mixed signal ic design notes set 3: more high frequency ......rc q1 q2 i1 i2 rf gm2 cbe2 rf gm1 rf...

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


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

))


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


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 ==


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


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


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….


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


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


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=?


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=?


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


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


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


Resistive feedback as 50 Ohm gain blocks

ips...relationshgain theNote


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


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...


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


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 ?


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 <


Cherry-Hoopers: DC bias variants

Rf

Rc

Q1

Q2

I1

I2

Rf

Rc

Q1

Q2

I1

I2

Rf

Rc

Q1

Q2

I1

I2


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

=+=


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=


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


Darlingtons 1

Why not just use emitter followers to buffer the stage input capacitances ????

Rc

Rc

Rc

Rc Rc


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


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


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


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


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….

mixed signal ic design notes set 3: more high frequency ......rc q1 q2 i1 i2 rf gm2 cbe2 rf gm1 rf...

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