Optimization of Electronic Measurements [1 ed.] 0805369066

Citation preview

PERE IT LIS

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OPTIMIZATION OF © Module 4 ELECTRONIC © ayaen aie MEASUREMENTS — =xeriments

T D A T E S K M N L E A M UCH K C I L -HOR CRO

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SELECTED PHYSICAL CONSTANTS Quantity

Symbol

Electron charge

Q,

1.603 « 10-1?9C

Faraday’s constant

ae

96487.0 C equiv—?

a

8.32 J mole—!

re

tant

“scones Planck’s constant Boltzmann’s

constant

Ice point

TABLE

Stand

Nr.

77771 23

rp)

4

h

6.63 « 10-4 J-sec

k

1.38 X 10-23 J °K7!

To

273.15°K

PREFIXES

FOR

UNITS Symbol

10

tera

T

10?

giga

G

mega

M

kilo

k

10?

hecto

h

10

deka

da

io

deci

d

10-4

centi

c

10-*

milli

m

10-*

micro

U

10>”

nano

n

Lo

~

0821 liter atm mole—? °K~?

Prefix

LO®

74073

OF

|

°K-}

Order

108

lnventar Nr,

Value

pico

p

145

femto

f

10-28

atto

a

OPTIMIZATION OF ELECTRONIC MEASUREMENTS

Instrumentation

For Scientists Series

OPTIMIZATION OF ELECTRONIC MEASUREMENTS

HOWARD

V. MALMSTADT University of Illinois

CHRISTIE

G.

ENKE

Michigan State University

STANLEY R. CROUCH Michigan State University GARY HORLICK University of Alberta

Os

W. Menlo

London

Park,

California

«: Amsterdam

A.

BENJAMIN,

* Reading,

: Don

Mills,

RE SRiK e

& wy, 3


T

10 kQ 0.22 na

33 kQ 100 kQ

220 kQ Reference

3

33 kQ

68 kQ

WW

10 kQ

WV

—WComparator

100 ke

—\V—

4 0.1 uF

100 ka

po

0.22

—10V

ae

33 kQ

33 kQ

symmetrical bipolar output square wave. Observe the output of the multiplier. Adjust the phase of the reference channel by fine tuning the tuned amplifier in the reference channel until the output of the multiplier shows the symmetrical synchronously demodulated waveform. Draw the_ signal, reference,

and

demodulated

waveforms

5

0.1 uF

HAH ins 10 ko

for correct

and

in-

correct adjustment of the phase. Observe the low pass filtered output on the servo recorder. Note that the output dc level is a measure of the amplitude of the input sine wave on the signal channel. The performance of this lock-in amplifier under conditions of low S/N can be tested by adding noise to the input sine wave. A simple noise generator using a Zener diode is shown in Fig. E4-23. Wire this circuit and observe the output noise. A low S/N signal for the lock-in amplifier can be generated by adding this noise signal to the input sine wave at OA1. Add sufficient noise to effectively “bury” the sine wave signal. Observe and draw the input to the signal channel tuned amplifier, its output, the output of the multiplier, and the output of the low pass filter. Use an output time constant of about 1 sec.

4+10V

Fig. E4—22

oO

recorder

Circuit for the lock-in amplifier.

Experiment

+15 V

0.1 uF

®

wv

10 kQ

—o

Fig. E4-23

T

2

To

neon bulb , on BIM

S)

Zener diode noise generator. A practical signal source can be set up, using the square wave of the DTM to drive a neon lamp on the BIM, and

JK-1

eM “shave

o1se

I1V

V

o—

167

100 ka

10 kQ

10 ka =

4-15

Reference

detecting the light intensity using a photocell or photodiode. The

circuit is shown

in Fig.

E4—-24.

Note

that the DTM

or plastic filters. Report your measurements

on this source.

output is first applied to a JK flip-flop to ensure symmetry. The light intensity can easily be varied using colored glass

100 ka WA

—O

||

Signal

Fig. E4-24 experiment.

Light

source

Experiment

4-15

Simple

Equipment:

signal for the lock-in

Boxcar

amplifier

Integrator

four OA’s two monostable multivibrators FET switch (eight-bit analog switch card) servo recorder SSG or function generator ADD oscilloscope

A simple boxcar integrator is constructed in this experiment, in which the position of the gating pulse on the signal waveform is manually adjusted. Simple monostables contro] the delay and gating times, and the signal is gated using a FET

switch. A sine wave generator and a random noise generator are used to test the S/N enhancement characteristics of the boxcar integrator. The boxcar integrator can be readily constructed in the ADD unit. The circuit diagram for the boxcar integrator is shown in Fig. E4—25a and the corresponding waveforms in Fig. E4-25b. The sawtooth waveform from the DTM serves as the signal. This is connected to input 1 of the circuit. The frequency of the sawtooth waveform should be 100 Hz. The gain of OA1 for this signal is 0.01 in order to simulate a small signal level. Input 2 of OA1 is used to add a noise signal to the sawtooth waveform. The SSG is used

to add

in a noncoherent

sine

wave,

and

is useful

in

168

Experiment

4-15

0.2 uF WW 10 kQ

100 kQ

WwW

1 MQ

100 ko

OW

or

Start

gate

1 MQ

10 kQ a \\\—

100 kQ bam \\

— recorder

A

Q

| OL Delay

Q ~

-\\-

FET

—\\\—

Signal 10 ka Noise

10 kQ

Gate

mono

>a

mono

|

(a)

:

OL

signe

Start

Delay mono

Fig. E4-25 forms

(b).

Boxcar

integrator

circuit

(a)

and

wave|

(b) testing the response of the boxcar integrator to specific interference frequencies. In addition, random noise may be added at this point from a random noise generator to simulate a low S/N measurement situation. The gain for this noise input is unity. The noisy signal is then inverted before being applied to the FET analog gate. The trigger for the boxcar integrator is obtained from the square wave output of the DTM. The square wave output and the sawtooth should have the relative phasing shown in Fig. E4-25b. The negative edge of the square wave signal is the actual trigger point. It fires the delay monostable which in turn triggers the gate pulse monostable. This pulse is used to control the FET analog gate. The position of this gating pulse with respect to the sawtooth waveform can be easily controlled by adjusting the delay monostable. For a 100 Hz input frequency the delay should be adjustable from about 1 msec to 10 msec. The width of the gate pulse should be set to about 0.5 msec. These waveforms are shown in Fig. E4Q—25b. These waveforms can easily be observed on a dual beam oscilloscope. Trigger the oscilloscope externally on the negative edge of the DTM square wave. Connect one

|

Gate

mono

beam to the DTM sawtooth output and adjust the time base

so that at least one cycle of the waveform can be Connect the second beam to the output of the monostable. Note that the position of the gating be set at any point along the sawtooth waveform ing the delay monostable. Draw the signal and waveforms.

observed. gate pulse pulse can by adjustgate pulse

Experiment

4—15

169

The gated signals are averaged by the final OA. The values of Rj,, R,, and C of this amplifier should be set to 100 kQ, 1 MQ, and 0.2 uF. The output of this amplifier can be recorded directly on the servo recorder with a full scale sensitivity of about 100 mV. The complete ramp can be sampled by successively setting the gate pulse at equally spaced intervals along the ramp and recording the output value on the recorder. The major division lines on the oscilloscope face can serve as convenient sampling points. Record the complete ramp waveform

the

(100

boxcar Hz

on

the

recorder

integrator

in this

case)

a

in

high

can

this

fashion.

speed

easily

be

Note

repetitive recorded

speed output device such as a servo recorder.

that

with

a

slow

waveform

on

The noise rejection properties of the boxcar integrator can be highly dependent on the specific frequency content of the noise. The characteristics are somewhat similar to those of the gated DVM integrator for dc and low frequency signals. Set the gate pulse at approximately halfway along the ramp and continuously record the output on the servo recorder. Apply from the SSG the specific sine wave frequencies

listed

in

the

table

below.

