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English Pages 973 Year 2000
RF/MICROWAVE CIRCUIT DESIGN FOR WIRELESS APPLICATIONS
RF/MICROWAVE CIRCUIT DESIGN FOR WIRELESS APPLICATIONS Ulrich L. Rohde " 4
David P. Newkirk 5#6
A WILEYINTERSCIENCE PUBLICATION
JOHN WILEY & SONS, INC. New York / Chichester / Weinheim / Brisbane / Singapore / Toronto
Designations used by companies to distinguish their products are often claimed as trademarks. In all instances where John Wiley & Sons, Inc., is aware of a claim, the product names appear in initial capital or ALL CAPITAL LETTERS. Readers, however, should contact the appropriate companies for more complete information regarding trademarks and registration. Copyright © 2000 by John Wiley & Sons, Inc. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic or mechanical, including uploading, downloading, printing, decompiling, recording or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without the prior written permission of the Publisher. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 605 Third Avenue, New York, NY 101580012, (212) 8506011, fax (212) 8506008, EMail: PERMREQ @ WILEY.COM. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold with the understanding that the publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional person should be sought. ISBN 0471224138 This title is also available in print as ISBN 0471298182. For more information about Wiley products, visit our web site at www.Wiley.com.
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CONTENTS
xi
='+ # '# $9 9 #6$ C 49 ' B## D ,2* ='+'* $ 8 D ,2* ='+'
6# 5## D ,2* ='+'2 8 # D ,22 ='+'(
86C # D ,2( ='+'= 5#$ B## D ,2= ='+'; "899 D ,( 6 Wireless Synthesizers
848
;'* $ 8 D ,(, ;' # ' # D ,(, ;''* %## D ,(, ;'' # DC >8 9# D ,=* ;''2 C #6# # I B88 D ,;2 ;''( '89'%# # ' # D ,;) ;''= . ##5 D ,); ;'2 C''#" ## D ,, ;'2'* 7 C' D ,, ;'2' "8'"8 ##7 >8 # D ,, ;'( " ## D ,,+ APPENDIXES A HBT HighFrequency Modeling and Integrated Parameter Extraction
900
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939
FOREWORD
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8 #6#9 /
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FOREWORD
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# 7 8 ### 9##/ 9 #8 /8 # #8/# 9E#F / : ## # 8 $/ #9 C998# 9 #8/# 7#/ ## # : # / 69 3 $455"" 6B # ##7# 8# 4""
PREFACE
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xvi
PREFACE
8 693 ## 8#
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9 # L 6 # # #89 ##8 # 6 / ' #4B"#/
# 6 ## #/ 8# 6# : #''# '# 6#9 8 # 4B"#98# / L5# # B 6 / 9# # 8D88# .CD".C6 >8 # . 6 6 / /
#' 989"L 0### L5# 4# # # / 9# 96 # /# L5#C37#4B"###6/# ## 7 9#9 # "L ### 68# L5# / 9# : # 6
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PREFACE
xvii
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PREFACE
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8 9
# 69 5#6 5$ 8# #4 " 9 8 # ! " 2' 44'µ>% @3 '% H; E E 9 +# H; G, % # NF $ ) DM = [133 − (8 + 10 + 10)]
8 = [105]0.4444 = 46.7 8 + 10
E/
Example 3. M % ' ' CIP4% 6' E'µ>%NFr6'% NF 6'D% #H; DM = [125 − (8 + 2 + 0)]
8 = [115]0.8 = 92 8+2
E
8 = [105]0.8 = 84 8+2
E
# H; DM = [125 − (8 + 2 + 10)]
( , ( )( G, @3' # @3 '% ' #'
L%$ # # ( NF NFr *
98
8
6 7
5
1 2 3 4
Example
HF receiver 16.0 HF receiver with 10dB pad 16.0 HF receiver with 2dB pad 16.0 Rohde & Schwarz XK 2100 40.0 shortwave transceiver XK 2100 with 10 dB of 40.0 unnecessary attenuation Satellite receiver 2.2 Wireless front end without 12.0 duplexer/filter losses Wireless front end with 3dB 12.0 duplexer/filter losses
System
Base IP3,in (dBm)
95.0
104.8 95.0
147.0
3.0
0.0 0.0
10.0
0.0 10.0 2.0 0.0
9.0
2.2 12.0
50.0
16.0 26.0 18.0 40.0
98.0
104.8 95.0
157.0
123.0 133.0 125.0 147.0
2.6
0.9 2.6
10.0
8.0 8.0 8.0 10.0
5.6
0.9 2.6
20.0
8.0 18.0 10.0 10.0
2.0
0.2 2.0
10.0
10.0 10.0 10.0 10.0
Resulting Resulting Base Base NFr Resulting IP3,in IP3,in Attenuation IP3,in (dB) (dBµV) (dBm) (dBµV) (dB) NFr (dB) NFant (dB) 123.0 123.0 123.0 147.0
Table 112 Eight dynamic measure cases compared
42.9
103.9 92.4
68.5
115.0 51.1 92.0 137.0
DMlab
42.0
103.7 90.4
63.5
105.0 46.7 84.0 127.0
DMsystem
17
SYSTEM SPECIFICATIONS AND THEIR RELATIONSHIP TO CIRCUIT DESIGN
99
! % ( + #
TripleBeat Distortion and CrossModulation. J'
" * % % # 3 * !; !; # #%
(> # % triplebeat distortion : ω ω #
ω4 # ω ω * % % $ % # M
%, % 9; ω4Aωω *+ ! #%
#, * ( # %
!; *
Figure 1107 Measured distortion components in a wideband (5–1000 MHz) amplifier. Figure 1108 shows a magnified view of the gaincompression region [15].
100
INTRODUCTION TO WIRELESS CIRCUIT DESIGN
*C7D ! # #
3/ % % % E;85
Noise Power Ratio. ( #
*+ ! %noise power ratioNPR%
( %#9;% $ # % $ % * 3 LargeSignal Effects. G, J'%
#
! * % 9; 4 % %% 3 J
#
N % *
#,#% # # #C2D
Figure 1108
Measured multiplesignal gain compression of the 5 to 1000MHz amplifier [15].
17
SYSTEM SPECIFICATIONS AND THEIR RELATIONSHIP TO CIRCUIT DESIGN
101
Figure 1109 Determining a network’s noise power ratio (NPR) involves the application of a test signal consisting of thermal noise [15]. (a) The reference measurementchannel noise power, P1, is then measured. (b) Next, a bandstop filter is placed between the noise generator and network under test to keep the test signal out of the measurement channel. Assuming sufficient filter attenuation, if the network were absolutely noiseless and linear, the ideal noise power in the measurement channel, P2, would then be zero. (c) In practice, the network’s own thermal noise and intermodulation between noise components outside the measurement channel result in an actual measurementchannel noise power (P3) greater than zero. The noise power ratio equals P1/P3.
AMtoPM Conversion. ( + AMtoAM distortion % *% *+ ? $ !; J; ! * % % 3 (
102
INTRODUCTION TO WIRELESS CIRCUIT DESIGN
Figure 1110 As a network is driven into compression, IM products at odd orders higher than 3 become significant, and phase shifts in powerdependent device capacitances cause curves and dips in the IM characteristics. The onset of these departures from IMresponse linearity occurs at generally lower input power levels for higher IM orders; their severity, and their position on the IM curves, differs among the various products of a given order and varies with network topology and tone spacing. Figures of merit based on straightline IM responses fail to usefully predict nonlinear network behavior under these conditions. This graph shows the simulated performance of a singleBJT broadband amplifier driven by two equalamplitude tones at 10 and 11 MHz.
Figure 1111 Driving a network into compression and saturation shifts the bias point(s) of its active device(s), changing their drivedependent reactances and shifting the phase of the output signal relative to its value at input levels below compression. This graph shows the simulated performance of a singleBJT broadband amplifier driven by a single tone at 10 MHz.
17
SYSTEM SPECIFICATIONS AND THEIR RELATIONSHIP TO CIRCUIT DESIGN
103
Figure 1112 Influence of differential phase error (AMtoPM conversion) on a QAM constellation.
% AMtoPM conversion%
#
Spectral Regrowth and AdjacentChannel Power Ratio. : # %% 9;H #9;
9; C/D #% adjacentchannel power ratio!1JB !1JB $ # !1JB * , #CD 34 %
#% !1JB ;G:3G( Phase Response Issues and Figures of Merit. # !; J; ' # all J; # % # %
* # Differential Group Delay. G#$ # *F # 9 #% #% * group envelope delay% #$ #" % *+ $ # 9 % *+ # % % %, %% * 3 7 ( *+ differential # # ( # #
# %
Effects of Phase Noise. !1 E % + F 3E 2 1 phase noise% $
104
INTRODUCTION TO WIRELESS CIRCUIT DESIGN
Figure 1113 Keeping adjacentchannel interference under control can involve a critical tradeoff between a wireless transmitter’s poweradded efficiency (PAE) and ACPR, as shown in this graph of the simulated behavior of the 1GHz MESFET power amplifier introduced into Figure 1101. As the amplifier is driven into compression, a peak occurs in the PAE response—in this case, at P–1dB—and the ACPR rises sharply.
Figure 1114 Closein amplitude and groupdelay responses for a 246MHz SAW filter designed for GSM applications [19]. This filter is well within its 3.0µs differential groupdelay specification across its passband (160 kHz at –3 dB); the peaks just outside the passband limits are characteristic of a network’s transitionband phase response.
17
SYSTEM SPECIFICATIONS AND THEIR RELATIONSHIP TO CIRCUIT DESIGN
105
Figure 1115 SSB phase noise. (a) An ideal signal generator would produce an absolutely pure carrier. (b) A real signal generator acts like an ideal generator driven by a noise generator, producing a noisemodulated carrier.
% 85 $ # % 3/" #%
# ! % %
, ::' E'?85 *85 M
#
% * reciprocal mixing% # + J
# #
' $ # # # * % 1M+ % $ # # % , 93 9 % + # *
9;H# " % ,
# 5 % % 9; # *
*
Figure 1121 Measured phase noise of the Rohde & Schwarz SMIQ signal generator at 1 GHz. This signal generator is optimized for all digital modulation capabilities and can be configured via appropriate programming. Above 10 kHz, the influence of the wideband loop becomes noticeable; above 200 kHz, the resonator Q takes over.
108
INTRODUCTION TO WIRELESS CIRCUIT DESIGN
Figure 1122 Reciprocal mixing occurs when incoming signals mix energy from an oscillator’s sidebands to the IF. In this example, the oscillator is tuned so that its carrier, at A′, heterodynes the desired signal, A, to the 455 kHz as intended; at the same time, the undesired signals B, C, and D mix the oscillator noise sideband energy at B′, C′, and D′, respectively, to the IF. Depending on the levels of the interfering signals and the noise sideband energy, the result may be a significant rise in the receiver noise floor.
3 4 # ( # input selectivity 3 % B=
f 2 QL √
( ,
' Q
Figure 1123 Block diagram of an analog/digital receiver showing the signal path from antenna to audio output. No AGC or other auxiliary circuits are shown. This receiver principle can be used for all types of modulation, since the demodulation is done in the DSP block.
17
SYSTEM SPECIFICATIONS AND THEIR RELATIONSHIP TO CIRCUIT DESIGN
109
Figure 1124 Principle of selectivity measurement for analog receivers.
( 93# # :! $ # E ;85 &85 # 7E;85 (# 2' : #Q LC% 93 # ±E ±E*85 9 B3 93 3 #
%93
E85 ;85 " % # 4 *85 ;85 ( %93 93
" % , # ( # 5 ( 93
34 % 5 93 9 % 93*E?4*85% $ *
%H:J $ #E?4*85
* 37 E #
(
#
# % # # # 5?QM # 5 $ : 37 9 37% F
Figure 1125
Principle of selectivity measurement for digital receivers.
110
INTRODUCTION TO WIRELESS CIRCUIT DESIGN
% # F B # F !1J # ! % % % % $# 3E
% B O: 5:;8NE ' , * 93 % #
+# #32 ( 93 , F 4' ,
Figure 1126 Dynamic selectivity versus IF bandwidth for (a) the Rohde & Schwarz ESH2 test receiver (9 kHz to 30 MHz) and (b) the Rohde & Schwarz ESV test receiver (10 MHz to 1 GHz). Reciprocal mixing widens the ESH2’s 2.4kHz response below –70 dB (–100 dBm) at (a) and the ESV’s 7.5, 12, and 120kHz responses below approximately –80 dB (–87 dBm) at (b).
17
SYSTEM SPECIFICATIONS AND THEIR RELATIONSHIP TO CIRCUIT DESIGN
111
Figure 1127 This graph shows the available dynamic range, which is determined either by the masking of the unwanted signal by phase noise or by discrete spurious signals. As far as the culprit synthesizer is concerned, it can be either the local oscillator or the effect of a strong adjacentchannel signal that takes over the function of the local oscillator.
! B3# % QM+ # # #
, all ,+B3 3 # 3/ 9
# %
+ F
Phase Errors. 9 J;# % # # % # # # * $ 3 ( % # # , % correlated #
* % 3Error Vector Magnitude. : 7%% ? + % 'GB # 34%4% 4 ! * error vector magnitudeEVM # ! +
% %$ #% % ## ? 344 G>;
112
INTRODUCTION TO WIRELESS CIRCUIT DESIGN
Figure 1128 Phase noise is critical to digitally modulated communication systems because of the modulation errors it can introduce. Intersymbol interference (ISI), accompanied by a rise in BER, results when state values become so badly errorblurred that they fall into the regions of adjacent states. This drawing depicts only the results of phase errors introduced by phase noise; in actual systems, thermal noise, AMtoPM conversion, differential group delay, propagation, and other factors may also contribute to the spreading of state amplitude and phase values.
Figure 1129 The noise sideband power of a signal that results from mixing two signals depends on whether the signals are correlated—referenced to the same system clock—or uncorrelated.
Figure 1130
Effect of gain imbalance between I and Q channels on a data signal’s phase constellation.
17
SYSTEM SPECIFICATIONS AND THEIR RELATIONSHIP TO CIRCUIT DESIGN
113
Figure 1131 Effect of quadrature offset on a data signal’s phase constellation.
Figure 1132
Effect of LOfeedthroughbased IQ offset on a data signal’s phase constellation.
Figure 1133 Representing errors in a digitally modulated signal’s inphase (I) and quadrature (Q) values relative to the ideal as a single error vector allows us to derive the resulting error vector magnitude (EVM), a sensitive indicator of transmission quality [20].
114
INTRODUCTION TO WIRELESS CIRCUIT DESIGN
18 TESTING 181 Introduction ( # % #
# ! , % & # # F * : %
' *
' ' & G4#$ Linear Diode Model. + 9/ & '9G ' #,& (,). ,7 % +.' 213 PIN Diodes
Introduction. ',7 ' & 0 ,7 2 0
136
MODELS FOR ACTIVE DEVICES
Figure 26
Junction capacitance range versus voltage.
,7C 0 & @&
" $ ,7 @ ,7 '
LargeSignal PIN Diode Model. + 9? ,7
'9K &
Figure 27
RF parameters versus localoscillator drive level.
21
DIODES
137
Table 24 Xband mixer diode data
"
' S %
' $ ' ' %!+% !4#$% Ω%
" 7+ %
4 46% 4 % ( 6% ( % ( 6% ( 6% ( % ( ( ( ( (
# # # 6 6 6 # # 6 6 " 6 6
!>! !>! !>! !9/ !9/ !9/ !K! !K! !9/ !9/ !=! !9/ !9/
!!! G!! !!! G! G! G! !! !! 9!! 9!! G! G! G!
G! K! GA KG KG KG KG KG GG K! KG KG KG
1 1 1 K K 9 / / K / G! / 9
! G ! G ! G !9! !9! !9! !9! !9! ! G ! = ! 9 ! / ! /
a
Specified for NF = 1.0 dB.
Basic Theory: Variable Resistance.  H I ( < * % * ( ( ' 2
9 =!!MC % 9A !>9:C⋅R) G0C⋅R) A!!!!!ΩC
( ,7 ) ,7 9! 9 &' !>G"Ω#
Figure 28
The linear diode model. This model is temperature dependent.
138
MODELS FOR ACTIVE DEVICES
Table 25 Linear diode model keywords
J
*
5
*
LP CB CP RS RJ CJ
,& ,& ) : :
!! !! !! !!
&
H I 
( ' ! ! &ΩC ,7 % !!! ΩC % 
H I ! @
, !
Notes on the PIN Diode Model ',7 2+ ,7
' 2"Q 2( 2 2 + 9 ! (BG?K 2(B9! K2"QBKG!!J B! 9>9 J9B !7B9!>> 9 ' '' ,7 F 1 A * & M M
Figure 29
The largesignal PIN diode model. This model is temperature dependent.
21
DIODES
139
Table 26 PIN diode model keywords
J
*
5
BV FC CJ0 VJ M GC1 GC2 GC3 TT K1 K2 RMAX KF AF FCP AREA
! ( . " & " & ) L : M M 9 M A ' M M " ,7 + & + & + &
RS CP CB LP
"# ! ( ,7 % ,& ,&
IS N IBV
* !.D = ! !.D !
C C9 CA
∞ !G !! ! !G !! !! !! !! !! ! !! !! ! ! !
!! !! !! !!
= ' ' 4) 4)9 4)A G ',7 :0 H(,).) T 2 ,7* I 07 ??9 K + ( "($1*2 $& ! 7T & & + 9 /
+ 9 ? ,7 G!Ω + 99! ,7 Q=
1 RsRvC 2π + √
9A?%
Figure 216
Simplified equivalent series circuit.
146
MODELS FOR ACTIVE DEVICES
Figure 217
Reverse series resistance Rv.
' &   2+  9GDA!
M#+ '
 π &
Example: A PIN Diode π Network for TV Tuners. ' '* !GA ,7π & 'M  ,7
π &+ 99>% 'M
=!D !!!"#$  ' ''* !GA ' "Q"5"2'74(3+7*M*56*3*.(
2 + B9GR) : (
Figure 227
A! G! 9G DGGW 9G
Internal circuitry of the TDA1053.
M R) R)
152
MODELS FOR ACTIVE DEVICES
Figure 228
Test and application circuit.
"Q"5"2'74(3+'#.π7.'032J
+ 99/
!!
R)
)#2)'.2(')(3+7*M*56*3*.('B9GR)
+ BG! + = GM * < = !B !!"#$ = !µB !!"#$
Figure 229
P 9 PG!!
M
G =
Ω &Ω
Attenuation and reflection attenuation versus control voltage.
21
Figure 230
DIODES
153
Attenuation versus frequency.
)#2)'.2(')(7'#.'.(')2)5'+452.99/%'B9GR)
M N =!D !!!"#$ < B GM D9M% BGM=DGM% 2 =!D !!!"#$
M
=GOAK% GP9% 9!O K%
' ,7 G!= & ' + 99/ ' + 99? + 9A! 214 Tuning Diodes
Introduction.  1&
1 3 ) D ) @ 3 #+ # 7
154
MODELS FOR ACTIVE DEVICES
Figure 231 (a) Basic PIN structure; (b) cross section of a reversebiased pn junction; and (c) density distribution of free charge carriers.
4 3 ' %
+
!K + %=%% &  & $ ' H I ' % ' $ % ' @ & $ D=M 7 3
@ + & & @
$ ) ! =
168
MODELS FOR ACTIVE DEVICES
, $ ( ,'* ,'* ( ,'* 3 % 6 ,'*  & 6 !! N ,'*
Distortion Products. 

+
CrossModulation. )
2 .9=9% C(V) =
! !
C0 (1 + V / ϕ)
n
9G9%
B B B!W B B
' S1 = v1 sin ω1t
9GA%
S2 = v2(1 + m cos ωmt)sin ω2t
9G=%
γ Output signal ~ v1 sin ω1t + γ sin (ω1 ± ωm)t
9GG%
21
DIODES
169
2
γ=
n(n + 1)mv2
4(V0 + ϕ)2
9GK%
+
%
' N A!N
+ 9=A +
Figure 243 Interfering signal (30% amplitude modulated) level versus bias for 1% crossmodulation for abruptjunction and hyperabruptjunction diodes.
170
MODELS FOR ACTIVE DEVICES
+ + 9=A
Intermodulation.  sin(2ω1t − ω2t) and sin(ω1t − 2ω2t)
9G/%
v(cos ω1t + cos ω2t)
9G?%
+ Intermodulation =
n(n + 1)v2 8(V0 + ϕ)2
9K!%
Crossmodulation = (2m) × Intermodulation
9K %
Harmonic Distortion. # *
9 v2 =
n v2 3(V0 + φ) 1
9K9%
+ 9== !N
Reduction of Distortion Products.   && + 9=G
( < For an Abrupt pn Junction (Alloyed Diodes) εε 1 1 V ) + (V + √ q C C
W=2 2
r 0
p
n
R
D
9KA%
21
Figure 244
DIODES
171
Signal level versus reverse voltage for 10% harmonic distortion.
For Linear pn Junctions (SingleDiffused Diodes, such as BA110BA112) εε (V + V ) √ aq
W = 3 12
r 0
R
D
9K=%
ε! //G× !D = ε ≈ 9 '
Figure 245 Backtoback diodes. CP is a fixed parallel capacitance, RB is a bias decoupling resistor, and the capacitor marked ∞ is a lowimpedance bypass.
172
MODELS FOR ACTIVE DEVICES
C=
εrε0S W
9KG%
$ C=
K (VR + VD)n
9KK%
,' C !G !AA %!>G + 9=K C 2 .9KK%< C = C0
m
A A + VR
9K>%
! =! ' & .9KK% . 9KA% 9K>%
0 1 1 C . 9KK% + 9=> '
Figure 246 Capacitance/voltage characteristic for (a) an alloyed capacitance diode, n = 0.5; (b) a diffused capacitance diode, n = 0.33; and (c) a widerange tuner diode (BB141).
21
Figure 247
Figure 248
DIODES
Capacitance/voltage characteristic of the BA110 diode.
Basic current/voltage and capacitance/voltage characteristics.
173
174
MODELS FOR ACTIVE DEVICES
Figure 249 Equivalent circuits for capacitance diodes: (a) complete circuit, (b) simplified circuit, and (c) further simplification for low frequencies.
Cmax Ctot(VRmin) = Cmin Ctot(VRmax)
9K/%
& 3 F &+ 9=/ C
' ^ ^ Vmin > V − VF and Vmax < V(BR)R − V
9K?%
'M ' C & ( 'M
Electrical Properties of Tuning Diodes.  = =9 Equivalent Circuit. ( F + 9=? ' + 9=?%
$
.$ =! ! + 9=?1  + 9=? Capacitance. + 9G! C = =9 &
21
DIODES
175
'
< ) = M =AM =9GM
) )
= +%
= +%
=9 +%
K 9D9AG
? A 99GD9KG
> 9 9DA
Useful capacitance ratio =
Ctot(3 V) Ctot(25 V)
= 4 to 6
3 B9GM ' + 9G 9GA+ 9G % $ + 9G9 $ + 9GA ' + 9G9 9GA U.9KK%V' 9MCR) '  )
Figure 250
Capacitance/voltage characteristic of diodes BB141 and BB142.
176
MODELS FOR ACTIVE DEVICES
Figure 251
Figure 252
Slope (normalized) as a function of the reverse voltage.
Capacitance (normalized) as a function of the junction temperature.
21
Figure 253
177
DIODES
Temperature coefficient of capacitance as a function of the reverse voltage.
