century journalistic missionary of applied electricity, felt obliged to include this prophecy in a n 1857 com68 Vicomte Th£odose A. L. du Moncel, Exposi des Applications de l'Eleclricile, 2' ed., vol. 3, pp. 110-112 (Paris, Hachette et О , 1857); also Le Telephone, p. 4 (Paris, Hachette e t ' O , 1878).

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pendium of applications of electricity, but he regarded the suggestion as so fantastic that he sought to protect the author's reputation by identifying him only by his initials. This slight was corrected later when the prophecy came true in the so-much-less-distant future that du Moncel himself was able to repeat the quotation and complete the identification in a small book he published in 1878 under the title Le Telephone. The only things needed to make Bourseul's prophecy come true were two electroacoustic transducers! Bell provided these, and his primary "reduction to practice" involved the reversible use of two identical moving-armature transducers. In one other very important respect Bell went beyond Bourseul's visionary prophecy by specifying that the motion of the transmitter diaphragm under the influence of the impinging speech wave should not interrupt the current, but that it should produce instead, for transmission to the receiver, an undulating current that would be an electrical replica of the sound-pressure variations in the speech wave. When one contemplates the sharp resonances that must have characterized all these early telephone instruments, it becomes evident that the word "replica" needs to be interpreted with a good bit of latitude. Nevertheless, all contemporary instruments were similarly afflicted so that no basis for discrimination among competitors could be based upon frequency infidelity. Bell's insistence upon the necessity of producing an undulating current was significant, however, and was ultimately to provide the basis on which his invention could be defined over the earlier telephone art disclosed by Philipp Reis. Reis's Telephone and the Doctrine of Undulation It cannot be known for sure whether Bourseul's prophecy ever came to Philipp Reis's attention, although it seems likely that it did since the article attracted considerable attention and an account of it appeared in Didaskalia,59 a 19th-century four-page news bulletin published daily at Frankfort, not far from Friedrichsdorf where Reis was serving as a young science teacher. But whether inspired by this suggestion or not, Philipp Reis seems to have been the first to undertake the actual construction of an instrument designed for the transmission of sounds — hopefully, even human speech — by electricity. In addition, Reis is often given credit for being the first to make use of the word "telephone" as a designation " A n article, "Elektrische Telephonie," signed by "L," Didaskalia, Blätter fur Geist, Gemiith und Publicität {Frankfurt) No. 232 (28 September 1854). N N E

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for such speech-transmission apparatus, a linguistic innovation more durable than his instrument designs; but Reis seems to have been "scooped" on this usage by the editor of Didaskalia, who captioned his paraphrase of Bourseul's article Elektrische Telephonies Reis 61 constructed his first "telephone" instrument in 1860 and demonstrated it before the Physical Society of Frankfurt am Main in the fall of 1861. In planning his transmitters, all of the various forms of which he built with his own hands, Reis was strongly influenced by a desire to make them resemble the human ear as closely as possible. To serve the function of the eardrum, he used a round membrane — the skin of a German sausage, as a matter of fact — in his initial experiments. The function performed by the small bones of the middle ear in forwarding the sound energy was taken over by a contact finger arranged to complete the external electrical circuit by bearing lightly against a small metal electrode attached to the center of the diaphragm. When the diaphragm vibrated under the action of an impinging sound wave, the quality of the electric contact varied. But as to exactly how it varied — this became a highly moot question whose scientific relevance expanded into a hotly contested legal issue. Sylvanus P. Thompson,62 a good many years later, took some pains to establish experimentally that a metal-to-metal contact of the sort Reis had used could exhibit a variation of contact resistance that was proportional to the contact pressure, but he could never gainsay the fact that the whole range of variation of the contact resistance was traversed within an extremely narrow dynamic range of variation of the activating sound pressure. Even under carefully contrived conditions, the proper adjustment of contact pressure was so difficult to attain and maintain 60 The word " telephone" actually made its appearance, in a somewhat different connection, as early as 1841: see, for example, Sir William Fothergill Cooke, The Electric Telegraph — was it invented by Professor Wheatstone?, Part ii, pp. 81, 121, 124 (in 2 parts, London, printed for the author and sold by W. H. Smith and Son, Part i [ " M r . Cooke's first pamphlet"], 48 p., 1854; Part i [revised to include "Mr. Wheatstone's Answer and Mr. Cooke's Reply," of 1856], 1857; Part ii [Arbitration papers and drawings], 1 8 5 6 ) . M C M 61 Johann Philipp Reis, "Ueber Telephonie durch den galvanischen Strom," Jahresbericht d. Physikalischen Vereins zu Frankfurt am Main, pp. 57-64 (1860—61) LC ; this paper and the critique by Wilhelm von Legat are translated by S. P. Thompson (see next reference); also quoted in translation in the reports of various litigations, e.g., 126 U. S. 33 and 126 U. S. 46 (cf. note 56). 62 Sylvanus P. Thompson, Philipp Reis: Inventor of the Telephone, pp. 131-153 (London, E. & F. N . Spon, 1883). The Reis and von Legat papers are translated at pp. 5 0 - 6 0 and 70-78.

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as to make its achievement largely accidental, owing in part to progressive as well as irregular changes in the condition of the metal surfaces at the point of contact and to the influence of temperature on the diaphragm itself. Many of the defendants in the various infringement suits brought by the owners of Bell's patents sought to show that Bell's invention had been anticipated by Reis, and several replicas of Reis's instruments constructed according to his "teachings" were exhibited in court. These demonstrations did little more than make it obvious that even an understanding of the nature of the required adjustment of the contact did not make it any easier to attain. Nor was it lost on the court that understanding what adjustment was required had to be based on Bell's conception of the method of speech transmission, not Reis's. If one spoke very softly to the Reis transmitter, so that the sound wave was moderate in intensity, and if the sound wave contained no component whose frequency was such as to excite resonance in either the diaphragm or the contact finger, and if the delicate adjustment of contact pressure was very nicely made, so that the contact resistance had some intermediate value between an open and a short circuit, THEN the contact resistance would vary around this intermediate value under the action of the sound wave and there would arise an undulating electric current of just the sort that Bell was claiming as an essential feature of his invention. Most of the time, however, the transmitter would either remain mute with the contact firmly made so t h a t no current variation was produced, or else the contact finger would bounce free a t the peak of each cycle of diaphragm movement, producing what would now be called "square-wave modulation" of the transmitted current. I n spite of stout efforts to show the contrary, no evidence could be found in Reis's writings that he ever contemplated any mode of operation of his transmitter other than one involving complete interruption of the current. What made this conclusion convincing was the additional fact that his receiver was so insensitive that it could not have produced an audible reproduction of speech even when his transmitter was in the rare condition of adjustment necessary for the production of an undulating current. The position that Bell took with regard to the requirement of an undulating current was a very firm one, and he testified under cross-examination on one occasion that the telephonic reception of intelligible speech would constitute positive evidence that the transmitter had pro-

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duced an undulating current.63 Studies of speech transmission conducted during and after World War II have revealed, however, that there is a substantial residue of intelligibility in speech waves that have been converted into square waves by infinite clipping,64 and in the light of these results Bell may have overstated the case for "undulation." It remained an uncontroverted fact, however, that it took either a Bell receiver to make Reis's transmitter talk, or a carbon transmitter of still later invention to make Reis's receiver speak. On the other hand, Bell's moving-armature transmitter did not even have any provision for breaking the circuit; instead, vibration of the armature simply induced in the coil of the transmitter a variable electromotive force. With the materials of construction available, this was a minute electromotive force indeed, but it did produce the required undulating current, and it did so every time, in just the manner and with just the result that Bell had clearly understood and claimed. The court decision summed up this situation in the fateful words: "To follow Reis is to fail; to follow Bell is to succeed." 65 The behavior of Reis's current-interrupting transmitter has been described in considerable detail, chiefly because it played such a prominent role in the legal attacks on Bell's telephone patents. From the point of view of transduction history, rather more interest should attach to the receiver of Reis's telephone, which comprised a coil surrounding an iron rod mounted on a resonating wooden box. Its action was almost certainly magnetostrictive; and because it was provided with a wooden diaphragm to augment the sound radiation and because it was designed for receiving speech signals (whether it ever did or not), it can be accorded the distinction of standing as the first magnetostriction loudspeaker — perhaps the first loudspeaker of any type. The description of Reis's telephone published by Inspector von 63 Bell's testimony on this point was set forth in his deposition taken in "Telephone Interferences A to L " and subsequently admitted as Item 2 of "Evidence for Complainants in Reply" in American Bell Tel. Co. v. Spencer et al., 8 Fed. Rep. 509. In many cases that attract wide attention, as this one did, additional reference material such as briefs and depositions is furnished by the litigants to various law libraries through privately printed publications such as American Bell Tel. Co. v. Spencer: Pleadings and Evidence (Boston, printed under direction of the Clerk, 1881). Bell's testimony appears in this reference at pp. 240-241. M J. C. R. Licklider and Irwin Pollack, "Effects of Differentiation, Integration, and Infinite Peak Clipping upon the Intelligibility of Speech," /.[ournal of the] Acoust[ical] Soc.pety of] Л ж. [erica] 20, 42-51 (January 1948). 85 126 U. S. 545. (see note 56).

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Legat 61 · 62 eventually became better known than Reis's original publication, but neither Reis nor von Legat was able to describe the action of this receiver in terms that showed any clearer understanding of its action than had been exhibited by the followers of Page nearly twenty years earlier. "All God's Chilluns Got Telephones"; or, The Telephone in Court

The work of Elisha Gray filled in part of the gap between Reis and Bell, and his claims eventually occupied a prominent place in the contests for priority of telephonic invention. For several years prior to 1872 Gray had been primarily concerned with telegraphic apparatus, but two incidents steered his interest toward the telephone. The first of these was his discovery that a sound could be produced when an interrupted current was passed between a metal surface and human tissue such as a hand or finger when the latter was kept in motion by drawing it lightly over the metal surface. The principal result of this discovery was a stimulation of Gray's interest in the transmission of musical sounds, and he was soon led to abandon his "animal-tissue" transducer (except for the bizarre patent 6 referred to above) in favor of a magnetic receiver. This receiver comprised an electromagnet, an armature, and an air gap, mounted together on a wooden resonator in such a way that the resonator was excited by the tractive force across the air gap acting against the inertial reaction of the magnet structure. This mode of action of the receiver does not appear to have been understood by Gray, however, since he described its performance in terms of the "well-known fact that an iron rod elongates when magnetized" — an explanation that might more appropriately have been applied to Reis's magnetostriction receiver. An iron pan was used as the diaphragm in another form of Gray's receiver, and this might indeed have served the telephonic function admirably if Gray had been able at that time to couple with it a suitable transmitter. The second incident that steered Gray toward the telephone was his personal discovery — presumably late in 1875 — of the so-called "lovers' telegraph" consisting of two membranes joined by a stretched thread or wire capable of transmitting longitudinal vibrations from one membrane to the other. This suggested to Gray a method of making a telephone transmitter, which he visualized as a diaphragm carrying a short needle partially immersed in a conducting liquid so that the area of contac between needle and liquid, and hence the electric resistance, would vary with the motion of the diaphragm.

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After a diversion of several weeks devoted to his multiple-telegraph interests (which he regarded as more pressing and important at that time), and before he had yet constructed a model of his new transmitter, Gray worked up a description of his invention in the form of a patent specification. This he filed with the U. S. Patent Office, on the afternoon of 14 February 1876, as a caveat 66 signifying his intention to proceed with a reduction to practice and his intention to file later a more complete specification as part of a formal application for a patent. In the meantime, however, Bell's completed application had already been filed in the Patent Office a few hours earlier on the same day. The sequence of filing was important in this case, since Bell's precedence, and the fact that his was a completed application, avoided the declaration of an interference and Bell's patent proceeded to final issuance within three weeks. Gray's legal position was not without substance, however, for although his receiver was less sensitive than Bell's, the "liquid transmitter" that he illustrated in his caveat embodied most of the features of a similar instrument that Bell had described in his application. The workability of such a transmitter was demonstrated by Bell himself when he used it for the first successful transmission of an intelligible sentence on 10 March 1876. The famous "first words" of that occasion — Mr. Watson, come here, I want you — were to become as well known in school textbooks as the more pontifical What hath God wrought with which Morse had opened commercial telegraph service more than three decades earlier. Yes, Gray's telephone would talk, but it was Gray's misfortune that Bell had invented it first. Thomas A. Edison 67 and Amos E. Dolbear,68 the latter a professor at Tufts College, were two others who had worked independently on both transmitters and receivers, and each could, and subsequently did, claim to have invented a complete telephone system. For more than a year 68 Elisha Gray's caveat of 14 February 1876 is quoted verbatim in George B. Prescott, The Speaking Telephone, Talking Phonograph and other Novelties, pp. 202-205 (New York, D. Appleton and Co., 1878). Bell's patent application of the same date is also exhibited for contrast, pp. 205-215. ST T. A. Edison communicated an account of his telephonic researches to G. B. Prescott, who published it at pp. 218-234 of the 1878 edition of his Speaking Telephone . . . (see preceding note). A further account of Edison's later work was added, pp. 126-174, in Prescott's retitled and revised edition, Bell's Electric Speaking Telephone (New York, D. Appleton and Co., 1884). 68 Amos Emerson Dolbear, The Telephone (Boston, Lee & Shepard, Pub., New York, Chas. T. Dillingham, 1877); see also Proceedings of the American Academy of Arts and Sciences 14 (of new series, 6) 77-91 (1878).

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following the sensation created by Bell's exhibition of his telephone at the Philadelphia Centennial Exhibition in June 1876, the Western Union Telegraph Company displayed a studied disinterest in Bell's experiments. When it became apparent during the latter part of 1877 that this new mode of communication posed the threat of serious competition, Western Union sought to protect its position by acquiring for its subsidiary, the Gold and Stock Telegraph Company, the services and patent interests of Professor Dolbear. A few months later the Gold and Stock Telegraph Company made arrangements to acquire Gray's interests also and the American Speaking Telephone Company was set up to exploit these interests by offering a competitive telephone service to the public. Early in 1878 they added to their arsenal the right to make use of Edison's newly developed carbon transmitter. In due course, as expected, the American Bell Telephone Company brought a suit for infringement against Peter A. Dowd, an agent of the pyramid of companies associated with Western Union. The defendants in this case elected to base their defense on Gray's claims for priority of invention, and voluminous testimony, running to more than 1,400 printed pages, was introduced during the two years this case was in preparation.69 The case never came on to be heard, however, for the testimony so clearly established Bell's position as the first inventor that the chief counsel for Western Union advised his clients to settle out of court on the best terms they could get. The first important case involving Bell's patents that actually reached the stage of adjudication was American Bell Tel. Co. v. Albert Spencer.™ In

this case, as in a long list of other cases brought in the Circuit Courts, the Bell patent was sustained. The most notorious of these was American Bell Tel. Co. v. People's Telegraph Co.,71 which was based on the extravagant claims of one Daniel Drawbaugh — claims that not only embraced Bell's original invention, but also several subsequent improvements contributed by Edison, Gray, Blake, and others. When it became apparent that all of these cases were scheduled to reach the Supreme Court on appeal at about ·· American Bell Tel. Co. v. Peter A. Dowd; a Bill (No. 1040) in equity filed 12 September 1878 in the U. S. Circuit Court, District of Massachusetts. Part I, Pleading and Evidence: Part II, Exhibits (Boston, Alfred Mudge & Son, Law Printers, 1880). Consent decree entered 4 April 1881 (first validation of Bell's famous Claim 5). For details concerning the "surrender" of counsel, see 126 U. S. 466. 70 American Bell Tel. Co. v. Albert Spencer, 8 Fed. Rep. 509 [1881]. 71 American Bell Tel. Co. v. Peoples Telegraph Co., 22 Blatchford 531, 22 Fed. Rep. 309 (1 December 1884).

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the same time, their pleading was consolidated, and the issue of priority was conclusively resolved by the Supreme Court in the decision referred to above.66 Transducers,

Telephonic and

Miscellaneous

While the decision in "The Telephone Cases" settled once and for all the basic question of who invented the telephone, there remained a rich field for the development of improvements in telephone instruments. Alternative methods for performing the various functions of telephony were avidly sought and it was under the impetus of this stimulation that the catalog of electroacoustic transducers was rounded out during the period between 1876 and 1880. The telephone receiver quickly achieved a relatively mature state of development. The first major improvement in the receiver was the introduction of a permanent magnet, which eliminated the necessity of transmitting a polarizing current over the line. Dolbear conceived this idea independently, but the permanent magnet had been mentioned explicitly in the second Bell patent 7 2 and these claims were eventually validated by the Supreme Court along with the famous fifth claim of Bell's first patent. Most of the modifications of the receiver that were produced within the four years following the issuance of Bell's patent represented little more than ingenious attempts to improve the geometrical configuration of the magnetic structure in order to overcome some of the inherent weakness of the permanent-magnet materials then available. By 1881 the bipolar moving-armature receiver had substantially acquired the definitive form it was to retain for more than 50 years, the changes to be incorporated during this long interval consisting principally of those made possible by basic improvements in the materials of construction. The transmitter was still the weakest link in the telephone chain in 1878, just as it had been in Reis's time. While still engaged in defending the Dowd suit for infringement of Bell's patent, the American Speaking Telephone Company began to supply its customers with a variablecontact-pressure carbon transmitter that had been designed for them by 72

A. G. Bell, U. S. Pat. No. 186,787 (filed 15 January 1877) issued 30 January 1877. [Telephone receiver using "permanent magnet with a plate of iron or steel, or other material capable of inductive action, with coils upon the end or ends of said magnet nearest the plate."]

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Edison.73 What proved downright embarrassing to Bell was that this instrument consistently outperformed the magnetic transmitter still being supplied by the American Bell Telephone Company. Thus, in spite of the fact that his magnetic transmitter had been substantially improved since its first exhibition in 1876, Bell's supporters stood in danger of losing before the public while winning before the Court. It is not surprising, therefore, that they seized eagerly the opportunity presented early in 1878 to acquire the rights in a carbon transmitter designed by Francis Blake.74 Another patent wrangle was in the offing, however, for Emile Berliner 75 had filed a caveat describing his claim to the invention (but see below) of a variable-contact-pressure microphone some two weeks before Edison had filed the application covering his version of the carbon microphone, and both applications predated the Blake disclosure. The prior date of Berliner's caveat automatically evoked an interference when Edison's application came in, so there was some delay — a very long one as it turned out — in determining who was the first inventor of the "loose-contact" microphone. The American Bell Telephone Company attacked this problem in an obvious and forthright way: Edison was already in the enemy's camp, but they could, and did, promptly acquire both Berliner's patents and his services; and they assigned him at once to the task of removing the instability that had already cropped up in the Blake transmitters. By a technical tour de force of considerable distinction, Berliner carried out this assignment within six weeks, not only solving the problem of manufacturability, but also that of making the performance of the modified Blake transmitter surpass that of the contemporary Edison instruments. When Berliner joined forces with Bell, he also brought with him his patent on the induction coil for use in conjunction with a low-resistance 73 Thomas A. Edison (assignor to Western Union Telegraph Co.), [the "variable pressure" carbon microphone] three U. S. Pats. No. 474,230 (filed 27 April 1877), No. 474,231 (filed 20 July 1877), and No. 474,232 (filed 18 February 1886 as a division of the application of 20 July 1877), all finally issued 3 M a y 1892. Also British Pat. No. 2909 [30 July 1877], French Pat. No. 121,687 [ 1 9 December 1877], and similar patents in 7 other countries. 74 Francis Blake, [carbon transmitter] U. S. Pats. Nos. 250,126 to 250,128 (filed 15 September 1881) and No. 250,129 (filed 31 October 1881) issued 29 November 1881. The subject matter of all four had been combined in British Pat. No. 229, dated 20 January 1879. 76 The text of Berliner's caveat filed in the U. S. Patent Office 14 April 1877 is given b y Frederic Wm. Wile in Emile Berliner, Maker of the Microphone, Appendix I, pp. 3 0 9 313 (Indianapolis, Bobbs-Merrill Co., 1926); the complete application was filed 4 June 1877 and Pat. No. 463,569 finally issued 17 November 1891.

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transmitter, and this instrument together with the Blake-Berliner transmitter was sufficient to make secure for nearly two decades the American Bell Telephone Company's position of leadership in the rapidly expanding field of telephony. There was more trouble ahead, however. Berliner had followed up his caveat with a completed application filed within two months, but, for some reason never satisfactorily explained, there was an extraordinary delay in resolving his interference with Edison. The interference was at last settled in Berliner's favor at the Patent Office level and his transmitter patent was finally issued in 1891. As soon as it became generally realized that the delayed issuance of the Berliner patent virtually extended the telephone monopoly for another 17 years, a storm of popular protest broke out. A few newspapers supported this agitation, which finally provoked an appeal to the Supreme Court in a legal action brought earlier by the Attorney General in an effort to cancel all of the controlling telephone company patents. This classic suit was in litigation during the 1890's, at a time when "big business" was engaged in laying a foundation for the bitterness that was to be heaped on its head with much less justice 40 years later. As a result, a good bit of ill-temper was displayed before the Supreme Court 76 finally exonerated both the Telephone Company and Berliner from any culpability in connection with the delays that inadvertently extended their monopoly. This decision was concerned primarily with the issue of fraud and delay, and it did not undertake to rule on the question of whether Berliner's loose-contact transmitter patent was actually valid or not. It turned out to be more than a little ironical when another decision handed down four years later in the Circuit Court held the Berliner patent to be invalid.77 As a consequence, by long-delayed accounting, it is Edison to whom credit finally returns for the invention of the variable-contactpressure carbon transmitter. By this time, however, the Telephone Company could take the position that such an interchange of inventors was a matter of relatively minor importance: they had already enjoyed the use and supposed protection of the Berliner patent for nearly its normal life expectancy; but, in the meantime, they had also acquired from Edison his residual rights in the carbon microphone. Two English inventors, Hughes and Hunnings, made substantial con76 United States of America v. American Bell Tel. Co. and, Emile Berliner, 167 U. S. 224 [1897]. 77 109 Fed. Rep. 976 [1901].

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tributions to the early development of the carbon transmitter, although each made his invention just too late to reap the rewards that go with being first. Hughes 78 was not concerned about this, however, since he had already entered a disclaimer by concluding his Royal Society paper with the comment, " I do not intend to take out a patent, as the facts I have mentioned belong more to the domain of discovery than invention . . . I have already my reward in being allowed to submit my researches to the Royal Society." What Hughes had discovered was the telephonic virtue of the variable-contact-pressure transmitter, whose remarkable sensitivity led him to introduce the apt word "microphone" to describe such a transducer. This was not a newly coined word — Wheatstone 79 had used it in 1827 to describe an all-mechanical vibration stethoscope — but it was free from the ambiguity associated with the word "transmitter" and its usage as a designation for the acoustic-to-electric transducer is now universal. Hughes also presented in his Philosophical Magazine paper the first published description of the "howling telephone." For these experiments Hughes had been making use of two telephone receivers connected in series with a microphone mounted on a resonant wooden sounding board. The condition of self-oscillation was discovered accidentally, Hughes remarking that "when one of these [receivers] is placed on the resonant board, sound comes from the other." In modern terminology this could be called a positive-feedback oscillator using electroacoustic transducers in the feedback path, and it is all the more worthy of notice because it is probably the first recorded examplar of this type of self-excited oscillator. Hughes was not unaware of the essential role played by amplification in such a self-excited system, for he added the remark that "it follows that the question of providing a relay for the human voice in telephony is thus solved." To call this problem "solved" at that point overstates the case a bit, to put it mildly, but to have made these observations at all under the circumstances represents a brilliant example of inspired insight. 78 David Edward Hughes, "On the Action of Sonorous Vibrations in varying the Force of an Electric Current," P r o c e e d i n g s of t h e ] Roy.[p.\~] Soc.[iety] (London) 27, 362-369 (1878); "On the Physical Action of the Microphone," Phil. Mag. [ 5 ] 6, 44r-50 (1878), and Proceedings of the Physical Society (London) 2, 255-261 (1878). ™ Sir Charles Wheatstone, [the "microphone"] in "Experiments on Audition," Quarterly Journal of Science, Literature, and Art (London) 24, 6 7 - 7 2 (July-October 1827); reprinted in The Scientific Papers of Sir Chas. Wheatstone, pp. 32-33 [published for the Physical Society of London] (London, Taylor and Francis, 1879).

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To Hunnings 80 goes the credit for inventing a carbon transmitter using a multiple loose contact, which soon took the form of a disk electrode projecting into a contact cup containing granulated carbon particles. From that time on, one improvement followed another in seemingly endless parade, but no further attempt will be made here to trace the successive stages in the development of the carbon microphone.81 Its present standing as an electroacoustic transducer can be summarized in two statements: More than 40 million of them continue to serve well and adequately the transmitter function in telephones throughout the world; yet the fundamental physics of the surface-contact phenomena on which their operation depends is still not fully understood. When the smoke of all the priority contests in telephony had cleared away, Thomas A. Edison emerged as the contributor of the carbon transmitter, one of the vital components of the modern telephone. His contributions to multiplex telegraphy had already been substantial and he further consolidated his claim to immortality by sharing the midwifery of the incandescent lamp during the period 1877-1880. But there was more; Edison 82 made two other inventions that were ultimately to play a major role in stimulating and providing a market for electroacoustical transduction, namely, the phonograph (1877) and motion pictures (1891). The latter came a little too late to fall within the golden age of transduction; but if further evidence is needed to establish the 1870's as vintage years for acoustics, one can always fall back on the fact that the first edition of Lord Rayleigh's Theory of Sound was published in 1877. The moving-armature receiver and the carbon microphone were not the only electroacoustic transducers to come in for attention during the latter part of the "transducing 1870's." In fact, under the stimulation provided by the objective evidence that "there was a future" in electro80 Henry Hunnings, [granulated-carbon microphone] British Pat. No. 3647 dated 16 September 1878; U. S. Pats. No. 246,512 (filed 14 May 1881) issued 30 August 1881, and No. 250,250 (filed 30 September 1881) issued 29 November 1881; both assigned to American Bell Telephone Co. 81 But see H. A. Frederick, "The Development of the Microphone," J. Acoust. Soc, Am. 3, Supplement (25 p.) to July issue (1931). 82 T. A. Edison, [phonograph] U. S. Pat. No. 200,521 (filed 24 December 1877) issued 19 February 1878, followed for the next 30 years by many others directed to improvements. This original application represents one of the few cases on record in the Patent Office wherein the Examiner could find no prior-art reference to cite; [motion pictures] U. S. Pat. No. 589,168 (filed 24 August 1891) issued 31 August 1897; reissued in two parts, as RE. 12,037 and RE. 12,038, both dated 30 September 1902; and again as RE. 12,192 dated 12 January 1904.

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acoustical transduction, the whole gamut of electrical manifestations was recanvassed in a search for useful mechanisms of transduction. A few of these are still of passing interest. For example, Edison 83 patented a frictional transducer, which capitalized on the fact that an impressed electric potential could alter the frictional drag of a metal band making contact with a portion of the periphery of a rotating cylinder of chalk. This was actually an invention delivered on request; in order to evade a nuisance patent dealing with a minor but essential feature of the ordinary telegraph relay, Edison came up with this scheme as a possible substitute for the electromagnetic relay itself. Edison recognized that it could also serve as an electroacoustic transducer, since, when one end of the metal brake band was connected to a radiating diaphragm and the other to a spring supplying polarizing tension, very substantial amounts of sound could be produced. Edison called this device an " electromotograph," and he incorporated such a contrivance in a so-called loud-speaking telephone. The fundamental nature of this transduction mechanism is still not well understood, but its principle of operation seems closely related to that of Gray's animal-tissue transducer, and it undoubtedly served as a point of departure for the friction-operated transducer mechanism described by Johnsen and Rahbek 84 in 1919. While these frictional-drive mechanisms would appear to be highly vulnerable to nonlinear distortion and to a variety of "noise" effects, practitioners of the servo arts might still find them worth considering as torque amplifiers. Several inventors attempted to produce telephone transmitters that made use of liquid jets. One of the first of these was described by JervisSmith.85 Later on, when there was a scramble to find methods of impressing voice modulation on the output of a "wireless" transmitter, F. J. Chambers 86 and G. Vanni 87 sought to use the same principle by 83 T. A. Edison, [the "electromotograph"] U. S. Pat. No. 158,787 (filed 7 August 1874) issued 19 January 1875; also [the loud-speaking telephone] U. S. Pat. No. 221,957 (filed 24 March 1879) issued 25 November 1879. 84 Alfred Johnsen and Knud Rahbek, "A Physical Phenomenon and its Applications to Telegraphy, Telephony, etc.," /.[ournal of the] J»ii.[itution of] £/ec.[trical] £reg[inee]w. {London) 61, 713-725 (July 1923); see also British Pats. No. 144,761 (filed 6 March 1919, complete specification accepted 7 June 1920), and No. 194,747 (filed 14 November 1921, complete specification accepted 14 March 1923). 85 F· J. [Jervis-]Smith; his "liquid rheostat" is briefly noticed in Nature 20, 552 (1879), and in the Telegraphic Journal 7, 321 (1879). 86 F. J. Chambers, "The Chambers Liquid Microphone," The Electrician (London) 66, 560-561 (15 July 1910). 87 Giuseppe Vanni, "Sur quelques experiences nouvelles de telephonie sans fil,"

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allowing the sound wave to produce a variation in the effective length or area of a jet column forming part of the electric circuit. In the meantime, the influence of a sound wave on the point at which a liquid jet would break up into droplets had been discovered in 1886 by Chichester Bell 88 (a cousin of Alexander Graham Bell), who later joined forces with Sumner Tainter in the contribution of the engraved, rather than the embossed, groove to the development of the phonograph. Bell had introduced two electrodes into such a variable jet in order to study its performance by observing the resistance variation, and although he recognized that this mechanism would perform as a telephone transmitter, he did not think it represented a very good one. Majorana 89 developed this type of jet transmitter more extensively and used it in carrying out one of the very early demonstrations of radio telephony (late 1903). Electroacoustics had already been allied with radio by Greenleaf W. Pickard,90 who had succeeded in transmitting intelligible speech by radio about a year earlier (6 September 1902). R. A. Fessenden reported later that he had carried out similar experiments as early as the summer of 1900. Each of these pioneers was forced to use a noncontinuous r.f. carrier furnished by a high-frequency intermittent spark having a repetition rate of 8 to 10 kc/s, and each reported poor speech quality (but intelligible!) and a signal-to-noise ratio that hardly exceeded unity. Fessenden 91 realized sooner than others did, however, that a continuous carrier Bulletin de la Societe Internationale des Electriciens (after 1918, the Societe Frangaise des Electriciens) [3] 3, 503-518 (1913); also, "Fenomeni presentati dae getti liquidi e loro applicazione ai microfoni idraulici ed alia telephonia senza file," Rivista Technica d'Elettricita (Milan) (formerly I'Elettricita) 44, part 2, pp. 149-151, 157-159 and 165167 (4 November 1915) . M C M 88 Chichester A. Bell, "On the Sympathetic Vibrations of Jets," Phil. Trans. Roy. Soc. (London) 177, 383-422 (1886). 89 Quirino Majorana, "Ricerche ed esperienze di telefonia elettrica senza filo," Atti della Reale Accademia Dei Lincei, Rendiconti [5] 132, 86-94 (1904); and II Nuovo Cimento [5] 8, 32-42 (1904); also British Pat. No. 14,314 [1905] (filed 11 July 1905, accepted 23 November 1905). 90 Greenleaf W. Pickard, "Hertzian Wave Transmission of Speech," dated 6 September 1902 — an unpublished memorandum from the files of the "Special Work" division of А. Т. & T. Co.'s Engineering Department. I am indebted to Mr. Pickard for calling my attention to this report, and to Lloyd Espenschied, of the Bell Telephone Laboratories, for access to it. F.V.H. 91 Reginald A. Fessenden, "Recent Progress in Wireless Telephony," Scientific American 96, 68-69 (19 January 1907); "Long Distance Wireless Telephony," The Electrician (London) 69, 985-989 (4 October 1907). Another account by John Grant, "Experiments and Results in Wireless Telephony," The American Telephone Journal 16, 49-51 (26 January 1907) and 68-70, 79-80 (2 February 1907).