Record

and

explain

the observed response. The frequency of the sawtooth should be 100 Hz and the gate pulse should be 0.5 msec wide, for all measurements except those indicated for 1 msec. Note that the noise rejection is dependent on the relation of the period and phase of the sine wave to both the gate pulse width and the waveform repetition time. In some cases it will be useful to observe more than one cycle of the sawtooth wave in order to explain the results of the measurements.

Test

frequencies

for boxcar

SSG 100 kHz 10 kHz 1 kHz

1 kHz (1 msec gate)

100 Hz 100 Hz (1 msec gate)

200 Hz

The noise discrimination capabilities of the boxcar integrator are quite impressive. Using the noise generator shown previously in Fig. E4-23, add noise to the ramp signal at the input OA. Manually step the boxcar integrator gate pulse as above, and record the output on the servo recorder. Estimate the S/N enhancement that can be achieved. Plot the output values vs. delay time in order to reconstruct the signal.

integrator SSG 150 Hz 100 Hz 50 Hz

2000 Hz

3000 Hz 4000 Hz

170

Experiment

Experiment

4-16

4—16

Digital

Scanning

Boxcar

Integrator

Equipment: ADD (two DTM’s and one BIM) three OA’s FET switch (eight-bit analog switch card) five monostable multivibrators two DCU cards or two SN 7490N decade counters

scaler card

(EU-800-KC)

three JK flip-flops two NAND cards two five-bit shift registers (SN 7496N) dual in-line card

(EU-50-MC)

servo recorder sci] OscIHOsScOpe

With the boxcar integrator of Experiment 4-15 it was necessary to manually adjust the delay time in order to measure the complete shape of a waveform. The boxcar integrator to be constructed and studied in this experiment is capable of automatically scanning the gate pulse of the integrator across a waveform. The self-scanning operation

is based

on a

digital

clocking

and

sequencing

system

con-

structed from a 10-bit circulating shift register. This register is circulated and shifted under control of a master clock and various counters in synchronism with the repetition

of the signal.

J Clear

Fig. E4-26

10-bit shift register

Circuit for the digital scanning boxcar integrator.

Experiment

Clear

Aut

Bat

Cout

16

15

14

13

u,

| |

D sect

Esai

12

11

10

| |

| |

|

Preset

| pqClock|

| qClock|

| ¢ Clock

Clear

Clear

Clear

addr

sure c

Clear

a

Clock

Dies

AR

[

L

2

3

Preset A

Preset B

EE

pur

£ From SB

4

4

J A

9 _|

Preset

cls

Bits

Clear

input

Preset

4sts

~d Clock | | dClock}

R

GND

,

Preset

l

Preset

>|s

+

|

5

6

7

8

Preset Cc

Vcc

Preset D

Preset E

Preset

Clear

Ai

Bout

16

15

14

L

of

Preset

Clear

Clear

ale

ble

2

Y

Preset

chs

cHuR

il

1

Diets

Preset

EL

o Clock

WR

pb

J

E

Clear

‘1

[

3

4

5

6

7

8

Preset

Vcc

Preset D

Preset E

Preset

Preset

To SA

_

[_

— ed Clock

| aClock]

R

Clear

_

pos

__|

|

[

Preset

Bltds

]

1

9

| Clock

Ales

Clear

|

10

Preset

l

s

R

11 _

“d Clock | | ;qClock}

From Q of Mono-5

input

|

~

To FET

eria

Boat

|

JK-3

© © gate

selial

Ds

'—

| ,

Preset

12

13

tc

|

FromJK-2Q

GND

Cout

To clear

> From Q JK-1

5-BIT SHIFT REGISTER 1

Light 0 O—

d

ll

4

.

171

; Serial

2

REGISTER

SHIFT

5-BIT

4-16

+5V

Detailed shift register connections for the digiFig. E4-27 tal scanning boxcar integrator.

The complete circuit of the digital scanning boxcar integrator is shown in Fig. E4—26. This type of boxcar integrator was discussed in some detail in Section 4-5.4. This section

of the text must

be read and

understood

before

at-

tempting this experiment. Wire this complete circuit. A detailed layout for the connections to and from the five-bit registers is shown in Fig. E4—27.

Several waveforms E4—28.

from this circuit are shown in Fig.

These will be discussed,

along with some

comments

on operating the circuit. A simple signal source to demonstrate the use of this circuit is the ramp output of the DTM. This waveform is shown in trace 2 of Fig. E4-28a. The negative edge (1-0 transition) of the square wave from the DTM is used as the start trigger. This signal is shown in

172

Experiment

4-16

register, is shown in Fig. E4—28b along with the signal. Note that its duration is equal to the period of the clock waveform (trace 4 of Fig. E4—28a). The

ee

ee

Te Re

ON

time of JK-1

(trace 3, Fig. E4-28a)

indicates

the total segment of signal which will be scanned by the boxcar integrator. With the 10-bit register the integrator will incrementally sample nine equally spaced intervals in this segment of signal. The length of the scanned segment may be varied relative to the period of the signal by increasing or decreasing the period of the signal or the master

ee

clock

rate. If the master

clock

rate is increased,

care must

be taken so that the two pulses from monostables 4 and 5

still fit in between

clock pulses

(Q of JK-2).

They

may

not

overlap for proper cycling of the circulating register. This

was

(b) Fig. E4-28 grator.

Waveforms

from digital scanning boxcar inte-

trace 1 of Fig. E4—28a. The Q output trace 3 of Fig. E4-28a. The 1 level master clock NAND gate is open. opens at a finite delay time after the Start trigger

(trace

1). The

duration

of JK-1 is shown in is the time that the Note that this gate negative edge of the

of this delay

is set by

monostable 1. After ten clock pulses have been generated at Q of JK-2, the master clock NAND gate is cleared by the modulo-10 counter. The group of ten pulses generated during a cycle of the circuit are shown in trace 4 of Fig. E4—28a, as measured at the Q output of JK-2. These are the actual clock pulses that cycle the register. The actual gating pulse, as observed at the output of the shift

illustrated in Fig. 4-103.

Also,

in all cases,

care

must

“1”.

This

boxcar

inte-

be taken to ensure that the total of the delay time and scan segment is not greater than the repetition period of the ramp signal. A master clock rate of at least 50 kHz is adequate. This master clock rate also ensures that the duty cycle of the integrator does not get too low. This frequency can be obtained from a DTM by using an external capacitor of about 0.01 uF. Except for monostable 1, all monostable times are short and constant. Mono 1 should be about 1 msec and variable, mono 2 < 200 usec, mono 3 < 500 ypsec and monos 4 and 5 < 10 usec. To operate the system: 1.

Set switch

C

(SC)

to “O”

and

clears the circulating register.

Fig. E4-29 grator.