Series Resistance, + " 3% ( 5
0 + 9=? 3 % < Q=
1 ωCtotrS + 1 / ωCtotR
9>!%
+ 9G= $ % 3 0 !D !!!"#$ + 9=?% .9>!% < Q=
1 ωCtotrS
9> %
 + 9GG3 =
=9'
B=>!"#$ B?+
G%
2πLS
+ = =9+ 9G> $ % ' < ( G .$ ( =9GM ! ) 3B =AM 3
=
=9
9G 9 9=
9G / K
# 4#$ 4#$
* 3B
Leakage Current, Breakdown Voltage. ' &  & = =9 & < Reverse breakdown voltage at IR = 100 µA: V(BR)R > 30 V ' A!M '&
/%
2
ω2LCS RC = RB 2 ω L(CS + CP) − 1
9>?%
' ) + 9K!
21
Figure 261
DIODES
183
Parallelresonant circuit with two tuner diodes.
C2S > CS(Ctot + CP) + CtotCP
9/!%
' $ 1' + 9G? + 9K!
 + 9K
'
H" * )
MI%& ' ) 4 RC = 4RB
9/ %
Capacitances Connected in Parallel or Series with the Tuner Diode. + 9G? 9K! $ # &
$ C∗ = Ctot
1 1 + Ctot / CS
9/9%
' 3 & 3 Ctot Q∗ = Q 1 + CS
9/A%
184
MODELS FOR ACTIVE DEVICES
' C∗max C∗min
=
Cmax 1 + Cmin / CS Cmin 1 + Cmax / CS
9/=%
3 ^∗ ^ v =v
1 1 + Ctot / C
9/G%
' & .9/A% ' 1 + 9G?9K 1 $
CP C∗ = Ctot 1 + Ctot
9/K%
'3 3
Figure 262
Diagram for determining the capacitance ratio and minimum capacitance.
21
CP Q∗ = Q 1 + Ctot
DIODES
185
9/>%
' < C∗max C∗min
=
Cmax 1 + CP / Cmax
9//%
Cmin 1 + CP / Cmax

' + 9G? '
'5774274.
Cmax fmax = fmin
1+ 1+
CP (1 + Cmax/ CS) Cmax
9/?%
CP (Cmax / Cmin + Cmax/ CS)
  .9/?% < fmax = fmin
1 + Cmax / CP 1 + Cmin / CP
9/?%
+ + 9K9 0
1 1
0 $
.9/=% ( 2 " $ & &
C2+ ' & $ & ' $
'2)J74
186
MODELS FOR ACTIVE DEVICES
df 1 dC0 1 d(L − L0) 1 dL0 n dVR =− − − + f 2 C0 2 2 L0 2 VR + VD L
9?!%
' !!C! !.!C.! !.D.!%C. ! (+)
Modulating the Diode Capacitance by the Applied ac Voltage.  ' * & ' %  i = ^i cos ωt
9? %
' ^i(1 − n) 1 / (1−n) sin ωt v = (VR + VD) 1 + − 1 ωCtotVR
9?9%
& ' + 9KA# + 9K )3",.7('74'.",.2'52.*.,.7*.7).
Figure 263
Capacitance increase as a function of the ac voltage drop across the tuner diode.
21
Figure 264
DIODES
187
Temperaturecompensation circuit with diode.
  1 ' @ 9MCR)'
+ 9K=( D9MCR) V = V0 + VD − VF 
& & '
+ 9KG
Dynamic Stability. ' 2+ n
f = f0
Figure 265
VR + VD VR0 + VD
Temperaturecompensation circuit with transistor.
9?A%
188
MODELS FOR ACTIVE DEVICES
' ! !(
&  &
% ( & & $ +
+ %
21
Figure 270
DIODES
193
Differential forward resistance as a function of forward current.
S U '
& ' = %
Diode Switch Data. ' 9=A 9==
! !!!"#$'
' & ' $ '9=A M#+ 9== 5#+ ('9 Resonant Circuits Incorporating Diode Switches. + 9> ( M#+   ) , '∞ .9
194
MODELS FOR ACTIVE DEVICES
Table 211 BA243/244 specifications
Maximum Ratings 2 + B9GR) : (
9! !! G! DGGW G!
M R) R)
P P !!
M
!>P % !=P!G%
Ω Ω
G
NC
Characteristics atB9GR) + B !! 6& = GM * BG!D !!! "#$ = !
BA243 BA244
2 ∆ !! ∆ +9−=! ) = GMB "#$
2 =>−9!MB !!"#$
∆ !!
(
.$
AP9%
+ NCM
∆ 9G
#
Figure 271 (a) Diode switch as bandswitch, shorting a partial inductance; (b) equivalent circuit with blocked diode switch; (c) equivalent circuit with conducting diode switch.
21
Figure 272
DIODES
195
Capacitance as a function of the reverse voltage.
$ 2+ ' = GM + + 9> ' ′ ' ′ + 9>9 &
! !GΩ+ 9>!%' + 9> ) C A' + 9> . .
.9 9 + 9>A % + 9>A %  & 7 .9 # '  2+  H I . &
21
Figure 274
DIODES
197
Schematic of a VHF television tuner with electronic band selection.
Use of the Diode Switch in a Television Receiver. + 9>= =/DK9"#$%C  >GD99="#$%'M ' 9=A .
2+ 
9 * ADK ' $ !%
'
2+& ' )2'
&
M#+C5#+ (
M#+C5#+ λC9 λC= 5#+ 'M#+ 5#+ " 'M + ' 2+
198
MODELS FOR ACTIVE DEVICES
22 BIPOLAR TRANSISTORS 221 Transistor Structure Types All current RF silicon transistors are of the bipolar npn planar epitaxial type. Briefly, the significance of each of these terms is as follows.
Bipolar. In its broadest sense, it is the basic structure shown schematically in Figure 275, that is, the familiar threesemiconductorregion structure. Bipolar specifically means that the charge carriers of both negative (electron) and positive (hole) polarities are involved in the transistor action. In way of contrast, unipolar types include the junctiongate and insulatedgate fieldeffect transistors, which are basically one or twosemiconductorregion structures in which carriers of a single polarity dominate. npn. This abbreviation is for negative–positive–negative and identifies the regions of the structure as to polarity of the dominant or majority carrier in each region. The other polarity type is pnp. (See Figure 275.) Silicon. Silicon (Si) is one of two elements from the fourth column of the periodic table that are in widespread use for transistor fabrication [the other is germanium (Ge)]. Other materials used include the compound gallium arsenide (GaAs). Although silicon is in predominant use because it results in the most favorable compromise among highfrequency, hightemperature, highreliability, and easeofuse attributes of the usable semiconductor material, silicon–germanium (SiGe) technology is increasingly important because it affords highfrequency performance unachievable with silicon alone. Planar. The term planar denotes that both emitter–base and base–collector junctions of the transistor intersect the device surface in a common plane (hence, a better term might be coplanar). However, the real significance of the socalled planar structure is that the technique of diffusing dopants through an oxide mask, used in fabricating such a structure, results in junctions being formed beneath a protective oxide layer. These protected junctions are less prone to the surface problems sometimes associated with other types of structures, such as the mesa.
Figure 275
Transistor structure schematic.
22
Figure 276
BIPOLAR TRANSISTORS
199
Bipolar transistor sign convention.
Epitaxial. This term, as it is commonly used, is actually a shortening of the term epitaxialcollector. That is, the collector region of the transistor is formed by the epitaxial technique, rather than by diffusion, which is commonly used to form the base and emitter regions. The epitaxial layer is formed by condensing a singlecrystal film of semiconductor material on a wafer or substrate that is usually of the same material. Thus, an epitaxial (collector) transistor is one in which the collector region is formed on a lowresistivity substrate. Subsequently, the base and emitter regions are diffused into the “epi” layer. The epitaxial technique lends itself to precise tailoring of collectorregion thickness and resistivity with consequent improved device performance and uniformity. 222 LargeSignal Behavior of Bipolar Transistors* In this section, the largesignal or dc behavior of bipolar transistors is considered. Largesignal models are developed for the calculation of total currents and voltages in transistor circuits, and such effects as breakdownvoltage limitations, which are usually not included in models, are also considered. Secondorder effects, such as currentgain variation with collector current and Early voltage, can be important in many circuits and are treated in detail. The sign conventions used for bipolar transistor currents and voltages are shown in Figure 276. All bias currents for both npn and pnp transistors are assumed positive going into the device.
Electrical and Performance Characteristics and Specifications. E l e c t r i c a l characteristics may be described as uniquely defined, measurable electrical transistor properties that are not a function of the measuring circuit or apparatus (except insofar as standard terminations and measurement accuracy are concerned). Performance or operating characteristics are also electrical properties but they are, in general, not unique because their values depend on the measuring circuit (in particular, source and load impedance, which may be arbitrary). As might be expected, the terms are often used somewhat loosely (and sometimes *
Portions of this section, Sections 223 through 225, and Sections 233 through 236 are based on Paul R. Gray and Robert G. Meyer, Analysis and Design of Analog Integrated Circuits, 3rd ed., ©1993 by John Wiley & Sons, Inc. Reprinted by permission of John Wiley & Sons, Inc.
200
MODELS FOR ACTIVE DEVICES
interchangeably), especially in cases where only subtle differences are involved. The terms are generally used on transistor datasheets to segregate (for emphasis) under performance or operating characteristics those properties most directly applicable to the primary intended application. Performance (Operating) Characteristics. Of the numerous performance characteristics that can be specified for highfrequency transistors, perhaps the most fundamental and pertinent characteristics are:
• Power gain and noise figure, for smallsignal applications • Power gain, power output, and efficiency, for largesignal applications All of these characteristics are, of course, functions of frequency, bias temperature, and so on, and to completely characterize a transistor over its full frequency, bias, and temperature ranges would be prohibitively costly. Consequently, characterization data are given only for restricted ranges of these variables. These data should portray sufficiently the capabilities of a particular device for its intended applications. In the case of maximum ratings, some applications may require additional characterization by the user or through applications assistance from the manufacturer. POWER GAIN
Gmax. Of the various definitions for the measurement of power flow in an active twoport device, such as a transistor, two are unique enough to allow specification without recourse to specifying the complete measuring circuit in detail. One of these definitions is termed maximum available gain (Gmax) and is the power gain obtained when the input and output ports are simultaneously conjugately matched to source and load impedances, respectively. Implicit in this definition is the assumption that the twoport is unconditionally stable; that is, that no combination of input/output tuning can result in increasing gain to the point of oscillation. S212. The other unique power gain is the gain realized when the transistor is inserted between a source and load with identical impedances (in practice, usually 50 + j0 Ω). This particular insertion of transducer gain happens to coincide with the usual definition of the twoport forward scattering parameter, S21. More precisely, it is equal to the magnitude squared of this parameter and is therefore often identified by the symbol S212. For wideband applications, S212 is important because wideband terminations “not too different from 50 Ω” are more easily realized than are wideband transforming networks that provide the matching required for Gmax. A common measure of the noise generated by an active twoport device— noise that sets a lower limit on amplifier sensitivity—is noise factor (F). This is defined as NOISE FIGURE.
F=
Input signalwtownoise ratio
(2110)
Output signalwtownoise ratio
or more generally as F=
Total output noise power Output power due to source resistance
(2111)
22
BIPOLAR TRANSISTORS
201
At high frequencies, spot noise factor or noise factor for a small fractional bandwidth (say, 1%) is used and is usually expressed as noise figure (NF), in decibels: NF = 10 log F
(2112)
As already discussed, noise figure is a function of source impedance (as well as functions of frequency, bias, etc.) and hence, there is an infinity of noise figures associated with a given device corresponding to the infinity of possible impedances that may be presented to the device input. The only unique one, in the sense that it does not involve arbitrary source impedances, is NFmin, the minimum noise figure obtained (at a given bias and frequency) when the input is tuned to optimize this parameter. This is the noise figure value commonly given on datasheets. In practical amplifiers that involve more than one stage, overall noise factor (FO) is given by
FO = F1 + where
Fn − 1 F2 − 1 +⋅⋅⋅+ G(n−1) G1
(2113)
n = number of stages Gn = gain of the nth stage Fn = noise factor of the nth stage
This expression emphasizes the important fact that for lownoise amplifiers, the first stage must be designed for the lowest noise figure and highest gain possible. [Note that the noise contribution of the second stage is divided (reduced) by the gain of the first stage.] Since the optimum source impedance and bias currents for optimum gain and noise figure do not often coincide, very careful circuit design is required to minimize overall noise figure. For more accuracy, we recommend the noise correlation approach. This characteristic is important for both amplifier and oscillator transistors. In both cases, it is extremely circuit sensitive. For amplifiers, maximum useful output is often limited to that power output level at which gain has compressed 1 dB, an indicator of the upper limit of the device’s linearity range. For oscillators, it is merely a quantitative measure of RF power for given dc input power.
POWER OUTPUT.
EFFICIENCY. In the most general sense, this characteristic expresses as a percentage the ratio of RF power output to the total circuit input power, both dc and RF. That expression is efficiency, η, defined as
η=
PO
Pi + Pdc
× 100
(2114)
where PO = RF output power Pi = RF input power Pdc = total dc power input Since for oscillator transistors there is no RF power input, and for amplifier transistors the maximum input RF power is calculable from the power gain and power output specifications,
202
MODELS FOR ACTIVE DEVICES
the inclusion of Pi in efficiency is redundant. Moreover, since the major portion of the dc power is dissipated by the transistor collector, a more restricted definition of efficiency is pertinent. This parameter, termed collector efficiency (ηC), is given by ηC =
PO × 100 PCC
(2115)
where PCC = VCC × ICC VCC = collector supply voltage ICC = collector supply current
Electrical Characteristics. Electrical characteristics may be conveniently classified into two main types, dc and ac. The importance of dc characteristics of highfrequency transistors lies primarily in biasing and reliability considerations. However, certain dc characteristics are also directly related to highfrequency performance. For example, highfrequency noise figure is affected by dc current gain. The dc characteristics discussed here are those usually found on highfrequency transistor datasheets. V(BR)CBO, ICBO. These two parameters serve to characterize the reversebiased collector–base pn junction and are defined as follows (with the aid of Figure 277a). The collector–base breakdown voltage, V(BR)CBO, identifies the voltage at which collector current tends to increase without limit, usually due to the high electric field developed across the junction. This voltage sets a limit on the maximum transistor operating voltage and, as mentioned before under maximum ratings, usually is the basis for the collector–base maximum voltage rating. V(BR)CBO should be specified at a value of IC = IC1 in the figure, which is within the avalanche (or high slope) region of the device’s reverse characteristic. Typical values of IC1 are in the 1–10µA region for highfrequency transistors. To further define the quality of the reverse I–V characteristic, a specification is usually placed on the collector cutoff current, ICBO, which is measured at some value of collector– base voltage less than V(BR)CBO. For a goodquality silicon junction (“sharp” instead of soft; see Figure 277a), ICBO is in the nanoampere range. V(BR)EBO, IEBO. These two parameters characterize the reversebiased emitter–base pn junction in an analogous manner to the collector–base junction parameters V(BR)CBO and ICBO, given above, and are shown in Figure 277b. No further discussion of these parameters will be given here. V(BR)CEO, ICEO. The collector–emitter breakdown voltage and cutoff current are somewhat more complex in nature than the collector–base and emitter–base parameters. In the latter two, only a single pn diode is involved. In the collector–emitter case, two diodes are involved. Moreover, each is influenced by the other through transistor action, since the reverse current of the collector–base diode flows through the emitter–base junction as forward current. Thus, the collector–base reverse current is amplified by the dc current gain of the transistor, resulting in: dc CHARACTERISTICS.
• ICEO being greater than ICBO (for a given voltage) • Typically, the familiar negativeresistance region in the I–V characteristic as shown in Figure 277c.
22
Figure 277
BIPOLAR TRANSISTORS
203
Transistor reverse I –V characteristics.
Consequently, V(BR)CEO is typically specified at collector currents one to three orders of magnitude higher than in the case of V(BR)CBO and V(BR)EBO to establish the minimum value of this characteristic. hfe. This parameter is simply the dc commonemitter current gain; that is, the ratio of collector current to base current at some specified collector voltage and current. ac CHARACTERISTICS. Of the numerous ac characteristics defined for transistors, only relatively few are commonly used in characterizing highfrequency transistors. Some of the more pertinent parameters are briefly covered here. S Parameters. By far the most useful and conveniently measured set of twoport parameters for transistor highfrequency (roughly 100 MHz and above) characterization is
204
MODELS FOR ACTIVE DEVICES
the Sparameter or scatteringmatrix set. These parameters completely and uniquely define the smallsignal gain and input/output immittance properties of any linear “black box.” (By definition, a transistor or any active device is linear under smallsignal conditions.) However, these parameters reveal nothing (except possibly indirectly and approximately) about largesignal or noise behavior. Simply interpreted (more general definitions and other interpretations abound in the technical literature), the S parameters are merely insertion gains, forward and reverse, and reflection coefficients, input and output, with driven and nondriven ports both terminated in equal impedances, usually 50 + j0 Ω. Such an interpretation tends to make S parameters very attractive, once some familiarity is gained, at high (especially microwave) frequencies, since the power flow or gain and reflectioncoefficient concepts are more intuitively meaningful than voltage and current conceptual schemes. It should also be mentioned that Sparameters can be converted through straightforward matrix transformations to other twoport parameter sets, such as h, y, and zparameters. Proceeding with more specific definitions, the Sparameters are defined analytically by b1 = S11a1 + S12a2
(2116)
b2 = S21a1 + S22a2
(2117)
b1 S11 S12 a1 b = S S a 2 21 22 2
(2118)
or, in matrix form,
where, referring to Figure 278 a1 = (incoming power at Port 1)1/2 b1 = (outgoing power at Port 1)1/2 a2 = (incoming power at Port 2)1/2 b2 = (outgoing power at Port 2)1/2 E1, E2 = electrical stimuli at Port 1, Port 2 From the figure and defining linear equations, for E2 = 0, then a2 = 0, and (skipping through numerous rigorous steps)
S11 =
Figure 278
b1 a1
Twoport Sparameter definition.
22
BIPOLAR TRANSISTORS
205
⁄2
1
Outgoing input power = incoming input power =
Reflected voltage Incident voltage
= Input reflection coefficient S21 =
(2119)
b2 a1 ⁄2
1
Outgoing output power = incoming input power
⁄2
1
Output power = Avai input power lable
= (Forward transducer gain) ⁄2 1
(2120)
or, more precisely in the case of S21: Forward transducer gain = GTF = S212
(2121)
Zi = Zo
(2122)
Similarly, at Port 2 for E1 = 0, then a1 = 0, and S22 =
b2 = Output reflection coefficient a2
(2123)
S12 =
b1 1 = (Reverse transducer gain) ⁄2 a2
(2124)
GTR = S122
(2125)
Since many measurement systems display Sparameter magnitudes in decibels, the following relationships are particularly useful: S11dB = 10logS112 = 20 logS11
(2126)
S22dB = 20 logS22
(2127)
S21dB = 10 logS212
206
MODELS FOR ACTIVE DEVICES
= 20 logS21 = 10 logGTF = GTFdB
(2128)
S12dB = 10 logS122 = 20 logS12 = 10 logGTR = GTRdB
(2129)
Figure 279 shows an example of the use of S parameters in transistor stage design. Transition Frequency. One of the better known, but perhaps least understood, figures of merit for highfrequency transistors is the socalled transition frequency, fT. Part of the misunderstanding that appears to exist is due to the use of the misleading (but common, for
Figure 279 Key parameters in applying a BJT in lownoise frontend, highgain, and linearpower stages. (a) The BJT characteristics that lead to optimum dc bias for a lownoise front end; (b) parameters characterizing device performance; (c) Γopt for the first stage, and S11 and S22 for the output stage as simulated by CAD software. The example is based on the Siemens BJTs BFP420 (lownoise stage), BFP450 (highgain stage), and BFG235 (output stage). Circuits to optimize stage noise, gain, and I/O matching are shown in (d). (Presentation based on Figure 14 in Charles A. Liechti, “Microwave FieldEffect Transistors—1976,” IEEE Trans. Microwave Theory Tech., vol. MTT24, pp. 279–300, June 1976.)
22
BIPOLAR TRANSISTORS
207
historical reasons) term shortcircuit gain–bandwidth product for this parameter. By definition, f T is that characteristic frequency described by the equation f T = hfe × fmeas
(2130)
where hfe is the magnitude of the smallsignal commonemitter shortcircuit current gain, and fmeas is the frequency of measurement, chosen such that 2 ≤ hfe ≤
hfe0
(2131)
2
where hfe0 is the lowfrequency value of hfe. To varying degrees of approximation, depending on the transistor type, f T is the frequency at which hfe approximates unity. It is not, in general, the frequency at which hfe is precisely equal to unity. To clarify these points further, consider the plot of hfe against frequency sketched in Figure 280. At low frequencies, f < < fB, hfe is constant and equal to hfe0. At fB, hfe has decreased to 0.707 hfe0; that is, fB is the 3dB cutoff frequency for commonemitter shortcircuit current gain, hfe. For frequencies such that 2fB < f < f T
(2132)
hfe varies inversely proportional to frequency. That is, the f T defining relationship holds: hfe × fmeas = constant = f T
(2133)
At frequencies approaching f T, other parameters, especially package parasitics, can cause hfe to depart significantly from this 1/f variation. Therefore, the frequency, f1, at which hfe actually equals unity can be somewhat different from f T. Applying these frequencygain characteristics to the commonemitter wideband, lowpass amplifiers gives rise to the terminology of f T being a “gain–bandwidth product.” However,
Figure 280
hfe frequency characteristics.