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was a prime requirement and he was the first to achieve an acceptable degree of freedom from noise in radio telephony by using such a carrier (the Brant Rock-Plymouth tests conducted before invited guests on 21 December 1906). Four days later, Fessenden made the first radio broadcast — an impromptu program of Christmas music and readings that was received with amazed delight by several radio-equipped boats of the New England fishing fleet. On the thermal front of transduction, Preece 92 devised a novel telephone receiver in which the signal current passed through a fine platinum wire stretched tightly between a fixed support and a sound-radiating diaphragm. The heat capacity of the wire was so small that its temperature could follow at least the low-frequency components of the signal current, and transduction took place through the variations in tension on the diaphragm produced by variations in thermal expansion of the fine wire. One can hardly be surprised, however, by Preece's report that " N o sibilant sounds whatever could be produced." A few years later, Forbes 93 carried out experiments on the microphone version of a thermal transducer, the mechanism of transduction in this case being the periodic cooling of a hot wire by the "local wind" corresponding to the particle velocity in the sound wave. Forbes mounted his hot wire in a transverse saw-cut at the closed end of a cylindrical wooden resonator. This scheme was revived 30 years later by W. S. Tucker, 94 who made a singularly effective sound receiver by mounting the hot wire in the narrow aperture of a Helmholtz resonator. By the ingenious trick of capitalizing on the diffraction "bright spot" behind an opaque circular obstacle, this receiver was endowed with directivity as well as sensitivity, and it was used effectively during World War I as an acoustic locator for enemy artillery. In the meantime, F. Braun, 95 otherwise distinguished as the inventor of the cathode-ray oscilloscope, had discovered that sound could be 82

Sir Wm. Henry Preece, "On some Thermal Effects of Electric Currents," Proc· Roy. Soc. (London) 30, 408-411 (1880). ,3 George Forbes, "A Thermal Telephone Transmitter," Proc. Roy. Soc. (London) 42, 141-142 (1887). 94 W. S. Tucker and Ε. T. Paris, "A Selective Hot-Wire Microphone," Phil. Trans. Roy. Soc. (London) A 221, 389-430 (1921); also W. S. Tucker, "The Hot Wire Microphone and its Applications to Problems of Sound," Journal of the Royal Society of Arts (London) 71, 121-134 (5 January 1923). " Ferdinand Braun, "Notiz über Thermophonie," (Wiedemann's) Annalen der Physik und Chemie 66, 358-360 (1898).

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generated by the alternate thermal expansion and contraction of the layer of air in contact with a metallic foil made so thin that its temperature would fluctuate in accordance with the instantaneous magnitude of an impressed alternating current. Although this was a feeble sound source, it had the rare advantage that the sound pressure produced could be calculated in terms of measurable nonacoustic physical constants, and such a thermophone was used to good advantage by Arnold and Crandall 96 for the absolute calibration of microphones. The capillary electrometer as a receiver for wireless telegraphy, the speaking incandescent electric lamp, the singing arc, and the talking flame — measures of desperation these were; yet each came in for its share of attention as the search continued — and still does, for that matter — for new and perhaps better methods of electroacoustical transduction. What this art needed, whether it knew it or not, was the blessing of electronic amplification! The last two of the " conventional" transducer mechanisms — the piezoelectric and the moving-conductor or "dynamic" — made their first definitive appearance during the period 1877-1881, and the electrostatic made a brief transitory reappearance. In the latter connection, both Edison 67 and Dolbear described complete telephone systems using electrostatic transducers to serve both transmitting and receiving functions. Dolbear 97 exploited this mode of transduction more enthusiastically, however, and went so far as to construct a complete electrostatic demonstration telephone which he displayed at the Paris Electrical Exhibition of 1881. He also sought to set up this substitution of mechanism as a defense in his portion of the consolidated Telephone Cases.66 This was a defense that would indeed have prevailed over most of Bell's conflicting claims; but of Bell's sweeping Claim 5, Dolbear's attorney could only say, "Without this we cannot operate." Claim 5 stood up, however, and since Dolbear's instruments offered no other unique advantage over those then being offered to the public, little more was heard of electrostatic transducers in connection with telephony until the con" H. D. Arnold and I. B. Crandall, "The Thermophone as a Precision Source of Sound," PAyi.[ical] Äei).[iew] [2] 10, 22-38 (July 1917); but see also, for associated difficulties, Stuart Ballantine, "Technique of Microphone Calibration," J. Acoust. Soc. Am. 3, 319-360 (January 1932). 87 A. E. Dolbear, "A new system of telephony" [with a full-page frontispiece of quaint illustrations], Scientific American 44, 388-389 (18 June 1881); also, U. S. Pats. No. 239,742 (filed 11 October 1880) issued 5 April 1881, and No. 240,578 (filed 24 February 1881) issued 26 April 1881.

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denser microphone 98 reappeared as a laboratory instrument of high precision in 1918. In the meantime, Fessenden 99 and Burstyn 100 each applied for patents on "talking condensers" for use as modulators or demodulators of radiofrequency signals. The piezoelectric effect was the last of the major mechanisms to make its bow on the transducer scene. Jacques and Pierre Curie101 are usually credited with first discovering, in 1880, the ability of certain crystals to develop spontaneous electric polarization under the action of mechanical forces. As for all the other electromechanical effects, however, there were a good many precursors of the Curies' singular observations. Part of this background was provided by the phenomena of pyroelectricity, which had been brought under casual study several centuries earlier through the observation that pieces of tourmaline would acquire the ability to attract bits of paper and the like when subjected to heating. The electric surface charges that appeared when certain natural crystals were cleaved had also been observed. Not very much of this early literature dealt directly with the somewhat different piezoelectric effect, in which surface charges appear that are quantitatively proportional to the applied mechanical stress. However, Coulomb is said to have speculated about the possibility of producing electricity by pressure; and Haüy, 102 the godfather of crystallography, and Antoine Cesar Becquerel 103 (the grandfather of the Nobel laureate, A. Henri Becquerel) each carried out systematic experiments that were as surely predictive of the piezoelectric effect as Page's observations of galvanic music had been of magnetostriction. The study of these disjointed observations in 1878 led Lord 98 Edward Christopher Wente, " A Condenser Transmitter as a Uniformly Sensitive Instrument for the Absolute Measurement of Sound Intensity," Phys. Rev. 10, 39-63 (July 1917). 89 R. A. Fessenden, British Pat. No. 13,678 [1905] (filed 3 July 1905, accepted 12 October 1905). 100 Walther Burstyn, German Pat. No. 207,949 (filed 4 April 1908) issued 12 May 1909, U. S. Pat. No. 1,148,827 (filed 25 March 1909) issued 3 August 1915, and British Pat. No. 7906 [1909] (filed 2 April 1909, accepted 31 March 1910). 101 Jacques Curie and Pierre Curie, "Developpement par compression de l'electricite polaire dans les cristaux hemiedres ä faces inclines," Bulletin de la Sociele Mineralogique de France 3, 90-93 (1880); also in Compt. Rend. 91, 294-295, 383-386 (1880). 102 Rene-Just Haüy, "Sur l'filectricitc Produite dans les Mineraux ä l'aide de la pression," Memoires du Museum d'Histoire Naturelle (Paris) 3, 223-228 (1817), reprinted in Ann. Chim. et Phys. [ 2 ] 6, 95-101 (1817). 103 Antoine Cesar Becquerel, "Sur le developpement de l'electricite dans les corps par la pression et la dilatation," Bulletin des Sciences, par la Societe Philomatique de Paris [3] 7, 149-155 (1820); "Sur le Developpement de l'electricit6 par la pression; Lois de се developpement," Ann. Chim. et Phys. [ 2 ] 22, 5-34 (1823).

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Kelvin 104 to postulate a state of permanent polarization in all crystals exhibiting these effects. The existence of such a background of antecedent studies and experiments does not reduce the credit due the Curies, since their discovery of piezoelectricity was in no sense accidental; instead, they were led by their own systematic studies of pyroelectric phenomena and of crystal symmetry to-predictthat the class of crystals exhibiting pyroelectricity would also develop polar electricity when subjected to pressure variations along specific crystal axes. They were able to show experimentally that such charges were indeed produced, and that they were proportional to the pressure and would disappear when the pressure was removed. There are interesting contrasts to notice between the postdiscovery development of piezoelectricity and the corresponding phase of the magnetostriction story. The sister sciences, especially thermodynamics, had made great strides since the middle of the century, and things could now move rapidly. The converse piezoelectric effect was predicted theoretically by Lippmann 105 within less than a year after the Curies' announcement, and the physical existence and the quantitative reversibility of the converse effect was experimentally verified by the Curie 106 brothers only a few months later. The Curies soon undertook to turn these effects to the useful purposes of transduction by designing a piezoelectric instrument 107 for measuring forces or electric charges. Kelvin's paper of 1878 and the Curies' pioneer observations aroused the interest of Röntgen,108 who took up the burden of wrestling with the 104

Sir Wm. Thomson (Lord Kelvin), " O n the Thermoelastic, Thermomagnetic, and Pyroelectric Properties of Matter," Phil. Mag. [5] 6, 4-27 (1878). 106 Gabriel Lippmann, "Sur le principe de la conservation de l'electricite," Compt. Rend. 92, 1049-1051, 1149-1152 (1881); also Journal de physique [1] 10, 381-394 (1881), and Ann. Chim. et Phys. [5] 24, 145-178 (1881). 106 Jacques Curie and Pierre Curie, "Contractions et dilatations produites par des tensions electriques dans les cristaux hemiedres ä faces inclinees," Compt. Rend. 93, 1137-1140 (1881), and Oeuvres de Pierre Curie, pp. 26-29 (Paris, Gauthier-Villars, 1908). 107 The "quartz piezo-electrique," described at pp. 392 et seq. in the article by Jacques Curie, Ann. Chim. et Phys. [6] 17, 385-134 (1889); also as the appendix of Kelvin's 1893 paper in Phil. Mag., pp. 340-342 (see note 110); and in Oeuvres de Pierre Curie, pp. 554-563 (see preceding note); also J. and P. Curie, French Pat. No. 183,851, dated 27 May 1887. los Wilhelm Konrad Röntgen, "Ueber die durch elektrische Kräfte erzeugte Aenderung der Doppelbrechung des Quarzes," (Wiedemann's) Annalen der Physik und Chemie 18, 213-228 (1883); "Ueber die thermo-, actino- und piezoelectrischen Eigenschaften des Quarzes," ibid. 19, 513-518 (1883); "Elektrische Eigenschaften des Quarzes," ibid. 39, 16-24 (1890).

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complexities of understanding the electric charges that appeared on various minor facets of different crystals undergoing stress. C. Friedel and J. Curie 109 made a further contribution to the problem, and, in due course, Kelvin110 acknowledged all these amendments of his earlier work and made another effort himself to wrap up the subject. In the meantime, the great physical chemist, Duhem,111 had already offered a brilliant formulation of the piezoelectric relations in terms of thermodynamic potentials. F. Pockels 112 also addressed himself to a similar task, as did the great crystallographer Woldemar Voigt.113 Voigt had a supreme command of the crystallographic aspects of the piezoelectric problem, and the general theory of piezoelectricity that he advanced in 1890 was not effectively challenged for more than half a century. His detailed formulation of the piezoelectric relations, however, did not go far — in fact, did not need to go far — beyond that given by Duhem. Electroacoustics

Goes ίο Sea

Scientific interest in piezoelectricity was sustained during the following two decades, but technological utilization of it did not really begin until the French physicist Paul Langevin took up the subject in February 1917. The initiation of preliminary experiments in this field was preceded, however, by another transitory period of preoccupation with electrostatic transduction. 108

Charles Friedel and Jacques Curie, "Sur la pyroelectricite du quartz," Bulletin de la Societe Mineralogique de France 5, 282-296 (1882); also in Com.pt. Rend. 96, 12621269, 1389-1395 (1883). 110 Sir Wm. Thomson (Lord Kelvin), "On the Piezo-electric Property of Quartz," Phil. Mag. [5] 36, 331-342 (1893); "On a Piezo-electric Pile," ibid., pp. 342-343; "On Electric Molecules for the Explanation of the Piezo-electric and Pyro-electric Properties of Crystals," ibid., p. 384; "On the Theory of Pyro-electricity and Piezo-electricity of Crystals," ibid., pp. 453-459. 111 Pierre Duhem, "Applications de la Thermodynamique aux phönomenes thermo61ectriques et pyro-61ectriques," Лии.[ales] S«.[entifique de L'JEcole iVom.[ale] 5и/>.[рёпеиге] [3] 2,405424 (1885), 3, 263-302 (1886); "Sur les pressions ä l'interieur des milieux magnetiques ou di61ectriques," Com.pt. Rend. 112, 657-658 (1891); "Sur la (^formation 61ectrique des cristaux," Ann. Set. Ecole Norm. Sup. [3] 9, 167-176 (1892). us Friedrich Pockels, "Ueber die Aenderungen des optischen Verhaltens und die elastischen Deformationen dielektrischer Krystalle in elektrischen Felde," Neues Jahrbuch für Mineralogie Geologie und Palaeontologie [Beilage-B awT] 7, 201-231 (1890). из Woldemar Voigt, "Allgemeine Theorie der piezo- und pyroelectrische Erscheinungen an Krystallen," Abhandelungen der Gesellschaft der Wissenschaften zu Göttingen 36, (Math. Classe, Part 2), 1-99 (1890): and, of course, Lehrbuch der Krystallphysik (Leipzig, B. G. Teubner, 1910, 1928).

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The stage for these experiments was set in 1912 by L. F. Richardson,114 a Briton who advanced two proposals for enhancing the safety of ocean transport. The first of these was a scheme for obstacle avoidance based on echo ranging with airborne sound. There can be no doubt about the particular obstacles Richardson had in mind, since he filed this proposal in the British Patent Office just five days after the Titanic's tragic collision with an iceberg. An ingenious feature of his scheme was a suggestion for discriminating between the transmitted signal and the echo by using a frequency-selective receiver detuned from the transmitting frequency by just the amount required to compensate for the Doppler shift arising from motion of the echo-ranging vessel. The second proposal, essentially an underwater analog of the first, was filed a month later and was directed toward "detecting the presence of large objects under water by means of the echo of compressional waves having a wavelength in water of 30 cm or less . . . directed in a beam . . . by a projector having an aperture of at least 3X". Richardson took no constructive steps himself to implement either of these proposals, and he was apparently not aware that R. A. Fessenden 115 was already engaged in designing a novel form of moving-coil transducer for operation at much lower frequencies but otherwise intended both for echo ranging and for signaling. Fessenden's preliminary experiments were agreeably successful and an iceberg was indeed detected by underwater echo ranging 116 on 27 April 1914 at a distance of nearly two miles. By the end of 1914 the impending submarine menace of World War I was directing attention toward the detection of a different kind of "ob114 Lewis Fry Richardson, [echo ranging with sound in air] British Pat. No. 9423 [1912] (filed 20 April 1912, complete spec. 18 October 1912, accepted 6 March 1913); [ultrasonic echo ranging with underwater sound] British Pat. No. 11,125 [1912] (filed 10 May 1912, complete spec. 10 December 1912, accepted 27 March 1913). 116 Reginald A. Fessenden, U. S. Pats. No. 1,207,388 (Appl. Ser. No. 744,793 filed 29 January 1913) issued 5 December 1916; No. 1,167,366 (Appl. Ser. No. 770,857 filed 13 May 1913 as a division of the parent Appl. Ser. No. 744,793) issued 4 January 1916; No. 1,213,610 (Appl. Ser. No. 53,896, filed 4 October 1915 as a division of the parent Appl. Ser. No. 744,793) issued 23 January 1917; and No. 1,213,611 (Appl. Ser. No. 53,895 filed 4 October 1915 as a division of Appls. Ser. Nos. 744,793 and 770,857) issued 23 January 1917. See also Long-Distance Submarine Signalling by Dynamo-Electric Machinery, a lecture delivered 25 February 1914 before a special joint meeting of the American Academy of Arts and Sciences and the Lawrence Scientific Association held in the test laboratory of the Submarine Signal Company (Boston), and published by the Lawrence Scientific Association, Boston, Massachusetts, June 1914. ш This echo-ranging "first" on 27 April 1914 is recorded in an official report by Captain J. H. Quinan appearing in the U. S. Hydrographie Office Bulletin for 13 May 1914.

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stacle" in the sea. A y o u n g Russian electrical engineer, Constantin Chilowsky, whose imagination had, like Richardson's, been fired b y the Titanic disaster, was then convalescing from tuberculosis in a Swiss mountain hotel where his thinking on this problem crystallized into a plan for detecting submarines b y echo ranging with high-frequency sound waves. W i t h the hope of bringing his scheme somehow to the attention of the French government, Chilowsky w e n t to Dr. Milhaud, a patriotic French citizen who was the Professor of Political E c o n o m y at Geneva University. Professor Milhaud, after testing Chilowsky's qualifications in a remarkable way, 1 1 7 agreed to forward his proposal. Within a m o n t h — which is probably about par for that course — it reached the sympathetic hands of the mathematician Painleve, who was Minister of the Bureau des Inventions and who recognized at once the merits of the scheme and forwarded it to the distinguished physicist Paul Langevin 118 (February 1915). Chilowsky's original scheme envisaged the use of a moving-armature magnetic transducer in which the diaphragm was to be finely laminated in order to reduce the eddy-current losses, b u t Langevin was not sanguine about the prospects of success with such construction. After a m o n t h of careful study, during which both magnetostriction 117 After examining Chilowsky's proposal, Professor Milhaud said, "This is tremendous, but I can't forward it to my friends in the French Government because I have no proof that it is not pure fantasy . . . Can you give me any proof that you are an inventor capable of such great things? . . . Come back tomorrow." When Chilowsky returned next day, Professor Milhaud was ready to propose a test: "Prove to me," he said, " that you have at least modest inventive ability... Go to my friend Dr. Guye, the Professor of Physics, and propose to him any even small invention. If he approves, I will forward your proposal to France." Chilowsky rose handsomely to the occasion and proposed to Professor Guye an induction-balance scheme for detecting bullets embedded in the body — two coils at right angles, one carrying alternating current, the other connected to a telephone receiver. Professor Guye set about at once to test the scheme, was astonished by its immediate success, and quickly gave his endorsement of Chilowsky's inventive caliber to Professor Milhaud. [Based on a private communication from C. Chilowsky J 118 The following account is based on Langevin's "Account of the Research Work Carried on in France," forming an attachment to the Report of an Inter-Allied Conference on the Detection of Submarines by the Method of Supersonics [held at Paris, 19-22 October 1918]. U. S. delegates to this conference included Professors H. A. Bumstead, J. H. Morecroft, К. T. Compton, and Lt. Cdr. E. C. Raguet, U.S.N. The Conference Report (Reference No. 161), submitted by К. T. Compton on 31 October 1918, has recently been declassified and a copy is now deposited in the Library of the National Research Council, Washington, D. C. A later account of this work, with particular emphasis on depth sounding, appeared in the Hydrographie Review (published by the International Hydrographie Bureau, Monaco) 2, No. 1, pp. 51-91 (November 1924). The same article was also published separately as " Special Publication No. 3 " (October 1924).

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47

and piezoelectricity were considered and then rejected, Langevin decided that it would be safer to fall back on the "singing condenser," and he recommended that full-scale experiments be undertaken at once (March 1915). Numerical estimates indicated that, if electric field strengths of the order of a million volts per centimeter could be maintained, electrostatic forces as large as a kilogram per square centimeter would (theoretically) come into play, and this pressure could be transferred to the water without diminution by using either a very thin front electrode or one just half a wavelength thick. In accordance with his proposals, an experimental program was launched late in March 1915 at Langevin's laboratory in the School of Industrial Physics and Chemistry (of the City of Paris). The French Navy Department made available the services of Capitaine de Fregate Colin, who made arrangements for using an experimental arc transmitter, designed originally for wireless telegraphy, as a source of high-frequency electric power. Preliminary experiments soon revealed that even when the "air gap" was evacuated the electric field was limited by field emission from the electrodes to a much lower value than had been assumed in the preliminary calculations of the available driving force. Much better results were obtained — which is equivalent to saying there were fewer breakdowns — when the insulated electrode was covered with a thin sheet of mica, against which a thin radiating electrode could be drawn by the vacuum. Eventually the metallic front electrode was dispensed with entirely, the water itself serving as the radiating electrode in direct contact with the mica. A torsion pendulum was used to measure the sound radiation pressure, which served as an index of the total sound energy emitted. This turned out (July 1915) to be a few tenths of a watt per square centimeter of active transducer surface — a very respectable level of electroacoustical performance even by present-day standards. A good bit of trouble was encountered in devising a suitable receiver for these high-frequency sound waves. Langevin reasoned, on theoretical grounds, that a similar mica-dielectric transducer, when suitably polarized with a steady bias voltage, could absorb completely an incident elastic wave. One can presume that Langevin had in hand at this point an analysis of the modification of the mechanical constants of his transducer due to electromechanical coupling. This line of attack might well have exerted a profound influence on the development of transducer theory if Langevin had pursued it further, but for reasons neither then nor now understood he was not able to verify the predicted behavior experimentally and the matter was dropped.

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ELECTROACOUSTICS

For want of any better receiver, it was necessary to fall back on the use of a carbon microphone, modified for submerged operation. In spite of persistent difficulties with instability, clear signals were received with the transmitter and receiver situated on opposite banks of the Seine river just below the Pont National (December 1915-March 1916). On the basis of these encouraging preliminary results, Langevin and Chilowsky 119 applied for a joint patent on the principle of their method and on the apparatus actually constructed. Chilowsky's eccentric genius had been measurably stabilized by the relative deliberateness with which Langevin approached physical problems, but each had a keen appreciation of his own ideas and their collaboration was less than entirely serene. As a consequence, Chilowsky detached himself from the experimental program, at Langevin's request, shortly after their joint patent application was drafted. At about the same time, plans were being made to shift the locale of the field experiments to a sea base at Toulon, where the work was reconstituted in April 1916. Captain Colin continued in charge of the arc-transmitter equipment and Marcel Tournier, who had joined the project in September 1915, continued his substantial contributions to the constructional and experimental phases of the program. The effective sensitivity of the microphone receiver was increased by mounting it at the focus of a concave mirror, and the output of the transmitter was increased to nearly a watt per square centimeter by superimposing a steady biasing voltage. Direct transmission over distances of 2 kilometers was then obtained and, for the first time, echoes were received from the bottom and from a sheet of armor plate suspended in the water at a distance of some 200 meters. Troubles continued to intrude, however; the instability of the carbon microphone was not improved by the pressure variations arising from vertical motion in the water, and there were recurrent electrical breakdowns in the mica transmitter, not to mention the insidious leakage of water — which has an uncanny way of finding a path to the interior of seagoing equipment designed by land-based scientists. The success of Langevin's preliminary experiments with ultrasonics had been communicated to the British by the Duke Maurice de Broglie (an elder brother of Louis de Broglie), who served as scientific liaison officer. Sir Ernest Rutherford called on his assistant, Dr. Robert W. ш Constantin Chilowsky and Paul Langevin, [echo ranging with electrostatic transducer] French Pat. No. 502,913 (demand6 29 May 1916, delivre 4 March 1920, publie 29 May 4 1920).

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49

Boyle,120 to organize a research group to study this application of ultrasonics. Boyle's team included B. S. Smith, later succeeded by W. F. Rawlinson, and P. V. Hunter. William Duddell lent his "electric singing arc" and S. G. Brown lent his laboratory at South Acton. By mid-1916 the British group was paralleling Langevin's work with explorations of various other methods of generating sounds in water. The base for the British work was later moved to the seacoast at Parkeston Quay, and still later to Dartmouth. The piezoelectric effect had turned up in the discussion during many conferences, both private and official, on both sides of the Channel, and one proposal for its use was set forth in a memorandum from Rutherford to the British Admiralty. Always, however, it had to be passed over with the lament, " b u t the effect is so small." Two fortunate circumstances made it possible for Langevin to break through this impasse during the early months of 1917: some high-frequency amplifiers became available as a by-product of the intensive development program carried out at L'Ecole Centrale de T.S.F. under the direction of General Ferrie of the French Signal Corps; and Langevin was finally able to persuade the optician Werlein to cut some slices about 10 X 10 X 1.6 cm in size from a beautiful 10-inch quartz crystal that had long served as a showpiece in Werlein's Paris shop. Langevin's first quartz receiver was made by embedding one of these crystal slabs in wax, with a foil electrode on the back and a protective sheet of mica on the front surface in contact with the water. Excellent results in reception were immediately obtained (February 1917), and by November 1917 signals had been received at 6 kilometers with the quartz receiver and the electrostatic (mica) projector. In the meantime (April 1917), experiments were carried out using the quartz transducer as a sound source, with results that could only have been regarded as spectacular. At the frequency of fundamental resonance (ca. 150 kc/s), the power emitted was estimated, on equivocal grounds perhaps, to be nearly 10 watts per square centimeter, or about one kilowatt for the 4-inch square crystal! Langevin reported that "fish placed in the beam in the neighborhood of the source operating in a small tank were killed immediately, and certain observers experienced a painful 120 Robert William Boyle, "Ultrasonics," Science Progress 23, 75-105 (July 1928). [ I n two interviews, hereby gratefully acknowledged, Dr. Boyle communicated orally to the author a first-hand account of the genesis of ultrasonic echo ranging during World War I. This material has been interspersed in this account with that drawn from the sources cited in note 118.]

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ELECTRO ACOUSTICS

sensation on plunging the hand in this region." The voltage required for such performance was too high for convenient field use and there was not much prospect of finding many other quartz specimens of comparable size and quality. Both of these considerations stimulated Langevin to devise the steel-quartz-steel sandwich construction in which mechanical resonance was determined by the thickness of the composite vibrator while only the thin "filling" of the sandwich had to be made of the precious quartz. Moreover, the quartz could be used in small pieces of irregular shape by assembling them in a mosaic on one of the steel blocks before cementing. Langevin 121 completed the assembly of such a transducer in February 1918. By using this transducer instead of the mica projector, the range for one-way transmission was increased to more than 8 kilometers and, for the first time, clear echoes were obtained from a submarine. The development of electronic circuitry also continued and within a few more months it had become possible to use the same quartz-steel-block transducer for both transmission and reception, and to extend the range at which an echo was received from a submarine to an occasional 1500 meters. The term "precious" was applied advisedly to the quartz that was required for these experiments. Langevin had turned over to Boyle one of the 10 X 10-cm slabs cut by Werlein and the immediately successful results obtained with it led Boyle to launch in England and elsewhere a determined search for usable specimens of quartz, a search that threatened for a time to culminate in a raid on all the crystal exhibits in British geological museums. Two display crystals were finally located, however, in the London shop of an optical manufacturer (Culver & Co.); and with these as raw material, and after the firm of Farmer & Grindley, London, had been taught how to do the cutting and polishing, Boyle also completed two mosaic quartz-steel transducers and obtained his first echo from a submarine within the same month that had brought Langevin to this stage of advancement. Boyle then pursued his quartz "find" in the reverse direction along the line of supply: to a French manufacturer of crystal spectacle lenses and chandelier pendants . . . "people don't seem 121 Paul Langevin, French Pat. No. 505,703 (demandi 17 September 1918, delivre 14 May 1920, publie 5 August 1920). [Directed to the same objectives as No. 502,913 (see note 119), but discloses the steel-quartz-steel transducer. Subsequent development of this equipment for depth sounding is claimed by P. Langevin and C. L. Florisson in French Pat. No. 575,435 (demande 27 December 1923, delivre 22 April 1924, publie 30 July 1924)].

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to buy crystal any more . . . but we have a warehouse . . ."; and so finally to a ladder leading to the loft of a Bordeaux warehouse . . . there to find a huge mound of natural quartz crystals piled up like coal! The armful of crystals picked out by visual inspection and carried away by Boyle on that occasion provided the piezoelectric material for the echoranging equipment of the first ten vessels of the British fleet to be fitted with "Asdic" gear. Through an exchange of embassy attaches, reasonably effective scientific liaison was maintained among the Allied Forces throughout the First World War. These normal channels of information exchange were augmented in the spring of 1917 by the visit to America of a FrancoBritish Commission that included Sir Ernest Rutherford and Professors H. Abraham and C. Fabry of the University of Paris. One of the conferences with this Commission was held in Washington on 15 June 1917 for the purpose of allowing a selected group of nearly fifty leading American scientists to hear a full account of the preliminary experiments with ultrasonics that were being carried out by Langevin and by Boyle. Among those attending this conference were representatives of the U. S. Navy, the Bureau of Standards and a few other agencies and institutions, the General Electric Company, the Western Electric Company, Westinghouse, and physicists from some twenty American universities. A good many of these scientists were already engaged in the substantial effort then being devoted to the development of binaural listening methods for submarine detection,122 but the exciting prospects suggested by Langevin's interim report stimulated the initiation of several programs of research directed toward further exploration of this new field. The most significant of the programs inspired by Langevin's work was that launched at the New London (Conn.) Naval Experimental Station (at various times, Professors Wills, Pupin, Morecroft, and Cady, S. L. Quimby, Lewi Tonks, et al.); but strong supporting programs were conducted at Columbia University (Professors Pupin, Morecroft, Wills, and Cady), at the General Electric Company laboratories in Schenectady (Drs. Hull and Cady) and in Lynn (where facilities were set up for grinding and processing quartz slabs), and at Wesleyan University, which was Professor W. G. Cady's "home base." (Cady's name appears also with the other groups because each relied on Cady's receiving devices, most of 122 Harvey C. Hayes, "Detection of Submarines," Proceedings of the American Philosophical Society 69, 1-47 (March 1920); "U. S. Navy MV Type of Hydrophone as an Aid and Safeguard to Navigation," ibid., pp. 371HL04 (December 1920).

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which made use of Rochelle salt crystals.) A similar research program was also launched in Italy under Professor LoSurdo, to whom Langevin lent one of the slices of quartz from Werlein's " m o t h e r " crystal. Still another program, directed particularly toward telephonic applications of piezoelectricity, was instituted a t the Western Electric Company (A. M . Nicolson). Prior to the close of the War, however, none of these satellite programs was able to accomplish very much more than to verify some of the results already obtained b y Langevin and by Boyle. T h e exploitation of ultrasonic echo ranging was ultimately to afford an outstanding example of the military application of an acoustical phenomenon, b u t it came to fruition just too late to be of tactical value in World W a r I. There was to be, alas, ample opportunity for its military value to be demonstrated before another quarter century had passed. Most of the a t t e m p t s to make practical use of piezoelectricity prior to the close of World W a r I involved the use of quartz, which was recommended b y virtue of its availability and its high degree of purity and mechanical stability. I t had long been known, however, t h a t m a n y other crystals besides quartz would exhibit piezoelectric effects, and among those known to be more active than quartz was the hydrated tartrate of sodium and potassium, more commonly known as Rochelle salt (since it was first discovered in 1672 by Seignette, an apothecary of the French seaport La Rochelle). T h e extraordinary piezoelectric activity of this crystal was strikingly exhibited in 1919 when Nicolson 123 described and demonstrated a variety of electroacoustical devices, including loudspeakers, microphones, and phonograph pickups, making use of Rochelle salt. The commercial exploitation of such devices did not get under way for nearly a decade, however, owing to delays in devising suitable mountings and discovering suitable crystal " c u t s , " not to mention the difficulty of securing pure and homogeneous crystal specimens of adequate size in adequate quantities. A good bit of effort had first to be devoted to the methods and techniques of growing suitable crystals. Rochelle salt finally did come into its own as an electromechanical transducer after С. B. Sawyer and С. H . Tower had solved the twin problems of growing Rochelle salt crystals of adequate size and purity on a commercial scale and of ш Alexander McLean Nicolson, "The Piezo-Electric Effect in the Composite Rochelle Salt Crystal," 7>a»u.[actions of the] Ant.[trican] /wrf.ptute of] Sec.[trical] £ « £ i n e e > j 38, 1467-1485 (October 1919), and Proc. Am. Inst. Eke. Engrs. 38, 13151333 (November 1919); see also U. S. Pat. No. 1,495,429 (Appl. Ser. No. 227,802 filed 10 April 1918) issued 29 May 1924.