Performance

then

back

of digital scanning

to

Experiment

2.

Set switch A (SA)

4-17

173

is reset with

mono-

to “1”, then back to “0”. This presets

bit A, the first bit of the circulating register. This may be confirmed by noting that lamp Q is on.

3.

Push PB1 to “1”. This sets JK-3, resets the modulo-K counter (K — 10°), and thus enables the circuit.

4.

When the bit has been fully by the modulo-10® counter, the E position of the second at JK-1 will simultaneously and JK-3, thereby disabling

cycled through the the occurrence of a five-bit register and clear the circulating the circuit.

register “1” at Q=1 register

An example of the performance of the circuit is shown in Fig. E4—29. Figure E4—29a is an oscilloscope trace of the original signal (the ramp from the DTM), and the output of the circuit is shown in Fig. E4—29b as recorded on a strip chart recorder. The master clock rate was 50 kHz and the modulo-K counter was set for 105. The S/N enhancement capabilities of the circuit are illustrated in Figs. E4—29c and E4-29d. Figure E4—29c is a scope trace of the same signal but with added noise. This noise can be obtained from the noise generator shown in Fig. E4—23 and added to the signal at OA1. The output as recorded on the servo recorder is shown in Fig. E4—29d. Record the output of the boxcar integrator for both these signals. Plot the amplitude vs. delay time. What amount of S/N enhancement can be achieved?

Experiment

Equipment:

4-17

Analog

Scanning

Boxcar

Integrator

six OA’s two monostables FET switch card NAND gate card ADD oscilloscope comparator card

An analog scanning boxcar integrator is constructed in this experiment. The self-scanning action is obtained by summing the outputs of two OA integrators and applying the sum to a comparator. One integrator has a very slow integration time which serves the purpose of slowly increasing the voltage at which the comparator will fire. The second integrator is triggered by the start pulse indicative of the beginning of the signal repetition, and it has an integration time comparable to the period of the signal. The integrator outputs are subtracted; thus the comparator fires at a slightly longer time on each signal repetition. The output of the comparator triggers a monostable which gates a signal segment to a low pass filter with a FET switch. The complete circuit of the analog scanning boxcar integrator is shown in Fig. E4—-30 and waveforms are shown in Fig. E4—31. The signal is the ramp from the DTM and the start pulse is the negative edge of the square wave from the DTM with the relative phasing as shown in Fig. E4—31

(traces

1 and

2).

Integrator

2

(OA2)

stable 1 (traces 3 and 4) which is triggered by the start pulse. Integrator 1 controls the total measurement time. Its integration time is long, several seconds to minutes. The time it takes integrator 2 to reach the same value that integrator 1 reaches at the end of the total measurement should be approximately equal to the signal repetition period. The waveform for integrator 2 is shown as trace 4 in Fig. E4—31 and the waveform for integrator 1 at a time ¢ after the measurement has begun in trace 5. Note that the measurement is begun by opening the shorting switch on integrator 1. When the sum of the two integrators reaches zero the comparator fires, generating the gate pulse (see traces 6 and 7 of Fig. E4-31). Observe the scanning action of the gate pulse. Observe and record all the waveforms shown in Fig. E4-31. Record the ramp (~100 Hz) waveform on the recorder. If desired, a low S/N waveform can be generated,

as in the previous experiments, and the S/N enhancement characteristics of the scanning boxcar integrator observed.

174

Experiment

4-17

Signal

Start pulse

r-WwWs—4 1 MQ

1 MQ

oT

ore

100 ka

100 kQ

10 kQ

:

100 kQ

|

100 ko

FET switch

~

WW 47>

100 ko

—O

Recorder

Q

| Mono

FET switch

poe)

O——

+4

0.1 uF

—15V 100 kQ 100 kQ

100 ka aw

100 ka Comparator

5

4+15V 100 kQ 100 kQ

fog 20 uF

;

Sa

Mono

100 kQ

—

10V

+10V

Fig. E4—31 Waveforms for analog scanning boxcar integrator.

Gate pulse

Fig. E4-30 Circuit for the analog scanning boxcar integrator.

Experiment

Experiment Equipment:

4-18

An

Analog

Multichannel

Averager

4-18

175

ADD (two DTM’s and one BIM) three monostables two JK flip-flops three OA’s DCU card or SN 7490N decade counter

A complete four channel analog averager for repetitive signals is constructed and characterized. The circuit averages four successive segments of a signal on four FET switched capacitors that are sequenced by a circulating shift register clocked in synchronism with the signal. The circuit diagram of the analog multichannel averager is shown in Fig. E4—32 and the waveforms in Fig. E4—33.

eight-bit analog switch card NAND gate card oscilloscope

input to the first OA is to enable the addition of noise to the signal. This may be from the noise generator shown in Fig. E4—23. The start pulse used to trigger the measure-

five-bit shift register (SN 7496N)

The

signal is the sawtooth

Delay

=p

Start

A

Q

Q

(open-

Mono-1l

close)

Master

TU

Mono-2

|>

Set

Clear}

J

Clear

Preset E

o—

| Clear Q

|

y

In

Q

T

DCU

JK-1

second

J]

Carr

S

The

Q

|,

clock

output of the DIM.

IK-2

5-bit circulating shift register

:

Mono-3

Q

bop

Cc

8

A

Clock

T

Oo

100 ka

100 kQ

WA

WW

100 k2

Signal

a

—/\\-—

—\\—
0 transition triggers a short monostable pulse that clears the gate flip-flop, closing the master clock gate. The bit now sits in location E until the sampling sequence is initiated again by another start pulse. The pulses that sequence the circulating register are shown in Fig. E4—33b along with a scope trace of the actual integrated signal segments. The gating pulse out of the shift register (output D) is shown in Fig. E4—33c. Detailed connections for the fivebit circulating register are shown in Fig. E4—34.

To

PBI

FET switch controls

A_

+

To Mono-3

Analog multichannel averager waveforms.

ment cycle is the negative-going edge of the square wave from the DTM. It must be phased to the sawtooth, as shown in Fig. E4—33a. The 1—0 transition of this waveform triggers a delay monostable which delays the generation of the four sampling pulses a set time from the beginning of the sawtooth waveform. Thus the sampling pulses can be set at any point along the waveform. The 1-0 transition of the delay pulse monostable triggers the start monostable. This monostable pulse is Short. It clears the modulo-20 counter and sets the gate control flip-flop. This opens the NAND gate, letting the master clock through to the modulo-20 counter. This master clock signal should be about 10 kHz, and it can be conveniently obtained from a second DTM. The output of the modulo-20 circuit is used to clock the circulating shift register. The modulo-20 counter is necessary in order to reduce the jitter present in the asynchronous master clock gate as it was in the digital scanning boxcar integrator. The signal repetition rate and the master clock are asynchronous in that they have no constant phase relationship. However, the sampling pulses must be accurately phase-related to the sawtooth waveform; otherwise coherent averaging of the signal information will not occur. Without the modulo-20 counter, the jitter in the relative position of the sampling pulses with respect to the signal could be as much as one period of the clock. Now, however, the jitter is only 1/20

| Clear

A out

Bout

15

14

16

__ i

—_

Lo

Ps

Preset

4s

Coat

GND

13

CL

Ds

12

+,

Preset

input

11

10

9

|

|

J

CL

Preset

Preset

pels

chéls

alts

Serial

Evut

Preset

£

-q Clock | | Clock Clock] | Clock Clock E DAR CHHUR BHR R AHWR Clear

—e

Ab

2

3

Clock

Preset

Preset B

From Q of JK-2

Fig. E4-34

A

7

od

l

tL jf

Clear

aa

Clear

Preset C

5

6

7

8

Vcc |

Preset D

Preset £

Preset

To Switch

+5V

fT |

+5V

|

Detailed shift register connections.