208
MODELS FOR ACTIVE DEVICES
this is an optimistic approximation at best, since the product of lowfrequency circuit gain and the 3dB cutoff frequency is reduced from f T by an amount that depends on circuit impedances. The real significance of f T lies in the fact that it is a measure of certain internal transistor parameters that do, in fact, affect highfrequency performance: for example, gain (though not in the convenient quantitative manner implied by the term “gain–bandwidth product”). In particular, good highfrequency noise performance requires that f T be high. Thus, f T is included on transistor datasheets primarily as a figure of merit, not as a parameter to be used directly in design. Collector–Base Time Constant, rgbCc. This is an internal device parameter that relates only indirectly to highfrequency performance. It is primarily a measure of internal feedback within the transistor. It also relates to transistor highfrequency impedance. As the name says (in symbols), it is a measure of transistor base resistance and collector capacitance in combination; however, except for certain lowfrequency transistors, it cannot be considered the simple twoelement lumped RC time constant implied by the terminology. (In highfrequency transistors, base resistance and collector impedance must be considered to be distributed when considered in detail). As a figure of merit, it is included on transistor datasheets to indicate how well base resistance and collector impedance have been minimized. It also allows the estimation of certain gain properties of the transistor (see the fmax parameter, which we’ll describe shortly). Collector–Base Capacitance, Ccb. This parameter is simply the total collector–base pn junction capacitance measured at a low frequency (typically, 1 MHz), where it can be considered a single lumped element. For highfrequency transistors it is, of course, desirable that Ccb be small from bandwidth and stability considerations as well as from gain considerations alone. Maximum Frequency of Oscillation, fmax. This is another figureofmerit parameter, as opposed to measurable parameters directly usable in the application of transistors. Its importance stems from the following approximate relationships (which will not be derived here): 1/2
fT fmax ≈ g 8πrbCC
2
fmax Gmax ≈ f oper
(2134)
(2135)
These expressions illustrate in a quantitative way the importance and the interrelationship between high fT and low rgbCC insofar as highfrequency gain is concerned. However, since they are approximations and since their derivation involves several assumptions that are not always valid, they must be interpreted with caution. For example, the expression for Gmax is obviously not applicable at low frequencies, since as f → 0, Gmax → ∞, according to this expression. As a rule of thumb, the Gmax expression is a reasonable approximation for frequencies such that 5>
fmax >1 foper
(2136)
22
BIPOLAR TRANSISTORS
209
For accurate analysis of transistor gain and stability, a complete set of twoport parameters must be employed in exact expressions, such as those from which the approximations shown above were derived. Datasheet Transistor Specifications. The following is a reprint of a Siemens microwave transistor datasheet. This 25GHz fT transistor will soon be replaced by a 40GHz family, based on a silicon–germanium design. Key parameters describing the transistor are:
• The dc parameters, such as maximum current and voltage and dissipation • Noise figure as a function of generator impedance, bias point, and frequency • Frequencydependent behavior, typically expressed in S parameters, and also as a function of bias point and frequency • Largesignal performance to be calculated based on a nonlinear model, such as the Gummel–Poon The transistor description typically gives details about packaging, as the Gummel–Poon model is intrinsic (without parasitics). Not only does the package determine the parasitics, it also affects the device’s ability to transfer heat to its heat sink. The following figures, reproduced with permission from the datasheet for the BFP420 transistor by Siemens (now Infineon Technologies), are a typical representation of the dcIC curves, S parameters, and noise parameters of a normal, packaged microwave transistor. Besides its dc parameters and capacitance, there are other critical parameters. A BJT’s noise figure is a strong function of its dc current gain, and one can determine a 3dB cutoff frequency referred to as fT, which shows the gain rolloff as a function of collector current and frequency. Another important measure or figure of merit is fmax, the maximum frequency of oscillation: fmax =
Y21
(2137)
16πRbbCbeCbc
Figure 281 shows a photograph of the die for the BFP420. Since the intercept point is an important figure of merit, Figure 282 shows intercept point as a function of bias point for the BFR93AW BJT. We wish more manufacturers would supply this information. 223 LargeSignal Transistors in the ForwardActive Region We saw in the diode case that its description is physicsbased and it is, therefore, logical to apply the same modeling for the transistors. The first complete modeling for transistors was described in the Gummel–Poon model, but many engineers use the somewhat more simpler Ebers–Moll model. By combining two diodes, the parasitic elements, and the base separating resistor, we can show the “intrinsic” nonlinear model for the bipolar transistor. Many equations that have been published contain some approximations, but for exact nonlinear analysis, we have to resort to the somewhat more complex or complete equations as shown in Appendix A for the bipolar model. Recently, some other models have been proposed by researchers, such as the MEXTRAM models (Philips), but the trouble with these models is that while they may give quite good results for RF applications, it is virtually impossible to obtain parameters for them. So far the only industrystandard model is the Gummel–Poon, and to the authors’ knowledge there
210
MODELS FOR ACTIVE DEVICES
22
BIPOLAR TRANSISTORS
211
212
MODELS FOR ACTIVE DEVICES
22
BIPOLAR TRANSISTORS
213
214
MODELS FOR ACTIVE DEVICES
22
BIPOLAR TRANSISTORS
215
216
MODELS FOR ACTIVE DEVICES
22
BIPOLAR TRANSISTORS
217
218
MODELS FOR ACTIVE DEVICES
Figure 281 Photograph of the BFP420 die (310 × 290 µm). The bonding pad for the base is at the upper right; for the collector at the upper left. The large, lower pad connects to the emitter.
Figure 282
IP3,out versus IC at five values of VCE for the BRF93AW BJT.
22
BIPOLAR TRANSISTORS
219
are no accepted or affordable parameter extractor programs available, not even to consider the cost of hardware for such extractions. HewlettPackard recently published a system with a hardware cost in the vicinity of $1 million. A typical npn planar bipolar transistor structure is shown in Figure 283a, where collector, base, and emitter are labeled C, B, and E, respectively. The impurity doping density in the base and the emitter of such a transistor is not constant but varies with distance from the top surface. However, many of the characteristics of such a device can be predicted by analyzing
Figure 283 (a) Cross section of a typical npn planar bipolar transistor structure; (b) idealized transistor structure; (c) carrier concentrations along the cross section AA′ of the transistor in (b). Uniform doping densities are assumed. (Not to scale)
220
MODELS FOR ACTIVE DEVICES
the idealized transistor structure shown in Figure 283b. In this structure, the base and emitter doping densities are assumed constant, and this is sometimes called a “uniformbase” transistor. Where possible in the following analyses, the equations for the uniformbase analysis are expressed in a form that applies also to nonuniformbase transistors. A cross section AA′ is taken through the device of Figure 283b and carrier concentrations along this section are plotted in Figure 283c. Hole concentrations are denoted by p and electron concentrations by n with subscripts p or n representing ptype or ntype regions. The ntype emitter and collector regions are distinguished by subscripts E and C, respectively. The carrier concentrations shown in Figure 283c apply to a device in the forwardactive region. That is, the base–emitter junction is forwardbiased and the base–collector junction is reversebiased. The minoritycarrier concentrations in the base at the edges of the depletion regions can be calculated from a Boltzmann approximation to the Fermi–Dirac distribution function to give [2] np(0) = npo exp np(WB) = npo exp
VBE
VT
VBC u0 VT
(2138)
(2139)
where WB is the width of the base from the base–emitter junction depletion layer edge of the base–collector depletion layer edge and npo is the equilibrium concentration of electrons in the base. Note that VBC is negative for an npn transistor in the forwardactive region and thus np(WB) is very small. Lowlevel injection conditions are assumed in the derivation of Eqs. (2138) and (2139). This means that the minoritycarrier concentrations are always assumed much smaller than the majoritycarrier concentrations. If recombination of holes and electrons in the base is small, it can be shown that the minoritycarrier concentration np(x) in the base varies linearly with distance [3]. Thus, a straight line can be drawn joining the concentrations at x = 0 and x = WB in Figure 283c. For charge neutrality in the base, it is necessary that NA + np(x) = pp(x)
(2140)
pp(x) − np(x) = NA
(2141)
and thus
where pp(x) is the hole concentration in the base and NA is the base doping density that is assumed constant. Equation (2141) indicates that the hole and electron concentrations are separated by a constant amount and thus pp(x) also varies linearly with distance. Collector current is produced by minoritycarrier electrons in the base diffusing in the direction of the concentration gradient and being swept across the collector–base depletion region by the field existing there. The diffusion current density due to electrons in the base is Jn = qDn
dnp(x) dx
(2142)
22
BIPOLAR TRANSISTORS
221
where Dn is the diffusion constant for electrons. From Figure 283c, Jn = −qDn
np(0) WB
(2143)
If IC is the collector current and is taken as positive flowing into the collector, it follows from Eq. (2143) that IC = qA Dn
np(0) WB
(2144)
where A is the crosssectional area of the emitter. Substitution of Eq. (2138) into Eq. (2144) gives IC =
VBE qADnnpo exp VT WB
(2145)
VBE VT
(2146)
qADnnpo WB
(2147)
= IS exp where IS =
and IS is a constant used to describe the transfer characteristic of the transistor in the forwardactive region. Equation (2147) can be expressed in terms of the base doping density by noting that [4] npo =
n2i
NA
(2148)
and substitution of Eq. (2148) in Eq. (2147) gives __ qADnn2i qADnn2i = IS = QB WBNA
(2149)
where QB = WBNA is the number of doping atoms in the base per unit area of the emitter and ni is the intrinsic carrier concentration in silicon. In this form Eq. (2149)__applies to both uniform and nonuniformbase transistors and Dn has been replaced by Dn, which is an average effective value of the electron diffusion constant in the base. This is necessary for nonuniformbase devices because the diffusion constant is a function of impurity concentration. Typical values of IS as given by Eq. (2149) are 10–14 to 10–16 A. Equation (2146) gives the collector current as a function of base–emitter voltage. The base current IB is also an important parameter and, at moderate current levels, consists of two major components. One of these (IB1) represents recombination of holes and electrons in the base and is proportional to the minoritycarrier charge Qe in the base. From Figure 283c, the minoritycarrier charge in the base is
222
MODELS FOR ACTIVE DEVICES
Qe =
1 n (0)WBqA 2 p
(2150)
and we have Qe
IB1 =
τb
=
1 np(0)WBqA 2 τb
(2151)
where τb is the minoritycarrier lifetime in the base. IB1 represents a flow of majority holes from the base lead into the base region. Substitution of Eq. (2138) into Eq. (2151) gives IB1 =
VBE 1 npoWBqA exp VT 2 τb
(2152)
The second major component of base current (usually the dominant one in the integratedcircuit npn devices) is due to injection of holes from the base into the emitter. This current component depends on the gradient of minoritycarrier holes into the emitter and is [5] IB2 =
qADp p (0) Lp nE
(2153)
where Dp is the diffusion constant for holes and Lp is the diffusion length (assumed small) for holes in the emitter. pnE(0) is the concentration of holes in the emitter at the edge of the depletion region and is PnE(0) = pnEo exp
VBE VT
(2154)
If ND is the donor atom concentration in the emitter (assumed constant) then pnEo u
n2i ND
(2155)
The emitter is deliberately doped much more heavily than the base, making ND large and pnEo small, so that the basecurrent component, IB2, is minimized. Substitution of Eqs. (2154) and (2155) into Eq. (2153) gives IB2 =
VBE qADp n2i exp VT Lp ND
(2156)
The total base current, IB, is the sum of IB1 and IB2: 1 npoWBqA qADp n2i VBE + IB = IB1 + IB2 = exp V N L 2 τ D p T b
(2157)
Although this equation was derived assuming uniform base and emitter doping, it gives the correct functional dependence of IB on device parameters for practical doublediffused
22
BIPOLAR TRANSISTORS
223
nonuniformbase devices. Secondorder components of IB, which are important at low current levels, are considered later. Since IC in Eq. (2146) and IB into Eq. (2147) are both proportional to exp(VBE / VT) in this analysis, the base current can be expressed in terms of collector current as IB =
IC
(2158)
βF
where βF is the forward current gain. An expression for βF can be calculated by substituting Eqs. (2145) and (2157) into Eq. (2158) to give βF =
qADnnpo / WB 1 2 = 2 Dp WB NA WB 1 npoWBqA qADpni + + L 2 N τb 2τbDn Dn Lp ND p D
(2159)
where Eq. (2148) has been substituted for npo. Equation (2159) shows that βF is maximized by minimizing the base width WB and maximizing the ratio of emitter to base doping densities ND / NA. Typical values of βF for npn transistors in integrated circuits are 50–500, whereas lateral pnp transistors have values of 10–100. Finally, the emitter current is
IC IC IE = − (IC + IB) = − IC + = − βF αF
(2160)
where αF =
βF
(2161)
1 + βF
The value of αF can be expressed in terms of device parameters by substituting Eq. (2159) into Eq. (2161) to obtain αF =
1 1 1+ βF
=
1 W2B
Dp WB NA + 1+ 2τbDn Dn Lp ND
u αTγ
(2162)
where αT = 1+ γ=
1 W2B
(2163)
2τbDn
1 Dp WB NA 1+ Dn Lp ND
(2164)
The validity of Eq. (2162) depends on W2B / 2τbDn < < 1 and (Dp / Dn)(WB / Lp)(NA / ND) < < 1, and this is always tr ue if βF is large [see Eq. (2159)]. The term γ in Eq. (2162) is
224
MODELS FOR ACTIVE DEVICES
Figure 284 Largesignal models of npn transistors for use in bias calculations. (a) Circuit incorporating an input diode. (b) Simplified circuit with an input voltage source.
called the emitter injection efficiency and is equal to the ratio of the electron current (npn transistor) injected into the base from the emitter to the total hole and electron current crossing the base–emitter junction. Ideally γ → 1, and this is achieved by making ND / NA large and WB small. In that case very little reverse injection occurs from base to emitter. The term αT in Eq. (2162) is called the base transport factor and represents the fraction of carriers injected into the base (from the emitter) that reach the collector. Ideally αT → 1, and this is achieved by making WB small. It is evident from the above development that fabrication changes that cause αT and γ to approach unity also maximize the value of βF of the transistor. The results derived above allow formulation of a largesignal model of the transistor suitable for biascircuit calculations with devices in the forwardactive region. One such circuit is shown in Figure 284 and consists of a base–emitter diode to model Eq. (2157) and a controlled collectorcurrent generator to model Eq. (2158). Note that the collector voltage ideally has no influence on the collector current and the collector node acts as a highimpedance current source. A simpler version of this equivalent circuit, which is often useful, is shown in Figure 284b, where the input diode has been replaced by a battery with a value VBE(on), which is usually 0.6–0.7 V. This represents the fact that in the forwardactive region the base–emitter voltage varies very little because of the steep slope of the exponential characteristic. In some circuits the temperature coefficient of VBE(on) is important and a typical value for this is –2 mV/°C. The equivalent circuits of Figure 284 apply for npn transistors. For pnp devices the corresponding equivalent circuits are shown in Figure 285.
Figure 285
Largesignal models of pnp transistors corresponding to the circuits of Figure 284.
22
BIPOLAR TRANSISTORS
225
224 Effects of Collector Voltage on LargeSignal Characteristics in the ForwardActive Region In the analysis of the previous section, the collector–base junction was assumed reversebiased and ideally had no effect on the collector currents. This is a useful approximation for firstorder calculations, but it is not strictly true in practice. There are occasions where the influence of collector voltage on collector current is important, and this will now be investigated. The collector voltage has a dramatic effect on the collector current in two regions of device operation. These are the saturation (VCE approaches zero) and breakdown (VCE very large) regions that will be considered later. For values of collector–emitter voltage VCE between these extremes, the collector current increases slowly as VCE increases. The reason for this can be seen from Figure 286, which is a sketch of the minoritycarrier concentration in the base of the transistor. Consider the effect of changes in VCE on the carrier concentration for constant VBE. Since VBE is constant, the change in VCB equals the change in VCE, and this causes an increase in the collector–base depletionlayer width as shown. The change in the base width of the transistor, ∆WB, equals the change in depletionlayer width and causes an increase ∆IC in the collector current. From Eqs. (2146) and (2149) we have IC =
__ qADnn2i
QB
exp
VBE VT
(2165)
Differentiation of Eq. (2165) yields ∂IC ∂VCE
Figure 286 transistor.
__ VBE dQB qADnn2i =− exp V dV 2 QB CE T
(2166)
Effect of increases in VCE on the collector depletion region and base width of a bipolar
226
MODELS FOR ACTIVE DEVICES
and substitution of Eq. (2165) in Eq. (2166) gives ∂IC ∂VCE
=−
IC dQB QB dVCE
(2167)
For a uniformbase transistor QB = WBNA and Eq. (2167) becomes ∂IC ∂VCE
=−
IC dWB WB dVCE
(2168)
Note that since the base width decreases as VCE increases, dWB / dVCE in Eq. (2168) is negative and thus ∂IC / ∂VCE is positive. dWB / dVCE is a function of the bias value of VCE, but the variation is typically small for a reversebiased junction and dWB / dVCE is often assumed constant. The resulting predictions agree adequately with experimental results. Equation (2168) shows that ∂IC / ∂VCE is proportional to the collectorbias current and inversely proportional to the transistor base width. Thus narrowbase transistors show a greater dependence of IC on VCE in the forwardactive region. The dependence of ∂IC / ∂VCE on IC results in typical transistor output characteristics as shown in Figure 287. In accordance with the assumptions made in the foregoing analysis, these characteristics are shown for constant values of VBE. However, in most integratedcircuit transistors the base current is dependent only on VBE and not on VCE, and thus constantbasecurrent characteristics can often be used in the following calculation. The reason for this is that the base current is usually dominated by the IB2 component of Eq. (2156), which has no dependence on VCE. Extrapolation of the characteristics of Figure 287 back to the VCE axis gives an intercept VA called the Early voltage, where VA =
IC ∂IC ∂VCE
Substitution of Eq. (2168) in Eq. (2169) gives
Figure 287
Bipolar transistor output characteristics showing the Early voltage, VA.
(2169)
22
VA = −WB
BIPOLAR TRANSISTORS
dVCE dWB
227
(2170)
which is a constant, independent of IC. Thus all the characteristics extrapolate to the same point on the VCE axis. The variation of IC with VCE is called the Early effect and VA is a common model parameter for circuitanalysis computer programs. Typical values of VA for integratedcircuit transistors are 15–100 V. The inclusion of Early effect in dc bias calculations is usually limited to computer analysis because of the complexity introduced into the calculation. However, the influence of the Early effect is often dominant in smallsignal calculations for highgain circuits and this point will be considered later. Finally, the influence of the Early effect on the transistor largesignal characteristics in the forwardactive region can be represented approximately by modifying Eq. (2146) to
VBE VBE exp IC = IS 1 + VT VA
(2171)
This is a common means of representing the device output characteristics for computer simulation. 225 Saturation and Inverse Active Regions Saturation is a region of device operation that is usually avoided in analog circuits because the transistor gain is very low in this region. Saturation is much more commonly encountered in digital circuits, where it provides a wellspecified output voltage that represents a logic state. In saturation, both emitter–base and collector–base junctions are forward biased. Consequently, the collector–emitter voltage VCE is quite small and usually in the range 0.05–0.3 V. The carrier concentrations in a saturated npn transistor with uniform base doping are shown in Figure 288. The minoritycarrier concentration in the base of the edge of the depletion region is again given by Eq. (2139) as
Figure 288
Carrier concentrations in a saturated npn transistor. (Not to scale)
228
MODELS FOR ACTIVE DEVICES
np(WB) = npo exp
VBC VT
(2172)
but since VBC is now positive, the value of np(WB) is no longer negligible. Consequently, changes in VCE with VBE held constant (which cause equal changes in VBC) directly affect np(WB). Since the collector current is proportional to the slope of the minoritycarrier concentration in the base [see Eq. (2142)], it is also proportional to [np(0) − (np(WB)] from Figure 288. Thus, changes in np(WB) directly affect the collector current, and the collector node of the transistor appears to have a low impedance. As VCE is decreased in saturation with VBE held constant, VBC increases as does np(WB) from Eq. (2172). Thus, from Figure 288 the collector current decreases because the slope of the carrier concentration decreases. This gives rise to the saturation region of the IC − VCE characteristic shown in Figure 289. The slope of the IC − VCE characteristic in this region is largely determined by the resistance in series with the collector lead due to the finite resistivity of the ntype collector material. A useful model for the transistor in this region is shown in Figure 290
Figure 289 Typical IC − VCE characteristics for an npn bipolar transistor. Note the different scales for positive and negative currents and voltages.
22
Figure 290
BIPOLAR TRANSISTORS
229
Largesignal models for bipolar transistors in the saturation region.
and consists of a fixed voltage source to represent VBE(on), and a fixed voltage source to represent the collector–emitter voltage VCE(sat). A more accurate but more complex model includes a resistor in series with the collector. This resistor can have a value ranging from 20 to 500 Ω, depending on the device structure. An additional aspect of transistor behavior in the saturation region is apparent from Figure 288. For a given collector current, there is now a much larger amount of stored charge in the base than there is in the forwardactive region. Thus the basecurrent contribution represented by Eq. (2152) will be larger in saturation. In addition, since the collector–base junction is now forward biased, there is a new basecurrent component due to injection of carriers from the base to the collector. These two effects result in a base current IB in saturation, which is larger than in the forwardactive region for a given collector current IC. Ratio IC / IB in saturation is often referred to as the forced β and is always less than βF. As the forced β is made lower with respect to βF, the device is said to be more heavily saturated. The minoritycarrier concentration in saturation, shown in Figure 288, is a straight line joining the two end points, assuming that recombination is small. This can be represented by a linear superposition of the two dotted distributions as shown. The justification for this is that the terminal currents depend linearly on the concentrations np(0) and np(WB). This picture of devicecarrier concentrations can be used to derive some general equations describing transistor behavior. Each of the distributions in Figure 288 is considered separately and the two contributions are combined. The emitter current that would result from np1(x) above is given by the classical diode equation
VBE − 1 IEF = −IES exp VT
(2173)
where IES is a constant that is often referred to as the “saturation current” of the junction (no connection with the transistor saturation described above). Equation (2173) predicts that the junction current is given by IEF u IES with a reversebias voltage applied. However, in practice Eq. (2173) is applicable only in the forwardbias region, since secondorder effects dominate under reversebias conditions and typically result in a junction current several orders of magnitude larger than IES. The junction current that flows under reversebias conditions is often called the “leakage current” of the junction. Returning to Figure 288, we can describe the collector current resulting from np2(x) alone as
VBC − 1 ICR = −ICS exp VT
(2174)
230
MODELS FOR ACTIVE DEVICES
where ICS is a constant. The total collector current IC is given by ICR plus the fraction of IEF that reaches the collector (allowing for recombination and reverse emitter injection). Thus,
IC = αFIES exp
VBC VBE − 1 − 1 − ICS exp VT VT
(2175)
where αF has been defined previously by Eq. (2162). Similarly, the total emitter current is composed of IEF plus the fraction of ICR that reaches the emitter with the transistor acting in an inverted mode. Thus, VBE VBC − 1 + αRICS exp − 1 IE = −IES exp VT VT
(2176)
where αR is the ratio of emitter to collector current with the transistor operating inverted (i.e., with the collector–base junction forward biased and emitting carriers into the base and the emitter–base junction reverse biased and collecting carriers). Typical values of αR are 0.5–0.8. An inverse current gain βR is also defined, βR =
αR
(2177)
1 − αR
and has typical values 1–5. This is the current gain of the transistor when operated inverted and is much lower than βF because the device geometry and doping densities are designed to maximize βF. The inverseactive region of device operation occurs for VCE negative in an npn transistor and is shown in Figure 289. In order to display these characteristics adequately in the same figure as the forwardactive region, the negative voltage and current scales have been expanded. The inverseactive mode of operation is rarely encountered in analog circuits. Equations (2175) and (2176) describe npn transistor operation in the saturation region when VBE and VBC are both positive, and also in the forwardactive and inverseactive regions. These equations are from the Ebers–Moll equations. In the forwardactive region, they degenerate into a form similar to that of Eqs. (2146), (2158), and (2160) derived earlier. This can be shown by putting VBE positive and VBC negative in Eqs. (2175) and (2176) to obtain
VBE − 1 + ICS IC = αFIES exp VT
(2178)
VBE − 1 − αRICS IE = −IES exp VT
(2179)
Equation (2178) is similar in form to Eq. (2146) except that leakage currents that were previously neglected have now been included. This minor difference is significant only at high temperatures or very low operating currents. Comparison of Eq. (2178) with Eq. (2146) allows us to identify IS = αFIES and it can be shown [6] in general that αFIES = αRICS = IS
(2180)
22
BIPOLAR TRANSISTORS
231
where this expression represents a reciprocity condition. Using Eq. (2180) in Eqs. (2175) and (2176) allows the Ebers–Moll equations to be expressed in the general form VBC VBE IS − 1 − IC = IS exp exp V − 1 VT T αR IE = −
VBE IS VBC exp V − 1 + IS exp V − 1 αF T T
(2181)
(2182)
This form is often used for computer representation of transistor largesignal behavior. The effect of leakage currents mentioned above can be further illustrated as follows. In the forwardactive region, we have, from Eq. (2179), VBE − 1 = − IE − αRICS IES exp VT
(2183)
Substitution of Eq. (2183) in Eq. (2178) gives IC = −αFIE + ICO
(2184)
ICO = ICS(1 − αRαF)
(2185)
where
and ICO is the collector–base leakage current with the emitter open. Although ICO is given theoretically by Eq. (2185), in practice, surface leakage effects dominate when the collector–base junction is reverse biased and ICO is typically several orders of magnitude larger than the value given by Eq. (2185). However, Eq. (2184) is still valid if the appropriate measured value for ICO is used. Typical values of ICO are 10–10 to 10–12 A at 25 °C, and the magnitude doubles about every 8 °C. As a consequence, these leakage terms can become very significant at high temperatures. For example, consider the base current IB. This is IB = −(IC + IE)
(2186)
If IE is calculated from Eq. (2184) and substituted in Eq. (2186), the result is IB =
1 − αF αF
IC −
ICO
(2187)
αF
But from Eq. (2161) βf = and use of Eq. (2188) in Eq. (2187) gives
αF
1 − αF
(2188)
232
MODELS FOR ACTIVE DEVICES
IB =
IC βF
−
ICO αF
(2189)
Since the two terms in Eq. (2189) have opposite signs, the effect of ICO is to decrease the magnitude of the external base current at a given value of collector current. 226 SmallSignal Models of Bipolar Transistors Figure 291 shows the smallsignal equivalent BJT model. It consists of an intrinsic model and a package model. Table 212 lists its keywords. In order to better understand the difference between the various technologies, we show Table 213, which allows the reader to compare their performances.