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53

developing practical methods of processing and machining such crystals with modified woodworking tools.124 Since that time, a major industry has grown up around the application of these crystals in phonograph pickups, telephone receivers, and other electroacoustical devices. Crystal Control of Frequency In the meantime, another major field of application for piezoelectricity was opened up by Cady, who continued his researches in this field after the scientific effort of World War I had been demobilized. While working with a quartz crystal connected in the circuit of a self-excited vacuumtube oscillator, Cady discovered that the frequency of self-oscillation could be stabilized over a small range by the vibration of the quartz crystal. In retrospect it appeared that a good many other experimenters had made use of crystals associated with vacuum-tube circuits with which they might have observed this stabilizing action; but most of them sought to avoid the "anomalous" effects that occurred in the neighborhood of resonance in the crystal, and it remained for Cady to discover this remarkable stabilizing action of a high-Q resonator. Cady extended these results by applying two pairs of terminals to the crystal and connecting these as a feedback path for a three-tube amplifier in such a way that the circuit would oscillate but only at the resonance frequency of the crystal. Cady communicated these results freely and promptly to his scientific colleagues and took immediate steps to publish 125 his findings. He also elected to file two patent applications 126 describing these inventions, but their processing to final issuance and their subsequent history were not to be uneventful. While these patent applications were still pending, Cady discussed their contents openly with prospective users or licensees, including engineers of the research laboratories of the American Telephone and Telegraph Company and the Western Electric Company, and of the Radio Corporation of America, the Bureau of Standards, and other 124

С. B. Sawyer and С. H. Tower, "Rochelle Salt as a Dielectric," Phys. Rev. 36, 269-273 (February 1930); C. Baldwin Sawyer, "The Use of Rochelle Salt Crystals for Electrical Reproducers and Microphones," Proceedings of the] /ni/.[itute of] Radio Eng.[mtt~\rs 19, 2020-2029 (November 1931). lm Walter Guyton Cady, "The Piezo-Electric Resonator," Phys. Rev. 17, 531 (A) (April 1921); Proc. Inst. Radio Engrs. 10, 83-114 (April 1922); also Piezoelectricity (New York and London, McGraw-Hill Book Co., Inc., 1946). ш Walter G. Cady, [crystal resonator] U. S. Pat. No. 1,450,246 (filed 28 January 1920) issued 3 April 1923; also [crystal stabilization, and a 3-tube oscillator controlled by a 4-terminal crystal] U. S. Pat. No. 1,472,583 (filed 28 May 1921) issued 30 October 1923.

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agencies who might be presumed to have a material interest in the precise control of frequency. Instead of seeking to acquire rights under Cady's inventions by license or purchase, however, the Western Electric Company elected to file a socalled divisional patent application,127 which purported to stem from an earlier application filed by A. M. Nicolson in 1918, but which contained four claims copied from Cady's two pending applications. Nicolson's attorneys later amended his application by adding two more of Cady's claims and requested (3 May 1923) an interference, which was duly declared.128 A motion on behalf of Cady to dissolve the Nicolson interference was immediately granted with respect to five of the six claims in interference. Another motion seeking permission to present testimony concerning the issues at stake had also been filed at the same time; but before a ruling had been made on the latter motion, Cady disposed of his patent rights to the Radio Corporation of America (January 1925), and his attorney later withdrew from the case. In the continuation of the interference action, a tactical error on the part of counsel for Cady's assignee resulted in denying to Cady the opportunity to present the testimony that might have established his right to the remaining claim in interference. Without such evidence, priority for the contested claim was awarded by default to Nicolson (20 December 1926) on account of the earlier effective filing date of his so-called parent application. In the meantime, applications had been filed 129 for the reissue of Cady's two patents in an effort to secure claims that would more adequately describe his inventions. Many of these additional claims were now rejected by the patent examiner on the basis of the award to Nicolson of priority with regard to Cady's Claim 1; and since the Nicolson application was still pending, Nicolson was able to take over without further contest some of the text and most of the subject matter of the revised and broadened claims that Cady had sought in his reissue applications. In the role of a disciple of frequency stabilization, to which missionary 127 A. M. Nicolson, Application dated 13 April 1923, filed as a division of Appl. Ser. No. 227,802 (see note 123), finally issued 27 August 1940 as U. S. Pat. No. 2,212,845. According to Judge Ford's decision cited below in note 135, this application introduced new material and cannot, therefore, be properly regarded as a "division" of the 1918 application. 128 Interference No. 50,545, Cady v. Nicolson, declared 9 February 1924. 129 Cady's U. S. Pat. No. 1,450,246 was reissued on 2 July 1929, in five divisions: RE. 17,355 (filed 2 April 1925), and RE. 17,356 — R E . 17,359 (filed 6 August 1925). Cady's Pat. No. 1,472,583 was reissued on 26 March 1929, in three divisions: R E . 17,245 (filed 8 April 1925), and RE. 17,246 — RE. 17,247 (filed 6 August 1925).

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55

task he devoted himself for several years, Cady described and demonstrated his crystal circuits (January 1923) to Professor G. W. Pierce of Harvard University. Pierce took up the study of such crystal-oscillator circuits immediately, and within a few months his experiments had led him to the invention of several improved forms of crystal oscillator in which a two-terminal crystal could be made to control uniquely the frequency of oscillation in a single-tube circuit. Pierce exhibited his results to Cady on the latter's return from a European trip in the fall of 1923. Cady was greatly impressed by this quick success, especially with the fact that a two-terminal crystal in thickness vibration could be made to control the frequency of an oscillator by the use of a circuit containing a single tube. Cady's colleague Professor K. S. Van Dyke, while still following Cady in the use of a four-terminal crystal, had succeeded (1922) in establishing controlled oscillations in a single-tube circuit. The following sequence of events fell into a now-familiar pattern. Pierce 130 published his findings immediately, filed patent applications describing his inventions, and in due course encountered an interference provoked by Nicolson on the basis of the same "divisional" application, which had by now been amended to include several claims copied from Pierce's applications. In this case, however, the contested claims were awarded 131 to Pierce on the ground that Nicolson had not disclosed the invention described by these claims. In the ensuing revision of claims, Pierce was careful to retain only those that were sufficiently restricted to read only on the "Pierce oscillator." Pierce was especially careful to avoid the adoption of any claims that would read on the pioneer work of Langevin or on the original Cady disclosures, since it was his belief that these inventors were entitled to such claims even though a good many of them were still attached to the Nicolson application. Pierce's applications became involved in a long series of further interferences, but the patents deriving from his parent application and all but one of its derivatives had been finally passed for issuance by the fall of 1938. When the much-contested Nicolson divisional patent was finally issued, in August 1940, the situation that prevailed on the "crystal130 George Washington Pierce, "Piezoelectric Crystal Resonators and Crystal Oscillators Applied to the Precision Calibration of Wavemeters," Proceedings of the American Academy of Arts and Sciences 69, 81-106 (October 1923); also U. S. Pat. No. 2,133,642, issued 18 October 1938, on a parent Appl. Ser. No. 695,094 filed 25 February 1924 (cf. note 132 below). 131 Board of Appeals, decision 24 October 1936 in Interference No. 67,863. Pierce v. Bailey v. Nicolson.

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oscillator front" could be summarized as follows: Pierce held a portfolio of patents 132 containing claims for the "Pierce oscillator" circuits, including several claims that had been supported by awards of priority over Miller ш and various others with whom he had been involved in interferences concerning individual circuit features, and some that had been established against Nicolson on the basis of nondisclosure; eight reissue patents containing relatively narrow claims had been issued in Cady's name and either had expired or were about to expire; and Nicolson had a "fresh" patent that carried many broad claims, some based on the default award of priority over Cady, and some that did not even deal with frequency stabilization but were based on a similarly suspect award 134 of priority over Langevin, who had not taken adequate steps to protect his American patent interests. The next chapter of this legal saga was put in the record as part of the decision returned in an infringement action brought by Pierce against American Communications Company. In handing down his opinion in this case, District Judge Ford presented an incisive review of the entire history of frequency stabilization, in which he found cause to state unequivocally that "Nicolson . . . teaches nothing about the control of the frequency of the oscillator," and that "although Nicolson may have believed he had a crystal-controlled oscillator, in fact he did not." Since Cady certainly did disclose and "teach the control of frequency," Judge Ford's decision appears to allow, or indeed to require, the assignment of unambiguous credit to Cady for being the first inventor of the crystal-controlled oscillator.138 In the improved form represented by the Pierce oscillator circuits, this type of frequency control is now almost universally used in radio transmitters and in many receivers. One can, in fact, say that the stabili1,1 G. W. Pierce, eight U. S. Patents issued upon divisions or continuations of the parent Appl. Ser. No. 695,094 (cf. note 130) as follows: No. 1,789,496 (20 January 1931), No. 2,112,863 (5 April 1938), No. 2,133,643 and Nos. 2,133,645 to 2,133,648 (18 October 1938), and No. 2,266,070 (16 December 1941); and Pat. No. 2,133,644, also issued 18 October 1938, on an original application filed 9 January 1928. 133 Interference No. 64,637 Miller [Pat. No. 1,756,000] v. Pierce, 97 F.2d 141 [6 June 1938]. 134 110 F.2d 687 [1 April 1940], Langevin v. Nicolson. ш Judge Ford's decision in the infringement action, Pierce v. Am. Comm. Co. Inc., et al., I l l F. Supp. 181 [19 March 1953], 97 U. S. Pat. Q. 60, was later reversed by the 1st Circuit Court of Appeals, 18 December 1953, 208 F. 2d 763,100 U. S. Pat. Q. 1. The reversal turned on a point of law, however, and did not impugn Judge Ford's findings of fact concerning priority of invention which were conceded by the appellants.

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zation, standardization, and precise control of frequency made available by such use of the electromechanical reactions of a vibrating crystal have had a profound effect on the whole evolution of the modern science of electrical communication. The growing demand for quartz to meet the needs of the communications industry has threatened to outrun the world supply of quartz of suitable "radio" quality, and has stimulated efforts (already moderately successful13e) to grow usable quartz crystals artificially. Substitute crystals suitable for frequency control and for filter applications have been sought avidly, the most satisfactory to date being ethylene diamine tartrate (EDT). A similar quest for crystalline materials 137 suitable for electroacoustic transducers has led to the exploitation for special purposes of ammonium dihydrogen phosphate (ADP), potassium dihydrogen phosphate (KDP), lithium sulfate (LH), and dipotassium tartrate (DKT). The most promising competitor of Rochelle salt, however, is barium titanate, with which minor additives (such as lead or calcium titanate) are sometimes advantageously combined. When this material is prepared in the form of a homogeneous polycrystalline ceramic, it can be endowed with piezoelectric properties in any chosen direction by the application of a strong electric polarizing field; and if the ceramic material is allowed to cool from an elevated temperature in the presence of the electric field, the internal polarization persists indefinitely unless the crystal is again heated or subjected to strong counter fields. In this respect the effect closely parallels the phenomena of ferromagnetism, and such synthetic piezoelectric materials are among those that are sometimes called ferroelectric. Electrodynamics

Takes Over

The last of the basic transducer mechanisms to be accounted for, and the most important in terms of modern commercial utilization, is the "dynamic" or moving-coil mechanism. A good many of the very early experiments with electromagnetism — for example, La Rive's "floating current" — might be regarded as antecedents of the moving-coil 136

Ernest Buehler, "Growing Quartz Crystals," Bell 246 (July 1953). 137 For a running account of the activity in this field, electricity" in the Institute of Radio Engineers Technical Progress" published annually in the March or April issue tute of Radio Engineers.

Laboratories

Record 31, 2 4 1 -

see the section titled "PiezoCommittee reports on " Radio of the Proceedings of the Insti-

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transducer principle. In its modern form, this motor mechanism consists of a circular coil of wire that lies in a radial magnetic field and is supported so that it can move axially. Ernst W. Siemens,138 the founder of the well-known German firm of Siemens & Halske, was the first to describe this arrangement, whose principal features are clearly set forth in the patent application he filed early in 1874 —• just a little more than two years before Bell's invention of the telephone. Siemens described his "magneto-electric a p p a r a t u s " as a means "for obtaining the mechanical movement of an electrical coil from electrical currents transmitted through it." Although the apparatus exemplifying this behavior was shown as the operating mechanism for a telegraph relay, Siemens pointed out that the action of the coil could also be used " f o r moving visible or audible signals." I t is clear, however, that he had no more articulate signals in mind than those of a bell or telegraph sounder. I t is also interesting to notice a t this late date that a pair of instruments of this sort would probably have provided more suitable apparatus for the discovery of telephony than the plucked reeds with which Bell experimented; but Siemens's attention, like Elisha Gray's, was apparently directed elsewhere at the time. Not long after Bell's invention of the telephone, Charles Cuttris and Jerome Redding, 139 of Boston, filed a U. S. Patent application describing what appears to have been the first moving-coil electroacoustic transducer. About two weeks later, applications were filed in Germany and in England on behalf of the same E. W. Siemens,140 who now redressed his failure to invent the telephone, as it were, by making a substantial disclosure setting forth many of the fundamental features that still characterize the typical moving-coil transducer mechanism. Each of these primitive " d y n a m i c " transducers made use of a permanent magnet for producing the radial magnetic field, and each proposed the use of a nonmagnetic parchment diaphragm as the sound radiator. Siemens went further and specified that the diaphragm was to have the general form of the frustum of a cone, but that it should have an exponentially flaring 138

Ernst Werner Siemens, U. S. Pat. No. 149,797 (filed 20 January 1874) issued 14 April 1874. 13S Charles Cuttriss and Jerome Redding, U. S. Pat. No. 242,816 (filed 28 November 1877) issued 14 June 1881. 140 Ernst Werner Siemens, German Pat. No. 2355 (filed 14 December 1877) granted 30 July 1878; and through representation by Carl Heinrich Siemens, British Pat. No. 4685 dated 10 December 1877 (provisional spec, filed 10 December 1877; "sealed" 1 February 1878; complete spec, filed 30 April 1878).

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profile "of trumpet form" — a shape sometimes characterized as "morning glory" form. The structure that Siemens proposed was so prophetic that many later workers in this field found the shadow of the Siemens patent athwart their path. Even after the basic features had reverted to the public domain with the expiration of the Siemens and the Cuttris patents, there were many opportunities for the next generation of pioneers to echo Rice's classic complaint that " the ancients have stolen our inventions." 141 Of course, a few small but important structural features now regarded as essential were missing in these primitives, such as a voice-coil centering spider (Pollak 142), nonmagnetic spacers to maintain the air gap between inner and outer poles (Lodge,143 and claimed later by Pridham and Jensen ш ) , and a compliant suspension for the base of the conical diaphragm, supplied later in a variety of forms by many inventors. Strangely enough, Siemens neglected to suggest, although Lodge, Brown,188 and others did later, that the diaphragm should be made large if it was desired to radiate sound into a room. On the other hand, if it appears that modern loudspeaker manufacturers are too ready to make undiscriminating claims to "high fidelity," apparently as a matter of routine, they are at least following an old and well-established tradition — as Siemens put it, with admirable restraint, these structures "produce articulate sounds with great distinctness." Siemens's patent specification of 1877 disclosed not only the movingcoil mechanism, but also the basic elements of the balanced-armature principle of magnetic transduction. I t might be more accurate to refer to the suggested configuration as a balanced-diaphragm mechanism, inasmuch as the structure he proposed more nearly resembles the one to which Hanna 1 4 5 later gave this designation than it does the definitive 141 This lament actually arose in quite a different connection and was addressed to E. W. Kellogg by Chester W. Rice (G. E. Co.), but its aptness will appeal to every frustrated reinventor. 142 Anton Polläk (a Hungarian living in Paris), U. S. Pat. No. 939,625 (filed 7 August 1908) issued 9 November 1909. 143 Oliver J. Lodge, British Pat. No. 9712 [1898] (provisional spec, filed 27 April 1898; complete spec, filed 13 December 1898, accepted 13 January 1899). The [British] Science Museum, South Kensington, has a model of this early loudspeaker drive mechanism, a photograph of which appeared in Wireless World 21, 807 (21 December 1927). 144 Edwin S. Pridham and Peter L. Jensen (Assignors to Magnavox), U. S. Pat. No. 1,448,279 (filed 28 April 1920) issued 13 March 1923. 146 Clinton R. Hanna, "Design of Telephone Receivers for Loud Speaking Purposes," Proc. Inst. Radio Engrs. 13, 437-460 (August 1925).

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form of balanced-armature structure proposed by Capps.146 Another early form of balanced-armature structure was described by Bell's assistant, Thomas A. Watson,147 but neither this pioneering effort nor that of Siemens gained their inventors any significant reward, since hardly any use was made of these configurations until so much later that the original patents had long since expired. Two other early disclosures are worthy of passing notice, although neither made use of the moving-coil principle. Ader,148 in a French patent of 1878, proposed the use of a large diaphragm which was to consist of a stretched membrane about 40 cm in diameter, and which was to be actuated by a circular array of moving-armature magnetic drive mechanisms. A few months later, J. W. Maxwell 149 proposed a mechanoacoustic transducer comprising a closed housing fitted with two opposed conical diaphragms, with ''cotton or wool placed around the vibrators within the box, in order to destroy the ring." Both of these concepts — the large direct-radiator diaphragm and the closed housing with damping material — were destined to reappear with all the freshness of brand new ideas some forty years later. Sir Oliver Lodge,143 in his British patent specification filed in 1898, described again, somewhat more specifically than Siemens had, the constructional features and the advantages of the moving-coil mechanism (including the nonmagnetic air-gap spacer referred to above). This was the same year in which Lodge was granted his famous patent for selective tuning apparatus for radio receivers — a coincidence that could be regarded as predictive of the close linkage of future developments in these two fields. Lodge referred to his moving-coil transducer as a "bellowing telephone," and he dared go so far as to propose that multiple units be used to drive the entire ceiling or wall of a room as a sound-radiating diaphragm ! This suggestion held the large-diaphragm honors for more than ten years, until it was decisively topped by a proposal advanced by the Hungarians, Klupathy and Berger,160 in which the entire side of a ship ue

Frank L. Capps, U. S. Pat. No. 441,396 (filed 7 April 1890) issued 25 November

1890. 147 148 us

T. A. Watson, U. S. Pat. No. 266,567 (filed 17 April 1880) issued 24 October 1882. C16ment Ader, French Pat. No. 127,180 dated 28 October 1878. Joseph W. Maxwell, U. S. Pat. No. 216,051 (filed 7 November 1878) issued 3 June

1879. 160

Eugen Klupathy and Christian Berger (Budapest, Austria-Hungary) U. S. Pat. No. 1,036,265 (filed 3 December 1910) issued 20 August 1912.

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was supposed to function as a "sounding board" for transmitting or receiving sounds in water. This scheme ought perhaps to be disqualified as a loudspeaker, since provision was made for transmitting only two or three relatively pure tones, and these were to be excited by plucking or by the rubbing of a friction wheel against a steel wire stretched from side to side within the ship. Garrett and Lucas 151 disclosed a somewhat more realistic scheme for using the side of a ship as a diaphragm, although the realism was tempered by their radical assumption that the hull would serve the acoustical function of a sound-transparent window rather than to behave as a more or less rigid diaphragm. They also proposed to use magnetostriction as the mechanism of transduction, suggesting that one end of a nickel rod surrounded by a pickup coil could be attached directly to the skin of the ship, while the inboard end of the rod could advantageously be mass loaded in order to enhance the inertial reaction. Several years later (ca. 1928), and with a nice instinct for showmanship, Professor G. W. Pierce contrived a novel large-diaphragm loudspeaker by attaching a magnetostriction transducer similar to that described by Garrett and Lucas to the under side of a large lecture table. Surprisingly good reproduction of demodulated radio signals comprising speech or music was afforded by this arrangement. On one fondly remembered occasion, Professor Pierce demonstrated the ruggedness of such a loudspeaker by climbing up on the lecture table and remarking to a startled colloquium audience, " See, you can even stand on the diaphragm of this loudspeaker without interfering with its operation!" Hardly less bizarre were the claims advanced by R. A. Fessenden 162 for " A loud-speaking telephone having its diaphragm arranged as a kinetoscopic screen."; and for " a loud speaking telephone having a diaphragm of the same order of dimensions as the cross section of said inclosure.", the inclosure having already been described as "adapted to contain an audience". Lodge included in his 1898 loudspeaker specification the description of an electrical amplifier which was to utilize one of his moving-coil transducers to actuate a carbon microphone, whose electric output would drive in turn another moving-coil transducer, which would drive another microphone, and so on. Edison had anticipated this basic conception by proposing more than twenty years earlier a similar microphonic ampli161 Thomas Alexander Garrett and William Lucas (of Reigate and Crouch End, England), U. S. Pat. No. 942,897 (filed 31 August 1909) issued 14 December 1909. 162 R. A. Fessenden, U. S. P a t No. 1,213,176 (filed 27 June 1916) issued 23 January 1917.

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fier actuated by the moving armature of a magnetic telegraph relay.163 Edison must have been less impressed by this invention than its prospects might have warranted, since it appears to have been one of the few inventions he made that was not published promptly in the form of a patent specification. Gilliland 154 did seek a patent a few years later for his similar "Improvements in Reproducers of Undulatory Electric Waves," but his proposal, although one of the earliest in the Patent Office, can hardly be said to have advanced the art significantly. If Edison was not impressed by the possibilities of the telephonic repeater, a good many others were, and a great deal of development effort was devoted to electromechanical, or "microphonic," amplifiers during the forty years following Edison's published correspondence on the subject. To say that these devices were afflicted with all the ills of the carbon microphone is also to suggest that every significant improvement in either the carbon microphone or the telephone receiver provided a new basis for alleged improvements in such microphonic amplifiers. One of the early contributions to this art was made by Trowbridge and Sheldon.145 Their contribution was rather more conceptual than practical, however, and Trowbridge himself pointed out the essential inoperability of their earlier device in two later patent disclosures,156 in which he proposed, incidentally, to make use of a balanced-armature actuating mechanism. During the first decade of the 20th century, patent applications literally by the score were directed toward the use of such electromechanical amplifiers as telephone repeaters, and much of the basic theoretical study 163 A brief notice of "Edison's Pressure Relay" appeared in The Telegraphic Journal [which became The Electrical Review after 1891] 6, 149-150 (July 1, 1877). A similar device was described by Edwin J. Houston arid Elihu Thomson in a letter titled "The relaying of the telephone," Chemical News 37, 255 (21 June 1878). A lively exchange of letters followed. Edison [Chemical News 38, 45 (26 July 1878)] declared "that the telephonic repeater described by Messrs. Houston and Thomson was invented by me over a year ago . . . " Houston, apparently unaware of Edison's pending patent application for the carbon microphone, replied [ibid., pp. 138-139 (13 September 1878)] that Edison could hardly have made the invention a year earlier since that would make it precede Hughes's description of the carbon microphone, Edison ignored the reference to Hughes and replied dryly [ibid., p. 198 (18 October 1878)] by quoting from the article in The Telegraphic Journal. ш Ε. Т. Gilliland, U. S. Pat. No. 247,631 (filed 8 July 1879) issued 27 September 1881. 166 John Trowbridge and Samuel Sheldon, U. S. Pat. No. 407,799 (filed 17 December 1888) issued 30 July 1889. 166 Professor John Trowbridge [of Harvard University], U. S. Pats. No. 756,436 (filed 18 May 1903) and No. 756,437 (filed 18 May 1904), both issued 5 April 1904; see also Pat. No. 814,411 (filed 14 July 1905) issued 6 March 1906.

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of the problems of self-oscillation and impedance balancing in long transmission lines was premised on the use of such amplifiers. To cite a typical example, Lindsey 167 proposed a particularly simple form of moving-coil carbon-button repeater of the same general type that Lodge had suggested earlier. The very minute mechanical displacement required to produce a useful amount of resistance variation in a carbon transmitter eventually invited the utilization of magnetostriction as an actuating mechanism, and telephone repeaters operating on this basis were proposed in due course, for example, by Warth 158 and by Rainey.159 A more novel method of obtaining amplification had been suggested earlier by Biggar,160 who proposed to use for this purpose the variation of electric resistance produced when a material such as bismuth is immersed in a magnetic field arranged to vary with the signal current. Still another novel scheme was put forth by Ehret, 161 who proposed to use the input signal currents to produce a splitphase magnetic field for an induction generator whose rotor was driven above synchronous speed. One of the patents granted to Ehret was notable for the allowance of a basic claim that defined his invention as " a n improvement in the art of reproducing signals. . . which consists in amplifying the current changes or fluctuations representing the messages or signals." — a claim that appears to be broad enough to have covered any signal-frequency amplifier in a communication system. It is often the case that the most useful new devices are produced not so much by the exploitation of novelty as by the application of sound engineering design and system planning directed toward the improved utilization of "conventional" principles. On such a basis one can say that the most significant contributor to the electromechanical-repeater art was Η. E. Shreeve.162 He appreciated, as Trowbridge had, that the 167 Lucius A. Lindsey, U. S. Pat. No. 901,974 (filed 20 March 1906) issued 27 October 1908. «» Nathaniel G. Warth, U. S. Pat. No. 1,022,519 (filed 28 January 1910) issued 9 April 1912. 168 Paul M. Rainey (W. E. Co.) U. S. Pat. No. 1,092,453 (filed 14 October 1913) issued 7 April 1914. 180 John Stuart Biggar, U. S. Pat. No. 543,843 (filed 16 November 1894) issued 6 August 1895. 161 Cornelius D. Ehret, U. S. Pat. No. 818,363 issued 17 April 1906 (filed 25 August 1905 as a division of Appl. Ser. No. 167,129 filed 27 July 1903 [on which Pat. No. 818,236 issued 17 April 1906]). The signal-frequency amplifier is broadly covered by Claim 5 of No. 818,363. 162 Herbert E. Shreeve (W. E. Co.), U. S. Pats. Nos. 791,655-θ (filed 8 July 1904) issued 6 June 1905, and ten others in the same field issued 1906-1915.

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clamped-edge diaphragms of both receiver and transmitter could be dispensed with and their resonances avoided, and a "Shreeve repeater" became the first of such devices to perform reliably enough to qualify for commercial service in a toll telephone circuit (New York-Chicago, from August 1904). To be sure, obsolescence as a telephone repeater started to overtake the electromechanical amplifier almost as soon as the thermionic triode made its bow on the scene in 1907; but this replacement could not be justified until improved vacuum pumps had made it possible to get rid of the residual gas that made the early triodes as capricious as the carbon microphone. While this issue still hung in the balance, another type of electronic amplifier using mercury-arc tubes 163 made a spirited but shortlived bid for acceptance as a telephone repeater. The high point in the development of the microphonic repeater was reached late in 1914. At that time a long, and often heartbreaking, program of research on many fronts was heading up to the climax represented by putting into commercial service the first transcontinental telephone circuit (25 January 1915). The commitment to launch this service, with due pomp and ceremony, as a feature of the Pacific-Panama Exposition held at San Francisco had been made long before anyone could be certain that high-vacuum tube repeaters would be either adequate or ready in time for such use. As it turned out, they were both adequate and ready; but in the meantime, electromechanical repeaters had been installed at each repeater station and were in readiness for service as alternates, or as replacements in case of trouble with the vacuum-tube repeaters. After commercial toll service had been established, the transcontinental circuit was operated for a period of a few days during 1915 with only the electromechanical repeaters in use throughout. This test was conducted ostensibly for the purpose of making measurements on over-all performance, but one can suspect that it may have been equally motivated by the desire of many who had shared in the repeater development to witness the fruition of their labors.164 For service in special applications requiring extreme compactness or 163

Harold D. Arnold (W. E. Co.), U. S. Pat. No. 1,118,176 (filed 7 May 1914) issued 24 November 1914. 184 John Mills, "The Line and the Laboratory," Bell Telephone Quarterly 19, 5-21 (January 1940); Frank B. Jewett, "Transcontinental Panorama," ibid, pp. 38-58 (January 1940). [Two of a series of articles commemorating the 25th anniversary of the opening of transcontinental telephone service.]] See also Thomas Shaw, "The Conquest of Distance by Wire Telephony," Bell System Гесй.[шса1] /.[ournal] 23,337-421 (October 1944).

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operation on low voltages, as in hearing aids, for example, the electromechanical amplifier continued to hold out stubbornly against the vacuum tube. Even for this service, however, its doom began to be sealed when the development of the "peanut tube" (Western Electric Co., 1922) made it feasible to design "carryable" vacuum-tube amplifiers for hearing-aid use. V. O. Knudsen 165 reported that by 1938 vacuum-tube hearing aids had taken over nearly half the market in England, where the "wearable" type of hearing aid appears to have been developed first. This trend was accelerated by the development of subminiature vacuum tubes just prior to World War II, and the postwar development of the transistor has already allowed the miniaturization of hearing aids to be carried to even greater extremes. The quarter century extending from Lodge's disclosure in 1898 to the mid-1920's was a relatively slack period for both the science and the art of electroacoustics. Perhaps it might better be called a period of gestation, of slumbering fertility and gathering strength. A good many minor developments appeared, however, and a few major innovations originated during this interval; and the pace finally began to quicken toward a climax during the early 1920's. The break-out came in 1925, and was spearheaded by Rice and Kellogg of the General Electric Company, about whose contributions there will be more to say later. But if this was a resting period in which electroacoustics was mustering its resources, it was a time for vigorous frontal attack on the problem of transmitting electric signals. Scientific evolution had to march with twenty-league boots to cover, within a score of years, the ground that lay between the coherer of Branly and Lodge and a technology adequate to sustain transatlantic radio telephony and domestic radio broadcasting. And while "wireless" was undergoing this fabulous transition, the network of telephone lines quietly snaked its way to the west, and to the north and south, and knit the nation together with threads of conversation reaching from coast to coast and border to border. These achievements constitute a distinguished chapter in man's conquest of his environment, but even to catalog its highlights would carry the present account too far afield. After those bold words it is anticlimactic — but relevant — to call attention to the fact that the expansion of both space and wire communication demanded thorough understanding of the fundamental behavior of selective circuits for signal transmission. John Stone Stone and 166

V. O. Knudsen, "An Ear to the Future," / . Acoust. Soc. Am. 11, 29-36 (July 1939).

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Ε. F. W. Alexanderson were early pioneers in this field, but the most substantial contributions to the fundamental understanding of transmission circuits were probably those made by G. A. Campbell, to whom can be given major credit for developing a physical theory of wave filters. The growth of sophistication with regard to electric transmission networks was in due course to spread its blessings to the field of electroacoustics. The concept of a complex electric impedance had been introduced only a few years before the turn of the century, but it had been quickly adopted and had greatly facilitated the systematic analysis of electric transmission systems. By 1920, the concept of impedance had been extended by Kennelly and by Webster to embrace also the fields of mechanics and acoustics.166 The adoption of familiar "impedance" terminology for the various complex ratios arising in mechanics and acoustics had been based, of course, on the similarities in the mathematical equations used to describe the behavior of these different systems. Then, with the guiding assistance of a terminology of similarity, it became natural to hope and ultimately to expect that details of the behavior of mechanical and acoustical systems could be interpreted usefully in terms of the better-known properties of their analogous electric-network counterparts. Such use of electric-network analogs for deductive analysis sprang up spontaneously in so many places at about the same time that it seems as useless as it would be difficult to establish who did it first. Hahnemann and Hecht, Aigner, Wegel, Harrison, and Norton are among those whose early use of these notions can readily be attested by patent disclosures or other publications.167 166 A. E. Kennelly made extensive use of both concepts in his studies of the telephone receiver, and he refers [in Chap. XIII of his Electrical Vibration Instruments (New York, Macmillan, 1923)] to his own use of the term acoustical impedance as early as 1917. He conceded priority in this usage, however, to A. G. Webster, "Acoustical Impedance and the Theory of Horns and of the Phonograph," Proceedings of the National Academy of Sciences (Washington) 6, 275-282 (1919). m Walter Hahnemann and Heinrich Hecht, of Signal Ges. m.b.H. of Kiel, "Schallgeber und Schallempfänger" (in 3 parts), Physikalische Zeitschrift 20, 104-114 (March 1919); 20, 245-251 (June 1919); 21, 264-270 (May 1920); and U. S. Pat. No. 1,507,171 (filed 21 July 1921) issued 2 September 1924; Franz Aigner, Unterwasserschalltechnik (Berlin W., M. Krayn, 1922); R. L. Wegel, J. Am. Inst. Elec. Engrs. 40, 791-802 (October 1921) [see note 1, Chapter 2], and U. S. Pat. No. 1,704,354 (filed 30 April 1923) issued 5 March 1929; Henry C. Harrison (W. E. Co.), U. S. Pat. No. 1,730,425 (filed 11 October 1927, as a continuation of [and, therefore, entitled to the earlier filing dates of] the subsequently abandoned Appls. Ser. No. 610,977 filed 6 January 1923, No. 628,168 filed 28 March 1923, and No. 33,619 filed 29 May 1925) issued 8 October 1929; Edward L. Norton (W. E. Co.), U. S. Pat. No. 1,681,554 (filed 24 November 1924) issued 21 August 1928.