Experiment

4-18

177

Random noise can be added to the signal, as in the previous experiments, to illustrate the effectiveness of this measurement instrument in enhancing the S/N. A noisy signal is shown in Fig. E4—35a. This signal can be observed at the output when the circulating register is cleared. With the multichannel averager working, waveforms such as those in Figs. E4-35b and E4—35c are observed. The two waveforms are for noisy and noise-free signals. The actual buildup of the signal in the sampled segments can be observed by erasing the capacitors and then viewing the multiple signal traces. This is best observed if the circuit is triggered only every tenth waveform. ‘This can be easily set up by putting a modulo-10 counter before the delay monostable. Multiple oscilloscope traces of the signal buildup are shown in Fig. E4~36a for the noise-free signal and in Fig. E4-36b for a noisy signal. The time constant has

(b)

(c) Fig. E4-35 ager.

Performance of the analog multichannel aver-

Fig. E4-36 averager.

Signal

(b)

on the 10 be

been

decreased

(R = 4.7

kQ),

so

that

the

difference

between successive traces is more evident. Draw the observed waveforms and report the S/N enhancement capabilities.

build-up

in

the

analog

multichannel

the setting of the delay monostable and their width on clock frequency. For this experiment a clock of about kHz and a signal repetition rate of about 50 Hz should used.

178

Experiment

Experiment

Equipment:

4-19

4-19

Correlator

This circuit is quite useful for studying some of the basic properties and results of simple correlations. A wide variety of binary waveforms may be entered into the registers and cross-correlated. Load each shift register with a six-bit rectangular pulse. This is done by setting the clock

ADD four OA’s FET switch (eight-bit analog switch card) two monostables scaler card or four SN 7490N decade counters

to a very slow rate

two five-bit shift registers (SN 7496N) two eight-bit shift registers (SN 7491AN) servo recorder

A correlator is constructed that is capable of evaluating the cross-correlation and auto-correlation functions for some simple waveforms. The waveforms are simple sequences of binary ones and zeros that are stored in circulating shift registers. The circuit diagram for the binary waveform correlator is shown in Fig. E4-37. The detailed connections to the 13-bit circulating shift registers are shown in Fig. E4—38. This type of correlator was discussed in detail in Section

4—5.6,

and this section

must

attempting this experiment.

be read and

understood

(~0.5

Hz),

and

even though the pulse is obscured by the noise.

Modulo-K Counter

7

0

O—

_

_

HT

| |

|

Q

:| | |

|

Q

|___Sealer____Mono-I___Mono-2 __|

circulating

shift register 1

A

I

SI

N

Clock

100 ka

Se

7—{+—-++

|

as

PO

Correlator for binary waveforms.

A

IMQ

FET

gate

Fig. E4-37

— Clock

VW

—w—

1 tet

|

Preset

100 ko

10 ka

Noise

circulating

|

A SI

A

10 kQ

WwW

13-bit

shift register 2

Preset

first bit

E4-23. Note that the correlation pattern can still be observed

_

Sew 13-bit

the

before

Master clock

N

presetting

of the registers after each of six consecutive clock pulses. The initial relative positions are not important as the circuit will keep recycling the auto-correlation pattern on the recorder. The clock rate should be increased to about 500 Hz once the registers are loaded. Observe the output correlation pattern on the recorder. Add noise to the pulse signal at the first OA using the noise generator shown in Fig.

1

uF

10

270

ka

—\\\—

27 ka NAA

—O

To recorder

Experiment

LQ

SC

LR

LS

LT

4-19

179

ty

p

1

Serial Clear

Aunt

16

15

Bou

Coa

4

13

GND

Dour

12

1

Eau

input

10

9

14

13

A

B

GND

CP

NC

12

11

10

9

8

R

@

racP

5

Oo RHIO

R

eb Q

AY pT _] ry} 27) 3]}] 4) s5]]} eo ]] 77]

sash Clock

Preset

Preset

LV

LW

Asi

Bont

Preset

Vcc

LX

Preset

Cit

Ss

QO

S

8

1

2

3

4

5

6

7

NC

NC

NC

NC

Veco

NC

NC To FET gate

LY Serial

Clear

CP

Preset

bbn

Preset

GND

Dour

Eau

Input

©

Q

AB

14

13

12

1

R

OFyre

racP

s

OR

A 1

iD Clock

Fig. E4-38 lator.

Detailed

1

Preset

o

Tf

Preset

Preset

shift register connections

@

Vcc

ie

Preset

for corre-

Preset

Preset

OR

GP

st4o

O

CP

ste

CP

NC

10

9

8

oHJr CP

@Q

GND

a CP

oH4s

REHHO

@

R

CP

OR

CP

ste

sto

CP

s

1

2

3

4

5

6

7

NC

NC

NC

NC

Veo

NC

NC

—o To

OA

180

Experiment

4—19

Load each shift register with the three one-bit pulses shown in Fig. 4-125 and repeat the above measurements.

Grounding

and Shielding

Appendix A

Grounding

Appendix A

and Shielding

When measuring low level signals, problems are frequently encountered which can be traced to improper grounding, poor choice of input amplifier, and improper or inadequate shielding. Such problems are often difficult to assess and their elimination remains

somewhat

of an art. However,

some

basic system interconnection guidelines are developed in this appendix which, when followed, will minimize the occurrence of grounding and shielding problems. Grounding

Voltage is not an absolute quantity but is the potential difference between two points. In order to establish and maintain reproducible and safe voltages in a circuit, a stable reference point from which all voltages are measured must be established. This single stable reference point is called the circuit common. When a circuit is linked to other circuits in a measurement system, the commons of the circuits are often connected together to provide the same common for the complete system. The circuit or system common may also be connected to the universal common, earth ground, by connection to a ground rod, water pipe, or power-line common (see Note 16, Module 1). The terms ground and common are often used inter-

changeably but are usefully distinguished as described above. Most of the problems with grounds or commons arise because two separate commons or earth grounds are seldom, if ever, at the same voltage. It is quite possible for two commons in the same rack of electronics to be at different voltages; and any time a signal source is somewhat remote from the input amplifier, as is often the case, it can almost be guaranteed that the signal source common will be at a different voltage than the measurement system common.

A simple voltage signal source is shown in Fig. A—-1a connected to an OA voltage measurement circuit. The signal common C1 is at a different 181

182

Appendix

A

Rin

—WRs

Ground

loop

Vs

+— Common

|

be -Vegp-——— (a)

Common

2

Ry

NA bm

Fig. A-1

different

(a)

Ground

commons.