Figure 291
Linear BJT model.
22
BIPOLAR TRANSISTORS
233
Table 212 Smallsignal equivalent BJT model keywords
Keyword
Description
Unit
A RE F T CE CI RCE RC RO CO RB1 RC1 RE1 RB2 RC2 CBE CBC CCE LB LC LE TJ NFAC FC
Intrinsic Model Ratio of IC to IE at dc Emitter resistance Current generator rolloff frequency Time delay Emitter capacitance Collector capacitance Collector–emitter resistance Collector resistance Extrinsic base–collector resistance Extrinsic base–collector capacitance Intrinsic base resistance (Rbb) Parasitic collector resistance Parasitic emitter resistance Parasitic base resistance Parasitic collector resistance Basetoemitter package capacitance Basetocollector package capacitance Collectortoemitter package capacitance Baselead inductance Collectorlead inductance Emitterlead inductance Chip temperature Noise factor proportional to drive Flicker noise (1/f noise) corner frequency
CBCP CBEP CCEP ZBT ZCT ZET LBT LCT LET
Package Model Basetocollector package capacitance Basetoemitter package capacitance Collectortoemitter package capacitance Base transmission line impedance Collector transmission line impedance Emitter transmission line impedance Base transmission line length at εr = 1 Collector transmission line length at εr = 1 Emitter transmission line length at εr = 1
Default
hertz
0.0 0.0 ∞ 0.0 0.0 0.0 ∞ ∞ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 298 1.0 50
farad farad farad ohm ohm ohm meter meter meter
0.0 0.0 0.0 50 50 50 0.0 0.0 0.0
ohm hertz second farad farad ohm ohm ohm farad ohm ohm ohm ohm ohm farad farad farad henry henry henry Kelvin
Notes: 1. A ≡ α = Ic / Ie; β = dc current gain = α(1 – α). 2. The bipolar current gain in this model is described by A = A(0) =
e−jωT 1 + j (f / F)
where ω = 2 πf and f is frequency. 3. The current source is controlled by the current through Re. The current generator has a cutoff frequency with respect to the total emitter current, IE: F = gm / 2πCe where gm = 1/Re. This frequency becomes infinite for the default value for Ce (0.0). The parammeter F specifies the frequency rolloff for the current generator with respect to the current through Re. Effectively, this frequency parameter may be used to model additional delays in the device.
234
MODELS FOR ACTIVE DEVICES
Table 213 Overview of current BJT technologies including BiCMOS
Parameter Emitter Size β Ft (GHz) Cje (fF) Cjc (fF) Cjs (fF) Re (Ω) Rb (Ω) BVceo (V) BVcbo (V) BVebo (V) VA (V) Minimum Tpd
Parameter Emitter Size β Ft (GHz) Cje (fF) Cjc (fF) Cjs (fF) Re (Ω) Rb (Ω) BVceo (V) BVcbo (V) BVebo (V) VA (V) Minimum Tpd
Parameter Emitter Size β Ft (GHz) Cje (fF) Cjc (fF) Cjs (fF) Re (Ω) Rb (Ω) BVceo (V) BVcbo (V) BVebo (V) VA (V)
MOSAIC 3
MOSAIC 5 2
MOSAIC 5SE 2
RFBICMOS1
TFSOI
0.3 × 0.9 µm 0.4 × 1.3 µm 0.1 × 1.2 µm2 0.95 × 3.2 µm 0.3 × 0.9 µm 150 150 90 80 40–65 14@ Vce = 1 V 14@ Vce = 1 V 27@ Vce = 1 V 16@ Vce = 1 V 8@ Vce = 2 V 19.9 4.3 3.8 5.1 1.5 25.1 2.8 2.8 3.7 0.34 49.6 4.3 3.6 7.4 0.95 22 36 50 34 72 462 578 583 462 n/a 6.5 7.0 4.8 6.0 >3.5 20 20 15 18 >10 5.2 4.2 3.8 6.0 4.3 30 48 20 >25 25–40 75 ps @ 1.5 36 ps @ 800 43 ps @ 300 µA 52 ps @ 25 µA 35 ps @ 800 mA µA µA TFSOI Ring Device
2
RFBICMOS3 Analog
RFBICMOS3 Digital
2
BiGCMOS3 Analog
BiGCMOS3 Digital
0.1 × 0.25 × 0.25 × 0.2 × 0.2 × 7.2 µm2 0.75 µm2 0.75 µm2 0.6 µm2 0.6 µm2 40–65 100 150 100 100 8 @ Vce = 2 V 15 @ Vce = 2 V 25 @ Vce = 2 V 15 @ Vce = 1 V 35 @ Vce = 1 V 3.4 1.8 1.8 1.7 1.7 2.8 1.1 1.1 0.2 0.3 2.4 12.0 12.0 4 4 26 140 140 113 113 790 n/a n/a 10 kΩ/sq. 15 kΩ/sq. >3.5 6.5 4 6.5 4.8 >10 15 15 20 15 4.3 4 4 4 4 30–40 40 25 40 20 75 ps @ n/a n/a 35 ps @ 22 ps @ 100 µA 50 µA 200 µA AT&T BEST2a
Fujitsu POSET 2
2
HP ISOSAT IIb
HP HP25 2
0.4 × 20 µm 1.0 × 2.0 µm 0.1 × 1.7 µm 100 110 75 23 @ Vce = 3 38 @ Vce = 3 V 28.5 @ Vce = 3 V V 5.0 3.5 42 5.0 2.2 37 8.0 n/a 123 25 25 n/a 10 kΩ/sq. 960 100 5.5 5.4 5.2 11 18.2 15 8.0 4.5 >5 24 n/a n/a
2
0.6 × ? µm 100 14/Fmax > 20 GHz n/a n/a n/a n/a n/a 15 25 2.0 25
Hitachi SMI 0.2 × 2.0 µm2 500 82@ Vce = 2 V 2.9 4.8 4.1 30 240 2.5 6.4 6.2 8
(continued)
22
BIPOLAR TRANSISTORS
235
Table 213 (Continued)
Parameter Minimum Tpd
Parameter Emitter Size β Ft (GHz) Cje (fF) Cjc (fF) Cjs (fF) Re (Ω) Rb (Ω) BVceo (V) BVcbo (V) BVebo (V) VA (V) Minimum Tpd Parameter Emitter β Ft (GHz) Cje (fF) Cjc (fF) Cjs (fF) Re (Ω) Rb (Ω) BVceo (V) BVcbo (V) BVebo (V) VA (V) Minimum Tpd Parameter Emitter Size β Ft (GHz) Cje (fF) Cjc (fF) Cjs (fF)
AT&T BEST2a 37 ps @ 2.1 mA 48 ps @ 600 µA
Fujitsu POSET
HP HP25
HP ISOSAT IIb
Hitachi SMI
21.5 ps @ 320 µA
n/a
n/a
16 ps @ Ig = 1.3
Mitsubishif
National ABIC V
0.5 × 5.7 µm2 90 20
0.5 × 0.5 µm2 85 13 @ Vce = 2 V
n/a 9 n/a n/a 155 6.2 n/a n/a n/a n/a
1.9 3.7 9.6 n/a 383 8.5 20 7.5 n/a 38 ps @ 1.8 mA
Philips QBiC2
Philips PRETg
0.4 × 7.6 µm2 0.2 × 1.6 µm2 0.6 × 40 µm2 0.5 × 1.2 µm2 n/a 120 80 100 17 43 51 20 @ Vce = 3 V 20 n/a 120 2.4 16 1.7 140 3.5 n/a n/a 160 6.5 n/a 80 n/a 120 43 220 55 700 Ω/sq. 3.3 2.7 6 4.5 n/a n/a 17 13 2 2.2 4.5 5.5 n/a n/a n/a 15 29 ps @ 19 ps @ n/a n/a 300 µA 300 µA Siemens B6HF Philips SiGeg Siemens B6HF Siemens SiGeg Plus
0.2 × 0.9 µm2 50 14 1.5 1.0 5.0 120 1 kΩ/sq. 7 12.5 5.5 20 n/a
IBM SiGec
Maxim GST1d Maxim GST2e
0.5 × 1.0 µm2 1.2 × 2.6 µm2 0.7 × 1.5 µm2 100 75 190 12.5 26 @ Vce = 4 V 41 @ Vce = 1 V 5.2 9 4 3.4 15 7 3.6 11 9 n/a n/a 80 300 600 710 3.3 >5 >4 9.5 >12 >14 n/a >4 >4 n/a 20 15 n/a n/a n/a
NEC BSA
0.4 × 1.4 µm2 100 45 @ Vce = 1.5 V 9.1 4.6 10.8
NEC SiGeg
NEC NESAT III
0.25 × 2.7 µm2 0.27 × 2.5 µm2 0.8 × 3.3 (drawn) µm2 >60 115 130 25 @ Vcb = 0 V 50 @ Vcb = 2 V 61 @ Vcb = 1 V 11 6.5 31
8.5 8.0 26.5
7.5 5.5 13
SONYh 0.2 × ? µm2 100 30 n/a n/a n/a
(continued)
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MODELS FOR ACTIVE DEVICES
Table 213 Overview of current BJT technologies including BiCMOS (Continued)
Parameter Re (Ω) Rb (Ω) BVceo (V) BVcbo (V) BVebo (V) VA (V) Minimum Tpd
Parameter Emitter Size β Ft (GHz) Cje (fF) Cjc (fF) Cjs (fF) Re (Ω) Rb (Ω) BVceo (V) BVcbo (V) BVebo (V) VA (V) Minimum Tpd
Phillips SiGeg Siemens B6HF
Siemens B6HF Plus Siemens SiGeg
n/a n/a 3.2 11 3.5 70–100 14 ps @ 6 mA
n/a 165 >3.5 n/a n/a n/a 25 ps @ 1.2 mA (CML)
n/a 14 kΩ/sq. 7 10.8 2.0 20 16 ps @ 2.0 mA (CML)
STM HSBi
STM HSB2A
iSTM HSB3g,j
0.35 × ? µm2 >50 n/a n/a n/a n/a n/a 10 kΩ/sq. 4.5 n/a n/a n/a n/a
0.35 × ? µm2 >50 20 n/a n/a n/a n/a n/a n/a n/a n/a >30 30 ps
0.2 × ? µm2 >50 ~50 n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a
SONYh
n/a n/a 8 kΩ/sq. n/a 2.5 4.0 9.9 18 3.0 3.5 130 10 11 ps @ 1.9 mA 21 ps @ Ig = 3.5 mA (CML) (CML) Toshiba
Toshiba Epi Baseg
0.4 × 5.0 µm2 0.6 × 5.0 µm2 60 105 22 @ Vce = 2 V 52 @ Vce = 3 V 9.0 16.1 3.6 14.1 11 n/a 14 22.7 90 205 6.2 4.1 14.8 9.5 4.2 n/a n/a 26.5 19 ps @ 1.2 mA n/a
1.0 µm Design Rule; NF = 3.25 dB, GA = 12 dB at IC = 2 mA, freq. = 2 GHz for 16 × 1 × 2 µm2; Resistors: 150 Ω/sq. (mono), 300 Ω/sq. (mono), 500 Ω/sq. (poly); Layers of metal, Schottky diodes, linear capacitor (silicided n+ poly/n+Si); Gate length = 0.68 µm (nch)/0.8 µm (pch), Gate Oxide = 12.5 nm (3 V)/15 nm (5 V), Vth = 0.65 V (nch)/–0.9 V (pch), Gm (µS/µm) = 204 (nch)/65 (pch). b 0.6 µm Design Rule; Gold metallization, ILD: polyimide; Inductors: Q > 10 for L ≤ 10 nH; Capacitors: Q > 25 for C ≤ 20 pF; Schottky diodes (fc = 100 GHz), Zener diodes, MIS capacitor, thin film resistors, and LPNP, 10 mask process. c Analog devices using this process. d LPNP Ft = 80 MHz; threelayer metallization; Schottky diodes (RsCj ~ 4 ps); Implanted resistors: 200 Ω/sq.; Poly resistors: 400/2000 Ω/sq.; NiCr thin film resistors (50 Ω/sq.) with laser trim option; MOS capacitor. e LPNP Ft = 85 MHz; twolayer metallization; Schottky diodes (RsCj ~ 0.8 ps); Implanted resistors: 170/600/1200 Ω/sq.; NiCr thin film resistors (50 Ω/sq.) with laser trim option; MOS capacitor. f Ln = 0.8 µm, Tox = 18 nm, Vth = 0.76 V (nmos), Vth = –0.78 V (pmos), 2polyMIM capacitor: 2.7 fF/µm2, Schottkys, inductors. g Not known if this process is in production. h 0.8 µm Design Rules; 2.5 fF/µm2 MIS capacitor; 600 MHz PJFET; 12L; Ft = 4 GHz VPNP; poly resistors 80/400/2000 Ω/sq. i Targeted for 900MHz GSM radio frontend blocks, a CT2 cordless singlechip radio, and DECT (digital enhanced cordless telephones). j Targeted for multimode 900MHz GSM, 1.8GHz PCN and 1.9GHz PCS based systems. Company is also evaluating integrating SiGe in HSB3. a
23
FIELDEFFECT TRANSISTORS
237
23 FIELDEFFECT TRANSISTORS Both diodes and pnp/npn transistors work on the injection principle, which means the base–emitter junction generates either free electrons or other carriers, which are being “collected” by the collector connection and the base connection controls it. While this is a fairly complex process, its physics is well understood, and its latest spinoffs, heterojunction BJTs and silicon–germanium transistors, seem to offer a bright future. In opposition to this, the fieldeffect transistor (FET) controls the electronic conduction in a solid by an electric field, and this concept actually predates the invention of the bipolar transistor. J. E. Lilienfeld filed for a patent on such a device in 1925 (U.S. Patent No. 1,745,175), and W. Shockley presented a comprehensive theory of the FET in 1952. It took until 1960 before the first commercially available FETs came on the market. Several types of semiconductor materials have been used for making FETs: silicon, germanium, gallium arsenide, and others have been used. By far the most widely used is silicon, followed now by gallium arsenide. The FET is a class of electronic semiconductor device in which the conduction of a “channel” between source (S) and drain (D) terminals is controlled by an electric field impressed on the channel via a gate (G) terminal. The conduction channel may utilize ntype carriers (electrons) or ptype carriers (holes). The electric field that controls the channel conduction may be introduced via a pn junction [for a “junction” FET (JFET)], a metal plate separated from the semiconductor channel by an oxide dielectric [for a metaloxide semiconductor (MOS) FET], or a combination of the two methods. The polarity of the controlling electrical field is a function of the type of carriers in the channel. A FET “family tree” is shown in Figure 292. For today’s microwave and RF integrated circuits, the JFET with its highfrequency problems (low cutoff frequency) and large variation in parameters, such as transconductance and pinchoff voltage, has fallen out of favor and is mainly used in discrete circuits such as twoway radios or other RF applications that tolerate these wide variations and temperature dependence. The mostused FET types are MOS for smallsignal applications, LDMOS (lateral diffused MOS) for power applications, and GaAs MESFET for lowerpower applications (lowvoltage applications) as well as highpower applications (recent advertisements by NEC have shown output power up to 100 W). Additional information on the FET family is shown in Figure 293. All members of the FET family are highimpedanceinput devices. Figure 294 shows the key operating parameters for MOSFETs and MESFETs in lownoise stages, highgain stages, and linearized power stages. The linearization also improves the matching. This figure is similar to its counterpart in Section 222. The following several pages present a typical example of a datasheet* for a JFET (U310) and the chip (NZA) on which it is based, followed by an example of a device with a much higher dynamic range (the CP640 family). The CP640 family and devices similar to them are being replaced by lowpower LDMOS, which are not yet welldocumented. At least one company, InterFET, is devoted entirely to producing discrete JFETs and JFETrelated hybrid and smallscaleintegration IC products. *
Reproduced with permission of VishaySiliconix.
238
Figure 292
“Family tree” of microwave FET types showing cross sections of their structures [7]. Copyright ©1976 IEEE.
239
Figure 293
Another FET family tree [8].
240
MODELS FOR ACTIVE DEVICES
Figure 294 Key parameters in operating a MESFET in a lownoise frontend stage, a highgain intermediate stage, and a linear power stage, showing (a) the device characteristics that lead to optimum dc bias for each service, (b) the parameters that characterize the device performance, (c) the optimum generator reflection coefficient that must be synthesized by each circuit, and (d) circuit arrangements that reduce the transistor’s input Q or stabilize it at low frequencies. Although this example is based on an HP MESFET with a gate length of 1 µm and a gate width of 500 µm, this principle applies to all members of the FET family [7]. Copyright ©1976 IEEE.
23
FIELDEFFECT TRANSISTORS
241
242
MODELS FOR ACTIVE DEVICES
23
FIELDEFFECT TRANSISTORS
243
244
MODELS FOR ACTIVE DEVICES
23
FIELDEFFECT TRANSISTORS
245
246
MODELS FOR ACTIVE DEVICES
231 LargeSignal Behavior of JFETs A section view of a junction fieldeffect transistor (JFET) is shown in Figure 295. This structure contains, between the source and the drain contacts, an ntype channel embedded in a ptype silicon substrate. If it is assumed that the pn junction forms a barrier to current flow, then it can be seen that channel conduction is a function of the channel width, length, and thickness and of the density and mobility of the carriers. In this structure, current can flow equally well in either direction through the channel; that is, the drain can be positive or negative with respect to the source. Since we have found that the SPICE models for JFETs are really incomplete and give poor answers, we will only briefly touch here on the JFETs performance. The modified Materka model, one of the best GaAsFET models, turns out to be best suited for JFETs because both transistors act similarly in the dc area. Both have a gatetosource diode that becomes conductive above 0.7 V at the input and they are also quite similar in other respects. Their equivalent circuits are also quite similar, as parameter extractions for both approaches have shown. In general, in a threeterminal device, the drain current ID is a function of two variables: VDS and VGS. This function is best represented by families of characteristic curves, as shown in Figure 296. These curves are for the common source configuration, with the drain as the output and the gate as the input. They reveal that for this device, if VDS is greater than about 2 V (but less than the drain breakdown), ID is primarily determined by the gate voltage VGS. Under these conditions it is valid for small signals to characterize the FET by a single transfer characteristic curve, commonly called the forward transconductance curve, such as the upper curve shown in Figure 296b. Some of the relationships between the forward transfer curve and the output characteristic curves of Figure 296a will be examined. The value of VGS that reduces ID to approximately zero is the gatesource cutoff voltage, VGS(off). With reference to the output curve, Figure 296a, note that the drain current at VGS = 0 tends to become saturated at a drain voltage approximately equal in magnitude to −VGS(off). This drain voltage is often referred to as the pinchoff voltage VP; however, in this section pinchoff voltage is used interchangeably with gatesource cutoff voltage. VP will have the same meaning as VGS(off). The symbol IDSS is commonly used to indicate the value of saturated drain current at VGS = 0.
Figure 295
Junction fieldeffect transistor [9].
23
FIELDEFFECT TRANSISTORS
247
Figure 296 Static characteristics of an nchannel JFET.
The forward transconductance characteristic of Figure 296b can be approximated by a power law relation expressed as n
VGS ID = IDSS 1 − VGS(off)
(2190)
if VDS ≥ −VGS(off). By differentiation the smallsignal transconductance gfs is given by n−1
VGS dID IDSS 1− = −n gfs = VGS(off) VGS(off) dVGS
(2191)
Some texts indicate a value of 32 for n; however, experimental measurements on a number of nchannel JFET geometries indicate that the exponent n is close to 2, which is the value derived in an approximate treatment by R. D. Middlebrook [10]. A useful relationship between gfso, IDSS, and VGS(off) is derived from the ratio of Eqs. (2190) and (2191): ggs = n(VGS − VGS(off))−1 ID At VGS = 0, ID = IDSS and gfs = gfso. Using 2 as the value of the constant n leads to
(2192)
248
MODELS FOR ACTIVE DEVICES
gfso = −2
IDSS VGS(off)
(2193)
For nchannel FETs IDSS is positive and VGS(off) is negative; for pchannel FETs IDSS is negative and VGS(off) is positive; thus gfs is a positive quantity for both p and nchannel FETs. Equation (2190) indicates that for VGS = VGS(off), ID = 0. In a real device this does not happen. Starting from zero, as the gate voltage is made more negative, the drain current decreases until it reaches a very low value equal to the drainleakage current. At this value, the source current will consist of sourcegate leakage. Any further increase in the magnitude of the negative gate voltage will result in an increase in ID leakage. For the smallsignal device illustrated, this minimum ID is on the order of 2 × 10−13 A. For some types of applications of the FET, it is helpful to understand the characteristics at very low values of VDS, such as those shown in Figure 297. A very low value is one that is small compared to the magnitude of VGS − VGS(off). In this region, VDS is small enough to have little effect on channel thickness, so that the ID / VDS slope is nearly linear. Since the slope is a function of VGS, the FET can be utilized as a voltagecontrolled resistor. The conductance slope (∆ID / VDS) at VDS = 0 is approximately a linear function of VGS − VGS(off). If gds at VGS = 0 is given the term gdso, then
Figure 297 Enlargement of nchannel output characteristic around VDS = 0.
23
Figure 298
FIELDEFFECT TRANSISTORS
249
JFET ID, gfs, and gds.
VGS gds = gdso 1 − VGS(off)
(2194)
with VDS = 0. A plot of this characteristic is shown in Figure 298, along with gfs and ID characteristics. The relationship between gdso, VGS(off), and IDSS is given by the equation gdso = −2
IDSS
(2195)
VGS(off)
where IDSS and VGS(off) are as indicated in Figure 296. It is important to note that Eqs. (2194) and (2195) and the gds curve of Figure 298 are valid only for the case where VDS is very small compared to VP. Drainsource conductance at higher values of VDS will be discussed later. FETs designed to be used as voltagecontrolled resistors typically have a high VGS(off) because the VDS / (VGS − VGS(off)) ratio should be low to keep distortion low. The actual largesignal JFET model as used in most simulators is shown in Figure 299, including a list of its intrinsic keywords (Table 214). Again, we had very little luck using this model as published by several SPICE CAD software manufacturers as offered. While we cannot judge on the quality of the parameters that came with the software, it was not possible to closely match even optimized sets of parameters to this largesignal model and obtain acceptable results. However, since the modified Materka model worked very well for this, we recommend that this popular JFET model not be used at frequencies above 10 MHz. 232 SmallSignal Behavior of JFETs Figure 2100 shows the smallsignal equivalent transistor model we would recommend. It consists of an empirical FET model and a package model. Table 215 lists its keywords. Its advantage is that its builtin noise model is very accurate, even for JFETs and metal semiconductor FETs.
250
MODELS FOR ACTIVE DEVICES
Figure 299 The nonlinear JFET model. Table 214 lists its intrinsic and extrinsic parameters. In our opinion, this model is limited to frequencies below 10 MHz; above this frequency, the modified Materka model should replace it.