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The best-known, and perhaps the first, use of electric-network analogs as a basis for the design of a mechanical system grew out of the efforts of Maxfield and Harrison to improve the performance of phonograph recording and reproducing equipment. One of the first fruits of this assignment, undertaken shortly after the close of World War I, was a scheme for using negative feedback around the electromechanical transduction link as a method of increasing electrically the effective damping in a mechanical system.168 A little later, Hanna 169 proposed a similar scheme for controlling the resonant response of his balanced-diaphragm loudspeaker unit. Incidentally, both of these disclosures anticipated by several years the recognition of the broad advantages accruing generally from the use of negative feedback in electronic amplifiers. The use of positive feedback around an electromechanical transduction link had been suggested even earlier by Lawther. 170 When the excitation for an amplifier supplying power to a transducer is derived from the vibration of the transducer itself, as proposed by Lawther, such a self-excited system can be made to function effectively at resonance even under wide variations of the resistance and reactance of the load. Theoretical studies undertaken in support of the Maxfield-Harrison experiments provided the basis for broad patents to Harrison and Norton 167 covering the principle of designing a transducer as a band-pass filter by using analog relationships between the mechanical system and the electric networks of conventional filter theory. Within a decade, these notions had been extended to embrace the use of the driving-point impedance of electromechanical resonators as reactance elements in lattice-type filter networks, and the use of multiple electric meshes coupled to one or more mechanical resonators 171 in such ways as to make 168

Joseph P. Maxfield and Henry C. Harrison (W. E. Co.), U. S. Pat. No. 1,535,538 (filed 3 January 1923) issued 28 April 1925. 169 Clinton R. Hanna (Westinghouse), U. S. Pat. No. 1,645,282 (filed 28 August 1924) issued 11 October 1927. 170 Harry P. Lawther (assignor to John Hays Hammond, Jr.), U. S. Pat. No. 1,518,123 (filed 29 August 1918) issued 2 December 1924. 171 Lloyd Espenschied (B.T.L.), U. S. Pat. No. 1,795,204 (filed 3 January 1927) issued 3 March 1931; Warren P. Mason (B.T.L.), U. S. Pats. No. 2,045,991 issued 30 June 1936, and Nos. 1,967,249 and 1,967,250 issued 24 July 1934, all three filed 26 January 1933 as continuations of abandoned Appl. Ser. No. 489,268 filed originally 17 October 1930, and No. 2,094,044 (filed 2 July 1935) issued 28 September 1937; also "Electrical Wave Filters Employing Quartz Crystals as Elements," Bell System Tech. J. 13, 405-463 (July 1934); also [magnetostriction coupling] Emory Lakatos (B.T.L.), U. S. Pat. No. 2,166,359 (filed 30 March 1937) issued 18 July 1939; and W. P. Mason. U. S. Pat. No. 2,170,206 (filed 8 M a y 1937) issued 22 August 1939.

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it possible to contrive selective filters in which all the internal electrical resonances arise as a result of electromechanical coupling. The earlier patent disclosures by Harrison and Norton do not appear to have been widely noticed in this connection, perhaps because they were issued later (although filed earlier) than the definitive paper by Maxfield and Harrison.172 The latter publication certainly was widely noticed, however, and it can be said to have brought the century-old courtship of electrical theory and acoustics to the happy climax of a successful marriage that shows no prospects of ever being put asunder. A premature effort to exploit commercially an early "MaxfieldHarrison" recorder (via a short-lived independent company operating under the name Phonic Laboratory, ca. 1921) had not been successful. However, the second phase of their development program yielded the socalled "rubber-line recorder" and the prototype of the phonograph reproducing equipment that was later to become widely known as the Orthophonic Victrola. The first record manufacturer to seek a license for the use of the electromechanical recording portion of this equipment was the Columbia Phonograph Company (ca. late 1924 or early 1925). Somewhat later, but still early enough for the Orthophonic Victrola and electrical recordings to reach the market in time for the 1925 Christmas trade, the Victor Talking Machine Company acquired a license for the use of both the rubber-line recorder and the new mechanical phonograph with its band-pass type of mechanical pickup and a folded exponential horn. The circumstances that led to the negotiation of the latter license illustrate an interesting moral that still retains a substantial measure of validity. Some of the executives of the Victor Talking Machine Company displayed relatively little interest in the new equipment at the outset, in spite of the fact that the phonograph industry as a whole was already beginning to feel the hot breath of radio's pursuit. The proffer of a license was all but rejected, even after a private demonstration had quickly convinced some members of the Board of Directors that the new Orthophonic equipment did indeed sound "more n a t u r a l " ; but on the other hand, it certainly " d i d n ' t sound like a phonograph," and they didn't think the public would buy it. Maxfield finally prevailed on Victor's Vice-President, 171 J. P. Maxfield and H. C. Harrison, "Methods of High Quality Recording and Reproducing of Music and Speech based on Telephone Research," Trans. Am. Inst. Flee. Engrs. 46, 334-348 (February 1926); also in Bell System Tech. J. 6, 493-523 (July 1926).

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who believed the new machines and records to be a marked improvement, to gather evidence with which the deadlock could be broken by taking the new machine and some samples of the new electrical recordings to his home so that he could try them out on a few of his neighbors. It was suggested that he play a few of the new records on the new machine, apologizing for them as something experimental; and that he should then tell his guests that they could now go back to the old machine and play some real records on a real phonograph. As he (and Maxfield!) had expected, his neighbors made it emphatically clear that they had no further interest in listening to the old records on the old machine, and they insisted on playing through each of the new records several times. Other executives, however, still remained skeptical until each had, in his turn, tried the same experiment in his own home. Maxfield laughingly recalls this incident by saying, "they finally shook their wise old white heads and said, 'well, we don't understand it, but if that's what the public wants, let's give it to them'; and so they signed the license agreement." 173 Thus was it demonstrated that "high fidelity" is its own best salesman. The tremendous advantages of electrical recording soon led to its universal adoption throughout the phonograph industry. The Orthophonic Victrola, on the other hand, had hardly been on the market for as long as a year when it began to encounter stiff competition from phonograph reproducing equipment using an electromechanical pickup, vacuum-tube amplifier, and some form of loudspeaker. The first of these all-electric phonographs to become available was the Brunswick "Panatrope" marketed by the Brunswick-Balke-Collender Company. The Majestic Company soon offered a similar machine for sale, and these were followed by many others. The mechanical pickup of the original Orthophonic had a frequency response at least as good as that of the early electromechanical pickups, but its sound output was necessarily limited to the modest power that could be delivered by the record groove. This was not enough to qualify it to survive long in competition with electronic amplification, and within less than a year, Victor was offering the Orthophonic with the optional feature of electrical reproduction, some models with a horn-drive unit actuating the original folded horn and some with a direct-radiator loudspeaker. The mechanical phonograph pickup had served the industry well, however, if only by furnishing a 173

This account is based on private communications from J. P. Maxfield.

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vehicle for establishing the use of electric-network analogs as a basis for the analysis and design of transducer systems — a fundamental contribution that survives as one of the most valuable tools in the kit bag of the designer of electromechanical transducers. Most of the innovations of the early phonograph art that had survival value for modern electroacoustics were those concerned with the materials, dimensions, and methods of manufacture of sound-radiating diaphragms. The now-familiar conical paper diaphragm that terminates at the base, or rim, in a section that is flat except for annular corrugations was first described by John Stroh 174 in a British patent of 1901. Stroh (along with a good many people since his time) was trapped into making the easy mistake of presuming that such annular corrugations in the flat mounting section (sometimes called the "surround") would increase the compliance for axial motion. More careful consideration of the way the material of the cone and its surround is required to stretch under axial motion will indicate that a contrary result is actually to be expected. Radial corrugations or radial slits would be required to accommodate the tangential stretching of the cone material associated with large axial motions, as was pointed out much later by Bostwick.175 Annular corrugations are still commonly used, however, and they do serve the useful function of stiffening the base of the cone, thereby raising the frequency below which the cone vibrates as a rigid whole. Lumiere 176 disclosed in 1908 a method of fabricating a 10-inch flat diaphragm reinforced with radial pleats that were introduced for the purpose of enhancing its rigidity. The mechanical effect of these radial folds, in practice, was probably influenced strongly by secondary factors, but it is certain that one could no more expect that such reinforcement would remove the resonances that characterize the response of a flat diaphragm than one could expect that a change in the shape of an auditorium would eliminate its reverberant modes of vibration. It has been well said that such changes do not remove the modes of vibration; they just re171 John M. A. Stroh, British Pat. No. 3393 [1901] (provisional spec. 16 February 1901, complete spec. 6 November 1901; accepted 14 December 1901). 176 Lee G. Bostwick (B.T.L.), U. S. Pat. No. 1,967,223 (filed 6 January 1933) issued 24 July 1934. 176 Louis Lumiere, of Lyon, France (assignor to Victor Talking Machine Co.), French Pat. No. 401,501 (demand6 25 July 1908, delivrt 27 July 1909), and U. S. Pat. No. 986,477 (Appl. Ser. No. 505,149 filed 30 June 1909) issued 14 March 1911, and Pat. No. 1,036,529 (filed 26 March 1910 as a division of Appl. Ser. No. 505,149) issued 20 August 1912.

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move any possibility of calculating them in advance! The Lumiere diaphragm was originally intended for use with a mechanical phonograph, but it was also incorporated in one of the first large-diaphragm loudspeakers to become commercially available (in England). A few years later the now-standard practice of constructing the paper cone and its corrugated rim in one piece was patented to Duncan, 177 who went so far as to claim an "acoustic diaphragm having a diameter of more than eight inches". This left the field open, at least so far as Duncan was concerned, for manufacturers who chose to market loudspeakers with diaphragms just slightly less than eight inches in diameter — and a few elected to do so. Another "diaphragm" invention directed originally toward the phonograph was disclosed in 1913 by Hopkins,178 who claimed, among other things, a clamped-edge conical diaphragm operating in a circular aperture 9 inches or more in diameter. The "clamped-edge" and the "circular aperture" were beginning to sound something like a baffle, but it was far from good baffle art since the clamped edge would have prevented the large excursions necessary for low-frequency radiation even if a proper baffle had been intended; and besides, Hopkins's phonograph couldn't deliver any significant amount of low-frequency excitation anyway. Even so, this patent might have been more troublesome — which is to say, more expensive — to the loudspeaker industry than it was had not the Supreme Court 179 finally ruled that Hopkins's claims were "narrowly confined by the prior art . . . and not infringed by a device in which the rim of the tympanum is made of limp leather or cloth." Even broader claims for a conical diaphragm flexibly supported and driven by a concentric voice coil were subsequently allowed in a patent to C. L. Farrand, 180 and over fifty suits against alleged infringers were promptly filed in various courts by his assignee. This attempt to dominate m

Harry L. Duncan, U. S. Pat. No. 1,442,215 (filed 9 M a y 1919) issued 16 January

1923. 178 Marcus C. Hopkins (assignor to Lektophone Corp.), three U. S. Pats, issued 2 July 1918: No. 1,271,527 (filed 14 July 1913, renewed as Ser. No. 224,048 on 22 March 1918); No. 1,271,528 (filed 24 December 1913, renewed 22 March 1918); and N o . 1,271,529 (filed 17 April 1918 as a division of the renewal Appl. Ser. No. 224,048). 178 Lektophone Corp. v. The Rola Co., and Miller Bros. Co. v. Lektophone Corp. (on the Hopkins Pat. No. 1,271,529), 282 U. S. 168 and 4 U. S. Pat. Q. 151 (1930). There is a good review of the prior art in the opinion returned in Lektophone v. Rola, 34 F.2d 764 (1929). 180 o f Farrand's many patents in the radio field, the one used as a basis for court action was U. S. Pat. No. 1,855,168 issued 19 April 1932 (filed 17 October 1929 as a division of Appl. Ser. No. 103,844 filed 22 April 1926).

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the industry backfired, however, when the Court held the claims in question to be invalid. More than a decade before this legal fiasco, the "Phonetron" had appeared as an embodiment of one of Farrand's earlier patents. 181 As the first coil-driven direct-radiator loudspeaker to reach the American market (ca. 1921), the "Phonetron" was well received and it began immediately to furnish lively competition for the table-model horn units that were already in demand by home constructors of the early 1920's who sought to free their radio-broadcast reception from the confining privacy of headphones. A more novel contribution to the diaphragm art was offered by Ricker,185 who suggested the use of two large wide-angle cones (3 feet in diameter!) cemented base to base to form a light rigid structure that was to be "freely suspended." For radiation at low frequencies, this "hollow diaphragm" was no more effective than the classical oscillating sphere of comparable size, but the large diameter that Ricker proposed would still have qualified it impressively in this respect. Huguet d'Amour 183 made a similar proposal and showed a practical method of supporting such a radiator by clamping it at the circle of truncation of one of the cones. The characteristic shape of this double-cone construction became well known during the 1920's when it was developed independently for the Western Electric Model 540AW "loudspeaking telephone." Lane 184 suggested a little later that an elliptic cross section for such direct-radiating conical diaphragms might yield a more uniform distribution of resonance frequencies. The elliptic shape still appears frequently in radio loudspeakers, but one can suspect that its use is more often dictated now by space considerations than by an attempt to secure the advantages claimed by Lane. 181 Utah Radio Products Co. v. R. T. Boudette, on certain claims of Farrand 1,855,168, held invalid, 78 F.2d 793; 22 U. S. Pat. Q. 358. The "Phonetron" was based on the earlier Pat. No. 1,847,935 issued 1 March 1932 (filed 17 October 1925 as a division of Appl. Ser. No. 464,009 filed 23 April 1921). It was briefly noticed in Scientific American 126, 154 (27 August 1921); see also "Cone Loud Speakers," Proceedings of the Radio Club of America 4, 3-7 (October 1926). 182 Norman H. Ricker (W. E. Co.), U. S. Pat. No. 1,859,892 (filed 6 October 1922) issued 24 May 1932. 183 Paul-Georges Huguet d'Amour, French Pat. No. 570,109 (demand! 6 November 1922, d!livre 12 January 1924), 1 n addition No. 28,223/570,109 (demand! 22 September 1923, d!livr6 21 October 1924); also British Pat. No. 239,245 [1923] (filed 22 September 1924, complete accepted 17 December 1925). 184 Clarence E. Lane (W. E. Co.), U. S. Pat. No. 1,913,451 (filed 30 July 1924) issued 13 June 1933.

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Continuing research on permanent-magnet materials having high coercive force and high energy storage has yielded results of broad general significance, but the bearing of these results on the transducer art has been primarily connected with the economics of loudspeaker manufacture. The exploitation of such new materials has not led to any significant alteration in the form or functional structure of the moving-coil species of loudspeaker motor, which has survived without important change since its original conception in 1874. Modified forms of the basic loudspeaker drive mechanisms have continued to appear, of course, from time to time, and some of these are still found to be useful in special applications. A basic improvement in the balanced-armature mechanism had been made in 1890 by Frank Capps,146 who was later to become better known as the inventor of the burnishing facet on the recording stylus used for engraving disk records. Capps's improvement consisted in using a stationary signal coil surrounding a light rocking armature, instead of winding the coil on the armature as Watson 147 had done much earlier. A few years later Halsey 186 proposed winding the signal coils on extensions of the magnetic pole pieces, which may have qualified for originality but certainly represented a backward step with regard to the efficiency of the magnetic circuit. Whether guided by sound reasoning about eddy-current losses or by a desire to blanket the field (if indeed he was aware of the prior art), Baldwin 186 adopted first one and then the other of these basic configurations in executing his designs for an improved headphone in which a light balanced armature was linked to a thin mica diaphragm. These units were relatively heavy and, as a consequence, were uncomfortable to wear for long periods; but the electroacoustic design set forth in his 1913 disclosure (Capps configuration) was excellent, and for many years after their first appearance "Baldwin" headphones were regarded by amateur pioneers in radio as the last word in effective instrumentation. A somewhat more rugged balanced-armature mechanism of the same type, designed a few years later by Egerton, 187 was used to drive the diaphragm of 186

Edward S. Halsey, U. S. Pat. No. 542,191 (filed 20 April 1894) issued 2 July 1895. Nathaniel Baldwin, U. S. Pats. Nos. 905,781 (filed 29 January 1908) issued 1 December 1908, No. 957,403 (filed 1 July 1909) issued 10 May 1910, and No. 1,153,593 (filed 27 March 1913) issued 14 September 1915; an elementary description in Ε. E. Bucher, Practical Wireless Telegraphy, pp. 168-169 (New York, Wireless Press, Inc., 1917, 1918). 187 Henry C. Egerton (W. E. Co.), U. S. Pat. No. 1,365,898 (filed 8 January 1918) issued 18 January 1921. lis

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one of the early table-model horn loudspeakers (WE Model 518W, ca. 1921). A year or two later, Wegel modified the same unit for service as the drive mechanism for the WE BJfiAW double-cone loudspeaker mentioned above. One might almost draw the conclusion that this unit was too good, and that its continued availability as a general utility motor mechanism may have dulled the incentive for improvement and delayed by several years the study of moving-coil systems by Western Electric and А. Т. & T. engineers. Lively competition for Baldwin headphones was furnished by another type of deluxe telephone receiver in which a light nonmagnetic diaphragm in the form of a small free-edge cone was linked to a moving-armature drive mechanism. This instrument was developed in England by S. G. Brown.188 A flat reed served as the magnetic armature, and a convenient knob projecting through the back of the housing made it possible to alter the air gap while the headphones were being worn. This adjustment, which resembled in its action the "tickler" control on a regenerative receiver, allowed the user to take maximum advantage of an increase in sensitivity that occurs whenever the air gap is reduced to the critical value for which a delicate balance is established between the mechanical stiffness of the reed and the negative stiffness 189 introduced by the magnetic polarizing field. A similar design feature was made available several years later in an inexpensive free-edge direct-radiator cone loudspeaker marketed by the Tower Manufacturing Company (Boston) during the mid-1920's. Still another ingenious type of moving-armature mechanism was described in 1910 by Evershed and Kilroy; 190 and an improved modification of the same functional structure was proposed a little later by Brown,191 who continued to pursue the trail of better drive mechanisms for telephone receivers. In the configuration that Brown suggested, the 188 Sidney George Brown (of London, England), British Pat. No. 29,833 [1910] (filed 22 December 1910, complete spec. 19 June 1911, accepted 22 January 1912); and U. S. Pat. No. 1,096,676 (filed 27 March 1911) issued 12 May 1914. The British specification shows a moving-coil version that does not appear in the U. S. Patent. 189 The principle involved is discussed below in Chap. 7. See also discussion by C. R. Hanna (note 145). 190 Sydney Evershed and Willie Dickson Kilroy (of London, England), U. S. Pat. No. 1,333,298 issued 9 March 1920 (filed 12 September 1916 as a division of Appl. Ser. No. 559,158 filed 3 May 1910 [which became Pat. No. 1,218,934 issued 13 March 1917]). 191 Sidney George Brown (of North Acton, England), U. S. Pat. No. 1,318,535 (filed 17 April 1918) issued 14 October 1919.

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pole pieces of the polarizing magnet are close together and have their faces ground on a concave arc. The free end of a pivoted armature overlaps the two pole pieces and moves parallel to their faces so that the length of the gap (but not its area) remains constant as the armature is deflected. The electromechanical action is thus exactly like that of a conventional electric motor in which the poles of the armature (rotor) move across those of the field (stator), except that for vibratory service either the armature current or the field current is reversed rapidly and the rotary motion is restricted to an angular displacement considerably less than that included by one pole pair. Evershed and Kilroy made extensive use of this analogy with an electric motor in describing the operation of their drive mechanism; and while Brown did not, he did illustrate a multipole structure; and each described both alternative positions for the signal coil. More than a decade later, Farrand 192 and Peterson 193 filed patent applications almost simultaneously showing modifications of the constantair-gap idea adapted for linear motion of the armature. Peterson disposed his signal coil around the moving armature, while Farrand arranged the signal coils on the pole pieces in such a way that, when used with a pushpull amplifier, the plate current would assist in providing the polarizing field. By a confusing, if not misleading, perversion of terminology, the constant-air-gap moving-armature drive mechanism had been referred to by Evershed and Kilroy as an "inductor" type of loudspeaker motor. The Farrand modification of this basic structure reached the market so designated, and enjoyed a modest degree of commercial success during radio's burgeoning predepression era (ca. 1928-1932). The designation "inductor type" might more properly have been reserved for the species of loudspeaker motor pioneered by Field 194 in 1894. In its basic form this type of vibratory induction motor consists of a stationary signal coil inductively coupled to a short-circuited voice coil. The latter drives a sound-radiating diaphragm in the usual way when the induced currents in the low-resistance voice coil interact with a steady polarizing field. A good many disclosures of similar nature appeared sub182

C. L. Farrand (Assignor to Farrand Inductor Corp.), U. S. Pat. No. 1,784,486 (filed 26 February 1929) issued 9 December 1930. ш Charles W. Peterson, U. S. Pat. No. 1,797,965 (filed 1 March 1929) issued 24 March 1931. 194 Stephen Dudley Field (Assignor to American Bell Telephone Co.), U. S. Pat. Nr S40,969 (filed 5 December 1894) issued 11 June 1895.

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sequently, but the basic principle had been so clearly described by Field that most of the later patents were limited to claims based on structural modifications. Among these may be mentioned Fay and Dorsey,195 Ringel,196 and Arkell.197 The major, and almost the only, objection to the prototype structure described by Field arises from its vulnerability to eddy-current losses produced by currents induced in the polarizing held structure. In the disclosure mentioned above,190 Evershed and Kilroy had included one modification that qualified as a true "inductor"; and they made a start on solving the eddy-current problem by mounting on the field structure a reversed compensating coil designed to cancel the net magnetic coupling between the signal coil and the field excitation winding. Fessenden 115 carried out this same idea more effectively by changing the configuration of the field structure so that the two halves of the primary coil could be wound in opposite directions. This ingenious scheme permitted the net coupling with the magnetic field winding to be annulled while still allowing both parts of the primary coil to be effective in inducing useful current in a single-turn "voice coil." Nordenswan and Curtis 188 achieved an equivalent result by means of an equally ingenious orthogonal orientation of the polarizing field structure and a laminated core that served to couple the signal coil and the voice coil. Two more recent efforts to exploit inductive coupling deserve brief mention. Barker 199 made use of a compliant support for the wire comprising the winding of a voice coil and relied on induced currents in the aluminum form on which the voice coil was wound for diaphragm drive 186

Richard D. Fay, U. S. Pat. No. 1,763,846 issued 17 June 1930; and Herbert G. Dorsey, U. S. Pat. No. 1,899,561 issued 28 February 1933: both patents assigned to R.C.A. and both applications filed 16 October 1926 as continuations of the joint Appl. Ser. No. 579,191 filed originally 2 August 1922 and subsequently abandoned. Also R. D. Fay, U. S. Pat. No. 1,780,349 (filed 10 December 1927) issued 4 November 1930. 188 Abraham S. Ringel (R. C. Α.), U. S. Pat. No. 2,007,746 issued 9 July 1935 (Appl. Ser. No. 263,378 filed 21 March 1928 as a division of Appl. Ser. No. 44,735 filed originally 20 July 1925 as a joint application with J. P. Minton [became Pat. No. 1,868,019 issued 19 July 1932]). ш Frederick G. Arkell (of England, assignor to General Electric Co.), U. S. Pat. No. 1,743,749 (filed 11 January 1929) issued 14 January 1930. An earlier application filed in Great Britain 25 January 1928 was later abandoned. 198 Robert Nordenswan and Alfred S. Curtis (W. E. Co.), U. S. Pat. No. 1,644,789 (filed 17 May 1924) issued 11 October 1927. 1M Alfred Cecil Barker, British Pat. No. 448,271 (appls. dated 5 December 1934 and 11 July 1935, combined in one complete spec. 21 October 1935, accepted 5 June 1936); and U. S. Pat. No. 2,164,374 (filed 15 November 1935) issued 4 July 1939. A brief nontechnical description of "The Magnavox Duode Speaker" appeared in Wireless World 38, 241-242 (6 March 1936).

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at high frequencies. St. Clair's 200 design objective was a resonant transducer with high power output. The vibrating element that he used was a free-free bar consisting of a solid cylinder of duraluminum driven at one end by a single-turn "voice coil" inductively coupled to a stationary primary coil, and situated as usual in a radial magnetic field. When suitably supported, such a vibrator can exhibit an extremely sharp resonance — so sharp, in fact, that it is virtually necessary to provide positive feedback, as suggested by Lawther, 170 so that the system as a whole will be self-excited for oscillation at its own resonance frequency. Transducers based on St. Clair's design have given a good account of themselves in various experimental studies devoted to the phenomena associated with very intense sound waves in air. One of the most interesting forms of induced-current drive mechanism for loudspeakers was embodied in the "tone generator" described by Hewlett 201 in 1921. Direct current in two opposed pancake-wound coils produced a radial magnetic field lying in the plane of a thin unstretched metallic diaphragm located between the coils. When a signal current of proper phase was superimposed on the polarizing current in the two coils, circulating eddy currents could be established in the metallic diaphragm, and their interaction with the radial polarizing field would produce a force reaction that was distributed almost uniformly over the entire surface of the diaphragm. Since the unstretched diaphragm itself was sufficiently "floppy" to have virtually no characteristic resonance of its own, the electroacoustical performance of the unit was remarkably good, even by present standards. These features, the light nonresonant diaphragm and uniformly distributed driving forces, are also characteristic of the modern form of electrostatic loudspeaker; indeed, the Hewlett tone generator can readily be shown to be in almost all respects a true electromagnetic analog of the electrostatic loudspeaker. It has remained a laboratory curiosity, however, owing to difficulties of construction and the low efficiency associated with its inherently poor magnetic circuit. A more primitive moving-conductor system utilizing electrodynamic forces distributed over the radiating surface had been disclosed by 200 Hillary W St. Clair, "An Electromagnetic Sound Generator for Producing Intense High Frequency Sound," Review of Scientific Instruments 12, 250-256 (May 1941). 201 C. W. Hewlett, "A New Tone Generator," Phys. Rev. [2] 17, 257-258 (February 1921); 19, 52-60 (January 1922); Journal of the Optical Society of America 6,1059-1065 (December 1922).

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Taylor 202 in 1885. In this case, the diaphragm itself was to consist of a thin flat single-layer spiral of wire with adjacent turns cemented together to form an acoustic seal. Two such flat spirals were provided and the actuating force was simply the attraction or repulsion between the adjacent current sheets. This configuration is almost precisely that of Kelvin's classical "current balance," and the quadratic nature of the force reaction would surely have produced serious distortion if the device had been operated with any other signal source than a carbon microphone whose bias current would provide a polarizing field. A loudspeaker was devised by Gueritot 203 and marketed by Gaumont during the early 1920's which made use of a similar single-layer spiral of wire disposed on a [conical] surface of revolution, adjacent turns being bonded together, as in Taylor's construction, so that the wire could serve as both voice coil and diaphragm. A good bit of ingenuity had to be displayed in the design of pole pieces that would provide the required polarizing field without blocking the radiated sound. The moving-conductor species of transducer was exhibited in still another novel configuration by Schottky and Gerlach,204 who sought to exploit the substitution of a single metallic ribbon for the conventional multiturn voice coil. In the loudspeaker they described in 1923-24, the driving system served also as the sound-radiating surface and consisted of a thin metallic ribbon lying in a magnetic field established between extended pole pieces. Transverse corrugations reduced the stiffness of the ribbon to such a small value that its motion was primarily controlled by its inertia throughout a wide frequency range. The importance of this 202 Theodore F. Taylor, U. S. Pats. Nos. 314,155 (filed 3 January 1884) and 314,156-7 (filed 7 January 1884), all issued 17 March 1885; subject matter of all three combined in French Pat. No. 160,135 dated 5 February 1884, and in a provisional British Pat. specification No. 2703 [1884] filed 5 February 1884 and subsequently abandoned. 20S Maurice Gueritot (assignor to Soci6t6 des Etablissements Gaumont, Paris), French Pat. No. 558,037 (demand6 17 February 1922) delivr6 16 May 1923, I го addition no. 26,807/558,037 (demande 5 July 1922) deli vre 26 November 1923; also U. S. Pat. No. 1,523,262 (filed 12 April 1922) issued 13 January 1925. 204 Erwin Gerlach (Siemens & Halske Akt.-Ges. in Berlin-Siemensstadt): German Pat. No. 421,038 (filed 13 January 1923) issued 14 November 1925; "Das SiemensBandmikrophon und der Siemens-Bandsprecher," Siemens Zeitschrift 4, 165-168 (June 1924); U. S. Pat. No. 1,557,356 (filed 12 January 1924) issued 13 October 1925. Walter Schottky (Siemens & Halske Akt.-Ges. in Berlin-Siemensstadt), German Pat. No. 434,855 (filed 21 December 1924) issued 1 October 1926. W. Schottky (Part I) and Erwin Gerlach (Part II): "Vorführung eines neuen Lautsprechers," Physikalische Zeitschrift 26, (I) 672-675, (II) 675-676 (15 December 1924); Zeitschrift für Technische Physik б, (I) 574-576 and (II) 576-577 (1924).

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innovation did not stem so much from its modest success as a loudspeaker, however, as from the utility that Olson 205 recognized it to have for service as the generating element of a bidirectional pressure-gradient microphone. Through continuing studies devoted to such instruments, Olson and his collaborators have succeeded in making "ribbon microphones" available in a wide variety 206 of useful forms. It is time now to introduce two of the principal characters in this tale of transduction. Early in the 1920's C. W. Rice suggested to his colleague E. W. Kellogg that they tackle the job of making the very best possible "hornless loudspeaker." Dr. W. R. Whitney, director of the research laboratory of the General Electric Company, endorsed the venture and agreed that the investigation should be conducted without imposing any restrictions based on considerations of commercial practicability. Thus encouraged, Rice and Kellogg undertook the work enthusiastically. With such a broad objective, it is not surprising that they should have discovered independently a good many of the items credited to others elsewhere in these notes. Neither is it surprising that they were largely unaware of this parallel activity, since the disclosures contained in contemporary patent applications, while uniquely valuable for establishing priorities, are often delayed in coming to the attention of other workers in the same field. It is fortunate for everybody that Rice and Kellogg had been freed of any concern over questions of priority and of patentable novelty, at least for the time being. This freedom meant that they could — and did — extend their studies into all sectors of the hornless-loudspeaker field. As a consequence, one of the features that made the definitive "Rice-Kellogg 207 paper" of 1925 so important was that it made available immediately and to everyone a concise summary of the 206 Harry F. Olson, "Mass Controlled Electrodynamic Microphones: The Ribbon Microphone," J. Acoust. Soc. Am. 3, 56-68 (July 1931); also U. S. Pat. No. 1,885,001 (filed 31 March 1931) issued 25 October 1932. 206 Julius Weinberger, H. F. Olson, and Frank Massa, " A Uni-Directional Ribbon Microphone," J. Acoust. Soc. Am. 6, 139-147 (October 1933): and H. F. Olson, "Line Microphones," Proc. Inst. Radio Engrs. 27, 438-446 (July 1939); " Polydirectional Microphone," ibid. 32, 77-82 (February 1944); "Gradient Microphones," J. Acoust. Soc. Am. 17, 192-198 (January 1946); also Elements of Acoustical Engineering, 2d ed., Chap. VIII (New York, D. Van Nostrand Co., 1947). 207 Chester W. Rice and Edward W. Kellogg, "Notes on the Development of a New Type of Hornless Loud Speaker," Trans. Am. Inst. Elec. Engrs. 44, 4614175 (April 1925); and " Discussion " of same, pp. 475-480. (The abridged version appearing in the AIEE Journal omitted several features of interest.)

