ECE145a / 218a Resistive Feedback Amplifiersclass notes, M. Rodwell, copyrighted 2009 ECE145a / 218a Resistive Feedback Amplifiers Mark Rodwell University of California, Santa Barbara

class notes, M. Rodwell, copyrighted 2009

ECE145a / 218a Resistive Feedback Amplifiersp

Mark RodwellUniversity of California, Santa Barbara y

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


Resistive Feedback For Line Termination

sferpower tran Maximum1)matching-impedancefor reasonsdifferent 2 are there:Recall

lines. on wavesstanding from ripple gain Avoiding 2)p)

s.reflection line eliminate order to inprovidesfeedback ,amplifiersfeedback resistive In ooutin ZZZ ==

gain. maximumr transisto theobtainnot do wehence sfer,power tran maximumfor designed *not* are These


World's Simplest Amplifier

lines.-nsmissionoutput tra andinput toconnected tees,bias andr transistoof consistsAmplifier

dlitlfamplifier; toexternal are lines-onTransmissi

ends.lineat areplanes reference


AnalysisparametersSfindTo

. withimpedances and gains compute we,parameters-S findTo

0ZZZ loadgen ==g

implicit. as elements bias DC theTake

model. devicesimplifiedhighly a -nowfor - Use

analyze Circuit to


Analysis

mout

CZjZg

VVS 0

21 122

:inspectionBy

−== 1/

1/1//1 11

−+−

=→=

t

oin

oingsin

ZZSR

ZZZZSCjZ ω

gsZZZgen CZjVLgen

021 1

0ω+

== 1/1/

22 +=→∞=

oout

ooutout ZZ

ZZSR

! needsour meet may it matching), (no G lower than is gain Though ?amplifier this with wrongisWhat

max

ripple. gain wavesstanding , large :problem serious More 2211 →→SS


Standing Waves

hfii / hwillendsline bothat sReflection

: formtheof varationsgain/phase cause

, 1

12

LSlje ΓΓ− − β

frequencywithandlengthcable both vary with willgain hence

fix this. toneed We

frequency. withand length cable


Eliminating Standing Waves

thus...directly, stages twomatchdirectly can we whileSo,

permanent. connection theandshort arelengths line if acceptableonly is ...this

. todevice each matchmust wechanged, be cansconnectionthat somodular,components or the long, are lines If

0Z


Types of Impedance Matches

0. tscoefficien Reflection:(lossless) MatchingImpedance Reactive

→

(maybe)gainavailablemaximumdeviceGainCircuitnetworks. matching in absorbedpower signal No

reflected.power No

=→

:(lossy) MatchingImpedance Resistive

(maybe)gain availablemaximumdevice GainCircuit =→

networksmatchinginabsorbedpowerSignalreflected.power No

0. tscoefficien Reflection →

gain available maximum device thanless GainCircuit networks.matchinginabsorbedpower Signal

→


World's Second Simplest Amplifier

parasiticsrtransistoofabsencetheIn. in atednow termin are lines

,parasiticsr transistoof absence theIn

0Z

:wastedisgainPower

.eliminated (nearly)now are sReflection

ons terminatiin ndissipatio signal: wastedis gainPower


Analysis

implicit) (biasCircuit

d ld ii lifi d( ) modeldevice simplified-(over)

0pick willWeelCiruit Mod

ZRR Lds =


Analysis

2

:always As

21out

VVS =

0

21

ZZZgenLgen

V==

11)2/(

:or MOTC analysis nodalBy

221

1021 sasa

sbZgS m +++

−=

[ ]s.frequencie highat very only relevant are and termsthe

)2/()2/1)(2/()2/( where1

12

00001

21

baZZgZCZCa

sasa

mgdgs +++=++

obviousbeshouldmeffect terMillerThe obvious.beshouldmeffect ter Miller The


Analysis

1 [ ])2/()2/1)(2/()2/( where1

1)2/( 000011

021 ZZgZCZCaaj

ZgS mgdgsm +++=+

−≅ω

12/1 af π= 1f

)2/( 0Zgm−

cornerdB3andslopedB/decade20-ithbehavior wPlotBodestandardtheNoteplane.complex thein semicirclea isy trajector that theNote

corner.dB3andslopedB/decade20-ithbehavior w Plot Bodestandard theNote

21S


Input Impedance

:ionApproximat Miller theUsing

circleG-constanta follows (almost) that thisNote

pole-singletheNotechart. Smith theon

circle G-constanta . ofbehavior

polesingle theNote

11S


Gain-Bandwidth Product

/2||||d tBWiS

0 if )2/(1/2 and )2/( |||| 00,21 π

fCfS

CZCfZgS gdgshighmbaseband →≅≅

only;ncalculatioroughA

/2||||productBW -gain So, ,21 τπ fCgfS gsmhighbaseband ===

.considered are parasitics deviceother whenbandwidthpoorer only;ncalculatio rough A


