ECE194J /594J notes, M. Rodwell, copyrighted 2011
Mixed Signal IC DesignNotes set 3:More High Frequency Amplifier Design
Mark RodwellUniversity of California, Santa Barbara
[email protected] 805-893-3244, 805-893-3262 fax
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Why do we care about impedances matched to 50 Ohms?
( )
terminated-well bemust lines or the lines,smission short tran havemust
Either we .)2exp(1 form theof ripples
gain/phase cause linesssion on transmi wavesStanding1−−ΓΓ− τfjLS
0 10 20 30 40 50 60 70 80 90 100freq, GHz
24
25
26
27
28
29
30
31
32
dB(S
(2,1
))
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Why do we care about impedances matched to 50 Ohms?
on waferblockscircuit major between cases) some(in or boundaries
chipat Ohms 50 e.g. tointerfacejust and ,interfacesinternal z-high usecan we,dimensions small has IC If
50 ohminterface(Zin=50)
50 ohminterface(Zout=50)
IC “core”with highZ interfaces
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Why do we care about transmission lines ?
*.*ignored be*cannot * parasitics itsbut lumped as modeled be can lineshort a hence
,* ,/ that aware bemust weBut,
lines. theon wavesstanding ignore can wemeans This
*.**lumped* as ctsinterconne all treat can we thenshort, are whichctsinterconne has IC theIf
.parameters-S and lines ion transmissignore tolike would we when timesare There
olinelineolineline ZLZC ττ ==
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Effect of lumped wiring parasitics on IC performance
RLRL
important more becomes ecapacitancct interconnehence and high for designing means I) (lowpower low
for designing , )/( isgain theSince
of timecharging RCan get weAnd ,* ,/
,parasitics BJT Ignoring lumped. as linesshort thesemodelcan weHere
wiring
L
LLm
Lline
olinelineolineline
RRqIkTRg
RC
ZLZC
=
=
==
τ
ττ
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Effect of lumped wiring parasitics on IC performance
response pulse andstability EF upon theeffect lsubstantia have...can ,*
thatunderstand will wedetail,in responsefrequency EF studied have weOnce
olineline ZL τ=
RLRL
RL RL
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Getting more bandwidth
At this point we have learned basics (MOTC etc)
How can we get more bandwidth…. ?Resistive feedbacktransconductance-transimpedanceemitter-follower buffers, benefits and headachesemitter degeneration…basicsemitter degeneration and area scalingft-doubler stages..distributed amplifiersft-doubler stages…simple, RL, power, with Darlingtonbroadbanding / peaking with LC networks….distributed amplifiersexamples….
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Broadband gain blocks: "worlds simplest amplifier"
better. much do can We limit". " theof origin theis This .2/ isproduct bandwidth-gain theand ,2/1 is bandwidth the, is stageper gain the n,combinatio & simplea as BJTeach model weIf cascade. stage CEa becomes thispath, signal aldifferenti
For thepairs. aldifferenti simple of cascadea Examine
τ
τππ
ffCg
CRRgCg
inm
inCCm
inm
=−
Rc
Rc2Rc
2Rc
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Broadband gain blocks: "worlds simplest amplifier"
τπfgC
g
min
m
2/ ratio by the e,capacitancinput of price theat comes *always* ctanceTranscondu ip.relationsh gain the
.henceresistor..a using a voltage intoback current output isconvert th toisstrategy designsimplest Our current.output
an into converted is ageinput volt An . ctancetranscondu provide tomade are sTransistor through.s think thiusLet
=
Rc
Rc2Rc
2Rc
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Resistive feedback stages, I: gain and impedance
.*)1( and /)1(set weif obtained are of sresistance
output andinput with (negative) ofgain stage-Per.lecture...in done be toanalysis dalgain....no voltage
into converting of way tedsophistica more a is This
//
/
outinfoutinm
outin
m
RARRAgR
A
g
−=−=
Rf
gm
Rf
gm
Rf Rf Rf Rf
gm gm gm gm
Rf
gm
RL
Rf
gmRgen
Rin=? Rout=?
