mixed signal ic design notes set 4: broadband design ...€¦ · ece194j /594j notes, m. rodwell,...

ECE194J /594J notes, M. Rodwell, copyrighted 2011

Mixed Signal IC DesignNotes set 4:Broadband Design Techniques

Mark RodwellUniversity of California, Santa Barbara

[email protected] 805-893-3244, 805-893-3262 fax


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 amplifiersbroadbanding / peaking with LC networks….examples….


Emitter Degeneration, I

./such that ncombinatio RCan want instead wefind will We.resistance

emitteran only using introduced on wasdegeneratiEmitter

mbeee gCCR =

Re Ce Re

ReCe


Emitter Degeneration, 2

later....back themadd and removed, etc ,ithcan work w wesuch that is topology that thenoteNext

cbbb CR

ReCe ReCe

CbegmVbe

Vbe

+

-


Emitter Degeneration, 3

( )

changedont y back...the added be nowcan etc and )1(

and )/1/( So,cancel) termsdependent frequency that the(note

*/1But

)( so :Vbe from Working

12

13

321

cbbb

Embeinin

mEbe

EmbeEEE

bebembembebe

CRRgCjCjZ

gRVI

RgVCjRIV

VCjgIVgIVCjI

−

−

+==

+=

=+=

+===

ωω

ω

ωω

ReCe

CbegmVbe

Vbe

+

-

Ve

Vb

I1

I2

I3


Emitter Degeneration, Summary

ReCe

CbegmVbe

Vbe

+

-

+

-

Rbb Ccbi

Ccbx

Rbb Ccbi

Ccbx

1)1( −+= Embein RgCC1

, )1( −+= Emmextrinsicm Rggg

Other element values do not change...


Emitter Degeneration, Unbypassed emitter resistance

1, )1( −+= Emmextrinsicm Rggg

can be shown by elementary nodal analysis, work through…Key observation: degeneration by this method results in a seriesinput resistance, which can increase Cbe charging time.

Rex

CbegmVbe

Vbe

+

-+

-

Rex

Cbe gmVbeVbe


Emitter Degeneration, combination case

ReCe

Cin

gmextVin

Vin+

-

Rex

CcbiCcbx

Rex

RbbCcbi

Ccbx

Rbb

CbegmVbe

Vbe

+

-

1)1( −+= Embein RgCC1

, )1( −+= Emmextrinsicm Rggg


Emitter Degeneration and Area Scaling 1

[ ]LLextmbbgencbbbgenbe

LextmV

RRgRRCRRCa

RgA

+++++=

−=

)1)(()( have then we

,gain a desire weIf stage. CS heConsider t

,1

,

emitter area =Aecurrent density =JeCurrent =Ae*Je=Ietransconductance=gminput capacitance=Cbecollector capacitance=Ccbbase resistance=Rbb



Ce Reemitter area =Aecurrent density =JeCurrent =Ae*Je=Ietransconductance=gminput capacitance=Cbecollector capacitance=Ccbbase resistance=Rbb

Bigger transistor, before degenerationemitter area =kAecurrent density =JeCurrent =kAe*Je=Iketransconductance=kgminput capacitance=kCbecollector capacitance=kCcbbase resistance=Rbb/know degenerate:Re picked such that (1+gmRe)=kintrinsic transconductance=kgmextrinsic transconductance=kgm/(1+gmRe)=gminput capacitance=kCbe/(1+gmRe)=Cbecollector capacitance=kCcbbase resistance=Rbb/k



Ce Re

[ ] [ ]

bandwidthhighest thegives and Ccb, vsRbb with associated sdelay term exchangesk of choice eappropriat So,

)1()1(

)1(

1:Kby Rbb decreased and 1:Kby Ccb increased havebut Cin, and gm original theleft with are We1.:Kby ddegenerate

then bigger, K timesr transisto themade have We

,,1

,1

LLextmgencbbbbe

Lextmbbcbbegen

LLextmbb

gencbbb

genbe

RRgRkCkRCRgRCCRa

RRgk

RRkCk

RRCa

++++++=

++

++

+=


Emitter Degeneration and Area Scaling 4: Emitter Follower Case

? thisdo want tomight weWhy


Emitter Degeneration and Area Scaling 5: Emitter Follower Case

( )

this.address tomethod one is above as generationscaling/de Area limit.bandwidth major a becan and , 2/1 timesseveral is

HBTan ofconstant time tedundegenera that theNote

1...

stage, CE with theassociated a1in only terms gConsiderin

1,2

2,1,2

21

τπfCR

Rk

RCRRgRk

RkCa

bebb

outbb

beLLextmoutbb

cb

++

++

++=

R1RL

Rbb1Rbb2

Ccb1Ccb2

Cbe1Cbe2


Ft-doubler stages….the Darlington Revisited

R1 RL R1 RL

Q1Q2

Cbe1 Cbe2Ree Ree

R1 RL

Rbb1

Rbb2Cbe1 Cbe2

Ree

Recall the improvement in Damping provided by Ree….…is there a larger lesson here ?