(b)

loop

resulting

Elimination

of

from

Rin

—Ww

the

ground loop by establishing a single common.

enw)

Rs

V;

L

(b)

voltage than the amplifier common C2, and thus a ground loop is present which can give rise to an erroneous signal. This can be particularly troublesome if the two commons are unstable with respect to each other. Ground loops can be eliminated by connecting all commons toa single point as shown in Fig. A-1b. However, it is important that the connections to common have very low resistance and high current carrying capacity so that ohmic drops along the connections are minimized. Typically a large Copper wire or foil is used. This is particularly important if a number of connections to a single common point are made and if some of the connections are long, as they would be when the signal source must be remote

from the measurement

circuits. Even so, at RF frequencies the resistance

is increased by the skin effect, and inductive reactance can be very large. While only two components of a measurement system (signal source and input amplifier) are shown in Fig. A-1, a single common should be established for all circuits in the measurement system in order to eliminate

Grounding

Signal

source aa

Input

amplifier ree,

and

Signal

modifier Ea aay

Shielding

183

Output device

GSES

Fig. A-2 ment

Vv

Single

system.

common

for

a

measure-

and minimize ground loops. This is shown in Fig. A—-2. In complex systems the necessity of low resistance to ground or common is very important, since ultimately a single connection must carry the sum of all the currents from every component in the system. It may in fact become impractical to have a single common point because the current carrying capacity cannot be provided. In this case it may be safer to have several stable grounds and tolerate some ground loops. This sort of compromise is often necessary in solving the ground problems associated with large installations and buildings, such as a computer center, or when the circuitry is subjected to interference which may cause large currents, such as interference from electrical storms.

However, even in laboratory measurement situations it may not be possible or practical to have a single common point, particularly if the signal source is remote from the measurement system. In these cases it is advantageous to use a differential input instrumentation amplifier as discussed in Section 3—2.1 of Module 3. The simple signal source of Fig. A-1 can be measured using an instrumentation amplifier, as shown in Fig. A—3.

Common Common

1

Fig. A-3 Instrumentation amplifier used to cancel out the effect of ground loops.

2?

184

Fig A-4 (a) Capacitive p ickup on input signal lines. Equal izat ization of pickup usi Ing a tw isted w ire signal pa Ir.

Appendix

(b)

A

Grounding

and

Shielding

185

Now, even though there is a difference in potential between the signal common and the amplifier common, the erroneous signals generated by the ground loops are common mode (common to both inputs) and as such are rejected by the differential amplifier. Therefore, it is unnecessary for the two common voltages to be stable with respect to each other. Note also that the input impedance of the instrumentation amplifier must be large with respect to the source resistance; otherwise, the common mode rejection ratio

(CMRR)

will be

degraded,

since

lines

two

the

are

Better common mode rejection (CMR) is achieved when balanced, as is the case with a Wheatstone bridge circuit.

not

identical.

the source is

Shielding

High CMR

mentation

depends on the equality of the two input lines to the instru-

amplifier.

As

mentioned

above,

a finite source

resistance

can

create an imbalance. It is also possible to pick up interfering signals on the input lines as a result of capacitive coupling to a disturbing line. Ground loops may also be established by capacitive coupling to ground. These problems are illustrated in Fig. A—4a. Differences in the amount of pickup can be significantly minimized by using a twisted wire signal pair as shown in Fig. A-4b. Now the capacitive coupling to the disturbing line and ground is approximately equal in both lines and high CMR is maintained. In addition to equalizing the pickup

as above,

the amount

of pickup

can be reduced by shielding the input lines. Shielding involves surrounding the input lines with a conductor. A high quality signal cable consists of a twisted wire signal pair, a foil shield, and a copper drain wire (see Fig. A-5). The shield should be connected to the signal ground (Fig. A—6a) so that the capacitance between the shield and the signal pair does not shunt the input impedance of the differential amplifier as it does in Fig. A-6b. In addition, the shield should not be connected to both the signal and measurement system commons, since this can establish a ground loop through Stranded copper drain wire Multiple layer foil shields Insulated outer jacket

\

™

Lyn Twisted signal pair Low

resistance

stranded

copper conductors

Fig. A-5

High quality signal cable.

186

Fig. A-6 (b)

(a)

Correct

shield

Incorrect shield connection.

connection.

Appendix

A

Grounding

and

Shielding

187

the shield and currents in the shield can induce currents in the signal pair via capacitive and inductive coupling. It is also possible to have a capacitively coupled ground loop to the shield which can in some cases result in induced currents in the signal pair. Some instrumentation amplifiers are equipped with an internal floating shield which surrounds the input section. This floating shield should be connected to the shield on the input twisted wire signal pair, which in turn is connected to the signal common. While signal lines are shielded as shown

in Fig. A—5,

instruments

are

shielded by their metal enclosures and chassis. In general, it is best if all shields are connected to the signal common, and no measurement system common is connected to the shield system except at the signal common. The arrangement is shown in Fig. A-7. Incorrect arrangements are shown in Fig. A—8. Since all the shields are capacitively coupled to ground, connecting a system component common to its shield can result in a ground loop as shown in Fig. A-8a. Also a system component common can be capacitively coupled to its shield, and connecting its shield to ground can result in ground loops both through the shield and the signal cables. Most of the considerations in this appendix concern analog signals with frequencies that are not very large, certainly less than 1 MHz. At higher frequencies and with most digital signals, coaxial cable is often used. Considerations with respect to digital signal transmission are discussed in Appendix C and Section 3—4.2 of Module 3.

--—-———

|

|

pT

| |

c=

|

|

|

|

|

____J

|

Too

|

| | Le

|

| |

1

Rin

|

WV-

Pe

| F

aw

I

t

|

i

|

=|

|

| Loo LL

Output

;

___

device 4

Loi

J

Shield connection

Fig. A-7

Shield around

a measurement

system.

J

188

Appendix

A

Output device

Output device

Fig. A-8

Two

incorrect shield connections.

Isolation

Occasionally it is desirable to isolate one circuit from another. For ac signals below about 5 MHz an isolation transformer can be used, as shown in Fig. A-9. At higher frequencies stray capacitance in the transformer makes the isolation ineffective.

Grounding

and

Shielding

VW

189

Ry

Ws Rin

WA

3

For digital signals excellent isolation can be achieved using optoisolators. These consist of a light source—detector pair which can couple binary signals. Typical light sources are tungsten bulbs, neon bulbs, and LED’s.

tectors. RF

Photoconductors,

phototransistors, or photodiodes

are used as de-

Shielding

High frequency interference in circuits is frequently referred to as RF (radio frequency) interference. Numerous sources of RF interference can be found in laboratory environments. Spark sources, flash lamps, and gaseous discharges for lasers are but a few. RF interference can be quite serious, rendering many digital circuits completely inoperable. Enclosing the circuit in a metal shield and using shielded cable can provide RF shielding. A conductor that has a high surface area (mesh or braid) makes an excellent RF ground. However, one main requirement of an RF shield clashes with that of the shield depicted in Fig. A—6a. The shield should be terminated at both ends, like the termination of a signal

cable for high frequency signals

Module

3). Thus

(see Appendix

C and Section 3-4.2 of

for best shielding two separate shields should

since the desired features for patible. One shield should be shield terminated at both ends termination prevents reflections

RF and low as shown in can be used of RF in the

be used,

frequency shields are incomFig. A—6a and a second RF around this first shield. The shield.

Fig. A-9

Isolation transformer.

Bibliography

Bibliography

Transform

Bracewell, Ron, The Fourier New York, N.Y., 1965.

and

Application,

Its

McGraw-Hill,

A classic reference work on the Fourier transform.

Technology,

Buus, R. G., “Electrical Interference,” in Design Hall, Englewood Cliffs, N.J., 1970, p. 381.