Table 214 Largesignal JFET model keywords
Keyword
Description
Unit
Default
Intrinsic Model NJF/PJF VT0 BETA LAMB IS PB FC CGS CGD T KF AF FCP SN AREA NOIS NAME
Channeltype selection (NJF = nchannel, PJF = pchannel) Threshold voltage Transconductance coefficient Channellength modulation Gatejunction saturation current Gatejunction potential Forwardbias depletion capacitance coefficient Zerobias gatesource junction capacitance Zerobias gatedrain junction capacitance Channel transittime delay Flicker noise coefficient Flicker noise exponent Flicker noise frequency shape factor Switch to turn device shot noise on (1) or off (0) Area multiplier Reference label to a set of noise data Required userspecified name up to 8 characters
volt ampere/volt2 /volt ampere volt farad farad second
NJF 2.0 1.0E4 0.0 1.0E14 1.0 0.5 0.0 0.0 0.0 0.0 1.0 1.0 1 1.0
Extrinsic Model RD RS
Drain ohmic resistance Source ohmic resistance
ohm ohm
0.0 0.0
23
Figure 2100
FIELDEFFECT TRANSISTORS
251
Linear FET model.
Electrical by equivalent noise _ _ generated within a_ JFET is usually represented _ noise sources, en and in. Both noise voltage en and noise current in are frequency dependent and have the characteristics shown in Figure 2101. _ An equivalent noise circuit is shown in Figure 2102. Above the frequency f1, en is approximately given by 1/2 _ 0.67 en ≅ 4KTB gfs
(2196)
252
MODELS FOR ACTIVE DEVICES
Table 215 Smallsignal FET model keywords
Keyword
Description
Unit
Default
Intrinsic model G CGS F T TDS GGS CDG CDC CDS GDS RI RG RD RS CGE CDE LG LD LS CGDE GDG TJ
Transconductance at dc, G0a Gatesource capacitance 3dB rolloff frequency Time delay Drainsource time delay Gatesource conductance Draingate capacitance Dipole layer capacitance Drainsource capacitance Drainsource conductance Channel resistance Gate resistance Drain resistance Source resistance External gate capacitance External drain capacitance Gatelead inductance Drainlead inductance Sourcelead inductance External gatedrain capacitance Gatedrain conductance Chip temperature
/ohm farad hertz second second /ohm farad farad farad /ohm ohm ohm ohm ohm farad farad henry henry henry farad /ohm kelvin
∞ 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 298
Package Parasitics LGB LDB LSB CGSB CDSB CGSP CDSP CGDP ZGT ZDT ZST LGT LDT LST FC FCP label
Gate wirebond inductance Drain wirebond inductance Source wirebond inductance Gate bondpad to source capacitance Drain bondpad to source capacitance Gate to source package capacitance Drain to source package capacitance Gate to drain package capacitance Gate transmission line impedance Drain transmission line impedance Source transmission line impedance Gate transmission line length for at εr = 1 Drain transmission line length for εr = 1 Source transmission line length for εr = 1 Corner frequency of flicker (1/f) noiseb Shape factor of the 1/f noise response Userdefined term that refers to temperature coefficient
henry henry henry farad farad farad farad farad ohm ohm ohm meter meter meter hertz
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 50 50 50 0.0 0.0 0.0 10 MHz 1.0
e−jωT where ω = 2πf and f The transconductance of this model may be approximately described by gm = G 1 + j(f / F) is frequency. b The flicker noise frequency dependence is given by 1 / (f / Fc)FCP.
a
23
FIELDEFFECT TRANSISTORS
253
Figure 2101 JFET noise characteristics.
where K = 1.374 × 1023 J/K T = absolute temperature in kelvins (273 K = 0 °C) B = frequency range in hertz gfs = transconductance of FET With the input shortcircuited, the noise voltage across the load RL resulting from the FET is _ Output noise voltage = enAV _ Below the frequency f1, en increases proportional to 1 / f n and is expressed as
Figure 2102
Equivalent noise circuit of the FET.
(2197)
254
MODELS FOR ACTIVE DEVICES
_ 0.67 en = 4KTB g fs
1/2 1 + f1 n f
(2198)
The lowfrequency corner frequency f1 for JFETs is typically in the 100Hz to_1kHz range, and the exponent n is usually between 1 and 2. As indicated by the equations, en is inversely proportional to the square root of gfs. _ The equivalent input noise current in is caused by the current in the gatetochannel junction. Its approximate value below f2 is _ in = (2qIGB)1 / 2 where
(2199)
q = 1.602 × 1019 B = frequency range in hertz IG = dc gate current
This expression is fairly accurate when IG is the result of the active device conductance. _ Typically, in will be lower than the calculated value because part of IG is due to conductance across the device package. At higher frequencies (above f2), 1/2 _ 4KTB in = RP
(2200)
where RP is the real part of gate input impedance. RP, in terms of Y11, can range from several tens of megohms (at audiofrequencies) to 1 kΩ or less (at VHF/UHF frequencies). The highfrequency corner f2 is typically in the range of 550 kHz and more than 100 MHz for highfrequency devices. Another form of noise is known as popcorn or burst noise, the causes of which have not been completely identified. It shows up as a random shortduration stepfunction change in drain current, equivalent to an input gatesource voltage change of a few tenths of a microvolt. It is not unlike big bubbles on the surface of boiling water. As far as the noise is concerned, we can also state that the Materka builtin proprietary noise model is significantly more accurate than the one mentioned above [1114]. This model is implemented, with minimal documentation of its inner workings because of its proprietary nature, in the linear portion of the circuit simulator in Ansofts Serenade Design Environment. In many cases, the manufacturer supplies only limited data, so it is most convenient that after SPICEtype parameter extraction is done by using the Scout program, one even gets good noise prediction for JFETs using the modified Materka model. 233 LargeSignal Behavior of MOSFETs Metaloxidesemiconductor fieldeffect transistors (MOSFETs) are important components in contemporary analog integrated circuits. Whereas initial applications were centered on allMOS processes, combined bipolar and MOS processes give the designer the best of both worlds. A major advantage of MOS processes for realizing analog functions is that complex, dense digital functions can be realized on the same chip.
23
FIELDEFFECT TRANSISTORS
255
Transfer Characteristics of MOS Devices. A cross section of a typical enhancementmode nchannel MOS transistor (NMOS) is shown in Figure 2103a. Heavily doped ntype source and drain regions are fabricated in a ptype substrate (often called the body). A thick layer of silicon dioxide is grown over the substrate material and a conductive gate material (metal or polycrystalline silicon) covers this oxide between source and drain. The operation of the device is very similar to that of a JFET in that the gatesource voltage is used to modify the conductance of the region under the gate. This allows the gate voltage to control the current flowing between source and drain, giving gain in analog circuits and switching characteristics in digital circuits. The enhancementmode NMOS device of Figure 2103a shows significant conduction between source and drain only when an ntype channel exists under the gate, and this is the origin of the nchannel designation. The term enhancement mode refers to the fact that no conduction occurs for VGS = 0, and thus the channel must be enhanced to cause conduction. MOS devices can be made equally well by using an ntype substrate with a ptype conducting channel. Such devices are called enhancementmode pchannel MOS transistors (PMOS). In technologies employing one or the other of these device types, the circuit symbol of Figure 2103b is commonly used for either one. In complementary MOS technology (CMOS) both device types are present and the circuit symbols of Figure 2103c will be used to distinguish them. In PMOS and NMOS technologies, the substrate is common to all devices, invariably connected to a dc power supply voltage, and usually not shown on the circuit diagram. In CMOS technology, however, devices of one type or another are fabricated in individual, separate isolation regions, which may or may not be connected to a power supply voltage. If these isolation regions are connected to the appropriate power supply, the symbols of Figure 2103c will be used and the substrate connection will not be shown. If the individual isolation regions are connected elsewhere, however, the devices will be represented by the symbols of Figure 2103d, where the substrate is labeled B. Finally, in NMOS technology an additional device type called a depletionmode device is usually available. This is a conducting channel implanted between the source and drain so that conduction occurs for VGS = 0. This device has characteristics that are almost identical to that of a JFET and will be represented by the symbol of Figure 2103e. The derivation of the transfer characteristics of the enhancementmode NMOS device of Figure 2103a begins by noting that with VGS = 0, the source and drain regions are separated by backtoback pn junctions. These junctions are formed between the ntype source and drain regions and the ptype substrate, resulting in an extremely high resistance (about 1012 Ω) between drain and source when the device is off. Now consider substrate, source, and drain grounded and a positive voltage VGS applied to the gate as shown in Figure 2104. The gate and substrate then form the plates of a capacitor with the SiO2 as a dielectric. Positive charge accumulates on the gate and the negative charge in the substrate. Initially, the negative charge in the ptype substrate is manifested by creation of a depletion region and resulting exclusion of holes under the gate. This is shown in Figure 2104. The depletionlayer width X under the oxide is 1/2
2εφ X= qN A
(2201)
256
MODELS FOR ACTIVE DEVICES
Figure 2103 (a) Typical enhancementmode NMOS structure. (b) Enhancementmode NMOS or PMOS circuit symbol when one device type only is present. (c) NMOS and PMOS symbols used in CMOS circuits. (d) NMOS and PMOS symbols used when the substrate connection is nonstandard. (e) Depletion MOS device symbol.
23
FIELDEFFECT TRANSISTORS
257
where φ is the potential in the depletion layer at the oxidesilicon interface, NA atoms/cm3 is the doping density (assumed constant) of the ptype substrate, and ε is the permittivity of the silicon. The charge per unit area in this depletion region is 2qNAεφ Q = qNAX = √
(2202)
When the potential in the silicon reaches a critical value equal to twice the Fermi level, φf K 0.3 V, a phenomenon known as inversion occurs [15]. Further increases in gate voltage produce no further changes in the depletionlayer width but instead a thin layer of electronics is induced in the depletion layer directly under the oxide. This produces a continuous ntype region with the source and drain regions and is the conducting channel between source and drain. This channel can then be modulated by increases or decreases in the gate voltage. In the presence of an inversion layer, and with no substrate bias, the depletion region contains a fixed charge 2qNAε2φf Qb0 = √
(2203)
If a substrate bias voltage VSB (source positive for nchannel devices) is applied between source and substrate, the potential required to produce inversion becomes (2φf + VSB) and the charge stored in the depletion region in general is 2qNAε(2φf + VSB) Qb = √
(2204)
The gate voltage VGS, required to produce an inversion layer, is called the threshold voltage Vt and can now be calculated. This voltage consists of several components. First, a voltage [2φf + (Qb / Cox)] is required to sustain the depletionlayer charge Qb, where Cox is the gate oxide capacitance per unit area. Second, a workfunction difference φms exists between the
Figure 2104 Idealized NMOS device cross section with positive VGS applied, showing depletion regions and the induced channel.
258
MODELS FOR ACTIVE DEVICES
gate metal and the silicon. Third, there is always charge density Qss (positive) in the oxide at the silicon interface. This is caused by crystal discontinuities at the SiSiO2 interface and must be compensated by a gate voltage contribution of Qss/Cox. Thus we have a threshold voltage Vt = φms + 2φf +
= φms + 2φf +
Qb Qss − Cox Cox Qb0 Qss Qb − Qb0 − + Cox Cox Cox
2φf 2φ + VSB − √ = Vt0 + γ √ f
(2205) (2206)
where Eqs. (2203) and (2204) have been used and Vt0 is the threshold voltage with VSB = 0. The parameter γ is defined as
γ=
1 √ 2qεNA Cox
(2207)
and Cox =
εox tox
(2208)
where εox and tox are the permittivity and thickness of the oxide, respectively. A typical value of γ is 0.5 V1/2 and Cox = 3.5 × 10−4 pF/ µ2 for tox = 0.1 µm. In practice, the value of Vt0 is usually adjusted in processing by implanting additional impurities into the channel region. Extra ptype impurities are implanted in the channel to make Vt0 K 0.51.5 V for nchannel enhancement devices. By implanting ntype impurities in the channel region, a conducting channel can be formed, even for VGS = 0. This MOS transistor is called a depletion device, with typical values of Vt0 in the range 1 to 4 V. If Qi is the charge density per unit area due to the implant, then the threshold voltage given by Eq. (2205) is shifted by approximately Qi/Cox. The preceding equations can now be used to calculate the largesignal characteristics of an NMOS transistor. For purposes of analysis the source is assumed grounded and bias voltages VGS, VDS, and VSB are applied as shown in Figure 2105. If VGS is greater than Vt, a conducting channel exists and VDS causes a larger reverse bias from drain to substrate than exists from source to substrate, and thus a wider depletion region exists at the drain. However, for simplicity, we assume that the voltage drop along the channel itself is small so that the depletion layer is constant along the channel. At a distance y along the channel the voltage with respect to the source is V(y) and the gatetochannel voltage at that point is VGS − V(y). We assume this voltage exceeds the threshold voltage Vt, and thus the induced electron charge per unit area in the channel is QI(y) = Cox[VGS − V(y) − Vt] The resistance dR of a length dy of the channel is
(2209)
23
Figure 2105
FIELDEFFECT TRANSISTORS
259
NMOS device with bias voltages applied.
dR =
dy WµnQI(y)
(2210)
where W is the width of the device, perpendicular to the plane of Figure 2105, and µn is the average electron mobility of the channel. The voltage drop dV along the length of the channel dy is dV = ID dR =
ID WµnQI(y)
dy
(2211)
If L is the total channel length, then substitution of Eq. (2209) into Eq. (2211) and integration gives VDS
L
∫0 ID dy = ∫0
WµnCox(VGS − V − Vt) dV
(2212)
This results in ID =
k′ W [2(VGS − Vt)VDS − V2DS] 2 L
(2213)
where k′ = µnCox =
µnεox tox
(2214)
Equation (2213) is important and describes the IV characteristics of an MOS transistor, assuming a continuous induced channel. A typical value of k′ for tox = 0.1 µm is about 20 µA/V2 for an nchannel device.
260
MODELS FOR ACTIVE DEVICES
As the value of VDS is increased, the induced conducting channel narrows at the drain end and Eq. (2209) indicates that QI at the drain end approaches zero as VDS approaches (VGS − Vt). This results in the same pinchoff phenomenon as occurs in a JFET, and further increases in VDS produce little change in ID. Equation (2213) is thus no longer valid if VDS is greater than (VGS − Vt). The value of ID in this region is obtained by substituting VDS = (VGS − Vt) in Eq. (2213), giving ID =
k′ W (V − Vt)2 2 L GS
(2215)
for an MOS transistor in the pinchoff region. As in the case of a JFET, the drain current in the pinchoff region varies slightly as the drain voltage is varied. This is due to the presence of a depletion region between the physical pinchoff point in the channel at the drain end and the drain region itself. If this depletionlayer width is Xd, then the effective channel length is given by Leff = L − Xd
(2216)
If Leff is used in place of L in Eq. (2215), we obtain a more accurate formula for the pinchoff region: ID =
k′ W (V − Vt)2 2 Leff GS
(2217)
The fact that Xd (and thus Leff) is a function of the drainsource voltage results in a variation of ID and VDS in the pinchoff region. Using Eqs. (2216) and (2217), we obtain ∂ID ∂VDS
=−
dLeff k′ W (V − Vt)2 2 L2eff GS dVDS
(2218)
and thus ∂ID ∂VDS
=
ID dXd Leff dVDS
(2219)
This equation is analogous to Eq. (2168) for bipolar transistors. Following a similar procedure, a voltage analogous to the Early voltage can be defined as VA =
ID ∂ID / ∂VDS
(2220)
and thus −1
dXd dVDS
VA = Leff
(2221)
For MOS transistors, the most widely used parameter for the characterization of output resistance is
23
λ=
FIELDEFFECT TRANSISTORS
1 VA
261
(2222)
As in the bipolar case, the largesignal properties of the transistor can be approximated by assuming that λ and VA are constants, independent of bias conditions. Thus we can formulate a better approximation to the IV characteristics as ID =
k′ W (V − Vt)2 (1 + λVDS) 2 L GS
(2223)
In practical MOS transistors variation of Xd with voltage is complicated by the fact that the field distribution in the drain depletion region is not one dimensional. A vertical component in the field distribution is introduced by the potential difference between the gate and channel and the gate and drain. As a result, the calculation of λ from the device structure is quite different [16], and it is usually necessary to develop effective values of λ from experimental data. The parameter λ is a linear function of effective channel length and is an increasing function of the doping level in the channel. Typical values of λ are in the range 0.050.005 V1. Note that, in the case of a JFET, the pinchoff region for MOS devices is often called the saturation region. A plot of ID versus VDS for an NMOS transistor is shown in Figure 2106. Below pinchoff, the device behaves as a nonlinear voltagecontrolled resistor, which is often called the ohmic or triode region. Above pinchoff, the device approximates a voltagecontrolled current source. Note that for depletion MOS devices, Vt is negative and ID is finite, even for VGS = 0. For PMOS devices, all polarities of voltage and current are reversed. The results as previously derived can be used to form a largesignal model of an MOS transistor. The model topology in the pinchoff region is the same as that for the JFET, but using Eq. (2215) for the controlledcurrent generator.
MOS Device Voltage Limitations. The voltage limitations of MOS transistors depend on the gate length L. For small values of L (less than about 10 µm), the draindepletion region
Figure 2106
NMOS device characteristics.
262
MODELS FOR ACTIVE DEVICES
exerts an appreciable influence on the channel. This causes ID to rise with increasing VDS in a similar fashion to the bipolar transistor curves of Figure 289. For long channel lengths, the draindepletion region has little effect on the channel and the IDversusVDS curves follow closely the ideal curves of Figure 2106. Eventually the drainsubstrate pnjunction breakdown voltage is exceeded and a sharp breakdown characteristic is obtained, which is similar to the JFET characteristic. In addition to VDS limitations, MOS devices must also be protected against excessive gate voltages. Typical gate oxides break down with about 2550 V applied from gate to channel, and this process is destructive to the transistor. 234 SmallSignal Model of the MOS Transistor in Saturation The preceding largesignal equations can now be used to derive the smallsignal model of the MOS transistor in the saturation or pinchoff region. The important equations are (2220) and (2206). Note from Eq. (2206) that the sourcesubstrate voltage VBS affects Vt, and thus ID. This is due to the influence of the substrate acting as a second gate and is called body effect. As a consequence, ID is a function of both VGS and VBS, and we require two transconductance generators in the smallsignal model as shown in Figure 2107. Variations in the voltage vbs from source to body cause current gmbvbs to flow from drain to source. Note that the body (or substrate) of an NMOS integrated circuit is usually connected to the most negative supply voltage and is thus an ac ground. However, the source connection can have a significant ac voltage impressed on it. Parasitic resistances due to the channel contact regions should be included in series with the source and drain of the model but are usually neglected in hand calculations. These resistances have an inverse dependence on channel width W and have typical values of 50100 Ω for devices with W of about 1 µm. The parameters of Figure 2107 can be determined from Eq. (2223) by differentiating. gm =
∂ID ∂VGS
= k′
W (V − Vt) (1 + λVDS) L GS
If λVDS 0?" 5
386
AMPLIFIER DESIGN WITH BJTs AND FETs
SFN. 7SRN.FN8 SFN 5 / & +
& / noise factor
F=
(S / N)input (S / N)output
≥1
$(.
 . 3 0 noise figure K F " &
3
404
AMPLIFIER DESIGN WITH BJTs AND FETs
Figure 324 Noise figure versus collector current, noise figure versus frequency, and source impedance for minimum noise figure versus frequency for the Siemens BFP420 transistor.
31
405
PROPERTIES OF AMPLIFIERS
Table 33 BFP420 commonemitter noise parameters
f
Fa
Gaa
D C.
,
,.
Γ
! . &.
RN
n
F)Ωb
U"(%(b
Ω.
,.
,.
)%@ )%$ )%% )%) )%% )%) )$)
%)( %%% %$( %4B %B$ (() $$)
VCET(KICT& )A %B (4 $) 4) ) E)
)A) %) %( %$B % %@ (()
() %( %$) %(% %)$ BE E4
)(B )() )() )(( )$$ )4 )$
4%) B() %(4) '%@) '%@) '%4() '%($)
B@ E@ ) ) %)
()$ %B %$ %%E A% @) $
a
Input matched for minimum noise figure, output for maximum gain. ZS = ZL = 50 Ω.
b
fT 3 /
"
/ 3 Pn = 2Iq
$@).
Pn I q %E)×%)'%A . $$
,#;4()
Noise Circles. # O5 2+ ; 2 P
 . transformation
6 #β #.
#α#. V
Y
&
Y
% )
) %
y%% y(%
y%( y((
'y%% 'y(%
% )
Z
z%% z(%
z%( z((
% )
) %
% )
'z%% 'z(%
A
) %
A%( A((
% )
'A%% 'A(%
% )
) %
31
PROPERTIES OF AMPLIFIERS
411
" Y.'%TZ. −i1 I1 V1 V = [Z] I + [Z] −i 2 2 2
$AE.
−i −i = [Z] 1 = [Tyz] 1 −i2 −i2
$A@.
i%i( + Y Z Z. $4 + 〈v v∗〉 〈v v∗〉 i1 ∗ ∗ 1 2 + 〈vv+〉 = 1 1 = [Z] 〈i [i1 i2]〉 [Z] ∗ ∗ 〉v1v2〉 〈v2v2〉 2
$AB.
[Cz] = [Z] [Cy] [Z]+
$AA.
v+ = [i∗1 i∗2] [Z]+
$%)).
/
+ 23$A).
#+
[Cz] = 2kT ∆f Re([Z])
$%)%.
[Cy] = 2kT ∆f Re([Y])
$%)(.
(kT + ABCD + 6 7%80 _ _ Y[Ca]Y + $%)$. F=1+ 2kT Re(YG) _ Y Y = G 1
412
AMPLIFIER DESIGN WITH BJTs AND FETs
2+ + F=1+
CA22( f ) + 2 Re{Yg( f ) CA12( f )} + Yg( f )2 CA11( f )
2kT0 Re{Yg( f )}
$%)4.
Y 3 F( f ) = Fmin( f ) +
Rn( f )Yopt( f ) − Yg( f )2 Re{Yg( f )}
$%).
5 3 + 3 ABCD +
 . F0 − 1 Rn − RnY∗0n 2 $%)E. [Ca] = 2kT − 1 F 0 2 2 − RnY0n RnY0n + 3 / 3 / 5
n / Ca + 2
Y0n =
Cii∗ Cui∗ Cui∗ − Im + j Im C Cuu∗ C uu∗ uu∗
F0 = 1 +
Cui∗ + Cuu∗Y0∗n kT
Ru = Cuu∗
Figure 327
$%)@.
$%)B. $%)A.
Noise figure measurement.
31
PROPERTIES OF AMPLIFIERS
413
Noise Figure Test Equipment. #$(@ /
5 3 %)'%B))! C. G :9. F1 = Fsystem −
F2 − 1 G1
$%%).
7%E8 0 + 2 0 F $%BE' . r≤
gm ω C1C2 2
≤
G ω2C1C2
$%BC'
G . gm " C& C/ . C& = C/ = Cm # F $%BC' 1 ωCm
>√ r
G
$%B2'
#
& / ωCm
gm Clapp circuit ClappGouriet circuit " %&% # 
Co C& C/
Figure 515
Circuit of a Clapp oscillator.
53
OSCILLATOR DESIGN
731
) C& C/ F $%BC'  Co ωo
ωoL −
1 1 1 =0 − − ωoCo ωoC1 ωoC2
$%B8'
Amplitude Stability. : # ; EH34 ) #
" D & &234 β # # . . . " %&H ) #
# Q/ 0
. Q/ ; Q/
Phase Stability. " longterm
# #
Figure 516
Twostage, emittercoupled oscillator.