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Resistive feedback stages, I: bandwidth and gain-bandwidth
( ) ( )( )
! stage CE simple aofbandwidth the*twice* is this,1for that Note
)....1/(21/)2/(2/1
,2/ and /)1( Since
3
/3
/
>>−=
−===−=
AAff
ACgCRffgCRAg
dB
moutindB
moutinm
τ
τ
πππ
Rf
gm
Rf
gm
Rf Rf Rf Rf
gm gm gm gm
Rf
gm
RL
Rf
gmRgen
Rin=? Rout=?
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Why have we nearly doubled the bandwidth ?
..bandwidth. the twicehence and , the1/2get we...soimpedance.given aat gain desired obtain the
to the1/2roughly need We.resistance loading physical ain current output t significan losing without of
impedance *output* provided hasfeedback resistive The
/
C
gR
m
outin
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Variations on resistive feedback.
amplifieran build ofeedback t resistiveor loading resistiveeither with used becan then block This
block. thebuild tors transistoof sets usecan We mg
Rf
gm
Rf
-gm
-gm
-gm
resistive feedback
resistive loading...
gm blocks
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Feedback with buffer
stage. EF theof escapacitanc additional by theoffset partially ist improvemen the
thoughstages, gain-lowfor bandwidth improves This
. / toreduced also is required The . biasing in easefor used often is This
/outinmm RAgg −=
Rf
gm
Rf
-gm
Av=1
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Resistive feedback as 50 Ohm gain blocks
ips...relationshgain theNote
ECE194J /594J notes, M. Rodwell, copyrighted 2011
High Speed Amplifiers
18 dB, DC-50 GHz
Dino MensaPK Sundararajan
8.2 dB, DC-80 GHz
-15
-10
-5
0
5
10
0 10 20 30 40 50 60 70 80
Gai
ns, d
B
Frequency, GHz
S21
S11
S22
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50
S22
S11
S21
ECE194J /594J notes, M. Rodwell, copyrighted 2011
2-stage differential amplifier
Rf
-gm-gm
First stage is resistively terminated, second stage has resistive feedback…this is because first stage is allowed to limit, or can have AGC applied, either of which would violate the feedback gain/impedance relationships...
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Cherry-Hooper Gm-Zt amplifier
( ) ( )
21
2
22
isgain Overall
. these)(derive is stage second of anceTransimped
./1)1/()( is stage 2nd
of impedanceInput .consistentnot are impedancesutinput/outp Here araint.feedback vpopular Very
Tmv
fCmfmfT
mcmfcin
ZgA
RGgGgRZ
gRgRRR
=
→+−=
→++=
Rf
-gm-gm
Rf
Rc
Q1
Q2
I1
I2 Rc
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Cherry-Hooper Gm-Zt amplifier
Rf
-gm-gm
Rf
Rc
Q1
Q2
I1
I2 Rc
Let us work through impedances and gainsboth carefully and by back-of-envelope……why is first order time constant so small ?