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existing state of the transducer art, including, as it turned out, the gist of a good many disclosures of prior work by others that had not yet become available in the form of published patent specifications. The second feature that made the Rice-Kellogg paper important was that they did succeed in producing a good loudspeaker — so good, in fact, that within a few years it had virtually driven all other types out of the market. What was perhaps even more important, however, the success of this laboratory research program played a major role in creating the market in which its triumph was to be scored. The way this came about makes this episode one of the contributing factors in the fabulous 20th-century growth of the modern communications industry. Prior to the early 1920's, nearly all reproduction of sound on a scale exceeding the capabilities of the telephone receiver was woefully handicapped by the difficulty of supplying adequate electric signal power. One need go back no further than 1924 to find it being said that "apparently we cannot yet get sufficient loudness for loudspeaking purposes without relying to a considerable extent upon resonance." 208 Rice and Kellogg were fully aware of this difficulty, and one of the first steps they took in launching their experimental program was to build a laboratory amplifier capable of delivering enough output power to permit the sensitivity advantage of resonance to be firmly abandoned. Only after this tool was in hand could they concentrate their attention on the question of "how faithful," rather than on the problem of "how loud." As a reasonable solution of the problem of fidelity began to emerge, it continued to be obvious that something would need to be done to augment the few milliwatts that represented the maximum power-output capability of any radio receiver then available in the commercial market. As a consequence of these considerations, the commercial version of the Rice-Kellogg loudspeaker reached the market in 1926 (designated by the trade name "Radiola" Loudspeaker Model 104) with a power amplifier yielding one watt of available signal power as a built-in feature. The next phase of this story really springs from the engineering decision to provide four extra terminals on the connection board at the rear of the 104 loudspeaker cabinet. It had turned up as a welcome dividend that the rectifier provided to supply the power requirements of the 104's !0 * A. O. Rankine, in his response to contributed discussions of the symposium on "Loud-Speakers for Wireless and Other Purposes," Ρroc. Phys. Soc. (London) 36, 114-151, 211-240 (1924); J. Inst. Elec. Engrs. (London) 62, 265-298, 373-375 (March, April 1924).

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amplifier and the loudspeaker field coil had enough surplus output capacity to supply at these auxiliary terminals all the d.c. power requirements of one of the superheterodyne radio receivers (Radiola 28) then in production. This combination of the Radiola 28 and the Radiola Loudspeaker 104 thus made available for the first time a complete batteryless radio receiver that could be operated like any other electrical appliance, merely by "plugging it in." The enthusiastic acceptance of this offering — even at the 1926 price of $250 for the 104. alone — indicated clearly that this was indeed what the public had been waiting for. This was also added fuel for the fires already lit under the development of new types of amplifier tubes especially adapted for a.c. operation, and the stampede toward their universal use in radio receivers gathered momentum quickly during 1926-1928. With the completion of the changeover to a.c. operation, the whole radio industry experienced the same kind of explosive release that follows removal of the key log in a jam, and into discard along with headphones and batteries went the last barrier between radio reception and a mass market that was soon demanding electroacoustic transducers by the millions. The design features that were responsible for the success of the RiceKellogg loudspeaker were based on the joint operation of two simple physical principles. These can be described, with a little oversimplification, as follows: Sound radiation gives rise to a mechanical resistance to the vibratory motion of a small diaphragm mounted in a baffle; this radiation resistance, and hence the radiated sound power, would increase with the square of the frequency if the vibratory velocity were maintained constant; but the square of the vibratory velocity (on which the sound power also depends) will decrease with the square of the frequency throughout the frequency range above resonance, where the motion of the system is primarily controlled by mass reactance. I t follows that if the fundamental resonance of the diaphragm system is made to occur below the lowest frequency of interest, the complementary variation with frequency of the two factors that jointly control the sound output will yield a uniform response throughout the middle range and up to some higher frequency at which the assumptions begin to fail. This was the acoustical virtue that Rice and Kellogg recognized and put to work, and it continues to be the basic precept that guides the design of all direct-radiator loudspeakers. The acoustical advantages of avoiding resonance by using the masscontrolled motion of a small diaphragm had been pointed out several

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years earlier by Sykes 209 in a broad disclosure directed toward electrical methods for microphone pickup and phonograph recording. From a patent point of view, this was an embarrassing anticipation, but its applicability to loudspeakers had to be inferred from incidental references to the reversibility of a pressure microphone using a mass-controlled diaphragm. Sykes considered carefully the equalization required in the electric circuits of such a microphone in order to compensate for the variation of velocity with frequency, but he failed to recognize that the variation of radiation resistance provides this compensation automatically for the loudspeaker. On the other hand, Riegger 210 and Wente 211 are each to be credited with the independent discovery of the unique loudspeaking virtues of the small coil-driven mass-controlled diaphragm in a baffle, and each made disclosures that were virtually as complete as that of Rice and Kellogg. As it turned out, however, neither Wente's patent specification nor the one Kellogg212 had filed a year earlier became available until long after the Rice-Kellogg paper had appeared and the Radiola 104 had played its stellar role in opening up the mass market for electroacoustic transducers; and the account of Riegger's work was published — one might almost say buried — in a journal of relatively limited circulation so that it has not even yet received the notice that it still deserves. There is a moral to be drawn here, perhaps, concerning the prompt utilization of effective channels of publication; but in any case, it must be said that neither of these worthy independent researches played any significant role in triggering off the commercial exploitation of the dynamic loudspeaker — credit for that belongs to Rice and Kellogg. The ability to achieve a reasonably broad midfrequency range of uniform response was quite enough to set into motion the machinery of 509

Adrian Francis Sykes (England), British Pat. No. 160,223 (five provisional specs, filed between 18 November 1919 and 8 October 1920; combined in one complete spec, left 18 October 1920; accepted 18 March 1921): U. S. Pats. No. 1,711,551 issued 7 M a y 1929 on a parent application filed 16 November 1920; and on three divisional applications, Nos. 1,639,713 issued 23 August 1927; 1,743,251 issued 14 January 1930; and 1,852,068 issued 5 April 1932. A fourth divisional application Ser. No. 319,299 was filed 14 November 1928 and subsequently abandoned. 210 Hans Riegger, "Zur Theorie des Lautsprechers," Wissenschaftliche Veröffentlichungen aus dem Siemens-Konzern 3, Part 2, 67-100 (1924). 211 Edward C. Wente (W. E. Co.), U. S. Pat. N0.1,812,389 (filed 1 April 1925) issued 30 June 1931. 212 Edward W. Kellogg (G. E. Co.), U. S. Pat. N0. 1,795,214 (filed 27 March 1924, renewed 10 November 1926) issued 3 March 1931; see also U. S. Pat. N0. 1,707,617 (filed 9 January 1925, renewed 18 May 1927) issued 2 April 1929.

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CONTEXT

83

mass production referred to above, but a host of problems had still to be dealt with at both the theoretical and the practical levels. Many of these were concerned with the implicit, as well as the explicit, assumptions invoked in describing the idealized behavior of a small radiator vibrating under mass control. For example, if a truly rigid diaphragm is to qualify as acoustically "small" at very high frequencies, it would need to vibrate with unreasonably large amplitude in order to radiate an adequate amount of sound at low frequencies. On the other hand, if a diaphragm is made large enough to be an effective radiator at low frequencies, its own higher modes of vibration will almost certainly obtrude a violation of the assumption of rigidity within the frequency range of interest. This obviously calls for a compromise — or for the invention of some scheme for making a vibrating diaphragm appear to have a different area, and perhaps for its voice coil to have a different mass, for different frequencies of excitation. I t is fortunate for modern loudspeaker manufacturers that nature smiles benignly on this need for compromise. The central portions of a conical diaphragm are relatively more stiff and more tightly coupled to the driving voice coil than are the outer, flatter portions of the conical surface. I t is normal behavior, therefore, for the outer zones of a conical diaphragm to become progressively decoupled at higher frequencies, leaving the stiffer central portion to carry the burden of sound radiation at the higher frequencies. A good bit of fumbling had to be endured, however, before the significance of this "variable area" principle was fully appreciated. Wegel 213 appears to have taken the first practical step toward deliberately assisting nature in the execution of this principle when he proposed in the design of the WE S4-0AW to make the central portion of the cone as light and stiff as possible while the outer zones were made more flexible and more highly damped. Martin 2 1 4 discussed the principle of frequency separation even more explicitly in a contemporary specification, but the structure he proposed was hardly more than a symbolic exemplification of the principle. Rice and Kellogg explored the idea of dividing up the conical diaphragm into elastically coupled annular seg213 Raymond L. Wegel (W. E. Co.), U. S. Pat. No. 1,926,888 (filed 5 February 1924) issued 12 September 1933; for conceptual anticipations, however, see S. G. Brown (note 188), and A. M. Nicolson, U. S. Pat. No. 1,624,357 (filed 15 June 1923) issued 12 April 1927. 214 William H. Martin (А. Т. & T. Co.), U. S. Pat. No. 1,536,116 (filed 1 April 1924) issued 5 May 1925.

84

ELECTROACOUSTICS

ments, but they reverted to letting nature take care of this problem in their final prototype. The notion of diaphragm segmentation was further elaborated a few years later by Parry 2 1 i in England, and by Bernard 216 in France. Parry's disclosure went somewhat further than the others by proposing that a separate voice coil be provided for driving each of the three annular segments into which the conical diaphragm was to be divided. A paraphrase of the Goldilocks legend is almost irresistibly suggested by such a neat array of voice coils nicely graded as to size: the little central cone had a little voice coil and it would go tweet, tweet; the middle-size conical section had a middle-size voice coil, and it would speak up with a middlepitched voice; but the big conical section on the outside had a great big voice coil, and it would go woof, woof, woof! In the meantime, the development of multiple-cone, multiple-voice-coil loudspeakers had been undertaken 217 in earnest at the newly established research laboratories of the Radio Corporation of America. This development effort has been sustained to such good effect that the variable-area diaphragm, and the corresponding feature of a variable-mass voice coil, are now established 218 as design features that can be invoked reliably whenever it becomes necessary to provide a single direct-radiator loudspeaker unit with uniform response over an extended frequency range. Variants on the variable-area principle have included the use of horns to enhance the acoustic loading of different segments of a radiating surface. Martin 2 1 4 had shown one interesting configuration in which the conical diaphragm for radiating low frequencies was to serve also as 216 Robert D. Parry (British Thomson-Houston Co. Ltd.), British Pat. No. 311,486 (filed 27 February 1928; complete Spec. 27 November 1928, accepted 16 May 1929); U. S. Pat. No. 1,980,957 (filed 27 February 1929, renewed 20 May 1933) issued 13 November 1934. 216 Marcel Bernard (Soci6t6 Francaise Radioelectrique, Paris), French Pat. No. 715,389 (demand6 14 August 1930) d61ivr£ 28 September 1931; also U. S. Pat. No. 1,897,294 (filed 30 July 1931) issued 14 February 1933. 217 See, for example, Abraham S. Ringel (R. C. Α.), U. S. Pat. No. 2,007,746 (filed 21 March 1928 as a division of Appl. Ser. No. 44,735) issued 9 July 1935: this development summarized by Harry F. Olson, " A New Cone Loud Speaker for High Fidelity Sound Reproduction," Proc. Inst. Radio Engrs. 22, 33-46 (January 1934). See also Α. V. Bedford, " A Concatenated Cone Speaker," J. Acoust. Soc. Am. 2, 251-259 (October 1930). 218 H. F. Olson, "Multiple Coil, Multiple Cone Loudspeakers," J. Acoust. Soc. Am. 10, 305-312 (April 1939); H. F. Olson and John Preston, "Wide Range Loudspeaker Developments," R. C. A. Review 7, 155-178 (June 1946), and /.[ournal of the] 5oc.[iety of] Motion Picture £»g[inee]«. 47, 327-352 (October 1946).

HISTORICAL CONTEXT

85

a horn to increase the radiation loading on a smaller high-frequency diaphragm — a scheme that could hardly be improved on as a method for generating objectionable Doppler-effect intermodulation. A coaxial construction less subject to this objection was revealed in principle by Fanger219 and disclosed in good engineering detail by Bostwick.220 In this scheme, which is still deservedly popular, a small high-frequency horn with its own driving diaphragm is nested either within or in front of the central pole piece of a large cone loudspeaker designed to carry the radiation load at frequencies below the cutoff of the small horn. An important variation of the multiple-diaphragm idea had already been put forward in 1917 by Fessenden,221 and again five months later by Langmuir.222 Each sought to produce the equivalent of piston action over a large radiating surface while avoiding at the same time the phase reversals and the variations of driving point impedance that would ordinarily be produced by high-order modes of vibration of a single large diaphragm. Details of their proposed solutions differed, but each, in effect, contemplated the subdivision of the active surface into elementary areas that were to be separately excited. Langmuir went on to point out that the flexibility of multiple-unit construction would facilitate control of the directivity of sound radiation. Such an idea has obvious applicability to the design of transducer arrays for underwater signaling. It serves also, for example, as a principle for guiding the use of small loudspeakers disposed in vertical arrays in order to improve the distribution of sound in speech-reinforcement systems. Fessenden sought later, and eventually was allowed, broad claims for the method of producing very sharp beams of transmitted sound by using a diaphragm whose dimensions are large in comparison with the wavelength. This basic idea had been anticipated to some extent by Richardson.114 However, Fessenden assumed explicitly, as Richardson did implicitly, that the diaphragm was to vibrate with uniform phase, and he recognized that this was a condition that could be maintained in prac219

Herman J. Fanger, U. S. Pat. No. 1,895,071 (Appl. Ser. No. 308,152 filed 25 September 1928) issued 24 January 1933, and Pat. No. 1,992,300 (filed 26 July 1932 as a division of Appl. Ser. No. 308,152) issued 26 February 1935. 220 Lee G. Bostwick (Β. T. L.) U. S. Pat. No. 1,907,723 (filed 28 September 1929) issued 9 May 1933. 221 Reginald A. Fessenden, U. S. Pat. No. 1,277,662 (filed 28 February 1917) issued 3 September 1918. The broad claims on highly directive radiators appear in Pat. No. 1,562,950 (filed 14 December 1918) issued 24 November 1925. 222 Irving Langmuir (G. E. Co.), U. S. Pat. No. 1,380,981 (filed 21 April 1917) issued 7 June 1921.

86

ELECTROACOUSTICS

tice only by invoking the principle of localized diaphragm excitation that he (and Langmuir) had enunciated. A more recent embodiment of this principle was described by Steinberger 223 in a proposal involving the segmentation of a large diaphragm to be used for radiating sound in water, and similar procedures are now — or should be — routine. The most frequently rediscovered feature of the loudspeaker art is the use of a baffle to avoid destructive interference between sounds radiated from the front and from the back of a radiating diaphragm. Stokes 224 had pointed out as early as 1868 that sound radiation could be materially increased by preventing the circulatory flow of air around the edges of a vibrating surface. A few years later, Rayleigh 225 recalled attention to Stokes's work, and also presented what is still regarded as the classic analysis of sound radiation from a rigid piston vibrating in an infinite baffle. The surprise with which one worker in this field after another tardily discovered Rayleigh's analysis of the baffle problem may possibly be related to the fact that by 1920 the second [1894] edition of his Theory of Sound had been out of print for a long time. The reprint edition of 1926 appeared in time to become better known to the following generation, but not in time to help the various experimentalists who discovered baffles before they discovered Rayleigh. Ramifications of the baffle art appear to be sufficiently numerous to have allowed a good many engineers to share in their discovery. For example, Button 226 filed an early disclosure of the dimensional considerations pertaining to the operation of a small diaphragm in a finite baffle. Keller,227 in an interference with Thompson,228 was awarded claims cover223 Raymond L. Steinberger (assignor to G. W. Pierce), U. S. Pats. No. 2,063,950 (Appl. Ser. No. 579,039 filed 4 December 1931) and Nos. 2,063,951 and 2,063,952 (filed 19 July 1935 as divisions of Appl. Ser. No. 579,039) issued 15 December 1936. For a primitive example of segmentation see Elisha Gray, U. S. Pat. No. 866,128 (filed 1 December 1899) issued 17 September 1907. 224 Sir George G. Stokes, "On the Communication of Vibration from a Vibrating Body to a surrounding Gas," Phil. Trans. Roy. Soc. (London) 168, 447-463 (1868). 226 John William Strutt, Third Baron [Lord] Rayleigh, The Theory of Sound, II, §§341 and 302 (in 2 vols., 8°, London, Macmillan and Co., Ltd., 1st ed. Vol. I, 1877, Vol. II, 1878; 2nd ed., revised and enlarged, 1894; reprinted, 1926, 1929; American reprint edition, 2 vols, bound as one, with a historical introduction by R. B. Lindsay, New York, Dover Publications, 1945). 226 Leroy R. Button, U. S. Pat. No. 1,506,562 (filed 20 December 1919) issued 26 August 1924. 227 Arthur C. Keller (А. Т. & T. Co.), U. S. Pat. No. 1,884,724 (filed 19 June 1923) issued 25 October 1932. 228 Roy E . Thompson (Hazeltine Corp.), U. S. Pat. No. 1,710,035 (filed 13 March 1926) issued 23 April 1929.

HISTORICAL CONTEXT

87

ing the use of an open-back cabinet to serve the functions of such a finite baffle. Frederick 229 proposed the use of a completely closed housing as one method of simulating the acoustical effect of an infinite baffle; and while he successfully asserted his priority over Rice 230 with regard to the use of a baffle, he lost to Minton 281 the claims covering a baffle enclosure with damping material. The function of an acoustic baffle is to do nothing — that is, to remain motionless — over as wide an area as possible. This is somewhat more than a purely passive role, however, since the baffle must supply any force reaction required in order that it not be set in vibration by sound waves reflected from it. When a finite baffle of modest size is used under listening conditions affording the usual amount of reverberation, the sound radiated from the rear of the diaphragm contributes more or less usefully to the total sound power output over most of the frequency range. This condition tends to break down, however, at low frequencies, which is usually just the portion of the range in which it would be most beneficial to contrive some way of assuring beneficial reinforcement. The most important innovation to come out of the research directed toward this goal has been the so-called "phase-inverter" housing or "bassreflex" enclosure. As is often the case with ideas that appear superficially to be simple, a good many loudspeaker designers discovered that they had already made this invention — after someone else had pointed out what the invention was. For example, there is a tendency to label as a forerunner of the bass-reflex principle any prior-art loudspeaker in which an incidental hole or side opening in the cabinet can be identified. The primitive disclosures of Finch 232 and Colby 233 are of this sort. Merrill and Hays 234 went a little further by exhibiting an enclosure containing holes intended to "prevent the formation of a dead-air cushion against a receiver diaphragm ". 229 Halsey A. Frederick (W. E. Co.), U. S. Pat. No. 1,955,800 (filed 5 May 1923) issued 24 April 1934. 230 Chester W. Rice (G. E. Co.), U. S. Pat. No. 1,631,646 (filed 27 March 1924) issued 7 June 1927. 231 John P. Minton (R. C. Α.), U. S. Pat. No. 1,827,994 (filed 12 June 1925) issued 20 October 1931. 232 Edwin D. Finch, U. S. Pat. No. 216,840 (filed 12 March 1879) issued 24 June 1879. 233 John W. Colby, U. S. Pat. No. 371,551 (filed 11 April 1887) issued 18 October 1887. 234 Albion Parris Merrill and Jenny Ward Hays, U. S. Pat. No. 669,944 (filed 10 January 1900) issued 12 March 1901.

88

ELECTROACOUSTICS

A more prescient anticipation of the bass-reflex principle was embodied in the telephone receiver devised in 1919 by Louis Steinberger.235 In this transducer, four small tubes were provided to connect the space behind the diaphragm to the volume of air enclosed at the front between the diaphragm and the opening in the ear cap, "whereby a better speech reproducing effect is secured." Weinberger and Wolff236 revealed a vague structural anticipation by specifying a vented cabinet, but their description of the placement of the vents was couched entirely in terms of the avoidance of destructive interference, and no mention was made by them of the extension of response to lower frequencies by a particular choice of cabinet dimensions and loudspeaker parameters. The basic disclosure of the bass-reflex principle was set forth in a patent to Thuras,237 an ingenious scientist of the Bell Telephone Laboratories whose untimely death in 1945 robbed electroacoustics of one of its stars. This patent gem is especially noteworthy for its simple exposition of the design of a compensated dynamic microphone in which the motion of the diaphragm is primarily controlled by the reactions of acoustic networks associated with the diaphragm and its housing structure. In another approach to the problem of making effective use of back radiation, High 238 proposed, in effect, to abandon the enclosure and to lead off the sound through a tortuous passage coupled to the rear of the diaphragm. High-frequency sounds were attenuated by selective absorption in the duct, but the low-frequency back radiation was discharged toward the front with enough time delay to provide reinforcement just above the extended low-frequency cutoff of the system. Such an acoustic labyrinth was further developed in commercial form by Olney 239 and was marketed during the late 1930's by the Stromberg-Carlson Telephone Manufacturing Company. m

Louis Steinberger, U. S. Pat. No. 1,366,067 (filed 28 February 1919) issued 25 January 1921. 231 Julius Weinberger and Irving Wolff (R. C. Α.), U. S. Pat. No. 1,760,862 (filed 31 March 1927) issued 27 May 1930; reissued 28 February 1933 as RE. 18,751. 237 Albert L. Thuras (B.T.L.), U. S. Pat. No. 1,869,178 (filed 15 August 1930) issued 26 July 1932. See also E. C. Wente and A. L. Thuras, "Moving-Coil Telephone Receivers and Microphones," J. Acoust. Soc. Am. 3, 44-55 (July 1931). Jurjen S. High (Westinghouse), U. S. Pat. No. 1,794,957 (filed 20 October 1927) issued 3 March 1931. Benjamin Olney (Stromberg-Carlson), U. S. Pat. No. 2,031,500 (filed 17 September 1934) issued 18 February 1936; also "A Method of Eliminating Cavity Resonance, Extending Low Frequency Response and Increasing Acoustic Damping in Cabinet Type Loudspeakers," J. Acoust. Soc. Am. 8, 104-111 (October 1936).

HISTORICAL CONTEXT

89

When the interior of the cabinet could be devoted wholly to the loudspeaker function, which is to say when the cabinet was not full of radio or phonograph equipment, the effectiveness of back loading could be enhanced by substituting for the labyrinth of uniform cross section a folded exponential horn. Such a combination of horn and direct-radiator loudspeaker 240 was marketed for monitoring purposes in the late 1930's as the RCA Model 64B. A good bit earlier, Williams 241 had suggested that two horns might be driven by the same diaphragm, a short highfrequency horn providing front-side loading and a long folded low-frequency horn the back-side loading. The same feature of dual horn loading was invoked later by Wente 242 and was still further exploited by Olson and Massa 243 in a compound horn system designed to improve the acoustic loading of a cone loudspeaker unit. It can be correctly inferred from the foregoing that provision for the radiation of large amounts of low-frequency sound was a more troublesome problem than the control of high-frequency radiation. Bass-reflex enclosures and compound horn systems, especially in combination with segmented cones and multiple voice coils — these were admirable expedients that made it possible to prescribe as much, or almost as little, compromise with ultimate perfection as economic restrictions would allow. The degree of success achieved with these expedients, however, could not disguise the fact that efficient energy conversion at widely separated frequencies demanded transducer mechanisms having quite different physical characteristics. Min ton and Ringel 244 had met this issue squarely as early as 1925, when they proposed a two-way or dual loudspeaker system in which electric filter networks were used to divide the frequency spectrum into two parts, the low-frequency signals being delivered to a "woofer" system and the high-frequency signals to a separate "tweeter." Such two-way (and later, three-way) systems were developed extensively 210 H. F. Olson and R. A. Hackley, "Combination Horn and Direct Radiator LoudSpeaker," Proc. Inst. Radio Engrs. 24, 1557-1566 (December 1936); also H. F. Olson (R. C. Α.), U. S. Pat. No. 2,224,919 (filed 31 March 1937) issued 17 December 1940. 241 Seiden Т. Williams (R. C. Α.), U. S. Pat. No. 1,943,499 (filed 6 April 1928) issued 16 January 1934. 242 Edward C. Wente (В. T. L.), U. S. Pat. No. 1,930,915 (filed 13 July 1932) issued 17 October 1933. 243 H. F. Olson and Frank Massa, "A Compound Horn Loudspeaker," J. Acoust. Soc. Am. 8, 48-52 (July 1936). 244 John P. Minton and Abraham S. Ringel (R. C. Α.), U. S. Pat. No. 2,084,160 (filed 9 June 1925) issued 15 June 1937.

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ELECTROACOUSTICS

for use in sound-motion-picture theaters by Wente and Thuras 248 and by Hilliard.246 Studies conducted with and on theater sound systems have yielded an increased appreciation of the importance of controlling the directivity of such sound sources. It is well established that the ear attaches more interpretive importance to directly transmitted sound than to reverberant sound received subsequently. One of the most useful methods of controlling the distribution of direct sound in either theater or home installations is to make use of a multicellular horn.247 Multiple-unit systems in which such a sectionalized horn is relied on for high-frequency radiation can be designed to yield a relatively high and uniform efficiency of transduction over a wide range of frequency, and they are still used almost universally for applications demanding the large-scale delivery of widerange sound reproduction. Unfortunately, at least from the acoustical point of view, a wide-range theater sound system is just a little clumsy to fit into the average living room. And just as certainly, no scientific sophistry can alter the physical relation between the wavelength of low-frequency sounds and the dimensions of the diaphragms or horns required to radiate them effectively. One ingenious approach to this problem, however, comes precious close to scientific sophistry; it has been described as building the living room into the mouth of the horn rather than installing the horn in the living room. The acoustical effects of confining the radiation from a sound source within a restricted solid angle had been well known for many years, but Maximilian Weil 248 appears to have been the first to point out that the common intersection of floor and walls at the corner of a room could serve to confine sound radiation in just this way. To change the language (but not the physics), these three diverging surfaces, as seen by looking outward from the corner, could be regarded as the bounding surfaces of the last stage of expansion of a flaring horn. A more explicit 245 E. C. Wente and A. L. Thuras, "Loud Speakers and Microphones," Bell System Tech. J. 13, 259-277 (April 1934). 246 John K. Hilliard, " A Study of Theater Loud Speakers and the Resultant Development of the Shearer Two-Way Horn System," J. Soc. Motion Picture Engrs. 27, 45-60 (July 1936); also C. Flannagan, R. Wolf, and W. C. Jones, "Modern Theater Loud Speakers and Their Development," ibid. 28, 246-264 (March 1937). 247 Edward C. Wente (B.T.L.), U. S. Pat. No. 1,992,268 (filed 11 April 1933) issued 26 February 1935. 248 Maximilian Weil, U. S. Pat. No. 1,820,996 (filed 8 December 1925) issued 1 September 1931.

HISTORICAL CONTEXT

91

disclosure of this "corner" concept was made by Sandeman249 and the idea was further explored by Kellogg.260 To analyze in detail the behavior of corner-mounted loudspeakers is not a simple problem, as can be appreciated by considering the equivocal conditions of acoustical termination that must be assumed when the mouth of the horn embraces half a room. Nevertheless, the excellent designs proposed by Klipsch261 have done much to establish the "corner horn" as an outstanding contribution toward the availability of wide-range sound reproduction in the home. These rambling remarks can well be terminated on such a hopeful note, for the level of research activity is high and the prospects are indeed bright. An intimidating array of books, research papers, and patents have been devoted to the science and technology of transducers since 1925, when audio — then video — began to lay siege to the home. Testimony regarding the scale of this activity is offered by the fact that the cumulative index of the Journal of the Acoustical Society of America con-

tains more than 1,400 entries referring to publications in the general field of transducers appearing either in its own Journal or in the contemporary literature during the 20-year period ending in 1948. The foregoing selective remarks do scant justice to this high level of research activity. More specifically, no attempt has been made in these notes to establish an adequate closure with regard to the current state of the transducer art as manifested in all the specific mechanisms of transduction. What little is to be said here about current practice is left to serve as introductory material for the following chapters. The loudspeaker designer has frequently been exposed to the cavil that his product is the weakest bond in the electroacoustic chain that links the performer and the listener. The designer has an impressive bag of tricks at his disposal, however, and he is better qualified now than ever before to defend himself by declaring that the problems of fidelity, or infidelity, in sound reproduction have become problems of architectural acoustics rather than electroacoustics. But that's another story . . . 249

Edward K. Sandeman (Stand. Tel. & Cables, Ltd.), British Pat. No. 322,470 (filed 29 August 1928, complete spec, accepted 29 November 1929); U. S. Pat. No. 1,984,550 (filed 25 May 1929) issued 18 December 1934. 260 Edward W. Kellogg, "Means for Radiating Large Amounts of Low-Frequency Sound," J. Acoust. Soc. Am. 3, 94-110 (July 1931). 251 Paul W. Klipsch, "A Low Frequency Horn of Small Dimensions," J. Acoust. Soc. Am. 13,137-144 (October 1941); "Improved Low Frequency Horn," ibid. 14, 179-182 (January 1943): also U. S. Pats. No. 2,310,243 (filed 5 February 1940) issued 9 February 1943, and No. 2,373,692 (filed 3 October 1942) issued 17 April 1945.

CHAPTER

2

Electromechanical Coupling — General The science of electroacoustics is based on the experimental observation that an electrical system can be associated with a mechanical system in such a way that a unique functional relation exists between the variables that characterize the electrical system and the variables that characterize the mechanical system. The existence of such a relation lies at the core of elementary electrodynamics, as exemplified by the role of mechanical quantities (such as force and work) in the definition of the basic electrical units. The analysis of electromechanical systems can begin then with the consideration of a simple but quite general case in which an electric circuit comprising a single mesh is coupled, through some sort of "black box" called a transducer, to a mechanical circuit having a single degree of freedom. Two equations will be required to describe the behavior of the system: one will need to be written in terms of the electrical variables and must include the electrical effects arising from motion in the mechanical system; and one will be written in terms of the mechanical variables and must include all the mechanical effects arising from currents or voltages in the electrical system. The symbols Tem and Tme appearing in Fig. 2.1 represent Z e (elect.)

ι

Transducer —I

z m (mech.)

FIG. 2.1. Schematic representation of an electromechanical transducer.

transduction coefficients that describe the electromechanical coupling, the direction of transfer being indicated by the subscripts. (As a useful mnemonic, read per, or due to, between the two subscript symbols.) Thus, Τem is defined as the electromotive force appearing in the electrical

ELECTROMECHANICAL COUPLING

93

mesh per unit velocity in the mechanical mesh. Similarly, Tme is defined as the force acting in the mechanical mesh per unit current in the electrical mesh. Assuming the steady state, in which variation with time enters always as е*а1, these defining relations allow the equations for the system to be written at once in the canonical form,1 E = ZeI+ T^v, F = TmeI + zmv.

(2.1)

Physical Realizability If equations of this sort are to be written down arbitrarily, it is pertinent to inquire what restrictions must be imposed in order that the equations may describe a physically realizable system. It can be taken as axiomatic that a physical system can neither have negative kinetic energy nor store negative potential energy, so the positive-definiteness of the kinetic- and potential-energy functions is at least a necessary condition for physical readability. It is equally axiomatic that the energy dissipation function for a passive system must also be positive-definite. In order to interpret these criteria in terms of the realizability of any particular network configuration, one must proceed to set up the most general type of network and to write down a total-energy function representing all the energy supplied from external sources or stored in the network. It is then straightforward2 to show that this total-energy 1 Poincare seems to have pioneered in pairing two linear equations, to describe the coupling between an electrical and a mechanical system, in his "Etude du recepteur t616phonique," L'Eclairage Electrique 60, 221-372 (16 February et seq. 1907). R. L. Wegel, in his "Theory of Magneto-Mechanical Systems as Applied to Telephone Receivers and Similar Structures," / . Am. Inst. Eke. Engrs. 40, 791-802 (October 1921), was the first to make use of mechanical as well as electric impedances in this connection, so that the equations for the coupled system could be displayed in the symmetric form shown here. 2 Most of the literature on this electric-network problem represents a paraphrase of the corresponding problem of small oscillations in dynamics. See, for example, A. G. Webster, The Dynamics of Particles and of Rigid, Elastic, and Fluid Bodies, 2nd ed., Chapter V (New York, G. E. Stechert, 1922; 3rd ed., Leipzig, B. G. Teubner, 1925); or Ε. T. Whittaker, Analytical Dynamics, 4th ed., §§ 76-78 (reprinted, New York, Dover Publications, 1944); also M. Bocher, Introduction to Higher Algebra (New York, Macmillan, 1927). The mathematical essence of the problem has been redistilled more recently by R. A. Frazer, W. J. Duncan, and A. R. Collar, Elementary Matrices, pp. 3032 (New York, Macmillan, 1946) and by E. A. Guillemin, Mathematics of Circuit Analysis, Chapter IV (New York, Technology Press [ M I T ] and Wiley, 1949). A comprehensive and self-sufficient discussion of physical realizability in electric networks is given by H. W. Bode, Network Analysis and Feedback Amplifier Design, Chapter VII (New York, Van Nostrand, 1945).