732
RF/WIRELESS OSCILLATORS
Figure 517
Phase plot of two openloop systems with different resonator Q values.
shortterm
(
D phase stability ) )
dφ / df " %&C 9&234 )
. &34 34 ) &C34 " %&C ∆f/ &34 GH/ ∆f& GH& # dφ / df f = fo
)
* " %&2 " Vo( jω) I( jω)
Figure 518
=
R 1 + jQ[(ω / ωo) − (ωo / ω)]
Parallel tuned circuit for phaseshift analysis.
$%%3'
53
OSCILLATOR DESIGN
733
ωo =
1 √ LC
and
Q=
R ωoL
$%%&'
# arg
Vo
I
ω ωo = θ = tan−1 Q − ωo ω
$%%/'
ω2 + ω2o dθ 1/Q = dω 1 / Q2 + [(ω2 − ω2o) / ωoω]2 (ωoω)2
$%%E'
ωo
Figure 519 Diagram for a feedback oscillator illustrating the principles involved, and showing the key components considered in the phase noise calculation and its contribution.
734 Figure 520 Phase noise with oscillator output taken from collector (upper trace) versus emitter (lower trace) of a BJT oscillator.
54
2Q dQ = dω ω = ωo ωo
OSCILLATOR CIRCUITS
735
$%%B'
# SF dφ / dω ∆ω / ωo # SF = 2Q
$%%%'
SF
F $%%B' Q # Q # # $ ' . " %&8 # twoport #
"
D L pulling ) . # . SSB phase noise . $ ' &0 " %/3 D
54 OSCILLATOR CIRCUITS 541 Hartley " %/& 0
)
 542 Colpitts " %// *
736
RF/WIRELESS OSCILLATORS
Figure 521
Hartley oscillator.
543 Clapp–Gouriet " %/E *9O : * *9O
D * # *9O !"
55 DESIGN OF RF OSCILLATORS 551 General Thoughts on Transistor Oscillators
$%%H'
>  $
" %&8' # , @ 0 &8C2 0 :
LL
Figure 522
Colpitts oscillator.
55
Figure 523
DESIGN OF RF OSCILLATORS
737
Clapp–Gouriet oscillator.
#
. A f 20 £(fm) = 10 log1 + (2fmQload)2
fc FkT 2kTRK20 + + 1 fm 2Psav f 2m
$%%C'
P(fm) J &0 fm 7 fm J f3 J fc J Q J Q F J kT J B& × &39/& E33 Q $ ' Ps J R J $ /33 Ω &3 Ω' K J # $ L' fC IC 7=# IC( .) &3 IC $ '
fC $0 '
3/% 3% & / %
& /CB BE H/C 8E
; fC " Q" @)*F IC # fC $
F. & @ %E&' 7=# IC IC Q" 7=#
# fC , fC
A ( Q 10" $
738
RF/WIRELESS OSCILLATORS
Figure 524
Phase noise of oscillators using different semiconductors and resonators.
& O0 '
$&3 0 &3 0 ' fC O fC A ="F# %3 0 D !" 7=# &9&3 0 $ 'D L(@"F# &39&33 0 D O"F# &39&33 L0 " %/B F $%%C' ! G/I #
+*( > . D " . 4
sφ( fm) =
+
+
αRF0 + αE(F0 / 2QL)2
f 3m (2GFkT / P0) (F0 / 2QL)2 f 2m 2αRQLF30 f 2m
+
αE 2GFkT + fm P0
G J F J k J 7 T J
$%%2'
55
DESIGN OF RF OSCILLATORS
739
P3 J $ ' F3 J fm J QL(= πF3τg) J Q
αR αE J ) LC . LC
: A & 1 / 1 >
# Q. # LC LC F $
! ? @ 0 7 F L' 0 L 02HB3 #
1 " LC " %/% ! ? @ @L,1 ) 0 02HB3 # # . # "F#
F $%%H' # #
* ) "F# @
740 Figure 525
A 118–198MHz oscillator from the Rohde & Schwarz SMDU signal generator.
55
Figure 526 generator.
DESIGN OF RF OSCILLATORS
741
Photograph of the helicalresonator system from the Rohde & Schwarz SMDU signal
"L
" .
/ $&B39&H3 L0 ' /3 0 .
% 0 " %/% 7 fT
.
LC ="F# %33 L0 D /33 %33 L0 &333 L0
" %/H
.
552 TwoPort Microwave/RF Oscillator Design
Q ) # ME MB
. !" @
" %/C #
; Q )
742
RF/WIRELESS OSCILLATORS
Decouples resonator from load variations Similar devices for Q1 and Q2 PoutQ2 > Pout Q1. Figure 527
Buffered oscillator design.
#
&A 1 / SC11 = ΓG
$%%8'
S12S21ΓL S11 − DΓL = 1 − S22ΓL 1 − S22ΓL
$%H3'
# SC11 = S11 +
1 − S22ΓL 1 = = ΓG SC11 S11 − DΓL
$%H&'
7 . F $%H&' ΓGS11 − DΓLΓG = 1 − S22ΓL ΓL(S22 − DΓG) = 1 − S11ΓG ΓL =
$%H/'
1 − S11ΓG S22 − DΓG
# SC22 = S22 +
S12S21ΓG 1 − S11ΓG
1 − S11ΓG 1 C = S22 S22 − DΓG
$%HE' $%HB'
* F $%H/' $%HB' 1 / SC22 = ΓL
$%H%'
/D # ΓL # n A Γ1SC11 = Γ2SC22 = Γ3SC33 = ⋅⋅⋅ = ΓnSCnn
$%HH'
55
DESIGN OF RF OSCILLATORS
743
7 " %/C # A & / $k R &' E B # 0
S)O #
A & @ #
S
/ @ k R &
k R &
E @ TSC&&T > & ) %3Ω B ! ΓGSC&& = & # SC// ) " "F#
S// %3Ω 0 S// %3Ω #
k R &D TSC&&T > & .
$0/33&' . / O0 #
S
# %& 1 " %/2
Table 51 S parameters and stability factors (VCE = 15 V, IC = 25 mA)
LB J 3
LB J 3% 0
S&& J 38B ∠&CB4 S/& J &83 ∠9/24 S&/ J 33&E ∠824 S// J &3& ∠9&C4 k J 9338
&3B ∠&CE4 /33 ∠9E34 33BE ∠&%E4 &3% ∠9&24 932E
744
RF/WIRELESS OSCILLATORS
Figure 528
Oscillator example at 2 GHz.
ΓL = 0.62 ∠30° SC11 = 1.18 ∠173° # G J /3 " ) S)O
Q S)O
" $,!(' ΓG ≈ &3 / ∠−&CE4 ΓG SC// C TS//T > & #
" %/8 . B O0 " %E3 #B&B33
Figure 529
Oscillator design flowchart.
55
Figure 530
DESIGN OF RF OSCILLATORS
745
A 4GHz lumpedresonator oscillator using the AT41400.
3% 0 #
@ B O0 /3H " ΓG = & − 3 ∠−&ECC4 SC// SC// = 3HEC ∠BB%4 # + /34 @ * &/2 " SC// = &&H ∠−%%4 ΓL = 32H& ∠%%4 #
" %E& 553 CeramicResonator Oscillators $*!'
# *! . # . &3 Ω 7 . ε
# Q # +*( /33 L0 E B O0
(
Figure 531
Completed lumpedresonator oscillator (LRO).
746
RF/WIRELESS OSCILLATORS
Figure 532
Ceramic resonators.
)
L " %E/ %EE K
" %EB # 22
B339&%33L0 # . $233 L0 /% O0 ' ε E2 $&9B% O0 ' ε /& O
A
Figure 533
Standard round/square ceramicresonator packaging and dimensions.
55
Figure 534
747
DESIGN OF RF OSCILLATORS
Modern ceramicresonator oscillator for handheld cellular phones.
! !
εr J /& l =
&HH f
εr J E2 l =
&/H f
εr J 22 l =
2/ f
# $ K4*'
&3
H%
2%
9E U&/
9E U&/
9E U&/
233
%33
B33
&9B% O0
2339/%33 L0
B339&%33 L0
# Q "
Calculation of Equivalent Circuit. # Rp =
2(Z0)2 R∗l
$%HC'
Z3 J l J
∗ R J
.
C∗ =
εr 2πε0εr = 55.61 × 10−12 loge(D / d) loge(D / d)
$%H2'
748
RF/WIRELESS OSCILLATORS
L∗ =
µrµ0 D D = loge = 2 × 10−7 loge d 2π d Z0 = 60 Ω
= 60
$%H8'
D 1 loge √ εr d
1 6 loge 2.5 88 √
= 5.6 Ω
$%C3'
. εr J 22 B%3 L0 C∗l = 49.7 pF 2
$%C&'
Lp = 8L∗l = 2.52 nH
$%C/'
Rp = 2.5 kΩ
$%CE'
Cp =
" %E% " %EH %EC
7  .
$::' " %E2 :: @ L * 7 Q . .
+ 9&%3 7K0 & L0 # . 554 Using a Microstrip Inductor as the Oscillator Resonator* Q GE9%I # @ ; ;&CCC 7=# )
F $%%H'
1 4Q2L
$%CB'
#
&3N Q
/3N
Q. ( V 7 @ K@ !" *
; ;&CCC 5:+ " F *A @H3& @H/36 /3 &88C 1
55
DESIGN OF RF OSCILLATORS
749
Figure 535 Schematic of a highperformance ceramicresonatorbased oscillator that can be used from 500 MHz to 2 GHz.
# )*
Increasing Loaded Q. " %E8 @H/3 )* . " Q 1/2
CT QL = RP L T
$%C%'
Figure 536
Simulated phase noise of an npn bipolar 1GHz ceramicresonatorbased oscillator.
750
RF/WIRELESS OSCILLATORS
Figure 537
Measured phase noise of a ceramicresonatorbased oscillator.
1 1 + RP = RT  RC = RT RC
−1
$%CH'
RT LT CT $ ' RC ) LT CT $ Q' RT RC @H/3 RP >
Figure 538
Miniature PLLbased synthesizer manufactured by Synergy Microwave Corporation.
55
Figure 539
DESIGN OF RF OSCILLATORS
751
Oscillator portion of Philips SA620 frontend IC with external resonator.
RP ZC $ RC ZC ' , L C ) 8 &3 $& / ' C
VCC # L " %B3 L # CT 1/2
LT2 ^ +1 RP = RP LT1
$%CC'
QA 1/2
LT2 +1 QL = QL LT1
$%C2'
"
!" LT CB H # 833 L0
W
HighQ Microstrip Inductor. ! L Q Q #
752
RF/WIRELESS OSCILLATORS
Figure 540
Oscillator portion of SA620 IC with tappedmicrostrip resonator.
# . Q CKL !
(
l $ ' w $ '
l L = [5.08E − 3] l ln w
w + 1.193 l
GEI $%C8'
L 0K #
( Q 5 6 QC = 0.63h[σfGHz]1 / 2
GBI $%23'
h
σ @K f O0 # Q .
C33 w h . &D wKh X & #
F $%C8' # 56 wl CS = Kε0εr h
$%2&'
55
DESIGN OF RF OSCILLATORS
753
CS ε3 J 22HF 9&/ $"K '
εr 5 6 K $ /9&%N' #
UHF VCO Using the TappedInductor Differential Oscillator at 900 MHz. # " %B& "
!" LT& LT/ $ & / 'D # & / 8 &3 $
' 7 $ H' . # 5 6 LT/
& / 8 &3 56 Q
7 L ( Q &/ O0
&H O0 . Q
. # Q !" #
& / Q #
Q. F $%23' Q # A
Figure 541
Differential oscillator with tappedmicrostrip resonator.
754
RF/WIRELESS OSCILLATORS
" . 833 L0 Q C%3 *
$ W' Q /E3 ) Q Q #
* RF& ) @ RF&
RF& # .
B E3 Ω @ VCC
Q VCC /% + > Q # VCC &3 + +*(  L. :( ,
# 5 6A ) & L
/33 H/ LKC
%33 ; 5LKC 6 & Q CKL # 5LKC 6 Q QL G
F $%C%'I 0 Q CT Q . Q. # . QL H/ "!% %3 E33 .
CT BE " 8%3 &333 L0 CKL C% " .
&9/ 7
8%3 L0 # # &
$ C& C/ ' / # / L QL #
QL CT Q , % 7 @@7
;3 Q ;3 # E CT 0 Q % 7 L
C& C/ H $ 7' !" ; QL !" !" 833 L0
E33 " # !" . 833 L0
755 Figure 542
Philips SA620 application board schematic showing the tappedmicrostrip resonator.
756
RF/WIRELESS OSCILLATORS
Figure 543 “Walking stick” microstrip Hartley resonator as used by Plextek in the 800–1500MHz range. Below 800 MHz, the resonator’s physical size becomes impractical; above 1500 MHz, the transistor’s parasitic reactances make the Hartley configuration problematic.
) * !" "
"** &% $ ' " %B/ @H/3 )* 555 Hartley Microstrip Resonator Oscillator O @ @ " . *
# * 0 $ '
# $" %BE' . Q . 23 # %/
556 Crystal Oscillators L " .
$ '
Table 52 Achieved oscillator phase noise versus tuning range
# ! 3%9E + /EN &HN &3N
# ! &9E + &HN &&N 2N
; /30 ( 9&33 7K0 9&3E 7K0 9&3H 7K0
55
DESIGN OF RF OSCILLATORS
757
Figure 544 Electrical equivalent of a piezoelectric crystal resonator, showing fundamental (1) and overtone (3, 5, 7, . . .) resonances. (Courtesy of Roger Clark, Vectron International.)
Table 53 Approximate crystal parameters
Crystal Q Approximations (F in MHz) ; "
*A % × &3H / × &3H 7 A Q = >A Q = F F * 0 QA &/ × &3H &3 × &3H @*A Q = # *A Q = F F Crystal Resistance (r) for 10MHz, ThirdOvertone Example Using Precision Crystal
r =
/πFC&
Approximation (F in MHz and C& in pF)
Q
r = H8HB
Typical Crystal Parameters &3L0 "
A C& J 33/ " C3 J EH " Q J E%3333 r J /% Ω L J 33&/HH% 0 %3L0 # ( A C& J 333/H " C3 J B/&/ " Q J &33333 r J &E Ω L J 333E28C 0 &33L0 "( A C& J 3333% " C3 J //% " Q J 23333 r J B3 Ω L J 333%3HH 0 &%%L0 0" "
A C& J 333% " C3 J &% " Q J /3333 r J &/ Ω L J 333/&32 0 Source: Roger Clark, Vectron International.
758
RF/WIRELESS OSCILLATORS
$ ' ) &3 L0 # Q = L C . .
Fundamental D overtone $E % C '
" %BB # %E . .

. " %B%
#
" %BH D " %BC $" %B2' Q $" %B8' @
" %%3 %%& $0*,' 557 VoltageControlled Oscillators +*( $" %E%'
#
Figure 545
A 3–30MHz Colpitts crystal oscillator.
759
Figure 546 As with every oscillator, the crystal oscillator’s input impedance is negative and real at resonance. This graph plots the real and imaginary components of the test voltage injected by the Oscillator Design Aid tool in Ansoft Serenade 8.0. Compare this graph with Figure 57, which plots an oscillator’s input impedance with the resonator absent.
760 Figure 547
Simulated phase noise of the crystal oscillator.
55
Figure 548 reduction.
DESIGN OF RF OSCILLATORS
761
This alternative output tap uses the crystal’s high selectivity for improved harmonic
# varactors voltagesensitive diodes. 7 . C=
K (VR + VD)n
$%2/'
Figure 549 Comparison of the crystal oscillator’s simulated output spectrum as obtained at the transistor emitter (dark gray, fundamental –26.7 dBm) and crystal (light gray, fundamental –29.1 dBm). At the emitter, the second harmonic is down only 4.3 dB relative to the carrier; at the crystal, the second harmonic is down 36 dB relative to the carrier.
762 Figure 550 A 100MHz VCXO suitable for ultralowphasenoise applications. The HSMS2800 hotcarrier diode (HCD) provides noise reduction.
763
Figure 551
Phase noise of the VCXO with and without the noisereduction diode.
764
RF/WIRELESS OSCILLATORS
Figure 552 Capacitance–voltage characteristic for an alloyed capacitance diode (n = 0.33), a diffused capacitance diode (n = 0.5), and a widerange tuning diode (BB141).
K. # .
K 3% 3EE $ ' 3C% pn  GH CI " %%/ 9 ! F $%2/'A m
A C = C0 A + VR
$%2E'
C3 VR J 3 A
#
. m . n F $%2&' # Cmax Ctot(VR,min) = Cmin Ctot(VR,max)
$%2B'
(
55
DESIGN OF RF OSCILLATORS
765
# L D @
O # %B " %%E 558 DiodeTuned Resonant Circuits
Tuner Diode in ParallelResonant Circuit. " %%B %%%
) " %%B RB @ CS L . CP # @
Rc "
. 2
Ctot Rc = RB 1 + CS
$%2%'
Table 54 Example tuning diodes (Siemens)
L.
!
* $TA J /% 4*'
#
VR IF CT VR CT $+' $ ' $"' $+' $"'
77BE8 77%E% 77%B% 77HE8 77HE8* 77HB3 7723B $ ' 772&B $ ' 772EE 772E% 778&B $ ' 77S%& $ ' 77S%&3E> 77S%&3C $ ' 77S%/ $ ' 77S%/3E> 77S%E $ ' 77S%E3E>
E3 E3 E3 E3 E3 E3 /3 /3 E3 E3 /3 C C C C C H H
/3 /3 /3 /3 /3 /3 %3 %3 /3 /3 %3 /3 /3 /3 /3 /3 /3 /3
/8 &2C /3 E2E E8 H8 BBC% BBC% 8E 8& BEC% %E3 %E3 %E3 &C% &C% %E3 %E3
E & & & & & / / & & / & & & & & & &
%3 /& /3 /H% /%% E3% /H&% /32 3C% 3H/ &2C E&3 E&3 E&3 &/% &/% /B3 /B3
VR $+' /% /2 /2 /2 /2 /2 2 2 /2 /2 2 B B B B B E E
* VR C IR $' $+' * %2 28 &33 &B% &%E //H &C& /&% &/B &BC /EB &C% &C% &C% &B3 &B3 //3 //3
≤/3 ≤&3 ≤&3 ≤&3 ≤&3 ≤&3 ≤/3 ≤/3 ≤/3 ≤&3 ≤/3 ≤&3 ≤&3 ≤&3 ≤&3 ≤&3 ≤&3 ≤&3
/2 E3 E3 E3 E3 E3 &H &H E3 E3 &H H H H H H B B
@(,E/E @(,E/E @(,E/E @(,E/E @(,E/E @(,E/E @(#/E @(#/E @(,E/E @(,E/E @(#/E @(#/E @(,E/E @(#&BE @(#/E @(,E/E @(#/E @(,E/E
Y * Q 7 ; F ( " O 0 0 0 ) ) : :
766
RF/WIRELESS OSCILLATORS
Figure 553 Diode capacitance CT versus reverse voltage VR for the diodes shown in Table 54. The curve labels correspond to the chip codes called out in the table.
) ω 2
ω2LCS Rc = RB 2 ω L(CS + CP) − 1
$%2H'
) " %%% #
# RB
O
. Rc = 4RB
Figure 554
$%2C'
Parallelresonant circuit with tuner diode, and bias resistor in parallel to the diode.
55
Figure 555
DESIGN OF RF OSCILLATORS
767
Parallelresonant circuit with two tuning diodes.
Capacitances Connected in Parallel or in Series with the Tuning Diode. " %%B
) CS 0
.
7 CS
C C∗ = Ctot
1 1 + Ctot / CS
$%22'
# Q Q Ctot Q∗ = Q1 + CS
$%28'
# C∗max C∗min
=
Cmax 1 + Cmin / CS Cmin 1 + Cmax / CS
$%83'
C . C . ( ^∗ ^ v =v
1 1 + Ctot / C
$%8&'
. C . #
768
RF/WIRELESS OSCILLATORS
. F $%28' # CP " %%B %%% 7 CP
CS
CP $%8/' C∗ = Ctot 1 + Ctot # Q Q CP $%8E' Q∗ = Q1 + Ctot # A C∗max C∗min
=
Cmax 1 + CP / Cmax Cmin 1 + CP / Cmin
$%8B'
)
Figure 556
Diagram for determining capacitance ratio and maximum capacitance.
55
DESIGN OF RF OSCILLATORS
769
Tuning Range. # $ " %%B'
# 1/2
fmax fmin
Cmax 1+ ( + ) C C / C 1 P S max = C max 1 + CP(Cmax / Cmin + Cmax / CS)
$%8%'
) ) F $%8%' A
Figure 557
Oscillator and switching section of the Rohde & Schwarz ESH2/ESH3 test receiver.
770 Figure 558
A 40–70MHz VCO with two coarsesteering ranges and a finetuning range of 1 MHz.
55
DESIGN OF RF OSCILLATORS
771
1/2
fmax 1 + Cmax / CP = fmin 1 + Cmin / CP
$%8H'
" " %%H >
$ . '
> CS F $%83'
Tracking. >
559 Practical Circuits
Oscillators with Coarse and Fine Tuning.
" %%C # ! ? @ F@;KF@+;B3
0"&3E3 * *
@ , # & L0 D @ A
Figure 559
Schematic of the dccoupled oscillator.
772
Figure 560
Phase noise of the dccoupled oscillator operating at 897 MHz.
773 Figure 561 Schematic of the Siemens VCO. This oscillator (simulation) works with such high voltagedivider capacitances (C2 and C3) only because the circuit’s largesignal transistor model, which was obtained under contract, exhibits unrealistically high gain at the frequency of oscillation. Actual capacitors with values on the order of those shown for C2 and C3 typically exhibit parasitic resistance and inductance of 0.3 Ω and 0.2 nH, respectively; the resulting series resonance would make any actual such capacitor act as an inductor at UHF. Obtaining practical “UHF useful” capacitances with values on the order of those shown for C2 and C3 would therefore necessitate the use of multiple, smallervalue capacitors in parallel—4 × 15 pF at C2, for example.
774
Figure 562
Simulated phase noise of the VCO. The frequency of oscillation is 1.052 GHz.
55
Figure 563
DESIGN OF RF OSCILLATORS
775
Implementation of the Siemens VCO.
& # # . " Q K3 7 / ) # LKC C # Q L $
' >
)
. " %%2
dcCoupled Oscillator. )* , : L " %%8 " %H3 7=#
Siemens Colpitts Oscillator. * " %H&
776
Figure 564 A recommended verylowphasenoise VCO that operates in the 1GHz region. The V436 stage is a constantcurrent generator responsible for improved phasenoise performance.
777 Figure 565 Phase noise of the lownoise VCO. The “ledges” from 100 Hz to 1 kHz and from 10 kHz to 100 kHz reflect the noisecleanup effects of a dualloop synthesizer; the superimposed line from 1 kHz to 2 MHz shows the oscillator’s noise characteristic with both loops unlocked. The closedloop response is noisier than the openloop response at offsets above 60 kHz because a wide loop bandwidth is used to achieve a faster switching speed.
778
RF/WIRELESS OSCILLATORS
@
* " %H/ L " %HE
# . $!C " %H&'
* S G2I
dcStabilized Oscillator. " ! ? @ @LOK@L0 " %HB
" %H% )
56 NOISE IN OSCILLATORS ) 
D # 561 Linear Approach to the Calculation of Oscillator Phase Noise @
$" %HH' . F F G8I
F=
(S / N)in (S / N)out
=
Nout NinG
=
Nout GkTB
$%8C'
Nout = FGkTB
$%82'
Nin = kTB
$%88'
N
# &0 f3 + fm $" %HC' ∆θpeak =
Vn RMS1
Vs,av RMS
∆θ1RMS =
1 √2
fKT =√ Ps,av
FkT √ P
$%&33'
$%&3&'
s,av
@ . f3 − fm
∆θRMS total = √ FkT/ Ps,av
$%&3/'
56
Figure 566
NOISE IN OSCILLATORS
779
Noise power versus frequency of a transistor amplifier with an input signal applied.