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Cherry-Hooper Gm-Zt amplifier--limiting behavior
Rf
-gm-gm
Rf
Rc
Q1
Q2
I1
I2 Rc
feedback.by provided constants)short time (hence impedances low maintainsoperation
signal-large encestage....h Zt not the stage, gm on thelimit always willamplifier this)(derive If 21 II <
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Cherry-Hoopers: DC bias variants
Rf
Rc
Q1
Q2
I1
I2
Rf
Rc
Q1
Q2
I1
I2
Rf
Rc
Q1
Q2
I1
I2
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Cherry-Hooper bandwidth---zero'th order
Rf
Rc
Q1
Q2
I1
I2 Rf
gm2Cbe2
Rf
gm1
Rf
gm2 gm3 gm
CLgm1
( )
paper.... Hitachiin analysis detailed moreMuch NOT. isconstant order time-second
small, isconstant order time-firsty that immediatel Notelecture)in example detailed more(work /
,inspectionBy
222
221
mLbeL
mLbe
gCCRagCCa
=+=
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Gm-Zt amplifier: understanding time constant behavior
-gm
Rf
1/1 of impedanceoutput andinput has This
moutin gRR ==
-gm-gm -gm-gm -gm-gm
1/ ofconstant timecharging hascapacitor each So mgC
-gm-gm -gm-gm -gm-gm
Rf Rf Rf
C1 C2
.)/( form theof are a2in termsso
constant timecharging C1 themakes C2 Shorting
12
1
fm
f
RCgCRC=
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Cherry-Hooper bandwidth---with Ccb
damping improved has andbandwidth reduced has Ccb that note
))(/())(/())(/(
//
23223222
23221
fcbmbefcbmbefbembe
fcbmbembe
RCgCRCgCRCgCaRCgCgCa
++=
++=
CcbCcb
Rf
gm2ViCbe2
Rf
gm1
Rf
gm2 gm3 gm CL=Cbe3gm1
Ccb
Vi
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Darlingtons 1
Why not just use emitter followers to buffer the stage input capacitances ????
Rc
Rc
Rc
Rc Rc
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Darlingtons 2
R1 RL R1 RL
R1 RL
Q1Q2
Rbb1
Rbb2
Ccb1Ccb2
Cbe1 Cbe2
( )
...)/()()(()!0()(
)1)(()(
... and 0Rex Taking
2111112122
1111
2122
1221
++++=+++
+++++=
∞==
bbeebbebbbebe
bebbcb
LLmebbcb
ebbbe
RrrRRrRCCaCRRC
RRgrRCrRCa
β
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Darlingtons 3
dampingcircuit in reduction consequentwith constant, order time-second in the **reappear*must *
)( that (2) and )later! on this (more minimum aat is for timecharging the(1) that reveals
ion considerat detailed more aBut ry texts.introductoin givencommonly Darlington for the motivation theis This
)( of instead )(:for timecharging reducedgreatly theNote
12222
2
12211221
2
RRCRCC
RRCarRCaC
bbbebbbe
be
bbbeebbbe
be
+
+=+=
R1 RL
Rbb1
Rbb2
Ccb1Ccb2
Cbe1 Cbe2
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Darlingtons
damping of lossin result response broadband to..attemptsrough...)...(work th
constant order time- second not thebut small,ery constant vorder time-first themakecan weNote ./ ratio theto
alproportion isfactor damping The ./A gain that and that note then stages, of cascade a have weIf
Then zero). are parasitics BJTother (all alone ofeffectat look tshard....le is problemexact Clearly,
21
21
1
11122
121
aa
rRRR
RrCCarCa
C
e
L
ebebe
ebe
be
===
==
R1 RL
Cbe1 Cbe2
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Darlingtons: improving the damping
( )( )( ) ( )( )( )( ) ( )( )
ee
122
112,1112
,22,1111
R of loading parallel the todue reducedare ) (e.g. Cbe2, with associated a2in termsy,importantl
More increased. are Cbe1 with associated a1in terms theSo,
...1
...1
reduced isgain EF Q1 The effects. 2 has Ree ofAddition
R
RRRCARRCa
RRRCARRCa
bbeebeefvbbbe
efouteebbbeefvbbbe
++−+=
+++−+=
R1 RL R1 RL
Q1Q2
Cbe1 Cbe2Ree Ree
R1 RL
Rbb1
Rbb2Cbe1 Cbe2
Ree
ECE194J /594J notes, M. Rodwell, copyrighted 2011
Getting more bandwidth
At this point we have learned basics (MOTC etc)
How can we get more bandwidth…. ?Resistive feedbacktransconductance-transimpedanceemitter-follower buffers, benefits and headachesemitter degeneration…basicsemitter degeneration and area scalingft-doubler stages..distributed amplifiersft-doubler stages…simple, RL, power, with Darlingtonbroadbanding / peaking with LC networks….distributed amplifiersexamples….
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