Simple Resistive-Terminated Amplifier: General Form

sgeneralize stage Thisblock. any withuse to mg

isondegenerati urceemitter/so or witha transist

forctance tranconduextrinsic :Recall

R1

,, )/1(

is −+= xtransistormextrinsicm

x

Rgg

R


Broadband Feedback Amplifier

output andinput provide toused Feedback Resistive

0 of impedances Z

and / : wantWe 0ZZAVV invinout =−=

this.obtain tonecessary , findmust We

0

Rg fm

invinout

.get also will welucky, are weIf 0ZZout =


Finding Rf:

// :currentInput 0inininin ZVZVI ==

/)1(/)(/)( : inCurrent f

RAVRVAVRVVIR

++

:But

/)1(/)(/)(

iR

fvinfinvinfoutinR

II

RAVRVAVRVVIf

=

+=+=−=

/)1(/

:But

0 fvinin

inR

RAVZV

IIf

+=

)1(0 vf

f

AZR +=→


Finding gm :

f

ZVRVIR

// : inCurrent

f

inininR

R

ZVRVIf

: load inCurrent

// 0==

ovinoutout

f

ZAVZVI // 0 −==

ovininovinRoutinmg

m

ZAVZVZAVIIVgIg

fm/)1(//

:current output block

0 +−=−−=−=−=

ovm ZAg /)1( +=→


Finding Zout (harder):

/ incurrent incurrent

)/( 00

VgZVgRI

RZZVV

mftest

ftestin

+=

+=

11

/

0

0

ZIG

VgZV

t t

inmin

⎟⎞

⎜⎛

−=

11

11

0

00

0

AZG

gZRZ

ZVI

RG

v

mftest

test

outout

⎟⎟⎞

⎜⎜⎛ +

+=

⎟⎟⎠

⎞⎜⎜⎝

⎛−

+===

( )212

1)1( 0000

AZA

G

ZZAZZG

vout

vout

+⋅+

=

⎟⎟⎠

⎜⎜⎝

+++

=

!!!!12

0

0

ZG

ZA

out

v

=

+

matched-impedance isOutput


Broadband Feedback Amplifier: Summary

0

ibb i dihi

, / : wantWe ZZZAVV outinvinout ==−=

d1

:settingby obtained is This

A+

0

0

)1(

and 1

ZARZ

Ag

vf

vm

+=

+=

00

ifonlyand ifonly that note Though,

ZZZZZZZZ Lin

====

00 ifonly and ZZZZ genout ==


Broadband Feedback Amplifier: Why do it ?

this...doWhy

ovm ZAg /)1( +=

? thisof ...instead

ovm ZAg /2 ⋅=

).discussionlater a for (noise noise less bandwidth, more :Answer


Capacitance as the Price for Transconductance

πCgf 2/:model device

simplifiedHighly

=

τ

τ

ππ

fgCCgf

min

inm

2/2/

=→=

. device less less requiresamplifier feedback The. uctance transcondits alproportion is ecapacitancinput device The

inm

min

CggC

→


Capacitance as the Price for Transconductance

RgCC dminin )1/(~ +=

τπfgC

Rgggg

min

dmmm

dminin

2/~~)1/(~)(

=→

+=

uctance.transcond toalproportion is ecapacitancinput on,degenerati resistive withEven

p ppp

set) notesreview design analog from hips(relations


Broadband Feedback Amplifier: Bandwidth Analysis

ovinovmmin ZfACZAgfgC ττ ππ 2/)1( so /)1(but 2/ +=+==

2/)||( where2/1but 000113 ZCZZCaaf inindB === π

2

vdB A

ff+

=1

2 so 3 τ

bandwidth more less required Less →→ inm Cg


Compare to Simple Resistive Amplifier

ii ZfACZAgfgC ππ 2/2so/2but2/ ⋅=⋅== ovinovmmin ZfACZAgfgC ττ ππ 2/2 so /2but 2/

2/)||( where2/1but 000113 ZCZZCaaf inindB === π

f

vdB A

ff τ=3 so

b d id hlMi dM C bandwidthless Morerequired More →→ inm Cg


Bandwidth Analysis with Cgd or Ccb

ecapacitancfeedback include:model devicebetter Slightly

notes)(analogby MOTCshowtowardStraighfor( )( )})11({)}1({)2/(

})1({)2/(notes)(analogby MOTCshow towardStraighfor

0000

00001

vvgdgs

mfgdgs

ZAZAZCZC

ZZgZRCZCa

+++++=

+++≅

( )

)2(2)3)(1()2/(

})({)}({)(

00

0000

v

vvgdgs

vvgdgs

AAAZCZC

+++

+=

Documents

ECE145a / 218a Resistive Feedback Amplifiersclass notes, M. Rodwell, copyrighted 2009 ECE145a / 218a Resistive Feedback Amplifiers Mark Rodwell University of California, Santa Barbara