Figure 567
Phase noise added to carrier.
780
RF/WIRELESS OSCILLATORS
#
Sθ( fm) = ∆θ2RMS = FkTB / Ps,av
$%&3E'
B J & &0 1 kTB = –174 dBm/Hz
(B = 1)
$%&3B'
$ fm' # "
. U&3 7 H 7 Sθ( fm > fc) = −174 dBm + 6 dB – 10 dBm = –178 dBm
$%&3%'
( P(1# X3 7 . L $ ' &CB 7K0 $&0 ' " Sθ( fm) &Kf fc #
" %H2 # # Sθ( fm) =
fc FkTB 1 + (B = 1) Ps,av fm
$%&3H'
; LL #
" %H8 # #
Figure 568
Phase noise modeled by a noisefree amplifier and phase modulator.
56
Figure 569
NOISE IN OSCILLATORS
781
Equivalent feedback models of oscillator phase noise.
L(ωm) =
1 1 + j(2QLωm / ω0)
$%&3C'
ω0 / 2QL = B / 2
$%&32'
# D #
ω0 ∆θout( fm) = 1 + ∆θ ( f ) j2QLωm in m
$%&38'
#
2
1 f0 Sθ,out( fm) = 1 + 2 fm 2QL Sθ F $%&3H' " L(fm) 1 L(fm) = 2
1 1 + 2 fm
2
f0 2Q L
Sθ,in( fm) Sθ,in( fm)
$%&&3'
$%&&&'
782
RF/WIRELESS OSCILLATORS
Figure 570
Equivalent feedback models of oscillator phase noise.
# $ LL ' # Sθ
f3 / /QL ,
fc f3 / /QL " %C3 " Q Q L(fm) & / f E & / f / " Q & / f E & / f @ F $%&3H' F $%&&&' 2 fc 1 f FkT 1 L(fm) = 1 + 2 1 + f P 2 2Q fm m L s,av 2 2 fc FkTB 1 f fc 1 f = + 1 + dBc /Hz + fm 2Ps,av f 3m 4Q 2L f 2m 2QL
$%&&/'
F. F $%&&/'  A &Kf "L "L QL $ Q' . QL =
ωoWe
Pdiss,total
=
ωoWe Pin + Pres + Psig
=
Reactive power Total dissipated power
$%&&E'
We L C We = Pres =
1 CV2 2 ωoWe
Qunl
$%&&B'
$%&&%'
56
NOISE IN OSCILLATORS
783
$%&&H'
# .
GLL D
F $%%H'I # A & L. Q. / L.
!" LKC # ) L
1 L . # Q & 0 Q E $O*' Q. ) O* 1 B * # 1 "F# 7=# #
) "
)
H98 IC . H3983
fT E× %× # fT # A • 7"OH%KHC • 7"!&3HK8/D 7"B3%KB/3 @
• /@*EE%2KEE%H ;F* • 0Z#!B&3% 0
784
RF/WIRELESS OSCILLATORS
• #/&33 $' ="F# 1E&3 /;BB&HK&C /;%E8C ) LL)* LF@"F# O"F# # &3 L0 &33 L0 # %%
#/&33 /3O0 npn $@
O
B%O0 fT @O ' % "F# # H * # !"
&39E3 Ω B3 7 # C # 2 " O"F# 0= "F#
;F* ;FB/B2B D F $%&&H'
) &CB 7K0 0 ) 9&C3 7K0 > M @
Q LC ) # Q # .  Q F $%&&E' #
.
A
1 1 1 = + QT,load Qload Qdiode
$%&&C'
56
NOISE IN OSCILLATORS
785
Table 55 Linear and SPICE equivalent circuits for the Avantek AT21400 chip
a
These equivalent circuits are provided only as firstorder design aids. Their accuracy for critical designs at very high frequencies has not been validated. b S parameters are from the linear equivalent circuit. Below 10 GHz, they have been fit to measurements of die on a standard carrier with one bond wire to the base and four wires to the emitter.
786
RF/WIRELESS OSCILLATORS
56
NOISE IN OSCILLATORS
787
788
RF/WIRELESS OSCILLATORS
# f . RS  $
E +' #
Q 562 AMtoPM Conversion >
) # ) Ra ; Vn = √ 4kT0R ∆f
$%&&2'
kT3 = B/ × &3−/& E33 Q R ∆f Ra /33 Ω %3 Ω ) B × B/ × &3−/& × &3333 Vn = √ −2 &/8H × &3 + √ 0 # +*( K3 (∆frms) = K0 × (1.296 × 10−8 V) in 1Hz bandwidth
$%&&8'
# θd =
2 K0√ fm
(1.296 × 10−8) rad in 1Hz bandwidth
$%&/3'
&33 0 K+ θd =
0.00183 rad in 1Hz bandwidth fm
$%&/&'
" fm J /% 0 $ 
"L ' θc = CE/ × &3−2 # @@7 A θc L(fm) = 20 log10 = −149 dBc / Hz 2
$%&//'
" &3 L0 K+ /3 7 G&3 $&3 L0 ÷ &33 0 'I 0 77&3B Rn /33 Ω &3 Ω F $%&&2' kT3 = B/ × &3−/&
56
NOISE IN OSCILLATORS
789
4 × 4.2 × 10−21 × 200 Vn = √ = 1.833 × 10−9 V√ Hz
$%&/E'
" F $%&&B' &3 L0 K+ &0 θd =
2 1 × 107√
(1.833 × 10−9) rad
$%&/B'
0.026 rad in 1Hz bandwidth fm
$%&/%'
fm
θd =
> fm = /% 0 θc = &3B × &3−H F. A θc L(fm) = 20 log10 = −126 dBc / Hz 2
$%&/H'
# F $%&//' ! ? @ @L,1 0 2HB3
) D ! ? @ 0 7
&33 0 K+ "* ) # ) &L0 D
) +*( # ) +*( ) &9&3 L0 K+ # "
: .
! F $%&3H' " %C& Q QL J &33
QL J &33333 Q E × &3H " %C/ * &3 0 &3 0
& 0 /3 0
790
RF/WIRELESS OSCILLATORS
Figure 571
Noise sideband of an oscillator at 150 MHz as a function of the loaded Q of the resonator.
Figure 572 to 10 kHz.
Noisesideband performance as a function of the flicker frequency fc varying from 10 Hz
56
NOISE IN OSCILLATORS
791
Figure 573 Noisesideband performance of an oscillator at 150 MHz, showing the influence of various tuning diodes.
" %CE %CB Q * " %CE K3 &3 0 K+D
* 7 &33 0 K+ 9&BE 7K0
9&%% 7K0
* * &L0 K+ +*( /% 0 9&/E 7K0 # " %CB &BCL0 +*( 7 Q . +*( S " %CB ) +*( $" %C%'
//30 All !" Q
LKC O $" %CH'
$ ' !"
> !" $ '
792 Figure 574 Noisesideband performance of an oscillator at 147 MHz, showing the influence of a tuning diode operated at bias voltages from 1.8 to 2.4 V in 0.1V increments.
56
NOISE IN OSCILLATORS
793
Figure 575 The VCO schematic. Because the tuning diode is in series with the resonator, it passes all of the tank’s RF current and plays a disproportionately large role in determining the circuit’s phasenoise performance.
Figure 576 Graphing the tuning diode’s ac load line reveals that increasing the diode’s tuning bias (decreasing its capacitance) results in a disproportionally large increase in the RF voltage across the diode. At all tuning voltages, the RF voltage across the diode is slightly positive (relative to the anode) during part of each cycle.
794
RF/WIRELESS OSCILLATORS
Figure 577 Adding capacitance across the tuning diode reduces the effect of its nonlinearities on phasenoise performance. We have also revalued the resonator to 120 nH to maintain oscillation near 147 MHz.
L $" %CC' Q LKC >
.
A # $" %C2' " %C8 # !" $ '
Figure 578 Now that the tuning diode passes only part of the tank’s RF current, varying its capacitance does not result in the large change in phasenoise performance shown in Figure 574. Note also that the phasenoiseversustuningbias relationship has reversed relative to that shown in Figure 574: The highest tuning voltage now corresponds to the lowest phase noise.
56
NOISE IN OSCILLATORS
795
Figure 579 The ac load line for the tuning diode in Figure 577. Now the voltage swing across the diode is virtually the same at all tuning voltages. The RF voltage across the diode still goes positive (relative to the anode) during part of the cycle.
" %23 +*( ; # &29/B+ " %2& " %C% %CC " %2/ " %2& # .
Figure 580 Tank circuit reconfigured as per Figure 554 to lightly couple the tuning diode in parallel with the resonator, with the resonator inductance again decreased to maintain oscillation near 147 MHz. The 1000pF capacitor and gate choke of Figure 575 (5.6 µH in series with 330 Ω) are no longer needed.
796
RF/WIRELESS OSCILLATORS
Figure 581 Comparison of worstcase phasenoise performance obtained with the tank configurations of Figures 575 (Original), 577 (Rev 1), and 580 (Rev 2).
Figure 582 Figure 579.
Comparison of the tuning diode’s ac load line for the worstcase phasenoise curves of
56
NOISE IN OSCILLATORS
797
)
" %2& C&N $" %C% ' &2N $" %CC ' 33BHN $" %23' @ "
. Q @ !" $" %%%' 7
+*( ) " %2E &3L0 B3L0 LC 02HB3 %33 L0 E&39HB3L0 02HH/ /9HO0 S)O H O0
Figure 583 Comparison of noisesideband performances of a crystal oscillator, LC oscillator, cavitytuned oscillator, switchedreactance oscillator, and YIG oscillator.
798
RF/WIRELESS OSCILLATORS
563 Nonlinear Approach to the Calculation of Oscillator Phase Noise #
$ .' LL # . # 1 : ! *! * = O 5, ( :; ( 1 ; *, #6 IEEE Frequency Control Symposium Proceedings &88B %B29%%B # @@7
$07' # . #
. #
.
#
Noise Generation in Oscillators. G8I #
A
• ;
• ;
>
07
Equivalent Representation of a Noisy Nonlinear Circuit. " %2B #
; G89&2I Frequency Conversion Approach. #
ω3$ ' ; # . , . #
# #
56
Figure 584
NOISE IN OSCILLATORS
799
Equivalent circuit of a general noisy nonlinear network.
# L
• ) L ω−& ω → 3 ω → ∞ • " D # ) #
# ω # (δZB δZH) A ∂EB ∂EB ∂EH ∂EH
δXB = JB(ω)
$%&/C'
δXH = JH(ω)
$%&/2'
FB FH J 07 ZB ZH J $@+' $
Z
ω3' =B =H J
800
RF/WIRELESS OSCILLATORS
# B H " ω A
• #
F $%&/C' # . #
conversion noise G&89/&I
• @ ω #
F $%&/2'  δZH # =H . #
modulation noise. ( δZH δω3 δω3(ω)
&0 ω F $%&/2' 
) L ω−E ω → 3 3 ω → ∞ L #
. " %2% ωZ ωZ " %2H $ ' )" > )" # . " %2C #
. D
) # .
Figure 585
Oscillator noise components.
56
NOISE IN OSCILLATORS
801
Figure 586 Noise sources where the noise at each sideband contributes to the output noise at the IF through frequency conversion.
" %22
&3 0 233L0 #
%
Conversion Noise Analysis. # $ @ 2x' kth Harmonic PM Noise
〈δΦk(ω)2〉 =
Nk(ω) − N−k(ω) − 2 Re[Ck(ω)]
Figure 587
RISS 2 k
Noise mechanisms.
$%&/8'
802 Figure 588 Biasdependent measured and predicted phase noise at 10 kHz off the carrier of an 800MHz oscillator.
56
NOISE IN OSCILLATORS
803
kth Harmonic AM Noise 〈δAk(ω)2〉 = 2
Nk(ω) − N−k(ω) + 2 Re[Ck(ω)]
$%&E3'
RISS 2 k
kth Harmonic PMAM Correlation Coefficient (ω) = 〈δΦk(ω)δAk(ω)∗〉 = −√ 2 CPMAM k
2 Im[Ck(ω)] + j[Nk(ω) − N−k(ω)]
$%&E&'
2
RISS k
Nk(ω) N−k(ω) J k Ck(ω) J k R J I@@ J k k
Modulation Noise Analysis kth Harmonic PM Noise 〈δΦk(ω)2〉 =
k2 T 〈J (ω)JtH(ω)〉TtF ω2 F H
$%&E/'
kth Harmonic AM Noise 〈δAk(ω)2〉 =
2 2 ISS k 
TA k 〈JH(ω)JtH(ω)〉TtAk
$%&EE'
kth Harmonic PMAM Correlation Coefficient (ω) = 〈δΦk(ω)δAk(ω)∗〉 = CPMAM k
2 k√ T 〈J (ω)JtH(ω)〉TtAk 2 F H jωISS  K
$%&EB'
=H(ω) J ; #F J . I@@ J k k
Experimental Variations. > .
" %28 &3L0 ) Q 7 ( ) 0E3B2
804
RF/WIRELESS OSCILLATORS
Figure 589
Abbreviated circuit of a 10MHz crystal oscillator.
" %83
0 " %8& ) L 233L0 +*( )
. L " %8/ * !"
&%Ω
Figure 590
Measured phase noise for this frequency standard by HP.
56
Figure 591
NOISE IN OSCILLATORS
805
Simulated phase noise of the oscillator shown in Figure 589.
& "
7=#
& "
" %8E
" %8B %8% %8H I9V
Phase Noise Optimization. 7
#
$ &% Ω' L9L " %8C
233L0 +*( > .
E/ 7 /3 L0 #
LL G//9/BI ) $ '
806
RF/WIRELESS OSCILLATORS
" %82
Summary. # # Q +*( #
"F#
. &3L0 &O0 *!
#
Figure 592 Colpitts oscillator that uses RF negative feedback between the emitter and capacitive voltage divider. To be realistic, we used actual components rather than ideal ones. The suppliers for the capacitors and inductors provide some typical values for the parasitics. The major changes are 0.8 nH and 0.25 Ω in series with the capacitors. The same thing applies for the main inductance, which has a parasitic connection inductance of 0.2 nH in series with a 0.25Ω resistance. These types of parasitics are valid for a fairly large range of components assembled in surfacemount applications. Most engineers model the circuit only by assuming lossy devices, not adding these important parasitics. One of the sideeffects we have noticed is that the output power is more realistic and, needless to say, the simulated phase noise agrees quite well with measured data. This circuit can also serve as an example for modeling amplifiers and mixers using surfacemount components.
807
Figure 593
Comparison between predicted and measured phase noise for the oscillator shown in Figure 592.
808 Figure 594
Predicted output waveform for the oscillator shown in Figure 592.
809
Figure 595
Predicted output spectrum for the oscillator shown in Figure 592.
810 Figure 596
The ac load line and dc I–V curves for the transistor in the oscillator shown in Figure 592.
811
Figure 597
Phase noise of the 800MHz VCO before and after optimization.
812 Figure 598 Calculated phase noise as a function of the supply voltage for a BJT oscillator. The graph shows a distinct minimum for a particular bias, which could be translated into a collector current change. Such phasenoise minimization could also be accomplished by changing just the voltage applied to the bias portion of the oscillator.
57
OSCILLATORS IN PRACTICE
813
Acknowledgment. # 1@ ,
, L)L)*
+ ! ,
F F
) @ F
1 7 ) L , "
* ; =
57 OSCILLATORS IN PRACTICE 571 Oscillator Specifications )
A Frequency Pushing. "
!" +*(  : $ ' K +*( $ ± & +' Harmonic Output Power. #
# /3 7
# Output Power. # . 7
%3Ω # 3 7 ± & 7 Output Power as a Function of Temperature. & 7 Posttuning Drift. #
+*( Power Consumption. #
Sensitivity to Load Changes. #
+*( ) frequency pulling
. +@>! $ &C% %3 Ω' +@>! $ %3 Ω' "
+*(
814
RF/WIRELESS OSCILLATORS
@
Spurious Outputs. +*( .
7 spurs . @
harmonic output power. Temperature Drift. +*(
)
&3 0 K4* 0 K4* Tuning Characteristic. #
+*( )
@
tuning linearity. Tuning Linearity. " ) . 3 + @
tuning characteristic. Tuning Sensitivity, Tuning Performance. # .
$L0 K+'
+*( Tuning Speed. #
+*( 83N #
#
+*( . 572 More Practical Circuits 7
)* . # " %88 @
)* " %&33 " %&3& 9 " %88 # " %88 " %&3/ " %88 " %&3E 7=# " %&3& :,L(@ "F# ="F# " %&3B 7=# # "F# Q B33 L0 7 O"F# B % O0 " %&3% O )* " %&3H
57
Figure 599
OSCILLATORS IN PRACTICE
815
Schematic of the Siemens IC oscillator.
" %&3C
# L L*&/&B2 F*: )* L*&HB2 L L*&/&B2 983 7K0 /% 0 #
*, $" %&32' " %&32 two A L C )
816 Figure 5100
Phase noise of the Siemens IC oscillator. The frequency of oscillation is 1.051 GHz.
57
Figure 5101
OSCILLATORS IN PRACTICE
817
Basic push–pull oscillator underlying the circuit shown in Figure 599.
7 Q $ /339E33 H39C3 '
( Q " LC
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Silicon/GaAsBased Integrated VCOs and Possible Difficulties. ,
+*(
#
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818 Figure 5102 The basic version of the oscillator (Discrete curve) is a better phasenoise performer than the integrated version (Monolithic curve). The frequency of oscillation is 1.039 GHz.
57
OSCILLATORS IN PRACTICE
819
Figure 5103 A 1.04GHz push–pull oscillator using LDMOS FETs instead of BJTs. (LDMOS FET parameters courtesy of David K. Lovelace, Motorola, Inc.)
Figure 5104
Phasenoise comparison of the BJT and MOSFET oscillators.
820
RF/WIRELESS OSCILLATORS
Figure 5105 A 1.022GHz IC oscillator based on two differential amplifiers. With an RF signal fed to the bases of Q1−Q4 and Q2−Q3 in push–pull, and IF output extracted from the collectors of Q1−Q3 and Q2−Q4 in push–pull, the circuit would act as a Gilbert cell converter. In the circuit shown, we have modified the differential amplifiers’ collector circuitry to give singleended output and avoid cancellation of the oscillator signal.
821 Figure 5106
Phase noise of the twodifferentialamplifier oscillator circuit.
822
RF/WIRELESS OSCILLATORS
Figure 5107 This validation circuit models the oscillator topology at the core of Motorola’s MC12148 ECL oscillator IC.
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/ [&BN )* " O Q %D /3 #
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$A \33E . W' ) +*( # . @ %H/ # D O " %&&3 D Q. = &&0 && 0 W ) )* )*
823
Figure 5108 Comparison of measured versus simulated phase noise of the MC12148 differential oscillator. The simulation (1.016 GHz) predicts a phase noise of –89.54 dBc/Hz at an offset of 10 kHz (Real L and C curve), which agrees well with Motorola’s specification of –89.54 dBc/Hz (typical at 930 MHz) at this offset. The Ideal L and C curve plots the simulation’s phasenoise performance with ideal reactances, as opposed to the Real L and C curve, which graphs the results with realistic Q values specified for its reactive components (Q = 250 for its C values and Q = 65 for its L, all at 1 GHz).
824 Figure 5109 Phasenoise performance of a 2.3GHz BJT oscillator with a resonator consisting of an inductor (2 nH) and a 1/4 λ transmission line (11 Ω, approximating the behavior of a dielectric resonator) with bias from a constantcurrent source and a lowimpedance, resistive constantvoltage source.
58
DESIGN OF RF OSCILLATORS USING CAD
825
Figure 5110 Samescale comparison of space requirements for transistors, capacitors, inductors, and bond pads. For reference purposes, the coil diameter is 0.2 mm.
58 DESIGN OF RF OSCILLATORS USING CAD 581 HarmonicBalance Simulation 07 . # # " 07 A
• • • •
1 L. L
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826
RF/WIRELESS OSCILLATORS
STANDARD HARMONIC BALANCE
Figure 5111 MESFET circuit partitioned into linear and nonlinear subcircuits for harmonicbalance analysis. Applied gate and drain voltages, and relevant terminal voltages and currents, are indicated.
Figure 5112 mization.
Flowchart of a generalpurpose harmonicbalance design algorithm that includes opti
827
Figure 5113 BJT microwave oscillator entered into the schematiccapture module of a commercial HB analysis program.
828
RF/WIRELESS OSCILLATORS
Figure 5114
Figure 5115 simulator.
Calculated phase noise of the microwave BJT oscillator shown in Figure 5113.
S11 response of a 3.8GHz BJT DRO as modeled by Ansoft’s SuperSpice timedomain
829
Figure 5116
Output voltage of the BJT DRO as simulated by SuperSpice.
830 Figure 5117
Current through the BJT DRO’s equivalent resonator inductance from startup to amplitude stabilization.
59
PHASENOISE IMPROVEMENTS OF INTEGRATED RF AND MILLIMETERWAVE OSCILLATORS
831
582 TimeDomain Simulation @)*F
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59 PHASENOISE IMPROVEMENTS OF INTEGRATED RF AND MILLIMETERWAVE OSCILLATORS * 591 Introduction #
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832
RF/WIRELESS OSCILLATORS
£(fm) = 10 log1 +
fc 2 1 + f (2fmQload) m f 20
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P(fm) J &0 fm 7 fm J f3 J fc J Q J Q F J kT = B& × &3−/& E33 Q $ ' Ps J R J $ /33 Ω &3 Ω' K3 J > LC Sφ( fm) = [aRF40 + aE(F0 / 2QL)2] / f 3m + [(2GFkT / P0)(F0 / 2QL)2] / f 2m + 2aRQLF30 / f 2m + aE / fm + 2GFkT / P0 G J F J k J 7 T J P3 J $ ' F3 J fm J QL(= πF3τg) J Q
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59
PHASENOISE IMPROVEMENTS OF INTEGRATED RF AND MILLIMETERWAVE OSCILLATORS
833
Figure 5118 Reduction of transistor flickerofphase noise via use of local negative feedback (emitter resistance), showing, for a BJT, the flicker noise or corner frequency, as well as the phase noise that results from the flicker noise. The negative feedback from the unbypassed emitter resistor reduces the flicker noise by up to 40 dB [26, 27].
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834
RF/WIRELESS OSCILLATORS
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Figure 5119
AFC stabilization of an external oscillator.
59
PHASENOISE IMPROVEMENTS OF INTEGRATED RF AND MILLIMETERWAVE OSCILLATORS
835
Figure 5120 Display of a typical phasenoise measurement using the delay line principle. This method is only applicable where x = sin(x). The measurements above the solid line violate this relationship and therefore are not valid.
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) " %&/E %HΩ Y& Y/ Y& npn $7*2B2*' Y/ $7"!8E' Y&D 07# " %&/E
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836
RF/WIRELESS OSCILLATORS
Figure 5121 frequencies.
Dynamic range as a function of cable delay. A delay of 1 µs is ideal for microwave
Figure 5122 Noise reduction in an oscillator whose signal flickeroffrequency noise is primarily due to sustaining stage flickerofphase noise. A phase perturbation in the sustaining stage produces a frequency change in the oscillator, which produces a change in the signal phase shift through the resonator detected as the phase detector. The resonator may be operated simultaneously in transmission line and reflection modes in the oscillator in the oscillator and discriminator portions of the circuit, respectively.