2 Kinds of Darlington:

If collectors are tied together:AC collector currents of both transistors contribute to output :)Both transistor Ccb's undergo Miller multiplication :(

Rgen RL

Q1Q2

Ree

RgenRL

Q1Q2

Ree

Collectors tied togetherEF collector grounded


Ft-doubler stages 2

Ree=1/gm1

Cbe2

Cbe1gm1Vbe1

Vbe1

+

-

gm2Vbe2

Vbe2

Vin

Iin Ic1

Ic2Ie1

Iout


Ft-doubler stages 3

beminoutbembein

inbebebebeeembe

meembeeebeee

eebe

mbeeebemeebeeeebe

mbebemebemcbebein

CjgIIVgICjIVVVVVRgV

gRgCRCRRCjgCjRVgRCjRIV

gCjVgIVgIVCjI

ωω

ωωω

ωω

/2/ hence and 2/2/ so...)(

/1 hence.../ such that Choose)1()/1()1/(

)/1( , , :V fromWork

out

21112

1

112

111111

be1

=======

==+

+=+=

+===

Ree=1/gm1

Cbe2

Cbe1gm1Vbe1

Vbe1

+

-

gm2Vbe2

Vbe2

Vin

Iin Ic1

Ic2Ie1

Iout


Ft-doubler stages 4

.parasiticsother theseof presence given the bandwidth,circuit overall doubled have wenor will fmax, doublednot certainly have Ccb...we and Rbb ignored has analysis that thisNote

! doubled have ..we/2/2/

and 2/ out

τ

τωω

fjffCjgII

VgICjI

beminout

bembein

====

Ree=1/gm1

Cbe2

Cbe1gm1Vbe1

Vbe1

+

-

gm2Vbe2

Vbe2

Vin

Iin Ic1

Ic2Ie1

Iout

+

-

Cbe/2gmVin

Vin


ft-doubler vs Darlington…thinking in terms of current gains:

econductancinput negativebut gain current high giveswhich )/( as sfrequencielower at sgain varieCurrent

...)/()/(2)(2

/

)( Since/ where)(2/ isgain Current

2

222121

212121

212

2121

jffjffjff

gHH

gYVI

VgVVgVgVgIIIjffHHHII

mmininin

inmbebembembemccout

inout

τ

ττ

τ

=+

=+

==

=+=+=+==+=

Iin H21Iin

(1+H21)Iin

Cbe2

H21(1+H21)Iin

(2*H21+H21*H21)Iin


ft-doubler vs Darlington…thinking in terms of current gains:

)/2( as sfrequencie allat sgain varieCurrent

)2/2(2)/(22

/

)( Since/ where2/ isgain Current

21

212121

2121

jff

Cjff

jfgjff

gHgYVI

VgVVgVgVgIIIjffHHII

bemmm

ininin

inmbebembembemccout

inout

τ

ττ

τ

π=====

=+=+=+===

Iin H21Iin

(1+H21)Iin

Cbe2

H21IinIin

H21Iin

2*H21Iin


ft-doubler vs Darlington…current gains:


ft-doubler …correction for Base resistance

Ree=1/gm1

Cbe2

Cbe1gm1Vbe1

Vbe1

+

-

gm2Vbe2

Vbe2

Vin

Iin Ic1

Ic2Ie1

Iout

L=CbeRbb/gm

Rbb

L=CbeRbb/gm

The indicated inductance is necessary for equal current splittingbetween the 2 transistors in the presence of Rbb. In this case theinput impedance is Cbe/2 in series with Rbb/2…again notethat this correction is significant because RbbCbe>>Cbe/gm


ft-doubler vs Darlington

What is the conclusion of all this ? We can view the ft-doubler as a special case of the connected-collector Darlington with heavy emitter-follower loading: in this case the second-order (resonant) response is entirely suppressed. More generally we might vary the EF loading to vary the damping. (The particular case of power amplifiers favors the ft-doubler due to efficiency reasons…)


Tuning: to prevent reflections, to peak gain

gain andmatch input S21, and S11both hurt has ecapacitancinput The

1 where,2/1

2/

2/12/

0

011

021

=

+=

+−

=

CjZZ

CZjCZjS

CZjZgS

oin

om

ωωω

ω

Cin

Rin=Zo

Zo

Rout=Zo

Zo


Pi-section input tuning….