Vol. 1, Prentice-

An excellent discussion covering topics such as electromagnetic shielding, component interference reduction, interference reduction in cables and interconnections, and grounding

Carlson, Noise

A. Bruce,

techniques.

Communication

in Electrical Communication,

Systems: An

Introduction

McGraw-Hill,

New

York,

to Signals N.Y.,

and

1968.

A modern text on communication systems with excellent coverage of Fourier transform concepts as applied to signals, modulation, demodulation, and sampling. Cordos,

E., and

tion Measurement

Howard

V.

Malmstadt,

System for Atomic

Chemistry, 44, 2277

“Dual

Channel

Fluorescence

Synchronous

Spectrometry,”

Integra-

Analytical

(1972).

The synchronous integration measurement system can accurately subtract background and also average noise over a wide frequency spectrum. Hieftje, G. M., “Signal-to-Noise Enhancement Through Instrumental Techniques. Part I. Signals, Noise, and S/N Enhancement in the Frequency Domain,”

Analytical

Chemistry,

44,

No.

6, May,

1972,

p. 81A;

“Part

II. Signal

Averaging, Boxcar Integration, and Correlation Techniques,” Analytical Chemistry, 44, No. 7, June,

1972, p. 69A.

These two articles provide a good introduction to modern hardware-based signal processing techniques. Horlick, Gary, “Digital Data Handling of Spectra Utilizing Fourier Transformations,” Analytical Chemistry,

44, 943

(1972).

191

192

Bibliography

Smoothing, differentiation, transforms are described. tion in the Fourier domain Horlick, Gary, “Detection

and resolution enhancement of spectra using Fourier A discussion of the distribution of spectral informais included. of Spectral Information

Techniques,” Analytical Chemistry,

45, 319

(1973).

Utilizing Cross-Correlation

The application of cross-correlation techniques to the detection of a single spectral peak in a noisy base line and the detection of complex spectral features is discussed and illustrated. Kelly, P. C., and Gary Horlick, “Practical Considerations for Digitizing Analog Signals,” Analytical Chemistry,

45, 518

(1973).

The effects of sampling interval, sampling duration, quantization, digitization time, aperture time, and jitter are examined. Quantitative error criteria for sampling common peaklike signals are given. Malmstadt, H. V., and C. G. Enke, Benjamin, Menlo Park, Calif., 1969.

Digital Electronics

for Scientists,

W.

A.

A treatment of digital techniques directed toward instrumentation applications. Malmstadt, H. V., C. G. Enke, and E. C. Toren, W. A. Benjamin, Menlo Park, Calif., 1962.

Jr., Electronics for Scientists,

An earlier work containing several still-relevant sections on analog measurement techniques and devices. Morrison, Wiley, New

Ralph, York,

Grounding

N.Y.,

1967.

and

Shielding

Techniques

in Instrumentation,

A comprehensive treatment of grounding and shielding problems. Electrostatics, shielding, differential amplifiers, bridge systems, and magnetic and RF processes in instrumentation are among the topics discussed. Savitzky, A., and Marcel J. E. Golay, “Smoothing and Differentiation of Data by Simplified Least Squares Procedures,” Analytical Chemistry, 36, 1627 (1964). A classic paper on smoothing using weighted moving averages. Schuartz, Mischa, Information Hill, New York, N.Y., 1970.

Transmission, Modulation,

and Noise,

McGraw-

A general text on modern communication systems. Contains a brief but excellent discussion of equivalent bandwidth and the bandwidth-time inverse relationship. Tobey, G. E., J. G. Graeme, and L. P. Huelsman plifiers, McGraw-Hill, New York, N.Y., 1971.

(Eds.),

Operational

Am-

A comprehensive treatment of the design and applications of operational amplifiers. The applications discussion includes active filters, modulation, and demodulation.

Solutions to Problems

to Problems

Solutions

SOLUTIONS 1.

a)

IN SECTION

TO PROBLEMS

4-1

F(f) = 2f¢ f(t) cos 2nft dt f(t) = cos 2nf't . Ff)

= 2fF cos 2nf’t cos 2nft dt

From integral tables, sin (m — n)x

fcos (mx) cos (nx) dx =

sin (m+

2(m—n)

n)x

2(m + n)

In our specific problem, t=

..F(f)

f,

=

m=

2nf’,

n=

2nf.

sin 2x(f’ — f)t

sin 2x(f’ + f)t

2n(f’ — f)

2n(f + f)

For positive frequencies only the first term is significant. FG

b)

m

=

sin 2x(f’ — f)t

an(f — f)

t

0

The above function is plotted in Fig. S—1 for f/ = 100 Hz andt = 1

sec, and in Fig. S—2 for f/ = 100 Hz and t = 0.1 sec. Note that only the axes are different.

c) The power spectrum [F?(f)] is plotted in Fig. S—3 for f/ = 100 Hz and t = 1 sec. 193

qT

Amplitude o Ww So

LN 98

Fig, S-1_ Fourier transform of cos 2n/'t for f' = 100 Hz and t = 1 sec.

985

[™

YoY

99

I

|

99.5

100

I

100.5

101

|

!

101.5

102

Hz

5

] 120

Hz

Frequency

0.075 F 0.050 F 0.025

T

Amplitude

0.100 F

ZN

Fig. S-2 f =

MM

80

Fourier transform of cos 2zxf’t for

100 Hz and t = 0.1 sec.

Fig. S-3_

The

power

spectrum

f’ = 100 Hz and t = 1 sec.

85

90

ve

100

=105

LN NO

Frequency

[F?(f)]

for

9

985

99

995

100.

100.5

Frequency

10l

101s

10) He

Solutions

to

Problems

195

d) When ¢ gets large the spectrum is narrow, indicating that the longer cosine wave is composed of essentially a single frequency. When ¢ is small the spectrum is quite broad. 2.

Below is the complete table of values. The values are calculated using the equation A cos 2xft, where A is the relative amplitude,

f the fre-

quency, and ¢ the time.

Fre-

Time,

quency, Hz

0 0.125 0.250 0.375 0.500 0.625 0.750 0.875 1.000 =

| | | | | |

—2.0;

—1.5}|

0.52 0.00 |-0.84 0.00 0.44 0.00 |-0.14 0.00 0.03

sec

—1.0}

—0.5

0.52 0.52 0.38 0.71 |—0.59 0.00 |—0.58 | —0.44 0.00 | —0.43 0.24 | —0.18 0.00 0.00 |—0.03 0.05 |—0.03 0.03

O52 0.92 0.59 0.24 0.00 |—0.10 |—0.10 |—0.06 |—0.03

0.52 1.00 0.84 0.63 0.43 0.26 0.14 0.07 0.03

0.26

1.98

3.92

0.007)

1.96

0.01

0.01

0

0.5

| | | |

1.0

:

1.5

2.0

0.52 O52 | 0.52 0.52 0.92 0.71 0.38 0.00 0.59 0.00 |—0.59 | —0.84 0.24 | —0.44 |—0.58 0.00 0.00 | —0.43 0.00 0.44 —0.10 | —0.18 0.24 0.00 —0.10 0.00 0.10 | —0.14 —0.06 0.05 |—0.03 0.00 —0.03 0.03 |—0.03 0.03 1.98

0.26

0.01

0.01

1.96

0.007}

0.00

0.00

3.92 exp [—4(]n 2) #7] 0.00

3.