ELECTROACOUSTICS

94

function can always be separated into three quadratic forms, one in each of the three types of impedance coefficients. I t can then be shown t h a t the necessary and sufficient conditions for the positive-definiteness of each of these quadratic forms is that the determinants of the impedance coefficients of like type, and each of their principal minors, shall also be positive-definite. To illustrate this criterion by a simple example, assume that the several impedance coefficients of Eqs. (2.1) are of the general complex type: Ze = Re+jo>Le

+

;

zm = rm+j0, Гт rm

>0, IT LM

>0; CT

Cm

(2.3)

and rm > 0 ,

lm > 0,

cm >

0.

The sufficiency of this criterion of r e a d a b i l i t y can be demonstrated if a systematic procedure can be set up for finding physical configurations 3 that conform to any set of equations like (2.1) for which the impedance coefficients also satisfy Eqs. (2.3). In practice, interest often centers on the converse problem in which equations like (2.1) are written explicitly to describe a known physical system and are then used to study the behavior of the system for various allowable choices of the parameters. In this case, the criterion (2.3) can serve to determine what is "allowable" and thus to guard against setting up unrealizable design objectives. Motional

Impedance

The most distinctive feature of an electromechanical transducer, of course, is its ability to convert electrical energy into mechanical energy 8 Although this procedure has not yet been reduced systematically to practice in electroacoustic-transducer design, it has been elegantly demonstrated for electric networks by H. W. Bode, "A General Theory of Electric Wave Filters," Journal of Mathe-

matics and Physics 13, 275-362 (1934).

E L E C T R O M E C H A N I C A L COUPLING

95

and vice versa. Important properties of the electromechanical interaction can be revealed, however, by studying the driving-point impedance of the system at either its electrical or its mechanical terminals. The electric driving-point impedance at a terminal pair is always defined as the complex ratio of the voltage across the terminal pair to the current entering and leaving the pair terminals, when all other electromotive forces and current sources are suppressed. For the generalized system of Fig. 2.1, the driving-point impedance can be found by setting F = 0 in Eqs. (2.1) and then solving for the current I in terms of the terminal voltage E. This leads to /E\

Z ее = I -J I

Δ Zez,η TemTmg 7 = Τ" = = Z t -\

TmTme >

. (2.4)

\I/F- 0 An Zm Zm where Дц is the signed minor, or cofactor, 4 of the first row and first column of the impedance determinant Δ. In a similar way the mechanical driving-point impedance zmm can be written at once as W

=(-)

\V/ S = 0

= A =

Δ22

2m

+

Ze

(2.5)

Inspection of Eqs. (2.4) and (2.5) reveals that the usual electric and mechanical impedances would appear without modification at their respective terminals if either of the transduction coefficients were to vanish. Additive terms appear in each equation, however, that represent the modification of the impedance caused by the presence of bilateral electromechanical coupling. For example, in Eq. (2.5) the additive term represents a change in the mechanical impedance arising as a result of current in the coupled electric circuit. Note that the magnitude of this term (which would account for "dynamic braking" if the transducer were a conventional electric motor) varies inversely with the total electric impedance in the external electric mesh. The corresponding modification of the electric impedance is especially important because of its usefulness in connection with the design of electroacoustic transducers, and the additive term has been suggestively 1

See any standard mathematics textbook for a review of the use of determinants in solving simultaneous linear equations: for example, L. A. Pipes, Mathematics for Engineers and Physicists, pp. 69-76 (New York, McGraw-Hill, 1946); I. S. and E. S. Sokolnikoff, Higher Mathematics for Engineers and Physicists, 2nd ed., pp. 102-113 (New York, McGraw-Hill, 1941); L. E. Dickson, First Course in the Theory of Equations, pp. 101127 (New York, Wiley, 1922).

96

ELECTROACOUSTICS

designated as the motional impedance. This term can be incorporated in Eq. (2.4) by rewriting it as the sum of the motional impedance Zmot and the "clamped" or "blocked" impedance Zc, the latter designating the impedance that is observed at the electrical terminals when the mechanical system is prevented from moving by some external constraint; thus

The motional impedance is defined explicitly by Zmot

=

(

(2.6)

in which the mechanical admittance ym has been written for the reciprocal of the mechanical impedance, l/z m . The term motional impedance was first introduced by A. E. Kennelly and G. W. Pierce in 1912, when they were studying the variation of impedance with frequency for a telephone receiver and discovered that the electric impedance could be influenced by the motion of the coupled mechanical system.5 The circumstances of this discovery are not without interest. In making their measurements, one of the experimenters would balance the impedance bridge while the other tended the signal source, a not-alwaysreliable Vreeland oscillator that was located in a nearby room. Quite by chance, one of them would habitually lay the receiver on its side on the laboratory bench while adjusting the bridge. The other always turned it face down, thereby altering the acoustic loading on the diaphragm, its motion, and the electric impedance! It is easy to understand how alarmed they were when their measurements showed a complete lack of agreement at all frequencies in the neighborhood of resonance. In the course of pursuing the source of this discrepancy, they finally decided to abandon the careful nursing of the oscillator and watch each other balance the bridge, whereupon the difference in their procedures became apparent at once. Kennelly and Pierce both appreciated the physical significance of the effect immediately, and each succeeded in working out a substantially complete theoretical analysis of the phenomenon within a few hours.6 s A. E. Kennelly and G. W. Pierce, "The Impedance of Telephone Receivers as affected by the Motion of their Diaphragms," Proceedings of the American Academy of Arts and Sciences 48, 113-151 (September 1912); also, Electrical World (New York) 60, 560-565 (14 September 1912). ' Recalled for the author and privately narrated by G. W. Pierce.

ELECTROMECHANICAL

COUPLING

97

The motional modifications of the mechanical and electric impedances are seen to be proportional to the negative product of the two transduction coefficients. It follows that the magnitude and nature of the motional impedances will depend on the size of these coefficients and on whether they are real or complex. In order to study in detail the performance of any specific kind of electroacoustic transducer, it is obvious that the corresponding transduction coefficents must be evaluated explicitly. Even in advance of such explicit evaluations, however, a good bit of information of general applicability can be extracted from a preliminary study of Eq. (2.6). The general behavior of the motional impedance, and in particular its variation with frequency, can be studied by considering the behavior of the mechanical admittance ym. Subsequently the transduction coefficients can be introduced as a scaling operator (—TemTme). The usefulness of this procedure stems, of course, from the fact that the same general form of admittance function ym can be used to characterize a wide class of mechanical systems without regard to the type of motor mechanism employed for electromechanical transduction. The Vector Impedance Locus Consider first, then, the mechanical impedance zm whose generalized expression was given by Eqs. (2.2) in the form Zm = Гт + julm +

= Гт + jxm. JOSCm

(2.7)

The variation of this impedance with frequency can be exhibited most usefully by representing the impedance as a vector drawn from the origin in the real-imaginary plane. As frequency changes, both the magnitude and the phase angle of the vector will also change and the tip of the vector will trace out a curve which can be called an impedance locus. If the mechanical resistance rm does not vary with frequency, the impedance locus for zm will be simply a straight vertical line passing through a point on the real axis at a distance rm from the origin, as shown in Fig. 2.2(a). At very low frequencies the phase angle of zm is very nearly —π/2, corresponding to "stiffness control" of the mechanical system, while at very high frequencies the phase angle approaches +7t/2, as is characteristic for "mass control." The phase angle is zero, as usual, at the angular frequency of mechanical resonance ω§ = (1 /1тст)· For any specific values of the mechanical constants, a scale of angular frequency

ELECTROACOUSTICS

98

Motional impedance locus

ШЛ

Impedance pOocus a

η

Real axis

Impedance locus

FIG. 2.2. Stages in the evolution of the vector-impedance locus.

could be laid out along the impedance locus, but this would not be a uniform scale since the rate at which the phase angle changes with ω depends on the relative values of the coefficients rm, lm, and cm. More specifically, the rate of change of phase with angular frequency, at resonance, varies inversely with the damping constant; thus, Ш \

\du)L

=

2L


The normalized frequency variable ρ vanishes conveniently at the frequency of mechanical resonance, and so does Θ, the phase angle of the total mechanical impedance. Note that θ is shown explicitly by the last line of Eq. (4.17) to be the angle by which the motional-impedance vector deviates from 2β, the inclination of the resonance diameter. By further reference to Eqs. (4.12), the loaded and unloaded resonance diameters can be extracted from Eq. (4.17) by inspection, and the mechanical power-utilization factor can then be expressed readily, either in terms of these diameters or in terms of the loaded and unloaded values of ρ : Ul

=

s—;—η—> Rm + RL

'

=

+ XIem Rm '

RL _ Dy — DL ^ Qv — Rm + RL Dy Qy

(4.18)

QL

Return now to further consideration of the gross efficiency. With the help of Eq. (4.17), the efficiency equation (4.16) can be rewritten in either of the following two forms, the first of which is arranged to show the influence of the frequency variable p; the second is obtained by reverting to the primary variables and manipulating the expression so as to display the denominator factored in a useful way: Π= „ 17

4- Xem

. ,,

19\

RtRL{Rlm +Xln) lRe(Rm+RL)+RlmXRe(Rm+RL)-Xlm^Re(Xm+XL)+RemXemJ'

(4.20)

E L E C T R I C - I M P E D A N C E ANALYSIS

125

At the frequency of mechanical resonance, Ρ = 0 = XM + XL, and the motional impedance reduces to the diameter of the impedance circle. As a result, either of Eqs. (4.16), (4.19), or (4.20) may be used as a basis for writing the efficiency at resonance as _(DV-DL)DL_DV-DL '

VIE

DY

RM

DL DV

(R, + DL COS

.

2/3)'

.

>

The significance of these relations can be demonstrated with the help of Fig. 4.2 in which the impedance loci are plotted for both air and water

loading of an experimental magnetostriction transducer. It is of some interest to note that, in spite of the fact that this particular transducer had a relatively high-resistance winding, relatively high internal mechanical damping, and a considerable amount of leakage reactance, its motional impedance in the unloaded condition is such as to make the total input impedance remain capacitive over a substantial frequency interval. The various quantities appearing in Eq. (4.21) can be scaled off directly from these impedance loci and, since the efficiency is a numeric, they can be measured in any convenient units without regard for the actual values of resistance and reactance appearing on the abscissa and ordinate scales. In this way the mechanical power-utilization factor for the loading used for the "water circle" of Fig. 4.2 can be evaluated as approximately 0.66, and the over-all efficiency at resonance as 0.45.

ELECTROACOUSTICS

126

Conditions for Maximum Efficiency

While it is customary to assume that maximum efficiency always occurs at "resonance," a closer examination of Eqs. (4.19) and (4.20) reveals that a still higher efficiency can be obtained for some other value of frequency or reactance than the one for which Ρ = 0 = Хм + XLThus, if all variables remain constant except the frequency, the condition for maximum efficiency can be found by setting the derivative of the denominator of Eq. (4.19) equal to zero. Alternatively, if everything else remains fixed and only the total reactance can be varied, it is obvious that the reactance should be "tuned" in such a way as to make the squared term in the denominator of Eq. (4.20) vanish. Either approach leads to equivalent conditions for maximum efficiency, which are 0/-1J.

2 Q P =

~REMXEM

m^+Rb)

=

,

t

a

a

DL n

0

m

Sill 2/3 =

;

.

(4 22α)

·

{Xm + Xb) = ~RZXem·

(4.22 b)

When the dip angle is positive, as it is for electromagnetic transducers, Rem and Xem are always of opposite sign, and maximum efficiency occurs at a frequency somewhat higher than the resonance frequency, as may be seen by solving Eq. (4.22a) for the frequency parameter, . . tfWeff-

_ PL sin 2β

=

iReQb

{—Хтодтев _ -RemXem 2ReVMK iReQ

It may be noted that the value of p required for maximum efficiency is independent of the load, since load changes affect DL and QL proportionally, so it can be evaluated most easily in terms of the data for the unloaded impedance circle. The corresponding value of efficiency, when it is maximized by variation of either frequency or reactance, is to be found by putting conditions (4.22) or (4.23) into Eqs. (4.19) or (4.20). For the latter, this merely amounts to dropping the squared term from the denominator, with the result shown in Eq. (4.24a). A little algebraic manipulation then makes it possible to rewrite the maximum efficiency in terms of quantities that can be scaled off more easily from the impedance diagram, as shown in Eq. (4.24δ): Vmax

_ ReRbiRlm + Xem) - lRe(Rm + Rl) + Rim] lRe(Rm + Rl) - X%J =

(DV-DL) \

DY

Г /

DL cos 2 ВТ

/. „. ч K

>

1

L-Re + DL cos 0m cos (2/3 + 0m) J

1

'

;

E L E C T R I C - I M P E D A N C E ANALYSIS

127

The increase in efficiency made available by operating at the maximumefficiency point, rather than at resonance, is by no means trivial, and may amount to as much as two-to-one when the transducer is lightly loaded. The relative increase in efficiency can be evaluated explicitly by dividing Eq. (4.24b) by Eq. (4.21), which gives Чти _ η ГЕЕ

(Re + DL cos 2/3) Re + DL COS 0 m c o s (2/3 + вт)

_ m

(4.25) 8

_ (total resistance at resonance) cos 6m total resistance at maximum efficiency The operating point for maximum efficiency can be located on the motional-impedance locus by a simple graphical construction illustrated in Fig. 4.2. If the center of the loaded circle is projected horizontally to the point b on the vertical through 0', the vertical distance O'b can be identified as half the motional reactance at resonance. When the point b is joined to a, which lies on the horizontal through 0', the angle O'ab is just the mechanical phase angle 0m, as may be verified by reference to Eq. (4.22a). By drawing the line O'c so that it makes the same angle 0m with the resonance diameter, as shown, the intersection of O'c with the motional-impedance circle at с establishes the operating point for maximum efficiency under this particular condition of loading. By repeating this operation for different assumed values of DL, the graphical construction for each corresponding value of 0m can be carried out and the intersections they determine with the various DL circles can be identified as the sequence of points labeled c, d, E, / , g. A line drawn through these points then constitutes a maximum-efficiency locus, along which the frequency variable ρ has the constant value given by Eq. (4.23). The graphical construction for each of these assumed conditions of loading yields the quantities needed in order to use Eqs. (4.21) and (4.24ό) to calculate the maximum efficiency and the efficiency at resonance. As an alternative, the graphical construction can be avoided altogether by assuming arbitrary values of DL, using Eq. (4.22a) to find в т , and putting these results into Eqs. (4.21) and (4.24i>). The same results are obtained by either procedure and can be tabulated as in Table 1, or plotted as shown in Fig. 4.3. Examination of these results will show that the electromechanical factor in the efficiency equation can indeed exceed unity, as suggested in the discussion following Eq. (4.16). I t is also revealed — and this might have been expected at the outset — that the maximum efficiency and the efficiency at resonance

128

E L E C T R O ACOUSTICS TABLE 1. Computation of efficiency at resonance and maximum efficiency, under different assumed loading conditions, for the transducer of Fig. 4.2. RL

Point in Fig. 4.2

g f Ε d С

RL+RM Dl Dr 1.0 0.9 .80 .68 .575 .45 .34 .20

RL

R.

RM

DL

R. Dv Dv DL

DV-DL

Dy

DL

0 0.10 .20 .32 .425 .55 .66 .80

0 0.11 .25 .47 .739 1.22 1.94 4.00

COS

вщ

0.294 .33 .37 .43 .510 .65 .86 1.47

0.601 .646 .706 .7627 .833 .894 .959

7/гев

^max

tynax '/res

0 0.12 .23 .34 .421 .48 .48 .41

0 0.40 .56 .64 .662 .64 .57 .43

3.29 2.43 1.87 1.57 1.33 1.19 1.07

Numerical data from vacuum circle: (Dv/R,) = 3.40; 2/3 = 60°.

О

0.2

0.4

n

L

DV

0.6

0.8

1.0

E L E C T R I C - I M P E D A N C E ANALYSIS

129

each has its own maximum with respect to variation of the relative loading as measured by DL/DV or by Ri/Rm. The relative gain in efficiency obtained by operating at a frequency above resonance is greater for light loading since the peak of the maximum-efficiency curve occurs at lighter loads than does the peak for efficiency at resonance. The Potential Efficiency and Its

Determinants

The optimum, or max-max, value of efficiency with respect to variations of both frequency and load resistance is called the potential efficiency and the condition for its occurrence can be found by setting the RLderivative of Eq. (4.24a) equal to zero: thus,

(4.26)

where the subscript Ε identifies quantities associated with operation at the potential efficiency. By putting condition (4.26) back into Eq. (4.24a), the potential efficiency can, after some algebraic manipulation, be expressed in the forms

(4.27)

The potential efficiency is obviously an important performance criterion for any transducer, since it denotes the optimum efficiency of transduction that can be obtained under the most favorable conditions of external loading. It may be observed that all frequency and reactance variables have dropped out of the expression for potential efficiency, which is shown by Eq. (4.27) to depend only on the blocked electric resistance, the internal mechanical resistance, and the complex force factor. It may also be observed that Eq. (4.27) provides a simple neces-

130

ELECTROACOUSTICS

sary criterion of physical readability: since the efficiency can never exceed unity, it must always follow that Rm >

Xem ~ ·

(4.28)

Λ
0.

(4.32)

If Eq. (4.32) is now introduced into the expression for the potential efficiency, Eq. (4.27), the potential efficiency takes the form

P o t Eff

·= / — w k

< 4 · 33)

E L E C T R I C - I M P E D A N C E ANALYSIS

133

This expression makes it obvious that it is not the total effective mechanical resistance Rm that limits the attainable potential efficiency, but only the part of the resistance that is of purely mechanical — not electromechanical — origin and that can be shown to be represented by the excess of Rm over Xlm/Re. Obviously if R'm can be made to approach zero, the potential efficiency will approach 100 percent. However, the value of load resistance RL for which the potential efficiency is attained is also influenced by such an assumed reduction in R'm, as may be seen by introducing Eq. (4.32) in Eq. (4.26) to give (4.34) This would seem to lead to a relatively sterile situation in which perfect efficiency could be achieved, but only if the useful load were made to vanish. Such a result also suggests that operation at maximum efficiency may not necessarily coincide with the condition for maximum power transfer between a specified generator and a specified external load. A Generalized Equivalent Circuit It was pointed out above that the imaginary part of the complex force factor is intimately associated with some dissipative process associated with the primary mechanism of transduction. Prime examples of this effect are offered by eddy currents and hysteresis losses that occur in magnetostriction and electromagnetic transducers (such as the telephone receiver). When comparable effects are of relatively small magnitude (as they are in electrostatic, piezoelectric, and some electrodynamic transducers), Xem is very small, the dip angle of the motional-impedance circle approaches zero, and the mechanical-resistance component R'm is correspondingly small. And whether small or large, it will turn out that the mechanical-resistance component R'm is just the reflected effect of these losses "transduced," as it were, into the mechanical circuit by electromechanical coupling. Such a transduction of losses is bilateral, however, and a similar resolution of the blocked electric impedance Zt can be made into two components Z" and Z'e. The double-primed quantity, as before, will represent the blocked electric self-impedance that is independent of electromechanical coupling (for example, the ohmic resistance of leads and electrodes or windings, and leakage reactance, if any); the single-primed quantity represents the electric reactance and

134

ELECTROACOUSTICS

resistance that is inherently associated with the electric or magnetic fields that furnish the electromechanical coupling. The over-all situation is completely symmetrical, therefore, and may be represented by the three-terminal equivalent network shown in Fig. 4.5(a). The intrinsic inseparability of the electric-impedance com-

FIG. 4.5. Equivalent networks for a coupled electromechanical system in which there is a permanent electromechanical contribution to the self-impedance of each mesh.

ponent Z'e and the mechanical-impedance component Z'm from the elements of the T-network representing the transducing mechanism is expressed by requiring that a, b, c, d, and e be regarded as inaccessible terminals in the sense used in the discussion of Fig. 3.2 in the preceding chapter. With the help of the (a) —* (b) transformation of Fig. 3.3, the network of Fig. 4.5(e) can be redrawn in the equivalent form shown in Fig. 4.5(δ). In the process of carrying out this transformation, it can be recalled that when the series impedance Z'e is moved to the shunt position, an impedance (—T^/Z'e) appears in series on the mechanical side. By virtue of the manner in which Ζand Z'm have been defined, this negative impedance element automatically cancels Z'm. This is not to say that the electromechanical component of mechanical impedance has been eliminated, but rather that it is now represented by the electric impedance Z'e appearing on the other side of the ideal electromechanical transformer. It may be remarked, incidentally, that the transformation from Fig. 4.5(a) to Fig. 4.5(i) is one of a complementary pair; an equivalent form could be exhibited in which Z'm would appear in shunt on the mechanical side while only Ζ w o u l d appear on the left. It may also

E L E C T R I C - I M P E D A N C E ANALYSIS

135

be noted for future reference that the single-primed impedances are defined in such a way that Z Ä = + Γ 2 = - ZL.

(4.35)

A useful interpretation of the conditions for operation at resonance and at maximum efficiency can be made with the help of these circuit diagrams. Consider Fig. 4.5(c), which represents the circuit of Fig. 4.5(b) modified by transposing the electric impedance Z'E to the right-hand side of the electromechanical transformer. In the preceding discussion of the conditions for resonance, it was assumed that the blocked impedance would not change significantly within a small frequency interval around resonance. When interpreted with reference to Fig. 4.5(c), this assumption is equivalent to saying that Z'E can be regarded as substantially constant, and that Ζ " is likewise either constant or very small, or else it can be merged with the generator impedance. It follows that when Z'e is small enough to be negligible, or wholly resistive, the condition of resonance will occur when the total series reactance of the three elements standing on the right of the electromechanical transformer vanishes — that is when Ι „ + Χ'Ή + XL = 0, in agreement with the discussion following Eqs. (4.17) and (4.20). The conditions that must be satisfied to assure operation at maximum efficiency do not appear to be equally self-evident, except under restrictive conditions on Z'J and the generator impedance. The configuration of Fig. 4.5(c), in which Z'M appears in parallel with the series combination of Z'M and ZL, suggests, however, that it might be useful to examine the admittance of this combination. This procedure will, in due course, yield the expected information about maximum efficiency; but in the meantime, it will also afford an alternative frame of reference in which to reexamine broadly several aspects of the electrical analysis of transducer performance. Admittance and Impedance Diagrams The same physical information that is embodied in the vector locus of electric impedance can, of course, be expressed in terms of a corresponding admittance diagram, since admittance is merely the reciprocal of impedance. This is equivalent to saying that, since impedance and admittance are inverse with respect to unity, the admittance vector will describe a locus that is a geometric inversion, with respect to unity, of the corresponding impedance locus. The geometric figure produced by

136

ELECTROACOUSTICS

the inversion of a circle is also a circle, from which it follows that the vector admittance diagram will display a motional circle just as the impedance diagram does. It can also be expected that singular features of the motional-admittance circle, such as the magnitude and inclination of its diameter and the spacing in frequency of points around its contour, will be just as useful in revealing the characteristics of a transducer as the similar information extracted from a motional-impedance circle. It does not follow, however, that precisely the same information is obtained when identical procedures of analysis are applied to these two diagrams. The interpretive value of the admittance diagram stems, in fact, from just such differences. Only the total admittances or impedances presented at the external transducer terminals are accessible for measurement, and it is these observable quantities that are simply related by the unit inversion. A process of subtraction is required in either case in order to exhibit the motional values. Circuit elements that are connected in series, or in parallel, combine differently in the algebraic expressions for impedance and for admittance. As a consequence, it can not be assumed that the motional admittance is the reciprocal of the motional impedance. In fact, it turns out that there is no simple universal relation between these motional quantities, in spite of the fact that each is characterized by a circular locus. They do tend to be complementary, however, and it is often worth while to perform the numerical inversions and to plot both diagrams in order to facilitate the analysis of a single series of experimental observations. The total impedance Zee, the blocked impedance Ze, and the motional impedance, are simply related by Eq. (4.1), repeated here for reference; -Γ2 Zfn + ZL

ZL

(4.1)

The total admittance, the blocked admittance, and the motional admittance, can be defined explicitly, in a similar way, as (4.36) After a modest amount of algebraic manipulation, the motional admittance can then be expressed in the form ττ

Zeml'Ζ e

,

E L E C T R I C - I M P E D A N C E ANALYSIS

137

A little more of the same kind of algebraic juggling will allow the efficiency, previously expressed by Eq. (4.16) in the impedance form

jzee-ze|

RL I

Ree

ZM

+ ZL

(416)

I

to be rewritten in terms of the observable admittances, as follows: n=\Y~-r.\ V

Gee

\ Z

m

+ Z

L

RL

, 4 , 2 > ( R .») = JILL N. pc-S,d 8

*Rm=/>e-Sad >

After inversion with respect to (Bf),becomes (a)

_£oSd Л m= 2 1° E

c-Sd < . .гzS^ _T^m (/>c) d 8

After Inversion with respect to (BP),becomes

(Bt)2 I - X — ,I ,RP,2 -~г. а с ' sсг s R0 d' App- /3C d

Symbols:

ι - η 8α ._!_ •-Add- Ρ 3 l r Sd ι App-- Ρ„ 8b I зтг Sp Sp L Adp =/»·9· Sd'2irg2

£1 Add •1-4 V Sq /piston,hlgh freq. 'dS, pс R

APP-

R

Adp=

Sd-2rr9z

FIG. 5.9. The impedance reflected into the electric mesh (at the d-d terminals of Fig. 5.5) by the electromechanical transformation of the mechanical-impedance network of Fig. 5.8(b).

The significance of "tuning the box" by changing the dimensions of the port will be apparent now, since the value of (C'A) is seen to depend on the port dimensions. Note first that if the port were entirely closed, making Sp = 0, the reactance of (C'A) and the port radiation resistance (R' a ) would both go to zero. This would reduce the bass-reflex enclosure to a simple closed box whose acoustical influence would be manifested by the added stiffness represented in the circuit by the branch 4-5-6 containing the inductance (Lb). AS a small port opening is introduced, the capacitance (C'A) retreats from its infinite value and series resonance with the residual inductance in the (Z^-branch occurs at some low frequency. Reference to the general circuit configuration of Fig. 5.5 will recall that such a series resonance will lead to an increase in the fraction of the current I diverted to the load branch, and hence to a

ELECTRODYNAMIC

TRANSDUCERS

163

peak in the sound radiation represented b y the power dissipated in (R'a)· T h e vector locus labeled С in Fig. 5.10 corresponds to such an a d j u s t m e n t , and the auxiliary loop in this locus occurring a t a low frequency is the manifestation of the series resonance just described. As the area of the port is further increased, the port resonance moves

Resistance [ohms] FIG. 5.10. Typical vector-impedance loci illustrating the operation of a moving-coil loudspeaker in a bass-reflex enclosure: curves С, B, and A show stages of increase in the port area and the approach toward "correct tuning" of the enclosure.

upward in frequency and continues to contribute a response peak. T h e port branch has the further effect of influencing the location of the frequency a t which the diaphragm system has its primary mechanical resonance, the effective reactance of the port branch above its frequency of series resonance being of the right sign to shift the primary resonance upward. As the port area is increased toward its optimum size, therefore, its effect is to make the original peak appear to have been split into two peaks, one lying above and one below the original resonance frequency.

ELECTROACOUSTICS

164

It is the lower of these two peaks that accounts for the beneficial extension of response toward lower frequencies. The foregoing description has been focused on the location of critical frequencies of resonance. The height of the associated response peaks depends, of course, on the radiation resistance or other damping associated with each resonance. Examination of the expressions annexed to the various circuit elements appearing in Fig. 5.9 will indicate that enough variables are available to provide the necessary control of these damping terms. The optimum adjustment, of course, is one which makes the two peaks nearly equal and of a height that does not rise objectionably above the level of response at neighboring frequencies. The solid curve A of Fig. 5.10 exhibits the typical behavior of the vector impedance under an adjustment that is not far from optimum. Similar, though slightly less informative, guidance for proper tuning of a bass-reflex enclosure can be drawn from a graph of the variation with frequency of the absolute magnitude of the electric impedance. Three curves of this type are shown in Fig. 5.11. Comparison of the multiple maxima of curve В in Fig. 5.11 with the successive loops of the vector locus marked В in Fig. 5.10 permits a direct comparison of the quality of information made available by these two experimental procedures. The vector magnitude curves serve especially well the needs io.

— / /

Bj, B,

8

|, — — δδ δ— о—о °

\

Fib/—\

.Л

•__·

у

I

дДД A fp

\

У\\

*

r1

— г,

—-

C l o s e d box Front and back ports open open

* FFront r o n t plus s m a l l e r 3QC i p o r t 'back ' port

* 2 ol 20

40

60

80

100 Frequency

I го

140

160

ΙΘΟ

200

[c/s]

FIG. 5.11. Curves of the absolute magnitude of the electric input impedance of a directradiator loudspeaker in a bass-reflex enclosure; curves A and В correspond to curves A and В of Fig. 5.10.

ELECTRODYNAMIC TRANSDUCERS

165

of the amateur constructor, since the data can be obtained easily and without elaborate equipment — for example, by the expedient of supplying current to the loudspeaker from a very high-impedance source and simply observing the voltage developed across the input terminals as the frequency is varied. Virtually all of the foregoing discussion has been devoted to considerations affecting the low frequency response of the loudspeaker. A different, but no less serious, class of problems is encountered in dealing with the response at high frequencies. This is the portion of the spectrum in which the designer is victimized by shortcomings in the physical properties of available materials of construction. The first sign of trouble to appear usually takes the form of a failure of the idealistic assumption that the diaphragm moves as a rigid "piston." This often occurs, and other modes of vibration make their appearance, at frequencies well below those for which the diaphragm begins to be acoustically large. In some respects the failure of this assumption is a blessing in disguise; when the outer portions of the diaphragm move with reduced amplitude at high frequencies, the net effect is a partial approach to the decoupling of different annular zones of the radiator at high frequencies, as contemplated in the "variable-area" schemes advanced by Wegel, Parry, Ringel, Olson, et aV Decoupling of the outer zones arises because they are each in turn driven by a mechanical "transmission line" comprising the portion of the cone surface inside the driven zone; and since this transmission line has distributed mass and stiffness, it naturally behaves as a low-pass system having a cutoff frequency. Such decoupling does not come as an unmixed blessing, however. Unless special efforts are made to introduce distributed damping for flexural vibrations of the conical surface (and this is attended by its own difficulties), the mechanical driving-point impedance for the cone, its net effective radiating area, and the sound output, will each pass through pronounced maxima and minima as the frequency is increased. Eliminating these irregularities in response throughout the middle and upper range of frequency is one of the major and not yet fully solved problems of modern loudspeaker design. No complete analytical treatment of this problem has yet been given. A method of attacking it with the aid of equivalent circuits can be suggested, but the fruitfulness of such a mode of attack on this kind of problem is still to be established. In order to mount such an attack, » See notes 213, 215, 217, and 218 of Chapter 1.