)/1 (henceshort issection -pi thesuch that freqeuciesfor Effective

)2(2/2/

section-pi a into ecapacitancinput r transisto theAbsorb

0 CZf

ZZCZLZCCC

o

ooino

obein

π

ττ

<

=====

Cin=C/2

Rin=Zo

Zo

Rout=Zo

Zo

Cx=C/2

L

Gain flatness and match improved for f<fo, but made worsefor f>f0


T-section input tuning….

case...section -pi the torelative fo doubled have weCin,given afor that Note

)/1 (henceshort issection -pi thesuch that freqeuciesfor Effective

)2(/

section-T a into ecapacitancinput r transisto theAbsorb

0 CZf

ZZCZLZCCC

o

ooino

obein

π

ττ

<

=====

Cin=C

Rin=Zo

Zo

Rout=Zo

ZoL/2

L/2


T-section tuning in feedback amplifiers

stability. reducedisger FBAs...dan Ohm 50in used frequently is This

)1)(2/(

)1(:ionApproximatMiller By

ALLAZR

f

of

−=

−=

Cin=C

Rin=Zo

Zo

Rout=Zo

ZoL/2

L/2

Cin=C

ZoZo

L/2 Lf

Rf


Bridged-T-section input tuning….

case...section -T theasfrequency same about theat off rolls ssneverthele S21 zero.exactly is S11 Cbe,by

modeled impedanceinput an hasr transisto theasInsofar )2(/

ooino

obein

ZZCZLZCCC

=====

ττ

Cin=C

Rin=Zo

Zo

Rout=Zo

ZoL/2

L/2C/2


Bridged-T-section input tuning….

Karthik Krishnamurthi


Tuning Networks use Microstrip elements....

Cin=C/2

Rin=Zo

Zo

Cx=C/2

L

Cin=C/2

Rin=Zo

Zo L

Cin=C/2

Rin=Zo

Zo

Cx

L

Cx=C/2


Distributed Amplifiers : Theory

synthetic drain line

synthetic gate line

• HEMT input/output capacitances absorbed into artificial input/output lines• broadband circuit ; gain/bandwidth limited by

HEMT resistive parasitics (fmax)distributed structure Bragg frequencyinput/output transmission line skin-effect losses


Synthetic Transmission Lines

transmission line section

line section inductance

• synthetic input/output line formed by transmission line sections• transmission line

characteristic impedancecutoff (Bragg) frequency delay

line section capacitanceHEMT input capacitance

L/CZ =LCfB π/1=

LCT =


Transmission Line Loss

lossless line

frequency-dependent loss

frequency-independent loss

2/4 02

122 RZCfπ=α

RZ 2/0=α


HEMT Equivalent Circuit

• simplified equivalent circuit

gsm Cgf π=τ 2/ ids rrff 4/max τ=

• element values scale with HEMT size

•


CS HEMT TWA


CS HEMT TWA--LC equivalent


CS HEMT TWA--SS model


TWA…limits to gain and bandwidth...

problem... rs....no transistosmall very of lotshigh with very made be...can /1

Frequency Braggbandwidth-gain feasible sets limits, aboveer with ....togeth

)ratioon degenerati capacitive)(2/(GainFrequency -Low

right...design get werequires...just 90)MismatchDelay Output -Input

2/ becauselimit gain a sets...2/1NLoss Line (output)Drain

... becauselimit frequency high a ...sets 2/1N:loss e(input)lin Gate

21

0

d

22g

LCf

ZNgS

TN(T

RZ

RC

om

draingate

dsod

ig

π

αα

ωαα

<

=

<−

=<

=<


Undamped Darlington FBA

-20

-15

-10

-5

0

5

10

15

20

0 10 20 30 40 50

S22

S11

S21


Feedback Amplifier with Follower Driving ft-doubler

-15

-10

-5

0

5

10

0 10 20 30 40 50 60 70 80

Gai

ns, d

B

Frequency, GHz

S21

S11

S22


80 GHz HBT Distributed Amplifier

-20

-15

-10

-5

0

5

10

15

0 20 40 60 80

Gai

ns, d

B

Frequency, GHz

S21

S22

S11


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mixed signal ic design notes set 4: broadband design ...€¦ · ece194j /594j notes, m. rodwell,...

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