59
PHASENOISE IMPROVEMENTS OF INTEGRATED RF AND MILLIMETERWAVE OSCILLATORS
837
(a)
(b) Figure 5123 BJTbased oscillators with noise feedback. (a) The noise sampling is done in the transistor emitter; (b) the noise sampling is done in the collector using a variation of the active biasing circuit shown in Figure 5124.
838
RF/WIRELESS OSCILLATORS
Figure 5124
Phase noise of the oscillator in Figure 5123a with and without noise feedback.
Moving up into the millimeterwave area, one of the target oscillators is the Kaband MMIC voltagecontrolled oscillator designed for Kaband smart munitions applications (Figure 5127). This voltagecontrolled oscillator MMIC employs 0.25µm gate length, doubleheterojunction, pseudomorphic, highelectronmobility transistor (PHEMT) technology. This is a custom chip developed by Martin Marietta under the U.S. Government MMIC program. Ansoft Serenade tools were used in this design.
Figure 5125
Layout of the Motorola 800MHz monolithic differential oscillator IC in Si technology.
839
Figure 5126
Phase noise of the oscillator of Figure 5125. The noise floor is limited by the onboard isolation amplifier.
840
RF/WIRELESS OSCILLATORS
Figure 5127
Layout of the Kaband voltagecontrolled oscillator.
Features
• • • • • •
Fundamentalmode, differentialring VCO Electronically tunable Output power greater than 16 dBm Poweradded efficiency (PAE) of 13% Compact size for easy integration with power amplifier 0.25µm pseudomorphic HEMTs
Specifications
• Frequency range: Ka band • Output power: 16 dBm minimum When applying the same technology as shown in the previous bipolar example, the phase noise can be reduced significantly. Since fieldeffect transistors require a negative gate voltage, it is possible to sample the noise in the drain current using a resistor, amplify the noise with an appropriate loop amplifier, and modulate the gate voltage within a 1MHz bandwidth. A spectrum analyzer measurement of this oscillator type, as shown in Figure 5128, indicates a phase noise of 78.6 dBc/Hz at an offset frequency of 100 kHz at a center frequency of 38 GHz, while the closedloop phase noise of Figure 5129 using the compen
59
PHASENOISE IMPROVEMENTS OF INTEGRATED RF AND MILLIMETERWAVE OSCILLATORS
Figure 5128
Figure 5129
841
Spectrogram of the 38GHz freerunning push–pull VCO shown in Figure 5127.
Phasenoise performance of a 38GHz oscillator with phasenoise “cleanup” system.
842
RF/WIRELESS OSCILLATORS
Figure 5130 5129.
A 47GHz loopstabilized VCO with phasenoise performance similar to that of Figure
sation scheme indicates a phase noise of about 108 dBc/Hz at 100 kHz. This is consistent with reported results from other researchers who have used complicated phaselocked loops to achieve similar performance as seen in Figure 5130. 596 Summary A novel method of improving the phase noise of oscillators has been demonstrated. This approach works well for lowfrequency oscillators such as 1000 MHz up to the millimeterwave range. It only requires an additional wideband dc biasing circuit, which applies noise feedback. The correctness of the theory has been demonstrated by appropriate validation.
REFERENCES 1. Paul Danzer, ed., The ARRL Handbook for Radio Amateurs, 75th ed. Newington, CT: American Radio Relay League, 1997, Chap. 14, AC/RF Sources (Oscillators and Synthesizers). 2. Ulrich L. Rohde, Jerry C. Whitaker, and T. T. N. Bucher, Communications Receivers: Principles and Design, 2nd ed. New York: McGrawHill, 1997, p. 380. 3. G. Vendelin, A. M. Pavio, and U. L. Rohde, Microwave Circuit Design: Using Linear and Nonlinear Techniques. New York: Wiley, New York, 1990. 4. Samuel Y. Liao, Microwave Devices and Circuits, 2nd ed. Englewood Cliffs, NJ: PrenticeHall, 1985. 5. S. C. Peterson, 900MHz µStrip, Philips Semiconductors application document. 6. H. Keller, Electronic UHF Tuning in TV Receivers, RadioFernschPhonoPraxis, No. 3, 1967. 7. L. Micic, The Tuner Diode, Radio Mentor Electron., 32(5), 404405, 1966.
REFERENCES
843
8. KyungWhan Yeom, An Investigation of the HighFrequency Limit of a Miniaturized Commercial VoltageControlled Oscillator Used in 900MHz Band MobileCommunication Handset, IEEE Trans. Microwave Theory Tech., MTT46, 11651168, August 1998. 9. D. B. Leeson, A Simple Model of Feedback Oscillator Noise Spectrum, Proc. IEEE, 54, 329330, 1966. 10. U. L. Rohde, C. R. Chang, and J. Gerber, Parameter Extraction for Large Signal Noise Models and Simulation of Noise in Large Signal Circuits Like Mixers and Oscillators, Proceedings of the 23rd European Microwave Conference, Madrid, Spain, September 69, 1993. 11. C. R. Chang, Mixer Noise Analysis Using the Enhanced Microwave Harmonica, Compact Software Transmission Line News, 6(2), 49, June 1992. 12. T. Antognetti and G. Massobrio, Semiconductor Device Modeling with SPICE. New York: McGrawHill, 1988, p. 91. 13. R. J. Hawkins, Limitation of Nielsens and Related Noise Equations Applied to Microwave Bipolar Transistors, and a New Expression for the Frequency and Current Dependent Noise Figure, Solid State Electron., 20, 191196, 1977. 14. TzuHwa Hus and Craig P. Snapp, Low Noise Microwave Bipolar Transistor SubHallMicrometer Emitter Width, IEEE Trans. Electron Devices, ED25, 723730, June 1978. 15. R. A. Pucel and U. L. Rohde, An Accurate Expression for the Noise Resistance Rn of a Bipolar Transistor for Use with the Hawkins Noise Model, IEEE Microwave Guided Wave Lett., 3(2), 3537, February 1993. 16. See reference 3. 17. R. A. Pucel, W. Struble, Robert Hallgren, and U. L. Rohde, A General Noise Deembedding Procedure for Packaged TwoPort Linear Active Devices, IEEE Trans. Microwave Theory Tech., MTT40(11), 20132024, November 1993. 18. U. L. Rohde, Improved Noise Modeling of GaAs FETS: Using an Enhanced Equivalent Circuit Technique, Microwave J., Part I: 87101, November 1991; Part II: 8795, December 1991. 19. V. Rizzoli, F. Mastri, and C. Cecchefti, ComputerAided Noise Analysis of MESFET and HEMT Mixers, IEEE Trans. Microwave Theory Tech., MTT37, 14011410, September 1989. 20. V. Rizzoli and A. Lippadni, ComputerAided Noise Analysis of Linear Multiport Networks of Arbitrary Topology, IEEE Trans. Microwave Theory Tech., MTT33, 15071512, December 1985. 21. V. Rizzoli, F. Mastri, and D. Masotti, GeneralPurpose Noise Analysis of Forced Nonlinear Microwave Circuits, Military Microwave, 1992. 22. U. L. Rohde, Key Components of Modern Receiver Design, VHF Conference, Weinheim, Germany, September 1718, 1993. 23. C. R. Chang and U. L. Rohde, The Accurate Simulation of Oscillator and PLL Phase Noise in RF Sources, Wireless 94 Symposium, Santa Clara, California, February 1518, 1994. 24. U. L. Rohde, Oscillator Design for Lowest Phase Noise, Microwave Eng. Eur., 3140, May 1994. 25. Dieter Scherer, Design Principles and Test Methods for Low Phase Noise RF and Microwave Sources, RF & Microwave Measurement Symposium and Exhibition, HewlettPackard. 26. D. J. Healy III, Flicker of Frequency and Phase and White Frequency and Phase Fluctuations in Frequency Sources, Proceedings of the 26th Annual Symposium on Frequency Control, Fort Monmouth, NJ, June 1972, pp. 4349. 27. Michael M. Driscoll, Low Noise Oscillator Design Using Acoustic and Other High Q Resonators, 44th Annual Symposium on Frequency Control, Baltimore, MD, May 1990. 28. Ulrich L. Rohde, Microwave and Wireless Synthesizers: Theory and Design. New York: Wiley, 1997.
844
RF/WIRELESS OSCILLATORS
INTERESTING PATENTS Michel Fache and Claude Juliot, Tunable UHF Oscillator with Harmonic Limitation, Lignes Telegraphoques et Telephoniques (Societe), Paris Cedex, France, U.S. Patent No. 4,146,850, March 27, 1979. Thomas M. Higgins, Jr., Negative Resistance Oscillator with Electronically Tunable Base Inductance, HewlettPackard Company, Palo Alto, California, U.S. Patent No. 5,373,264, December 13, 1994. Osamu Ichiyoshi, VoltageControl Oscillator Which Suppresses Phase Noise Caused by Internal Noise of the Oscillator, NEC Corporation, Japan, U.S. Patent No. 5,351,014, September 27, 1994. Shankar R. Joshi, Ulrich L. Rohde, and Klaus Eichel, PhaseLocked Loop Circuits and Voltage Controlled Oscillator Circuits, Synergy Microwave Corp., Paterson, New Jersey, U.S. Patent No. 5,650,754, July 22, 1997. Joseph H. Kiser, WideRange Electronic Oscillator, VariL Co., Denver, Colorado, U.S. Patent No. 4,621,241, November 4, 1986. Joseph H. Kiser, Oscillator Voltage Regulator, VariL Co., Denver, Colorado, U.S. Patent No. 5,675,478, October 7, 1997. Charles Lewis, Low Phase Noise UHF and Microwave Oscillator, ZCommunications, Inc., San Diego, California, U.S. Patent No. 5,748,051, May 5, 1998. Larry R. Lockwood, LowNoise Oscillator, Tektronix, Inc., Beaverton, Oregon, U.S. Patent No. 4,580,109, April 1, 1986. Benedict J. Nardi, Low Phase Noise Reference Oscillator, WatkinsJohnson Company, Palo Alto, California, U.S. Patent No. 5,341,110, August 23, 1994. Leon Riebman, LowNoise Oscillator, AEL Defense Corp., Lansdale, Pennsylvania, U.S. Patent No. 5,166,647, November 24, 1992. Takeshi Saitoh and Hiroshi Hatashita, TV Tuner Oscillator with Feedback for More LowFrequency Power, Hitachi Ltd., Tokyo, Japan, U.S. Patent No. 4,564,822, January 14, 1986.
FURTHER READING Stanislaw Alechno, Analysis Method Characterizes Microwave Oscillators, Part 1, Microwaves & RF, 36(11), 8286, November 1997. P. Antognetti and G. Massobrio, Semiconductor Device Modeling with SPICE. New York: McGrawHill, 1993. W. Anzill, F. X. Kärtner, and P. Russer, Simulation of the SingleSideband Phase Noise of Oscillators, Second International Workshop of Integrated Nonlinear Microwave and Millimeterwave Circuits, 1992. Behagi, Piecewise Linear Modeling of SolidState VaractorTuned Microwave Oscillators, Proceedings of the IEEE Frequency Control Symposium, 1992, pp. 415519. Noël Boutin, RF Oscillator Analysis and Design by the Loop Gain Method, Appl. Microwave & Wireless, 11(8), 3248, August 1999. P. Braun, B. Roth, and A. Beyer, A Measurement Setup for the Analysis of Integrated Microwave Oscillators, Second International Workshop of Integrated Nonlinear Microwave and Millimeterwave Circuits, 1992.
FURTHER READING
845
C. R. Chang, M. B. Steer, S. Martin, and E. Reese, ComputerAided Analysis of FreeRunning Microwave Oscillators, IEEE Trans. Microwave Theory Tech., MTT39, 17351745, October 1991. Y. Cheng, K. Chen, K. Imai, and C. Hu, A Unified MOSFET Channel Charge Model for Device Modeling in Circuit Simulation, IEEE Trans. ComputerAided Des., 17, 641644, August 1998. J. Craninckx and M. Steyaert, A 1.8GHz LowPhaseNoise CMOS VCO Using Optimized Hollow Spiral Inductors, IEEE J. SolidState Circuits, SC32(5), 736744, May 1997. P. Davis, P. Smith, E. Campbell, J. Lin, K. Gross, G. Bath, Y. Low, M. Lau, Y. Degani, J. Gregus, R. Frye, and K. Tai, SilicononSilicon Integration of a GSM Transceiver with VCO Resonator, 1998 IEEE International SolidState Circuits Conference Digest of Technical Papers, pp. 248249. Alper Demir, Amit Mehrotra, and Jaijeet Roychowdhury, Phase Noise and Timing Jitter in Oscillators, Proceedings of the IEEE 1998 Custom Integrated Circuits Conference, pp. 4548. P. J. Garner, M. H. Howes, and C. M. Snowden, KaBand and MMIC pHEMTBased VCOs with Low PhaseNoise Properties, IEEE Trans. Microwave Theory Tech., MTT46, 15311536, October 1998. G. Gonzalez, Microwave Transistor AmplifiersAnalysis and Design, 2nd ed. New York: PrenticeHall, 1997. A. V. Grebennikov and V. V. Nikiforov, An Analytic Method of Microwave Transistor Oscillator Design, Int. J. Electron., 83, 849858, December 1997. Andrey V. Grebennikov, Microwave Transistor Oscillators: An Analytic Approach to Simplify ComputerAided Design, Microwave J., 42(5), 292300, May 1999. Ali Hajimiri and Thomas H. Lee, A General Theory of Phase Noise in Electrical Oscillators, IEEE J. SolidState Circuits, SC33, 179194, February 1998. Ali Hajimiri, Sotiriosw Limotyrakis, and Thomas H. Lee, Phase Noise in Multigigahertz CMOS Ring Oscillators, Proceedings of the IEEE 1998 Custom Integrated Circuits Conference, pp. 4952. Frank Herzel and Behzad Razavi, Oscillator Jitter Due to Supply and Substrate Noise, Proceedings of the IEEE 1998 Custom Integrated Circuits Conference, pp. 489492. Qiuting Huang, On the Exact Design of RF Oscillators, Proceedings of the IEEE 1998 Custom Integrated Circuits Conference, pp. 4144. Kamran Iravani and Gary Miller, VCOs with Very Low Sensitivity to Noise on the Power Supply, Proceedings of the IEEE 1998 Custom Integrated Circuits Conference, pp. 515518. K. M. Johnson, Microwave VaractorTuned Transistor Oscillator Design, IEEE Trans. Microwave Theory Tech., MTT14(11), 564572, September 1966. K. M. Johnson, LargeSignal GaAs MESFET Oscillator Design, IEEE Trans. Microwave Theory Tech., MTT27(3), 217226, March 1979. W. E. Kamali, J. P. Grimm, R. Meierer, and C. Trirons, New Design Approach for Wideband FET VoltageControlled Oscillators, IEEE Trans. Microwave Theory Tech., MTT34(10), 1059 1063, October 1986. F. X. Kärtner, Noise in Oscillating Systems, Second International Workshop of Integrated Nonlinear Microwave and Millimeterwave Circuits, 1992. T. Kashiwa, T. Ishida, T. Katho, H. Kurusu, H. Hoshi, and Y. Mitsui, VBand HighPower Low PhaseNoise Monolithic Oscillators and Investigation of Low PhaseNoise Performance at High Drain Bias, IEEE Trans. Microwave Theory Tech., MTT46, 15591565, October 1998. Peter Kinget, A Fully Integrated 2.7V 0.35 µm CMOS VCO for 5GHz Wireless Applications, 1998 IEEE International SolidState Circuits Conference Digest of Technical Papers, pp. 226228.
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RF/WIRELESS OSCILLATORS
J. Kitchen, Octave Bandwidth VaractorTuned Oscillators, Microwave J., 30(5), 347353, May 1987. A. Kral, F. Behbahani, and A. A. Abidi, RFCMOS Oscillators with Switched Tuning, Proceedings of the IEEE 1998 Custom Integrated Circuits Conference, pp. 555558. Vênceslav F. Kroupa, ed., Direct Digital Frequency Synthesizers. New York: IEEE Press, 1999. K. Kurokawa, Some Basic Characteristics of Broadband Negative Resistance Oscillator Circuits, Bell Syst. Tech. J., 19371955, July 1969. Fred Labaar, New Discriminator Boosts PhaseNoise Testing, Microwaves, 6569, March 1982. A. L. Lacaita and C. Samori, PhaseNoise Performance of CrystalLike LC Tanks, IEEE Trans. Circuits Syst. Analog Digital Signal Processing, 45, 898900, 1998. SenYou Liu and HueyRu Chuang, A 2.4GHz Transceiver RF FrontEnd for ISMBand Digital Wireless Communications, Appl. Microwave & Wireless, 10(5), 3248, June 1998. M. Madihian and T. Noguchi, An Analytical Approach to Microwave GaAsFET Oscillator Design, NEC Res. Dev., No. 82, 4956, July 1986. J. O. McSpadden, L. Fan, and K. Chang, HighEfficiency KuBand Oscillators, IEEE Trans. Microwave Theory Tech., MTT46, 15661571, October 1998. MiniCircuits Engineering, Designers Considerations for VCOs Used in PhaseLocked Loops, Microwave Prod. Digest, 24, 34, 36, 37, 40, February 1999. T. Nakagawa and T. Ohira, A Novel Phase Noise Reduction Technique for MMIC Frequency Synthesizers that Uses Newly Developed Pulse Generator LSI, NTT Radio Communication Systems Laboratories, 12356 Take, Yokosukashi, Kanagawa 23803, Japan. Mohamed K. Nezami, Evaluate the Impact of Phase Noise on Receiver Performance, Microwaves & RF, 41(5), 165172, May 1998. E. C. Niehenke and R. D. Hess, A Microstrip Low Noise XBand VoltageControlled Oscillator, IEEE Trans. Microwave Theory Tech., MTT27(12), 10751079, October 1986. Chris OConnor, Develop Trimless VoltageControlled Oscillators, Microwaves & RF, 38(7), 6878, July 1999. T. Ohira et al., A Compact Full MMIC Module for KuBand PhaseLocked Oscillators, IEEE Trans. Microwave Theory Tech., MTT37(4), 723728, April 1989. D. P. Owen, Measurement of Phase Noise in Signal Generators, Marconi Instrum., 15(6), 117122, 19xx. D. F. Page, A Design Basis for Junction Transistor Oscillator Circuits, Proc. IRE, 46, 12711280, November 1958. ByeongHa Park, 1 GHz, LowPower, LowPhaseNoise, CMOS VoltageControlled Oscillator with an Integrated LC Resonator, private communication with the author. D. F. Paterson, Varactor Properties for Wideband LinearTuning Microwave VCOs, IEEE Trans. Microwave Theory Tech., MTT28(2), 110119, February 1980. Matthew Pope, Russell Crouch, and Jeff Gudewicz, Dual Band Voltage Controlled Oscillators for Personal Communication, Microwave Prod. Digest, 52, 84, 85, May 1999. Nenad Popovic, Review of Some Types of Varactor Tuned DROs, Appl. Microwave & Wireless, 11(8), 6270, August 1999. R. A. Pucel and J. Curtis, NearCarrier Noise in FET Oscillators, IEEE MTTS International Microwave Symposium Digest, 1983, pp. 282284. S. Qi, K. Wu, and Z. Ou, Hybrid Integrated HEMT Oscillator with a MultipleRing Nonradiative Dielectric (NRD) Resonator Feedback Circuit, IEEE Trans. Microwave Theory Tech., MTT46, 15521558, October 1998.
FURTHER READING
847
M. Regis, O. Llopis, and J. Graffeuil, Nonlinear Modeling and Design of Bipolar Transistors UltraLow PhaseNoise DielectricResonator Oscillators, IEEE Trans. Microwave Theory Tech., MTT46, 15891593, October 1998. V. Rizzoli, F. Mastri, and D. Masotti, A General Purpose Harmonic Balance Approach to the Computation of NearCarrier Noise in FreeRunning Microwave Oscillators, MTTS, x, 309312, 1993. M. Runkel, Analyse und Vergleich Spannungsgesteuerter Oszillatoren für Mobilfunkanwendungen, Master Thesis, GerhardMercatorUniversistät Gesamthochschule Duisburg, Chaired by Prof. Dr. Ingo Wolff, August 1994. Carlo Samori, Andrea L. Lacaita, Francesco Vill, and Franco Zappa, Spectrum Folding and Phase Noise in LC Tuned Oscillators, IEEE Trans. Circuits Syst. Analog Digital Signal Processing, 45, 781790, 1998. Sarafian and B. Z. Kaplan, A New Approach to the Modeling of the Dynamics of RF VCOs and Some of Its Practical Implications, IEEE Trans. Circuits Syst. Fundam. Theory Applic., 40(12), 895901, December 1993. G. Sauvage, Phase Noise in Oscillators: A Mathematical Analysis of Leesons Model, IEEE Trans. Instrum. Meas., IM26(4), xx, December 1977. JwoShiun Sun, Design and Analysis of Microwave VaractorTuned Oscillators, Microwave J., 302310, May 1999. R. J. Trew, OctaveBand GaAs FET YIGTuned Oscillators, Electron. Lett., 13(21), October 1977. R. J. Trew, MESFET Models for Microwave ComputerAided Design, Microwave J., 33(5) 115128, May 1990. T. Yamasaki and E. Nagata, Microwave Synthesizer for Terrestrial and Satellite Communications, NEC Corporation, June 1989. N. L. Wang and W. J. Ho, XBand HBT VCO with HighEfficiency CB Buffer Amplifier, IEEE J. SolidState Circuits, SC27(10), 14391443, October 1992. ShingTak Yan and Howard C. Luong, A 3V 1.3to1.8GHz CMOS VoltageControlled Oscillator with 0.3ps Jitter, IEEE Trans. Circuits Syst. Analog Digital Signal Processing, 45, 876880, 1998. D. A Warren, J. M. Golio, and W. L. Seely, Large and Small Signal Oscillator Analysis, Microwave J., 32(5), 229246, May 1989. R. Winch, Wideband VaractorTuned Oscillators, IEEE J. SolidState Circuits, SC17, 12141219, December 19, 1982. Markus Zannoth, Bernd Kolb, Josef Fenk, and Robert Weigel, A Fully Integrated VCO at 2 GHz, 1998 IEEE International SolidState Circuits Conference Digest of Technical Papers, pp. 224225.
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" ' ' #$ 0' 1 0' !! ' charge pump " ' " ) /2 " 3 ' fractionalNdivision ' ' ' 4 " ' 848
62
PHASELOCKED LOOPS
849
Figure 61 Block diagram of an integrated frequency synthesizer. In this case, the designer has control over the VCO and the loop filter; the reference oscillator is part of the chip. In most cases (up to 2.5 GHz), the dualmodulus prescaler is also inside the chip.
:
' D 4 #$ ) /2 " ' %
Figure 68 Phase detector with two D flipflops and a NAND gate. In this book, this type of phase detector will be called a tristate comparator.
856
WIRELESS SYNTHESIZERS
Figure 69 Logic diagram of the tristate detector.
"
4 " ' " " 4 ' " ) /7 ' " ' ) / f2 G Bf f * f2 Q2
E7M % E7M ) /" f * " f2 Q2 D V
62
Figure 610
PHASELOCKED LOOPS
857
Transfer characteristic of the tristate phase/frequency comparator.
/=M f2 G Bf " " Vave = 1 −
f1 V f2
/E
f2 f D ) /2 f f2
Figure 611
Output waveform of the tristate frequency comparator for different input frequencies.
858
WIRELESS SYNTHESIZERS
Figure 612
Average output voltage as a function of frequency ratio.
" " 1 quadD % A ' "
#$ F D '% ) /B 0' %