166

ELECTROACOUSTICS

the lumped circuit elements appearing in Fig. 5.5 would need to be replaced by the input terminals of a "leaky" transmission line. Such a transmission line would almost certainly be nonuniform, since it would be required to simulate the distributed mass and all the elastic properties of the cone, including the effects of radiation loading. Mawardi 8 has made some progress toward the solution of a simplified problem of this type, but it does not appear likely that a solution specifically applicable to the geometry of construction of a cone loudspeaker will become available soon. It is possible that some progress might be made in dealing analytically with this situation by replacing the L-C circuit representing a diaphragm system having a single degree of freedom with a slightly more complicated network of lumped constants. For example, it might be feasible to use just enough circuit elements to provide a representation of the first few critical frequencies representing the low-order modes of vibration of the cone. At the outset, such a scheme would consist merely in simulating by a network configuration the mechanical behavior made known by other independent measurements. As to why such an effort might be useful — perhaps in due course such an electric-circuit model might be able to "talk back" to the designer and to provide clues concerning useful modifications of the mechanical structure from which the model was derived. The methods of impedance analysis described in Chapter 4 can be used to deduce a good bit of additional information about the performance of the loudspeaker used for the illustrative curves of Figs. 5.6, 5.10, and 5.11. Many of the embellishments of the procedures of impedance analysis are concerned with the phase shift that gives rise to a dip angle, and much of this algebraic complexity obligingly disappears when the dip angle is zero, as in this case. Unfortunately, the usefulness of these procedures for the study of a typical mass-controlled dynamic loudspeaker is restricted by other factors. For example, much of the analysis is based on the assumption of a single degree of mechanical freedom — a condition that in no sense describes the behavior of a system capable of giving rise to a vector-impedance locus like curve В of Fig. 5.10! As Wegel once put it, a little ruefully, while observing the queer motion of a too-long driving link in the motor mechanism of a primitive loudspeaker, "to describe that motion in terms of only six 8 Osman K. Mawardi, " A Physical Approach to the Loudspeaker Problem," J. Acoust. Soc, Am. 26, 1 - 1 4 (January 1954).

ELECTRODYNAMIC TRANSDUCERS

167

degrees of freedom would be a gross oversimplification." 9 On the other hand, the general formulation of the analysis might make it useful to study such complicated modes of operation by means of impedance measurements — might, that is, were it not for the fact that the motional impedance is so small a fraction of the total impedance over most of the frequency range of interest that the difficulty of measuring it accurately robs the method of any general utility. When the motional impedance can be measured with satisfactory accuracy, however, the machinery of impedance analysis is both applicable and useful. For example, the vacuum circle of Fig. 5.6 allows the potential efficiency for this loudspeaker to be evaluated as 43 percent. At resonance in the "infinite" baffle, the efficiency realized is only 35 percent. The latter figure is to be regarded as an electromechanical, rather than an electroacoustical, efficiency, since it was assumed that the internal mechanical resistance was not altered in going from vacuum conditions to a normal atmosphere. However, other computations based on these data confirm the suggestion made above that internal air losses may be relatively important at low frequencies. For example, the value of load resistance associated with the 35-percent efficiency is much higher than the load that would be predicted theoretically for radiation from both sides of a rigid piston in a plane baffle. The bass-reflex enclosure improves this load situation: the electromechanical efficiency (still including the parasitic internal losses of undetermined origin), at the lowfrequency response peak of curve A in Fig. 5.10, turns out to be 43 percent, or just equal to the potential efficiency within the precision limits imposed by reading data from the plotted curves. As for the efficiency at higher frequencies well removed from such response peaks, the motional impedance could not be (or at least was not) determined with enough accuracy to allow a meaningful calculation of efficiency to be made. Estimates of the least magnitude of the motional impedance that could have been observed indicate that the efficiency must have been less than 2 percent, but these are obviously not the circumstances under which impedance analysis shows up to good advantage. • A dark episode in the development of the "good old WE remembered by R.L.W. and privately confessed to F.V.H.

640AW," nostalgically

C H A P T E R

6

Electrostatic Transducer Systems Electrostatic mechanisms of electromechanical transduction have established a long, if not distinguished, record through more than two centuries of pioneering use in almost every branch of the transducer art. Yet, in spite of ubiquitous appearance on the frontiers of transduction, such systems have only within recent years been able to gain, and hold, command of first preference in any major area of the field. It is difficult to say which is the more remarkable, the consistency with which electrostatic motors and generators have yielded to other transduction mechanisms when they have competed for the same service, or the regularity with which electrostatics has been resurrected for service in special applications. The fundamental nature of electrostatic forces is direct mechanical action exerted on relatively imponderable electric charges. In this respect these forces contrast sharply with the body stresses that characterize piezoelectricity and magnetostriction, and with the magnetic and electromagnetic forces that act on massive conductors of magnetic flux or electric current. The relatively small magnitude of electrostatic forces, and the ease with which their action can be brought to bear uniformly over extended areas, marks this mechanism of transduction as one of inherently low internal impedance — a force generator of high internal mobility, to put it in terms of the "other" analogy. But since the acoustic impedance of air is likewise low, it follows that there should be an essential " Tightness " about the employment of electrostatic mechanisms for the transduction of airborne sounds. Of course, the mobility advantage that goes with utilizing the force reactions of very light charges is wholly lost when the charge-carrying vehicle of force transmission is itself massive in comparison with the acoustic medium. The ever-present limitations imposed by the materials

ELECTROSTATIC TRANSDUCERS

169

of construction must, therefore, be overcome before the prospective advantages of the "built-in" impedance match can be realized. It was this obstacle as much as any other that doomed to only modest success the extensive development effort devoted to electrostatic loudspeakers 1 during the decade 1925-1935. Electrostatic transduction does not die easily, however, and can hardly be expected to do so while the lure of that built-in impedance match continues to beckon the ingenious. The most recent revival of interest has been sparked by the postwar availability of synthetic diaphragm materials so light and thin that their superficial density is comparable with that of a film of air only a few millimeters thick. Even so light a diaphragm as this can not quite be regarded as acoustically negligible; but it is now possible to project designs that approach, more closely than ever before, the ideal situation in which electromechanical forces of transduction act directly on the sound-bearing medium without introducing any localized discontinuity in the properties of the medium. One electrostatic device that has earned a secure place for itself in the transducer art is the condenser microphone. Wente's "uniformly sensitive instrument" 2 of 1917 probably represents the first transducer design in which sensitivity was deliberately traded for uniformity of response, and it was almost certainly the first in which electronic amplification was relied on to gain back the ground lost by eschewing resonance. Its availability — and the availability of the amplifier on which it depended — ushered in a new and thrilling era for the quantitative measurement of acoustical phenomena. The principal changes introduced in the condenser microphone itself during the next three decades consisted of the virtual elimination of the cavity in front of the diaphragm and a drastic reduction in the size of the instrument. As will appear 1 See, for example, G. Green, "On the Condenser-Telephone," Phil. Mag. [7] 2, 497-508 (September 1926); 7, 115-125 (1929); V. F. Greaves, F. W. Kranz, and W. D. Crozier, "The Kyle Condenser Loud Speaker," Proc. Inst. Radio Engrs. 17,11421152 (July 1929); C. R. Hanna, "Theory of the Electrostatic Loud Speaker," J. Acoust. Soc. Am. 2, 143-149 (October 1930); P. E. Edelman, "Condenser Loud-Speaker with Flexible Electrodes," Proc. Inst. Radio Engrs. 19, 256-267 (February 1931); Hans Vogt, "Ueber die Erzeugung von Schallvorgängen durch das elektrostatische Feld," Zeitschrift für technische Physik 12, 632-639 (1931), "Der tönende Kondensator," Elektrotechnische Zeitschrift 62, 1402-1407 (12 November 1931); N. W. McLachlan, "The Stretched Membrane Electrostatic Loudspeaker," J. Acoust. Soc. Am. 6, 167-171 (October 1933). 2 See note 98 of Chapter 1; also Ε. С. Wente, "The Sensitivity and Precision of the Electrostatic Transmitter for Measuring Sound Intensities," Phys. Rev. 19, 498-503 СMay 1922).

170

ELECTROACOUSTICS

shortly, it is only the impedance level of the instrument that changes when all its dimensions are altered by the same scale factor; the sensitivity remains the same. Fortunately, improvements in the performance and reductions in the size of preamplifiers have kept pace with these scale changes, although it may represent acoustical vanity to phrase it that way; it could just as well be said that the amplifier developments made these scale changes feasible. In either case, the result is that the modern miniature condenser microphone has become an indispensable tool for the acoustics laboratory, since it can be made so small in size that it produces negligible distortion of the sound field that it measures and so uniform and stable in response that it can serve as a secondary standard for sound-pressure measurements. The Condenser Microphone — Design Features The typical condenser microphone comprises a tightly stretched metallic diaphragm exposed to the sound field and a closely spaced counterelectrode, usually relieved by annular and radial grooves. A moderately high polarizing voltage (ca. 200 v) is applied through a very high resistance, by virtue of which the charge on the condenser remains substantially constant. When the capacitance is changed by displacement of the diaphragm, the voltage difference between the insulated back electrode and the grounded diaphragm changes accordingly, and this change constitutes the output signal. If it is intended that the output be proportional to the pressure of the actuating sound wave, the usual relations governing the constant-force excitation of a simple mechanical system indicate that the motion should be stifness controlled. I t follows that the frequency of mechanical resonance of the diaphragm must lie at or near the upper limit of the frequency range for which the microphone is expected to exhibit uniform response. The extent to which the resonance frequency of the diaphragm can be raised by tighter stretching is sharply limited by the ultimate tensile strength of available diaphragm materials. For stainless steel (as employed in the popular WE 64DA.A*), this limit is approximately 7—8 kc/s. Duralumin, when rolled thin enough for the surface layer hardened by cold work to constitute most of the cross section, permits this limit to be pushed up toward 12 kc/s. 3 3 Theodore H. Bonn, "An Ultrasonic Condenser Microphone," J. Acoust. Soc. Am. 18, 496-502 (October 1946).

ELECTROSTATIC

TRANSDUCERS

171

An alternative method of obtaining a high resonance frequency consists in using a small thick plate as the deflecting diaphragm, the restoring force being furnished by elastic rigidity rather than by stretching. Details of construction of a contemporary high-quality microphone 4 of this type [the Altec-Lansing Model 21B~\ are shown in Fig. 6.1. The Slots to admit sound pressure to

19 Holes (no.60 drill) for cavity damping G l o s s diophragm 0 . 0 0 2 in. thick

diaphragm cavity

Evaporated gold s u r f a c e

Bronze c l o m p i n g spring S t a i n l e s s steel rings for: Centering Clamping d i a p h ; Adjusting backploje assembly Clamping adjusting ring Assembly lockup Backplate assembly mounting

Holes -adjustment wrench

Molded m y c a l e x insulation for back plate a s s e m b l y , grooved to increase leakage paths G u a r d ring

FIG. 6.1. Details of construction of a modern form of condenser microphone. (Courtesy of Allec-Lansing Mfg. Co.)

qualifying term " thick " is, of course, used figuratively — in this example the diaphragm is a glass disk only 0.002 in. thick. A very thin film of evaporated gold on the front surface of the diaphragm serves as the mobile electrode, and the interelectrode insulation provided by the glass diaphragm itself guards against short circuit even under blast conditions. At the same time, the relatively high dielectric constant of the glass leads to an effective interelectrode spacing that is not much greater than the thickness of the air film between the inner surface of the diaphragm and the stationary back electrode. With this scheme of construction, it is easy to modify the instrument for the measurement of very high pressure amplitudes (as required for explosion studies, for example) merely by increasing the thickness of the glass diaphragm. Other expedients are also used to control the dynamic characteristics of the diaphragm. The spacing between the diaphragm and the stationary 4 John K. Hilliard, "Miniature Condenser Microphone," J. Soc. Motion and Television Engrs. 64, 303-314 (March 1950).

Picture

172

ELECTROACOUSTICS

electrode is usually made quite small (ca. 0.001 in. = 25 μ [microns]) in order to enhance the ratio of the active or variational capacitance to the fixed, or stray, capacitance between the insulated back electrode and the grounded housing. The presence of so thin a film of air trapped in the narrow air gap can influence materially the motion of the diaphragm, either by adding its stiffness to that of the diaphragm or by damping its motion, depending on whether the air is merely compressed in the air gap or is allowed to flow laterally toward the reservoirs provided by the grooves and cavities cut in the back electrode. In the latter case, a very substantial amount of viscous damping can be provided since the channel for such lateral flow is very narrow. In designing a condenser microphone for maximum uniformity of response, the dimensions and disposition of these grooves in the back electrode are carefully selected 5 to provide just-less-than-critical damping of the principal diaphragm resonance. In this way the upper limit of the range of uniform response can be made to occur somewhat above the frequency of resonance. When a resonance peak in the response occurring outside the nominal range of coverage can be tolerated, the air-escape reservoirs can be omitted from the back plate and the stiffness of the air used to bolster up the stiffness of the diaphragm itself. This scheme finds its most interesting application in the case in which the diaphragm is made of a thin membrane of modest intrinsic strength for which most of the stiffness is contributed by the film of trapped air. For example, a small diaphragm 9 mm in diameter, made of the thin material described above, and backed up by a shallow cavity 0.5 mm deep, was found to have its principal resonance at 15.5 kc/s. 6 A more spectacular example of how far this line of attack can be carried is furnished by a report 7 of usable output obtained at frequencies as high as 1 Mc/s with a small condenser microphone in which the diaphragm was a thin plastic film and the air gap was only the thin layer of gas occluded on the polished surface of the stationary electrode. One of the features of the condenser microphone that contributes to its usefulness as a laboratory tool is the relative ease with which its 5

Irving B. Crandall, "The Air-Damped Vibrating System: Theoretical Calibration of the Condenser Transmitter," Phys. Rev. 11, 449-460 (June 1918). 6 Made and tested by Theodore J. Schultz, Acoustics Research Laboratory, Harvard University. 7 Privately communicated by Dr. Erwin Meyer, III Physikalische Institut, Göttingen.

ELECTROSTATIC TRANSDUCERS

173

pressure calibration can be established,8 either by reciprocity methods or by the use of an electrostatic actuator. For free-field use, however, diffraction effects must usually be taken into account even at frequencies well below resonance, and at frequencies above resonance the microphone can seldom be regarded as "small in comparison with the wavelength." Nevertheless, when these diffraction hazards can be adequately dealt with, and when the decrease in its response of 12 db per octave above resonance can be adequately compensated, the "standard" form of condenser microphone can serve usefully over a frequency range extending well up into the ultrasonic. The Electrostatic

Loudspeaker

— Design

Features

The electrostatic loudspeaker failed to gain wide commercial acceptance, in spite of extensive development activity 9 devoted to it during 1925-1935, for the very sound reason that several serious shortcomings still adhered to its design. Either the diaphragm or the air gap itself had usually been relied on to provide the protective insulation against electrical breakdown, but this protection was often inadequate and limits were thereby imposed on the voltages that could be used and on the specific power output. Close spacings, a film of trapped air, stiff diaphragm materials, and vulnerability to harmonic distortion combined to restrict to very small amplitudes both the allowable and the attainable 8 A. L. DiMattia and F. M. Wiener, "On the Absolute Pressure Calibration of Condenser Microphones by the Reciprocity Method," J. Acoust. Soc. Am. 18, 341-344 (October 1946); Stuart Ballantine, "Technique of Microphone Calibration," ibid. 3, 319-360 (January 1932); see also L. L. Beranek, Acoustic Measurements, Chapter 4 (New York, Wiley, 1949). • For example, Colin Kyle, U. S. Pats. No. 1,644,387 (filed 4 October 1926) issued 4 October 1927, and No. 1,746,540 (filed 25 May 1927) issued 11 February 1930; Ernst Klar (Berlin), German Pat. No. 611,783 (filed 22 May 1926) issued 5 April 1935, and U. S. Pat. No. 1,813,555 (filed 21 May 1927, renewed 14 November 1930) issued 7 July 1931 [insulating spacers, perforated plate coated with a dielectric]; Hans Vogt (Berlin), more than a score of contemporary and relevant German patents, for example, German Pats. No. 583,769 (filed 25 December 1926) issued 9 September 1933 and No. 601,117 (filed 17 May 1928) issued 8 August 1934, and U. S. Pat. No. 1,881,107 (filed 15 September 1928) issued 4 October 1932 [tightly stretched diaphragm between perforated rigid electrodes]; Edward W. Kellogg (G. E. Co.), U. S. Pat. No. 1,983,377 (filed 27 September 1929) issued 4 December 1934 [sectionalized diaphragm with inductances for impedance correction]; William Colvin, Jr., U. S. Pat. No. 2,000,437 (filed 19 February 1931) issued 7 May 1935 [woven-wire electrodes]; D. E. L. Shorter, British Pat. No. 537,931 (filed 21 February 1940, complete spec. 23 January 1941, accepted 14 July 1941) [diaphragm segmentation with external dividing networks for improving directivity and impedance].

174

ELECTROACOUSTICS

diaphragm motion; and as a consequence, large active areas had to be employed in order to radiate useful amounts of sound power, especially at low frequencies. But when large areas were employed, the sound radiation was much too highly directional at high frequencies. Several of the patents cited above 9 bear on one or another of these features, and it is now apparent that an integration of such improvements would have made it possible to overcome almost — but not quite — every one of these performance handicaps. Occurring singly as they did, however, no one of these good ideas was able by itself to rescue the electrostatic units from the burden of their other shortcomings. Taken together, however, with the newly available diaphragm materials and with the important addition of one or two new ideas, the modern form of electrostatic loudspeaker can so completely surmount these former handicaps that it merits careful consideration as a potential competitor for the moving-coil loudspeaker in many applications. The outstanding performance characteristic of the electrostatic loudspeaker is the unusual smoothness of its pressure response, as exemplified by the relative freedom from peaks and valleys in the curve displaying relative response as a function of frequency. The corresponding regularity of phase promotes the avoidance of waveform distortion in the reproduction of transient signals. Casual tests indicate that such smoothness of response is an important determinant of listener satisfaction, but no systematic study of this subjective aspect of electroacoustics has yet been undertaken. A second distinguishing feature of the performance of electrostatic transducers is their high intrinsic conversion efficiency. Sound radiation does not need to share the signal energy delivered to the transducer with magnetic-hysteresis losses, eddy-current losses, nor with heat losses in a voice-coil conductor; and since the condenser dielectric is chiefly air, the dielectric losses are, or can be made, significantly lower than for most piezoelectric materials. The widespread — but erroneous — impression that electrostatic devices are "inherently inefficient" stems from a misdirection of emphasis. It is true that the input impedance of an electrostatic transducer is primarily that of a capacitive reactance; and as a consequence, such devices usually operate at a low and variable power factor. The place where dissipation occurs, however, is not in the transducer, but in the internal resistance of the signal source, which must supply the "wattless" component of the condenser charging current. Several interesting proposals have been advanced for dealing

ELECTROSTATIC TRANSDUCERS

175

constructively with this problem; and if it can be solved, the electrostatic loudspeaker and its signal source will emerge as the most efficient member of the family of electroacoustic energy transducers. The several preceding discussions of the "variable-area" principle will at once suggest this as a useful approach to the problem of securing the simultaneous advantages of a large area for low-frequency radiation and a small area of comparable acoustical size for high-frequency radiation. The variable-area principle can be introduced effectively in either of two ways: the diaphragm may be segmented and used in conjunction with external electric dividing networks; or a thin conducting film of very high resistance can be utilized for one electrode of the condenser. In the latter case, electrical connection is made at the center or at one comer of this electrode; its high resistance and distributed capacitance then serve the functions of an R-C transmission line that enables the diaphragm to act as its own dividing network. In either case, it is important to notice that the principle of active-area variation serves not only to control the increase of directivity at high frequency, but also to reduce the variation of input impedance with frequency. Other features of the so-called "modern" electrostatic loudspeaker will turn up in the conditions and assumptions on which the following analysis is based. It may be useful to summarize these,10 however, in the form of a long serial sentence, many of whose parts will be selfexplanatory: Distinguishing features of an electrostatic loudspeaker can usefully include (a) an extraordinarily light and strong diaphragm material, (b) high polarizing voltages — high enough to produce dielectric breakdown were it not for (с) complete sheathing of the stationary electrode with an insulating layer having high dielectric strength, (d) acoustic transparency of the stationary electrode, (e) viscous damping of the stationary electrode to keep it truly stationary, (/) subdivision of the diaphragm into elementary vibratory units, or bays, (g) systematic variation of the diaphragm stiffness by adjustment of the lateral disposition of spacers, (A) systematic variation of the diaphragm separation from the backplate, (г) arrangement for the effective area of the dia10 A program of research on electrostatic loudspeakers has been pursued with varying intensity for several years at the Acoustics Research Laboratory, Harvard University. Continuity and many original ideas have been contributed by A. A. Janszen. This summary is taken from an interim report by A. A. Janszen, R. L. Pritchard, and F. V. Hunt, "Electrostatic Loudspeakers," issued as Technical Memorandum No. 17, 1 April 1950. See also A. A. Janszen, U. S. Pat. No. 2,631,196 (filed 5 October 1949) issued 10 March 1953.

176

ELECTROACOUSTICS

phragm to vary automatically with frequency, perhaps with (j) further control of area reduction by electrical segmentation of the stationary electrode. Electrostatic transducers can be either "single-sided," in which electrostatic forces act on only one side of the vibratile diaphragm, or "push-pull," in which electric forces act on both sides of the diaphragm. Constructional problems are usually simpler for single-sided units, and condenser microphones are almost invariably constructed in this way. Since the same electromechanical analysis will serve to describe the performance of either microphone or loudspeaker, the single-sided case will be dealt with first. The question of harmonic distortion will need to be considered carefully; and since electrostatic forces are inherently quadratic, some care must be taken to establish criteria for the control of this hazard. However, since the analytical machinery needed to deal with the nonlinear-distortion problem is relatively more cumbersome, the fundamental-frequency mode of operation for a single-sided unit will be considered first. The Single-Sided

Electrostatic

Transducer

Consider first the mechanical mesh of the system described by the diagrammatic sketches of Fig. 6.2, and begin by recalling the elementary expressions for the force of attraction between oppositely charged condenser plates and for the capacitance of a parallel-plate condenser, to which can be added the basic relation between the charge on and the voltage across any condenser. These relations can be written (6.1)

The minus sign appears in the expression for the mechanical force of electrical origin/«because this stress is a tension and acts in the negative ж-direction. Using the notation defined by the schematic diagram of Fig. 6.2(6), the differential equation for the motion of the diaphragm can be written at once by setting the sum of the applied external (acoustic) force and the force of electrostatic attraction equal to the sum of all the mechanical reaction forces arising from diaphragm motion; thus,

(6.2)

ELECTROSTATIC

TRANSDUCERS

177

d = initial s p a c i n g without b i a s Light

(

mass.fm compliance,Cm resistance, r m orea.S - М д , e x t e r n a l (acoustic) force >| ^ - C h a r g e , q

flexible diaphragm

Rigid back-plate, perforated and sheathed in i n s u l a t i n g dielectric

Dielectric c o n s t a n t , e Q Capacitance,С = Protective resistance — W V — '

ΒΙΊΨ-

B i a s voltage

—СШУΠΓϋΤΠ

Blocking

1

condenser

I

1

o . e . signal input

(a)

(b)

FIG. 6.2. (a) Electric circuitry for isolating the signal source and the biasing circuit for a single-sided electrostatic loudspeaker. (b) Schematic diagram establishing the nomenclature for analyzing the performance of a single-sided electrostatic transducer.

The differential equation for the electric mesh can be written in a similar way by setting the sum of the impressed polarizing and signal voltages equal to the voltage "drops" across the electric impedances; thus, E0+e=

Lq+Rq

+ t, (6.3) «»J

The presence of the φ term in Eq. (6.2) and of the xq term in Eq. (6.3) brands these as nonlinear differential equations. The nonlinearity is of a mild variety, however, and a valid first-order solution can be approximated by "linearizing" the equations at the outset. This amounts to neglecting the product of the variational part of q multiplied by itself or by x. For well-behaved physical systems (and this one is), another approach can be used which has the advantage of making it possible to evaluate the distortion products generated by the nonlinearity. This procedure involves assuming that each of the variables can be expanded in a Fourier series. When these series are introduced in Eqs. (6.2) and

178

ELECTROACOUSTICS

(6.3), pairs of equations can be extracted that will describe the behavior of the systems at the zero, fundamental, and harmonic frequencies. This procedure will be carried through in detail later. It will be useful to consider first, however, just the conditions of equilibrium and the fundamental-frequency mode of operation. For this purpose, only the first-order terms of the Fourier series will be required, and these can be written most conveniently as the sum of two conjugate exponentials. The assumed form of the solution can then be expressed by the following four equations: x = Xo + \x\e>at + \x%e~jat, /а = W '

e=

K 1

+

+ iEfe-'"' =

cos ω/.

Inspection of Eqs. (6.2) and (6.3) reveals that the square of q and the product xq will also be required. These can be written out explicitly with the help of Eqs. (6.4) as follows: , ,

., ,

ial q*2 =ql1 + 5qoqie 1

+**

*

· , , ["terms in higher"! + powers of f ω J

^

The following abbreviations will also prove useful: Co = ,e»< [(,W m + +

+ J

L

+

[ ( м » - rm

(6.8) ·

In order that this pair of equations may be satisfied at all instants of time, the coefficients of the exponentials having like powers of ωί must individually satisfy each equation. As a consequence, two pairs of equations can be extracted from Eqs. (6.7) and (6.8), one representing the steady or zero-frequency solution and one representing the solution for the assumed fundamental frequency ω. The steady terms in Eqs. (6.7) and (6.8) can be collected as follows: .

=

qo(d + xq) _ go (

toS

Co

(6.9a) (6.96)

The first of these merely yields the unexciting information that the normal relation between charge and voltage holds with regard to the bias condition. The second contains more interesting information concerning the equilibrium position, or static deflection, of the diaphragm under the influence of polarization. If the polarizing charge qa is expressed in terms of the more easily measurable polarizing voltage, it turns out to be necessary to solve a cubic equation in order to compute the equilibrium displacement XQ. This will be discussed below at greater length. Consider next the fundamental-frequency mode of operation. Since the positive and negative exponentials in Eqs. (6.7) and (6.8) have conjugate coefficients, they can be combined to yield explicitly a real cosinusoidal function; but alternatively, and more simply, it can be recognized by reference to Eqs. (6.4) that the coefficient of e'at alone carries complete information about the complex amplitude of the cosine function. Using either method, and with the help of the notation defined by Eq. (6.6), one obtains the two electromechanical equations in the canonical form (6.10a)

ELECTROACOUSTICS

180

(6.10Ä)

ft = -2» h + ZmVl. joieoS

It can be seen at once that the transduction coefficient is symmetric and may be written explicitly in the alternative forms: Τ

= Τ m

= Τ = m

"

q

°

jbXoS

Eo

=

Γ

j{d + xo)

m

voIts

=

newtonsl

L eter/second

ampere J

(6.11)

The appearance of the time-phase quadrature factor j is to be duly noted. The force factor, or coefficient of j, is real in this case, since no dielectric dissipation was included in the expression for the relation between the current into and the voltage across the capacitance C. It is also to be noted that, since the angular frequency ω appears in the denominator of T, the transduction coefficient itself can be represented as the reactance of a condenser Cem, whose value is defined explicitly through 1 «о5 d + χо (6.12) T = Cem joiCe, ίο —

With the help of Eqs. (6.10) and (6.12), the equivalent-circuit diagram can be drawn at once as shown in Fig. 6.3(a), wherein the transduction R L y - W W W ) - j | ZL z;

"Cem

1[

—II

c

m

^m

r

m

II—ПЛЛГ^АЛЛл-т(α)

FIG. 6.3. Typical equivalent electric circuits for an electrostatic transducer.

coefficient is represented explicitly as a capacitance. The ideal electromechanical coupling transformer can then be introduced in the usual way by moving the equilibrium capacitance C0 into the shunt position as shown in Fig. 6.3(b). The turns ratio of this ideal transformer is, as

ELECTROSTATIC TRANSDUCERS

181

usual, the quotient of the transduction coefficient divided by the impedance moved into the shunt position; and since in this case these are like reactance elements, the turns ratio is real. It follows, incidentally, that such a transformer would permit direct "modeling" with an analogous electric circuit. Alternative expressions for the turns ratio, and its dimensions, are shown in the following equation: Γ _ Co_ _ CQEQ _ Q0 Tnewtons _ amperes ~1 , * Z'e Cm d + xо d + xü [_ volt meter/secondj One of the most notable features about the equivalent circuit of Fig. 6.3 (b) is the appearance of a negative capacitance, representing a negative mechanical compliance, on the mechanical side. As discussed in the preceding chapter, the shunt position for the static electric capacitance Co is mandatory in this case because the influence it has on the effective mechanical impedance will always be present so long as a fixed polarizing voltage is maintained across the condenser, even though the electrical terminals are otherwise on open circuit. Thus, when an external force acts to move the diaphragm from its position of mechanical equilibrium in the direction of reduced spacing, the force is opposed by the mechanical stiffness but is assisted by the increase of electrostatic attraction due to reduced spacing, and vice versa. The amount by which the effective mechanical compliance is modified as a result of the presence of a polarizing voltage can be evaluated by merging the positive and negative compliances shown in Fig. 6.3(i) into an effective mechanical compliance c'm, whose value is given by

c:= 1+

k (t)T=(Ä)·

The numeric k is identified as the electromechanical and is defined explicitly through

coupling

(6Л4) coefficient

(6.15) If the diaphragm is to be mechanically stable, it is obvious that k2 must be equal to or less than 1, since if this were not true, the net effective compliance would become infinite or negative and the diaphragm would collapse into contact with the fixed electrode. This stability condition is equivalent to requiring that k2


CQEQ + xof

EPTOS {d + хоУ|3

(6.16)

ELECTROACOUSTICS

182

It is useful to compare this condition with Eq. (6.9b), which is a static force equation from which the equilibrium displacement x0 can be obtained. Equation (6.9b) can be rewritten, for comparison, in terms of the polarizing voltage and the spacing: cm

ql __ CqEQ 2eoS 2eoS

ElepS 2 (d + x0)2

°2

xA* d/ '

This equation cannot be solved explicitly for the equilibrium displacement Xo, because the equation is cubic in this variable, but a graphical

Diaphragm displacement, -jFig. 6.4. Typical variation of the elastic- and electric-force components that determine the initial displacement under bias and the conditions of static equilibrium for a singlesided electrostatic transducer.

solution can easily be found. In the typical experimental situation, the polarizing voltage is the independent variable, in which case the situation will correspond to that illustrated in Fig. 6.4, where the dashed straight line represents the elastic restoring force given by the left-hand member of Eq. (6.17). The family of parabolic curves represents the electrostatic-attraction force given by any of the right-hand members of the serial Eq. (6.17) for different values of E0. The intersection of the straight line with any one of these parabolic curves, as at A, B, or C, determines a corresponding equilibrium value of the normalized displacement xo/d, which will always be negative since the positive indirection was selected to be opposite to that in which the diaphragm is drawn by the polarizing voltage.

ELECTROSTATIC TRANSDUCERS

183

An instability boundary is reached when the parabolic curve for —/«. just comes tangent to the straight line, as at C. Of course, the slope of the parabolic curve and of the straight line must be the same at the point of tangency, as may be verified analytically by observing that the derivative of Eq. (6.17) with respect to Xo yields the limiting equality relation of Eq. (6.16). As a further consequence of the geometrical relations exhibited by these curves, the upper limit for xa can be generalized by solving Eq. (6.17) for the reciprocal compliance and comparing the result with the inequality requirement of Eq. (6.16). Thus: J_ _ cm

—-Ε&ο^

·>

2(d + xa) x 2 0

EpepS {d + xaf

, °

K

» J

It follows then, from Eq. (6.18), that the stability criterion can be expressed by the simple requirement that = ? < f ·

(6.19)

In order to solve Eq. (6.17) graphically in a practical case, the magnitude of the compliance cm must be known. The simple form of expression for the restoring force appearing on the left-hand side of Eq. (6.17) embodies the assumption that this compliance is constant, corresponding to a linear restoring force. If the normalized equilibrium displacement Xo/d can be measured directly, this assumption can be submitted to test. It turns out that this can be done quite simply, merely by measuring the capacitance at some moderately high frequency well separated from any diaphragm resonance so that the measurement will not be significantly affected by any residual motion of the diaphragm. Then, by defining the equilibrium capacitance in the absence of polarization as Coo, the capacitance with polarization as C0, and the difference between these as AC, the following relations can readily be established: ίοS . π coo = ~r j АС = со — Coo; ΛΓ / \ ρ (6.20) XQ = AC _ Λ ^ j = coo d Co ' \ dj Co A test of this kind was carried out 11 with an experimental electrostatic /oudspeaker «nit (abbreviated ESLU hereafter, for convenience) and о=

toS

;—;

Y-T

1 1 1 am indebted to A. A. Janszen and J . F. Hersh for the experimental measurements shown in Figs. 6.5, 6.7, 6.12, and 6.14. F . V . H .