Vims = =

0.00

(4kTR Af)1/2 (4x

1.38 x

= 4.069 « 4.

10-73 & 300 & 100 « 10° x 10)?/2 V

10-*° V

Ave = 57.00,

o = 8.6,

S/N = 6.6.

From Fig. S—4, max ~ 67, min ~ 45. max — min 5

67 — 45 5

—

oo OLN c= 37/442

13

n 2x? — (2x,)? Note:

o? =

n(n — 1)

70

j

60F

_ —s

4.4

a

Vy

PuESage ms s

50

Ss

40+ Fig. S—4 Plot of values Section 4—1.

for Problem

4 in

196

Solutions

SOLUTIONS

Ls

to

TO

Problems

PROBLEMS

IN SECTION

a)

4-2

Vo = AVin — IR,

According to Eq.

(4-17), vin = Vsig + Bvo. -. Vo =A

(Vig + BY.) — IR,

Vo = Avuig +

BAv, — IR,

vo [1 — BA] = Avyig — IR,

Vo

AVsig 1 — BA

=

IR, 1 — BA

This final equation describes the output v, of the amplifier when feedback is present, and is analogous to the starting equation for the output

when no feedback was present. Note that the gain of the amplifier is 1/(1 —BA) of what it was without feedback (same results as before) and that the effective output impedance R, is also 1/(1 — BA) of what it was without feedback. This reduction of the output imped-

ance is another desirable characteristic of negative feedback.

b)

Equation

(4-17)

is vin = Vsig + Bvo. Rearranging yields Vsig

Vin

=

By.

—

Assuming no load is connected or that the IR drop across the output is very small: Vo = AV,

". Vaig = Vin — BAVin

Vsig = Vin [1 — BA] Dividing by the input current ij, yields Vaig

=—

Lin

Vin

[1-84]

lin

Or

Raig

Thus

the

creased

input over

[1 — BA].

impedance

that

of the

=

Rin

of the

amplifier

[1

—

BA].

amplifier without

with

feedback Ryig is infeedback R;, by the factor

Solutions

to

Problems

197

Therefore, in addition to achieving gain stabilization with negative feedback, the input impedance is increased and the output impedance is decreased, both of which are desirable in a voltage amplifier.

.

Equation

(4-13)

can be written

20 log (gain) = —20 logf — 20 log 2nRC.

If the gain decreases 6 dB, the frequency must increase to a new value

f’:

20 log (gain’) = —20 log f’ — 20 log 2nRC. Subtracting these two equations must give a 6 dB difference. 6 = — 20 log f + 20 log f’

Thus

- =

20 log

f

6

7

lo

a,

—>

=

0.3

F _ 1995. f

Thus decreasing the gain 6 dB results in a factor-of-two increase in the

frequency on the Bode plot.

Voltage gain Vour/Vin expressed in dB is 20 log

Vout

= 20 log (gain) in dB.

in

If the gain decreases 6 dB, the new gain becomes 20 log (gain’) in dB.

Subtracting these two equations must give a 6 dB difference. Thus

6 — 20 log (gain) — 20 log (gain’) 0.3 = log (gain) (gain’) gain

gain’ Therefore, a 6 dB decrease in gain is equivalent to reducing the linear gain by a factor of two.

198

Solutions

to

Problems

Another way to see this is to construct a table as follows: Gain,

dB

Gain

Oo.

(Vout/Vin)

1.00

1.995 3.98 7.94

6 12 18 SOLUTIONS

1.

TO

PROBLEMS

IN SECTION

4-3

M,(t)

= [1+ A, cos (2nf,t)]A, cos (2nf,t)

M.(t)

= A, cos (2nf,t) + A,A,cos

M.(t)

=

i

A.A,

A, cos

(2afct)

2

$a

cos aah + fat

(2nfst) cos (2xf,t)

cos 2n(f,

—

fe)t

The last step requires the trigonometric identity cos a cos B = 3[cos (a + 8) + cos (a — B)].

Negative frequency terms are avoided. 2.

Dt)

=[1 + A, cos (2xf,t)]A? cos? (2xf.t)

Dt)

= A?® cos? (2nf,t) + A A? cos? (2xf,t) cos (2nf,t)

With the trigonometric identity cos? a =

A? DY

A?

= a cos (4xf,t) + = +

A A?

+

With

the trigonometric

(a

6)1,

—~

Ay

D,(t) = >

+

+

(cos 2a + 1)/2,

A.A? a

cos (2nf.t)

cos (4nf.t) cos (2nf,t).

identity cos a cos B = 3[cos (a + B) + cos

AA? A A’

At

cos (2xf.t) + x

7s

2n(2fe — fs)t +

A A?

cos 2n(2f, + f,)t.

es (4xf,t)

Solutions

SOLUTION

1.

The

TO

PROBLEM

sampling

taken from

IN SECTION

rates for 1%

Table 4—2

are:

The

Gaussian

peak

Problems

199

4-4

maximum

Gaussian Lorentz Exponential

to

error in the peak

height

as

2.2 samples/sec 3.6 samples/sec 50 samples/sec

will fall to 0.01

of its maximum

value

which can be calculated by solving the following equation:

in a time t,

0.01 = exp [—4(In 2) 2?] —4.605 = —2.7732? t? = 1.661 t =

Therefore,

1.289

the total time over which samples

sec (both sides of the peak)

must be taken

is 2.578

and the total number of samples should

be 5.67.

For the Lorentz peak, 0.01 = (1 + 4f2)-1 1

0.01

—

1+ 42 0.01 + 0.0472 — 1 0.0412 — 0.99 t? = 24.75 = 4.97.

Therefore, the total time for the Lorentz peak is 9.94 sec and a of 35.8 or 36 samples should be taken.

total

For the exponential peak,

0.01 = exp [—2(In 2)|e|]

—4.605 = —1.386t fe=

3,323.

Therefore, the total time for the exponential peak is 6.645 sec and 332 samples should be taken.

Index

Index

Accuracy, 20 Active filters, see Filters Aliasing, 100-102 Amplifiers active filters, 41-47 bandwidth, 33 distortion, 33, 34 frequency response, 33, 34 gain, 32 gain-bandwidth product, 33 instrumentation, Appendix A lock-in, 118-125 noise in, 34, 35 notch, 49-50 selective, 122-123 tuned, 47-50 Amplitude modulation, 66-71 Analog filters, see Filters Analog-to-digital converters in computer-based techniques, 160 in cross-correlation, 153-154 digitization time, 105-106 in multichannel averaging, 141-143, 144-148 quantizing errors, 18-20 resolution enhancement, 144-148 Apodization, 104

Averaging (see also Integration) analog multichannel, 143-144 digital multichannel, 141-143 improvement of S/N by, 144-148 multichannel, 140-141 Bandwidth (see also Filters) amplifier, 33 noise equivalent, 15,37, 41, 116 system, 13-15 Bessel filter, 42-43, 45, 47 Binary correlator, 158-159 Bode diagram, 28 Boxcar integrator analog scanning, 135-137 applications, 137-140 computer-based, 160 digital scanning, 130-135 dual channel, 138-139 manual, 127-130 Bridged T network, 48 Butterworth filter, 42-43, 45, 47 Common mode rejection ratio, Appendix A Converters analog-to-digital, 18-20, 105-106, 201

202

Index

142, 144-148 digital-to-analog, 160 time-to-digital, 19 Convolution, 112 Correlation, 110-112 auto, 110, 152-153 cross, 110, 113, 126, 148-152 differentiation by, 150 instrumentation, 153-160 pattern detection by, 150-152 resolution enhancement by, 150 techniques, 148 Damping factor, 39-43 Data domains, 5 Decibel, 21-22 Demodulation diode envelope, 70 FM, 72-75, 79-80 synchronous, 69, 78, 123-125 Digital filtering, 161-163 Digital-to-analog converters in computer-based techniques, in correlators, 153-155 Digital voltmeter, 115-117 Digitization time, 105-106

161-163 Frequency bandwidth, 13-15 domain, 5 lower cut-off, 46 modulation, 71 multiplication, 76 oscillation, 53-54 rejection, 47-50 resonant, 38, 42, 46 shifting, 77 spectrum, 4-12 upper cut-off, 28, 42 Gaussian peak, 8, 11, 101-103, 113 Ground loops, 17, Appendix A Grounding, 16-17, Appendix A Hollow cathode lamps,

160

Feedback multiple, 38 negative, 31-35 positive, 35-36, 50-55 Filters active, 41-47 bandpass, 47-50 Bessel, 42-43, 45, 47 Butterworth, 42-43, 45, 47 digital, 161-163 high pass, 45-47 low pass, 36-45, 112-115, 123-125 noise bandwidth of, 37, 41 notch, 49-50 passive, 36-37 RLC, 38-41 Tchebyscheff, 45 Flame emission spectrometer, 3-4 Fourier domains, 5 Fourier transform, 5, 7-12, 111-112,

138-139

Integration, 113-118 boxcar, 125 by counting, 117-118 digital voltmeter, 115-117 Operational amplifier, 114 RC, 114-115 Isolation, Appendix A Lock-in amplifier, 118-125, Lorentzian peak, 101-103

160

Minicomputers, 160-163 Modulation amplitude, 68 double sideband, 66-67 frequency, 71 with lock-in amplifiers, 121-122 pulse amplitude, 80-82 pulse code, 84 pulse duration, 82-83 single sideband, 70-71 vestigal sideband, 70-71 Multipliers in correlation, 154 for demodulation, 69, 119, 123-125 for modulation, 66-68, 82 in S/N enhancement, 109

Index

Noise, 3, 8-24 amplifier, 34-35 amplitude spectrum, 9-12 bandwidth, 13-15, 37, 41, 116 excess, 16-17 interference, 8-9, 16-17, Appendix A Johnson, 12-13 phase spectrum, 9-12 photomultiplier, 3, 14-15 power spectrum, 8-9 quadratic sum, 20 quantizing, 17-20, 144-148 rms, 23 shot, 14-15 spectral equivalent power, 22-23 white, 8-9 Nyquist sampling theorem, 99-102 Oscillator, 35-36, 50-55 crystal, 54-55 feedback, 51-52 phase shift, 52-53 twin T, 53 Wien bridge, 53-54 Pattern detection, see Correlation pH measurement, 5-6 Phase spectrum, 9-12 Phase-locked loop, 75-78 Photomultiplier tube, 15, 117-118, 138-139 Photon counting, 117-118 Phototube, 14 Power spectrum, 5-12, 115-117 Precision, 20, 23 Pulse modulation, 80-84 Quality factor, 40-43 Quantization error, 18-20 level, 18-20 noise, see noise time, 105-106

203

Rate meter demodulator, 72-73 Recorder, see Transient recorder RLC circuits, 38-41 damping factor, 39-41 quality factor, 40-41 Sampling aperture time, 104-106 in boxcar integrators, 126 in computer-based techniques, 160 criterion, 99 duration, 103-104 in multichannel averaging, 144 rate, 99-102 Shielding, 16-17, Appendix A Signal-to-noise ratio, 20-24 expression of, 21-23 measurement of, 23-24 relation to precision, 23 Signal-to-noise ratio enhancement boxcar integration, 128-129, 133134 computer-based techniques, 160-163 correlation techniques, 148-149, 152-153, 157-158 filtering, 112-115 integration, 113-118 lock-in amplification, 124-125 principles, 24, 109 Smoothing, 161-163 Tchebyscheff filter, 45 Transducers input, 29-30 output, 30 photomultiplier tube, 15 phototube, 14 Transient recorder, 141, 143 Truncation, 103-104 Twin T network, 47-50, 53 Twisted wire pair, Appendix A Wien bridge, see Oscillator

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SYMBOLS

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Quantity or property

UNITS

FOR

QUANTITIES

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PROPERTIES Abbreviations of units

Symbol(s)

Units

m

kilogram (gram)

velocity

u

meter second?

m sec?

force

F

newton

N

ampere

A

(ampere centimeter~*)

(A cm-?)

mass

length time charge

1 t Q,q

work power

W P, p

current

Li

current density voltage

J

Vev

electric field

resistivity

conductance

conductivity capacitance

R

p

G

6

Am?

ampere meter?

Vv

volt volt meter~?

Vm-?

ohm

Q

(volt-centimeter ampere—?)

(V-cm A-?)

volt-meter ampere?

$

magnetic field

B

frequency

f,v

phase angle

6

temperature

T

w

a

(V cm—?)

V-m A-?

mho

Q-1

(ampere volt—! centimeter—*)

(A V-} cm-*)

ampere volt—? meter—?

mho ohm

Y

area

J WwW

joule watt

B Zz

admittance

angular velocity

(cm sec!)

farad

L X

magnetic flux

(centimeter second—?)

C

inductance reactance

susceptance impedance

m (cm) sec C

(volt centimeter—?)

strength

resistance

kg (g)

meter (centimeter) second coulomb

AV-'m"! F

henry ohm

H Q

mho

Q-1

weber

weber meter~?

a Q

(gauss)

hertz

degrees, radians

radians second—*

degree Kelvin (degree Celsius)

meter? (centimeter?)

Wb

Wb m~? (gauss)

Hz

°, rad

rad sec—* °K (°C)

m?(cm?)

a

THE MALMSTADT-ENKE INSTRUMENTATION FOR SCIENTISTS SERIES Optimization of Electronic Measurements is the fourth publication in this series, edited by H. V. Malmstadt and C. G. Enke. Eventually to include a wide variety of material, the series will be organized simultaneously in module and textbook form. Each module will. contain both text and laboratory material, and, in addition, the text portions will be available separately. This open-ended series provides maximum versatility in that the modules can be used inde-

pendently or in configurations of three or four, as ‘“‘packages,”’ each on a different area of instrumentation. The first package is entitled Electronic Measurements for Scientists and is made up of the following modules:

1) Electronic Analog Measurements and Transducers

,

(Malmstadt-Enke-Crouch) 2) Control of Electrical Quantities in Instrumentation (Malmstadt-Enke-Crouch) 3) Digital and Analog Data Conversions (Malmstadt-Enke-Crouch) 4) Optimization of Electronic Measurements (Malmstadt-Enke-Crouch-Horlick)

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It provides a unified treatment of the major measurement and control concepts that are universally applicable in all laboratories, and establishes a solid foundation from which to pursue subsequent

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studies in analog and digital electronics and instrumentation.

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W. A. BENJAMIN, INC. Menlo Park, California London

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Reading, Massachusetts *

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