ELECTROACOUSTICS

184

gave the results shown in Fig. 6.5. The experimental ESLU consisted of a single "bay" comprising a thin circular diaphragm 5 inches in diameter, sandwiched between two stationary electrodes. The diaphragm material was Saran (vinylidene chloride), having a measured superficial density of 0.03 kg/m2, a nominal thickness of 12μ, and an elastic modulus „250 С 8ό н

T

-

Fell in Equilibrium separation with no bias, 955 μ

a. .2200

/

•Л

150

t

%

2 100 0 Μ 1 50

O.I

0.2

Total force

/je|_C|\ 2i 0 s /

0.3

0.4

FIG. 6.5. Measurements showing typical values of diaphragm displacement, as a function of the electrostatic force due to the bias voltage, for a singlesided electrostatic loudspeaker; displacements inferred from measured change of capacitance.

[newtons]

of 3.5-5.5 Χ 108 newtons/m2. The fixed electrodes were made acoustically transparent by perforations and each was completely sheathed in a sprayed-on plastic film of high dielectric strength. The two stationary electrodes were 4.5 inches in diameter and each was mounted in such a way that its separation from the vibratile diaphragm could be nicely adjusted. By altering the external connections, this experimental ESLU could be used for tests of either single-sided or push-pull operation. The initial slope of the displacement-force curve of Fig. 6.5 is seen to be linear, within the precision of measurement, thus confirming the appropriateness of this convenient assumption. This linearity also suggests that the diaphragm, while it was not intentionally stretched any more tightly than seemed necessary in order to guard against wrinkling, must nevertheless have been under sufficient tension to make it behave

ELECTROSTATIC

TRANSDUCERS

185

as a stretched membrane, since it is for this case that theory predicts a linear restoring force. If the supported-membrane mode of operation is used, that is, if the diaphragm is mounted so that it is under no tension except that arising from deflection, the restoring force can be expected to vary with the cube of the deflection, according to the relation ( f m / S ) = α p ^ ] **;

χ >

2h

(6.21)

where (f m /S) is the force per unit area applied normal to the equivalent flat plate, χ is the average displacement of the plate, F 0 is Young's modulus of the membrane material, 2h is the thickness of the membrane material, 2a is the distance between supports (for example, for a circular membrane supported circumferentially, 2a would be the diameter of the mounting circle), and α is a numerical constant depending primarily on the geometry, but including also the effect of Poisson's ratio. In some experimental ESLU's that have been tested, the diaphragm has appeared to behave as if it were partially "supported" and partially "stretched," but no attempt has been made to resolve the restoring force systematically into linear and cubic components. In order to do this, it would probably be necessary to take into account the nonplanar shape of the deflected diaphragm and the corresponding variation of electrostatic force on different annular zones. I t is easy to show that, for the case of a cubic restoring force, a stability limit of f would be imposed on the equilibrium displacement —xo/d, instead of the limit § predicted by Eq. (6.19) for the linear case. In practice, "fall-in" usually occurs at values of —xa/d substantially less than the theoretical limit. For example, in the test shown in Fig. 6.5, fall-in occurred at a value of —Xo/d of about 0.22. I t was not determined whether this premature collapse was caused by the perturbing forces introduced by the signal used for capacitance measurement, by transient vibratory or acoustic forces, or by the fact that the curvature of the diaphragm allows its central portion to reach the critical spacing while the average spacing deduced from capacitance measurements is still less than the critical value, but the latter cause seems most likely. A convenient method for assessing the electromechanical coupling is also provided by measurements of the kind shown above. If the mechanical compliance given by the equality standing on the left in Eq. (6.18) is substituted in the defining relation [Eq. (6.15)] for the coupling coefficient, the latter can be written in the form

ELECTROACOUSTICS

186

k*=2

Coi-Xo) «051

2(-Xo) d + X0

(6.22a)

Then, in terms of the quantities defined by Eq. (6.20), the coupling coefficient can be evaluated by any of the following alternative relations: = 2

\Coo

- l) = 2 ψ- = 2 · / Coo 1 + {xo/d)

(6.22Ö)

A graphical representation of Eq. (6.226) is shown in Fig. 6.6 by a curve giving the coefficient of electromechanical coupling as a function of the ratio of the change in capacitance arising from polarization to the equilibrium capacitance without polarization. Equation (6.22b) can also be used, in conjunction with the data for Fig. 6.5, to study the variation of the electromechanical coupling coefficient with polarizing 1.0 -

1 1

11 1 1

—Γ "Γ- ТТТГ

1 1 II

^ 05

1 1 1 1 1 1 1 1 ι

•= 0.2 0.1 :

£ 0.05

-

^

о 0.02

Q0002

1

ι

11 1 1 I 1 Ι I 11 1 1 0.0005 0.0001 0.002 0.005 0.01

~»o d

0.02

1 1

1 1 II Q05 0.1

0.2

:

" -

= :

1 1 1 I 1 1 li. I/ 0.5

ДС

Coo.

Fig. 6.6. The coefficient of electromechanical coupling for a single-sided electrostatic loudspeaker as a function of the change in capacitance produced by application of the polarizing voltage.

voltage. This relation is shown in Fig. 6.7 along with the relation between the normalized equilibrium displacement and polarizing voltage. It is notable that even for polarizing voltages no greater than 80 percent of the fall-in limit the magnitude of the coupling coefficient is substantially in excess of that obtained with even the most active of magnetostrictive or piezoelectric materials. More conservative values of

ELECTROSTATIC

TRANSDUCERS

187

polarization, such as half the fall-in limit, can still yield coupling coefficients of the order 0.25.

a

:

K—

Μ

:

у1 L

-*o d ~S

:

s*

:

Г

/ -

-

/ -

r -

0.5

1.0 E0[kilovolts]

The Push-Pull

2.0

Electrostatic

25

FIG. 6.7. The electromechanical coupling coefficient and the equilibrium displacement under polarization, displayed as a function of bias voltage for an experimental electrostatic loudspeaker unit.

Loudspeaker

A variety of different circuit arrangements can be used to provide double-sided operation of an electrostatic loudspeaker, but the configuration shown12 in Fig. 6.8 has been found to have novel advantages. It will be observed that the two stationary electrodes flanking the vibratile diaphragm are each at ground potential, except for the a.c. signal voltage. The latter is assumed to be divided equally between the two meshes containing the "active" condensers Ca and Съ, as it would normally be if the signal is delivered at the terminals of a center-tapped coupling transformer as indicated. One of the practical virtues of this circuit 12 Carlo V. Bocciarelli of the Philco Corp. suggested this circuit to us and argued qualitatively the advantages of "constant-charge" operation. The analysis given below shows the performance to be even better than predicted. The circuit itself, though not its unusual virtues, has been proposed in various patents and other publications dating back at least to H. Riegger's disclosure in German Pat. No. 398,195 (filed 10 March 1920) issued 2 July 1924.

188

ELECTROACOUSTICS

arrangement is that the electrode bearing the high polarizing voltage is prevented from becoming a shock hazard by the protective housing formed by the rugged stationary electrodes. As before, the electricimpedance elements La, Ra, Lb, and Rb are included for generality. The resistance Ro in the common leg of the circuit serves as the high resistance designated as "protective" in Fig. 6.2(a). The impedance in this branch is common to the two meshes and, as will be seen later, it turns out to have an important influence on the performance of the ESLU.

FIG. Θ.8. Schematic diagram establishing the nomenclature for analysis of the push-pull electrostatic loudspeaker.

By way of whetting interest in the analysis to follow, one remarkable feature of the push-pull ESLU can be described at the outset in qualitative terms. I t is customary to regard electrostatic devices as inherently nonlinear, since the tractive force between condenser plates maintained at a constant potential difference varies inversely as the square of their separation. Consider, however, the situation presented by Fig. 6.8, and assume that a large charge has been placed on the mobile diaphragm. If the charging circuit is now disconnected — or, what is equivalent, if R0 is made so large that the time constants RaCa and RoCb are very long — then the force acting on the diaphragm will be determined only by the magnitude of the unvarying charge on the diaphragm and by the electric field established by the signal voltage between the stationary electrodes, and will be independent of the position of the diaphragm in the space between these electrodes. As a consequence, many of the

ELECTROSTATIC

TRANSDUCERS

189

limitations previously regarded as "inherent" to electrostatic systems will not limit the performance of an ESLU in this mode of operation. For example, in so far as linearity requirements are concerned, it will no longer be necessary to restrict the allowable motion of the diaphragm to a small fraction of the initial separation. Moreover, the restriction on the allowable ratio of signal voltage to polarizing voltage will also disappear. Confirmation of these remarkable performance features will constitute the objective of the following analysis. Three basic equations will be required to describe the electromechanical system of Fig. 6.8 — one for the single mechanical mesh and one each for the two electric meshes identified by subscripts a and b. With the help of Eqs. (6.1)-(6.3) above, these can readily be written by inspection. Alternatively, the energy functions can be formulated so that Lagrangian equations can be written in the appropriate variables. By either procedure, the basic equations emerge as FA -

zmv

-

FE

+E0 + I = (La + L0)qa - L0qb + (Ra + Ro)q« ~ R^b + ~,

(6.24a)

-E0 + I = (Lb + Lo)qb - L0qa + (Rb + R»)qb ~ R0qa + γ, · £ Cb

(6.240)

The letter symbols and the algebraic signs used in these expressions are defined by Fig. 6.8. The following definitions are also implied: C 0 = ,€°f ; ia = qa; (I'd T" 3C

Сь =

; X

%=

da + db= 2d.

(6.25)

Solutions of these nonlinear differential equations can be sought, as before, by assuming that each of the variables can be expressed in the form of a Fourier series, which can be written most conveniently in complex exponential form, as follows: ж= 2

- xneinat,

(6.26a)

-00 e " where | x„ | is the peak amplitude of the rath harmonic, x~n = xt, and €„ is the Neumann factor and has the value 1 if η = 0, but the value 2 if η И 0;

190

ELECTROACOUSTICS +00 j - 0 0

in

= 2 f. - F » e , w - F°> — 00 t n .Сл . , , XM . e = —i c»»' + - i е-"·" = El cos wt.

(6.26Ö)

(6.26c) (6.26

jnuxn = »„;

ZLn = mechanical impedance presented by radiation loading at the wth harmonic frequency.

192

ELECTROACOUSTICS

An Aside: Harmonic Distortion Products for the Single-Sided ESLU It is timely now to take another look at the electromechanical circuit of Fig. 6.8, and to observe that if the connection to the right-hand stationary electrode is broken, so that the δ-mesh is removed, the remaining α-mesh corresponds exactly to the single-sided case considered above. By the same token, Eqs. (6.23) and (6.24a) reduce to the equivalent of Eqs. (6.2) and (6.3) if дъ and its derivatives are set equal to zero, and if (La + Lo) is identified with L of Eq. (6.3) and (Ra + R0) with R. The relations needed for a study of harmonic distortion in the singlesided ESLU can be marshaled, therefore, in terms of this reduced form of Fig. 6.8. The extension to the push-pull case can then be made simply by replacing the terms omitted from Eq. (6.24a) and adding Eq. (6.246). N =

0.

o=

Cm

2«о£

£ _ qao(da + Xq) _ да о | eaS Cao N = 1.

0 = (Zml + ZL1)vi + TaJal, E\ = TaiVi + ZeaJa 1-

N = 2.

~ ^

=

(2m2

+

ZL2)V

*+

TaiTd2

(6.30a)

(6.306)

' (6.30c)

— N = 3.

-

~ Taify + ZeasJal· = (Zm3 + zL3)v3 + TaZIo3,

[ХЩЛ + XlQai) rj, ι ν τ 1 1 a3Vz 2e0S ' ^eaZlaZ-

(6.30O

Note first that the "impressed," or "forcing," quantities appearing on the left in Eqs. (6.30c) and (6.30J), which are written here as they emerge from the algebraic "mess" referred to above, can be expressed in terms of the corresponding currents and velocities by using the elementary relations juqa = Ia and jwx = v. The tactical advantage gained by discarding the terms in (N + 2) and higher will now become apparent. The fundamental-frequency components of velocity and current can be found by solving Eq. (6.306), since the only forcing function is the impressed signal Ei. With νχ and I\ in hand, the forcing functions for the

ELECTROSTATIC

TRANSDUCERS

193

second-harmonic components of v e l o c i t y a n d current are known, and E q . (6.30c) can be solved for ®2 a n d h- T h e n , w i t h vh

h, and h known,

the third-harmonic components can be evaluated from E q . (6.3(W), and so on. T h e f a c t t h a t these harmonic components can be evaluated in this w a y does not gainsay the f a c t t h a t there are too m a n y physical variables involved to m a k e it easy to interpret the results in general terms. T h e q u a n t i t y t h a t is p r o b a b l y of most interest is the ratio of the second-harmonic v e l o c i t y to the velocity a t the f u n d a m e n t a l frequency. B y a tedious procedure of the sort often referred to euphemistically a s " a little algebraic manipulation," the relative second-harmonic velocity can be expressed in the form

13

ИШ(1+7) i(M ЬдО €0-J N

= 1.

=

2.

—^

"

=

" TblVl

(Zm2

+

- g § = + N = 3.

^ -

Xl9a2

= ^

-

TaJai

= TalVl + (Zeal + Z 0 l)/ a l -

(IIN

С bo

0 = (2ml + Zü)ül + ( j f j

(6.32a)

— Zoi/al

2

ω)»2

+

+

(Zeb 1 +

Τ ail αϊ —

Tb\hl,

1,

Z01Ib

Z(,l)Ibl·

Гм/и,

+ (Zeo2 + Z 02 )/ o2 - Z 02 / W) —TbiVi

— Zoil

+ (Zeb2 +

a.2

(6.326)

(6.32c)

Zm)Ibi·

= (zm3 + 2L3)f3 + Tasla3 ~ ТьзЬз,

^J*qal = + =

Static

~^b3Vs

+ (Zea3 + Z03)/a3 - Z03/b3, ~

Equilibrium:

Zo3la3

+

N

{Zeb3 +

=

(6.32d)

Ζο3)/δ3·

0

The zero-frequency Eqs. (6.32a) will, as before, yield information about the conditions of static equilibrium. For this case, the time constants R0Ca and R0Cb are of no consequence since the charges qaо and qw will eventually adjust themselves to bring both Ca and Cb to the full bias voltage Eq. The q's can be eliminated then from the first of Eqs. (6.32a), by using the other two relations, whereupon the equilibrium condition can be written as

ELECTROSTATIC TRANSDUCERS —

77 — - rТ?m o —— —Г е0 =

195

qlo - дЬ> 2ео5

1 Ео«о5 2 {da + Хо)2

1 (db - Χα)2

(6.33)

Note carefully the algebraic signs attached to Fm0, the elastic restoring force acting on the diaphragm, and to the electrical force Fe0. Equilibrium requires, of course, that the sum of these be zero, which is just what Eq. (6.33) says. As before, this is a cubic in Xo, so a graphical solution would appear to be indicated; but it will be useful to consider first the general behavior of the electrical force Fea. At this point it will be prudent to insist temporarily on structural symmetry so that it can be assumed that da — db — d. The electrical-force part of Eq. (6.33) can then be manipulated into the following form:

[δ + 2δ3 + 3 δ 5 + · · · ] , where δ [ = x0/d] has been introduced as an abbreviation for the normalized displacement coordinate. It is at once apparent that the equilibrium Eq. (6.33) is satisfied by xo = S = 0; which is to say that there will be no shift of diaphragm position when bias voltage is applied. It is also apparent that the electrical force is linear for small displacement, and that it acts in the direction of the displacement. It constitutes, therefore, a negative stiffness whose magnitude is given by the derivative of Feо with respect to x0. If the electrical stiffness is defined as 1 fc e , it can be evaluated readily from Eq. (6.34) as 1 _ dFe0 ce d(— xo)

dFeо db db dxo'

(6.35)

The typical equilibrium conditions prescribed by Eq. (6.33) are exhibited graphically in Fig. 6.9. The elastic force Fm0 and the electrical force F a are shown by the solid-line curves; the electrical force is shown

196

ELECTROACOUSTICS

also with reversed sign (dashed curve) so that its intersection with the straight line representing Fm0 can display the equality demanded by Eq. (6.33). Note that all three solutions of the cubic equation are in evidence; but note also that the two intersections marked A are not only unstable but also inaccessible, since the electrical negative stiffness will

FIG. 6.9. Typical variation of the electric and mechanical forces affecting static equilibrium for the push-pull electrostatic loudspeaker.

have exceeded the mechanical positive stiffness, and "fall-in" will have ensued, before the points A can be reached. The boundaries of the region of stability are indicated by the points marked B, at which the slope of the (—i,e0)-curve matches that of Fm0. These points can be located analytically by first expressing the fact that the mechanical stiffness must exceed the electrical negative stiffness, and then by solving for the critical value of S in the limiting equality. Thus, with c6 given by Eq. (6.35),

i >\

Cm

Ce /

J_> Cm ~

(6.36) (1 + 6 δ 2 + 1 5 δ 4

d3

+

О-

ELECTROSTATIC

TRANSDUCERS

197

Note how this result compares with the corresponding criterion for the single-sided case given by Eq. (6.16) above. B y introducing the (theoretical) critical limit x0 = —d/3, Eq. (6.16) can be solved for the value of E% at which fall-in would occur; this yields

In the push-pull case, the diaphragm remains undeflected in spite of increasing bias, but its stiffness is progressively neutralized and fall-in would occur for the value of E0 given by Eq. (6.36) with δ set equal to zero, namely, (£o)cr,t..p.p.

/1 dz = ί2 ' ^ s )

=

L 3 0

(-EoWas.

(6.370)

I t was observed experimentally for the single-sided ESLU that the diaphragm fell in at values of δ that were only § of the theoretical limit, but since both critical voltages are likely to be influenced in a similar way by the perturbations that hasten diaphragm collapse, the advantage in this respect would appear to remain with the push-pull case. The generality sacrificed by requiring that da = db can now be recouped. If a little asymmetry were introduced — by moving the mounting frame for the diaphragm a little to the left, for example, so that da < db — the effect would be to shift correspondingly the neutral axis-crossing point 0 ' for the Fmo curve, as shown by the short dashed line drawn parallel to Fm0 in Fig. 6.9. The equilibrium prescribed by Eq. (6.33) would then occur at D, the new intersection of Fm0 and (~Fe0); and this point will always lie farther from the central position than the distance to which 0 ' was shifted by the structural asymmetry. The extent to which the asymmetry is exaggerated in this way depends on the relative slopes of these curves, that is, on the extent to which the mechanical stiffness is neutralized by the negative electrical stiffness. The boundaries of the region of stability are still located symmetrically with respect to the mid-point between the stationary electrodes, however, so that one effect of the structural shift is to reduce the effective width of the stable region. For single-sided operation, diaphragm collapse was found to occur always at a particular critical value of —xo/d. In the push-pull case, on the other hand, the slope of the f V c u r v e increases progressively on either side of the central position and may yield a critical value of x0/d

ELECTROACOUSTICS

198

that is either large or small depending on the bias voltage [cf. Eq. (6.36)]. This effect may be measured, as before, by defining a coefficient of electromechanical coupling in terms of the relative values of the mechanical and electrical contributions to stiffness. Equation (6.14), the defining relation for the coupling coefficient k, can easily be transposed to the form

The initial value of the electrical stiffness can be found by setting 5 = 0 in Eq. (6.35); and when this is introduced in Eq. (6.38a), the coupling coefficient becomes ι»

2Elt0Scm _ 2cmCoo

2cmCoo

οοιλ

The introduction of Cm in this expression anticipates the identification of the transduction coefficient that will turn up in connection with the fundamental mode of operation. One basic feature of the foregoing deserves reömphasis. When the diaphragm is displaced by some external agency, the electrical forces indicated by the Fe0 curve of Fig. 6.9 can come into play only in so far as it is possible for electric charge to flow to or from the diaphragm in the amount required to keep the condensers Ca and Съ charged just to the bias voltage E0. For example, if the time constant i?0Co were very long, and if an external force acted suddenly to deflect the diaphragm to a position even beyond the point marked A in Fig. 6.9, the initial effect would be an increase in Ca and a drop in the voltage across Ca (with corresponding converse changes for Съ). Instability and fall-in would not manifest itself until enough time had elapsed for the charge on Ca to rebuild its voltage back toward Ε ϋ far enough to reach the critical voltage for the assumed diaphragm displacement. It follows that diaphragm excursions of any extent will not precipitate static instability or fall-in provided their "dwell time" in the unstable region is short in comparison with the time constants. The foregoing can be summarized briefly by two statements: (a) the stability criterion given by Eq. (6.36) must be observed in order to assure the stability of static equilibrium; (b) but instability will not be precipitated even by large excursions occurring under dynamic conditions at frequencies for which the half-period is negligible in comparison with

ELECTROSTATIC

TRANSDUCERS

199

the time constant of the biasing circuit, that is, for frequencies that satisfy the criterion

/»

1

(6.39)

2RqC0iI

The Push-Pull ESLZJ at Fundamental Frequency: N = 1

The set of equations for N = 1 [Eqs. (6.32J)] display an agreeable symmetry. The two electric meshes are coupled by the common impedance Zoi, and each is coupled to the single mechanical mesh by a (symmetric) transduction coefficient. A three-mesh configuration such as that shown in Fig. 6.10(a) would appear to satisfy these coupling requirements, but one must always set up such trial circuits with caution until it is verified that all the algebraic signs and the assumed

I

Coo -T. ППЯГ1—'\ΛΛ—j \—C±J z

eal I L R Г ,, ° ° Gt-Hlji-j—ЯЯЯР^-ЛЛ/У

+ τ ηa,I = Τ

Zoi

I Г+

(da + x0)

-T M = j

«С -т-^о

_

. .

'

m

G -p^c

-VWTnnrv AA/VinnPR ü МЛ RX Mx Fig. 7.12. An equivalent mechanical-impedance network representing the mechanical and acoustic elements associated with diaphragm motion in the ring-armature receiver. [After Mott and Miner, reference 3 J {Courtesy of the Bell System Technical Journal.)

MOVING-ARMATURE TRANSDUCER SYSTEMS

235

Some of the structural design features of the ring-armature receiver can be discussed most conveniently in terms of the equivalent circuit shown in Fig. 7.12. A low-frequency cutoff in the response is introduced deliberately by providing a small hole in the center of the dome-shaped diaphragm. This has the useful effect of eliminating a good bit of interfering noise without impairing speech intelligibility. Since the hole serves to divert part of the volume current that would otherwise be delivered by the diaphragm to the chambers beyond, it must appear in the circuit diagram as the shunt-connected branch MH,RH· In a similar way, another portion of the volume current may be diverted by compression in the chamber SM between the diaphragm and the flexible dust-sealing membrane. There is opportunity for still another fraction to be diverted by compression in the grid-membrane chamber SA', and the residual volume current is finally delivered to the ear coupling chamber Sc through the impedance elements RG,MG that represent the holes in the grid and the receiver cap. Similar rationalization will then account for the components of volume current that return to the other side of the actuating diaphragm through the parallel paths comprising the chambers SA,SB,SX· This circuit configuration is obviously not one for which optimum values of the various circuit elements can be inferred by inspection. On the contrary, the large number of disposable parameters makes the task of finding optimum values by cut-and-try precalculation a problem of almost unmanageable complexity. I t is in just such cases that it is most rewarding to adopt the expedient of modeling the mechanoacoustic structure with an all-electric network analog. In effect, this amounts to attacking the optimum-value problem by using the equivalent circuit as an analog computer. The adequacy of such a procedure was demonstrated by using it successfully to establish the structural and dimensional constants for this commercial receiver. I t has taken nearly a century of progress in all the sciences to bring within reach the goal epitomized by comparing the primitive 19thcentury transducers, such as Reis's magnetostrictive knitting needle surrounded by a coil and mounted on a wooden box, with such beautifully adapted transducing mechanisms as those described above. One of the objectives of this book has been to demonstrate that much of the empiricism that characterized early assaults on the transducer problem has already disappeared. The task of removing the remaining empiricism continues to stand as a stubborn challenge to all who would seek to advance still further the frontiers of electroacoustics.

APPENDIX

A

Dimensions and Units Quantity

Basic Dimensions

Symbol

QMLT

QVLT

Energy

U

ΜΙ/Γ-»

QV

Power

W

ML2X-3

= QVT-l

Mass

Μ

Μ

QVPL" 1

Potential Current

V I

Q- l ML s T-» Q X -1

V QT-l

Transduction coefficient Force factor

Τ

Q-'MLT" 1

VTL - 1

A

Q - 1 MLT - 1

VTL - 1

Magnetic flux Magnetic flux density Magnetic field vector Magnetization Magnetomotive force Magnetic reluctance

Φ В Π Μ SF (R

Q - 1 ML 2 T _ 1 MQ^T" 1 QL-ιχ-ι QL-IT-I Q T -1

VT VTL" 2 QL-IT-I QL-lT-l

Inductance

L

Q^ML 2

Q-iy-p2

Susceptibility Permeability of free space Relative permeability

X Mo

Numeric Q^ML

Numeric Q-I V T 2 L -I

Μ

Numeric

Numeric

6

Numeric

Numeric

«о

Q2 M -1 L - 3T 2

Ε D Ρ С

Q- l MLT-i QL - 2 QL-» (^Μ-^-Τ1

Relative dielectric constant Permittivity of free space Electric field Electric displacement Electric polarization Capacitance

QT- 1 QV-iT" 1

VL" 1 QL" 1 QL_i QV"1

Units in which quantity is expressed, and dimensional equivalents joules = newton meters = coulomb volts watts = joule seconds = ampere volts = coulomb volts/second kilograms = newton seconds'/meter volts amperes = coulombs/second newtons/ampere = volt seconds/meter newtons/ampere = volt seconds/meter webers = volt seconds webers/meter 2 amperes/meter amperes/meter ampere turns = coulombs/second ampere turns/weber = coulombs/volt seconds' henries = webers/ampere = volt seconds2/ coulomb 4тг X 10-» = 1.257 X 10"« henries/meter

ι 8.854 Χ ΙΟ"15 = 3 ^ Х Г farads/meter volts/meter coulombs/meter' coulombs/meter2 farads = coulombs/volt

D I M E N S I O N S AND U N I T S

237

Electric impedance, resistance, reactance

Ζ R X

Q-^ML'T" 1

Q-'VT

ohms = volts/ampere = volt seconds/coulomb

Force

F

MLT-s

QVL - 1

Pressure Density

Ρ Ρ

ML-»T-» ML" 3

QVL - 3 QVPL-5

Stiffness

s

MT" 1

QVL - 1

Compliance

Cm

Μ-φ

Q-'V-'L 1

Specific acoustic impedance

pc

MLrT-1

QVL" 4

Mechanical impedance Acoustic impedance

Sm

MT-1

QVL^T

ZA

ML^T"1

QVL^T

newtons = joules/meter = coulomb volts/meter newtons/meter' = joules/meter3 kilograms/meter3 = newton seconds2/meter4 newtons/meter = coulomb volts/meter1 meters/newton = meters'/coulomb volt kilogram/meter' second - coulomb volts/meter4 = newton seconds/ meter3 newton seconds/meter = kilograms/second newton seconds/meter1 = kilograms/meter4 second = ohms (acoustic)

APPENDIX В

Conversion Charts* The conversion charts presented in this Appendix were prepared to facilitate conversions between the various units most frequently encountered in electroacoustical computations. Included are charts for angular, linear, area, and volume measure; force, torque, pressure, and density; and compliance and mechanical impedance. In addition, there are charts for the inverse of several of these measures. The charts of inverse measure are used for all conversions of the type X per unit A to X per unit B. An example of this case is volts per inch to be converted to volts per meter. It is sometimes possible to use the charts for multiple conversions when the specific units are not available on any of the charts. Thus, degrees per ounce inch torsional compliance can be expressed as radians per newton meter by first converting to radians per ounce inch and then to radians per newton meter. The desired over-all conversion factor is the product of the two f a c t o ^ 1.745 X 10-2 (degrees to radians) times 1.416 Χ ΙΟ2 (X per ounce inch to X per newton meter) giving number of degrees per ounce inch times 2.471 equals number of radians per newton meter. The following values for the fundamental constants were used in the preparation of the charts: 1 meter = 39.37 inches. 1 pound = 0.453592 kilograms. Acceleration due to gravity = 980.665 cm/sec2. Density of H 2 0 at 4°C = .999973 grams/cm3. Density of H g at 0°C = 13.5951 grams/cm3. Density of sea water at 0°C = 1.028 grams/cm3. * Reproduced from a manual of Technical Data with the kind permission of Brush Electronics Company, Cleveland, Ohio.

CONVERSION CHARTS

239

LENGTH

4 Multiply \\№uiiber

Centimeter*

Ж e

Ж ?

Millimeter·

1

10

10S

2.540-1Ö*2

2.540*10

3.048* 102

Centimeter·

ίο"1

1

io2

2.540*10*»

2.540

3.048*10

Meter*

ΙΟ'»

10-*

1

2.540-10*5

2.540*ΙΟ*2

3.048*10*^

II

Obtain (

g»

? r•

I

«»

>Ί

MU*

3.937*10

3.937-10*

3.937 104

1

ίο»

1.200-104

Inche*

3.937-10*2

3.937-10*1

3.937-10

10-J

1

1.200*10

Feet

3.281*10*»

3.281-10*2

3.281

в.ЗЗЗ-Ιθ"5

8.333-10*2

INVERSE LENGTH

Зч ff« •β 4

X Per Inch

X Per Foot

X Per Millimeter

1

ίο*1

10-»

3.937*10

3.937Ί0*2

3.281*10'»

X Per Centimeter

10

1

10-2

3.937-10*

3.937-10"1

з.гаыо"2

X Per Meter

10»

102

1

3.937-104

3.937*10

3.281

X Per MU

2.540* 10*2

2.540*10*»

2.540*10*®

1

10*»

8.333-ю"5

X Per Inch

2.540*10

2.540

2.540-10*2

10s

I

8.333-ю'2

X Per Foot

3.048*102

3.048*10

3.048 10*1

1.200-104

1.200*10

1

-оьшп ί

Ж

X Per Meter

s*

X Per Millimeter

ч Multiply \ \ number

I

240

APPENDIX В

AREA

1

10 2

ioe

ί.οβτιο*4

β.452·10 2

9.290-10 4

Square Centimeters

ίο'»

1

10 4

5.067·10" β

6.452

9.290 10 2

Square Meters

ίο'8

io"4

•

5.067-10

6.452Ί0* 4

9.290-10~ 2

Circular Müs

1.973-Ю3

1.97310 5

1.97310 9

1

1.27310 6

1.833-Ю®

Square Inches

1.550*ΙΟ*3

1.55010"'

1.550-103

7.8S4-10' 7

>

1.440 10 2

Square Feet

1.07610" S

1.07610 - 3

1.07610

S.454-lo" 9

6.94410" 3

1

Obtain 1 \

Μ

i f

π I»

-10

Square Feet

Square Millimeters

ТО

Square Inches

Circular Mile

Square Meters

5 η

Square Centimeters

Multiply ОчNumber \ \ of

INVERSE AREA X Per Square Inch

X Per Square Foot

1

io·2

io"e

1.973·10 3

1.550 Ю" 3

1.076-10" S

X Per Square Centimeter

10 2

1

«0- 4

1.973 10 5

1.550-10" 1

i.076'10* 3

X Per Square Meter

10 е

,o4

1

1.97S-109

1.550-103

1.076-10

X Per Circular MU

5.0β7·10" 4

5.067-10*®

5.067*10

1

7.854-Ю" 7

5.454-10*®

X Per Square Inch

6.452 Ю 2

6.452

6.452·10 _4

J-.27J-10®

1

6.944-10* 3

XPer Square Foot

9.290Ί0 4

Θ.290-102

9.280·10' 2

i.ess-io®

1.440-ΙΟ2

1

X Per Circular MU

X Per Square Meter

X Per Square Mllllmeter

Obtain

X Per Square Millimeter

X Per Square Centimeter

. Multiply \ \ N umber \ \ of

-10

CONVERSION

Radian·

Degree·

ы Seconds et

%

/ y

О © о

Μ

.4

I О

9.136 χ К

m о

-

Ounces Per Inch Per Second

\\

Dynes Per Centimeter Per Second

4·0 Η ю 01 о

Newtons Per Meter Per Second

Per Dyne

Meton (Meters Per Newton)

о

Newtons Per Meter Per Second

Multiply 4 \ N umber \\ of

«О

-

Centimeter

|V4 \N