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

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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

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VVS 0

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:inspectionBy

−== 1/

1/1//1 11

−+−

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oin

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021 1

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22 +=→∞=

oout

ooutout ZZ

ZZSR

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

max

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: formtheof varationsgain/phase cause

, 1

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frequencywithandlengthcable both vary with willgain hence

fix this. toneed We

frequency. withand length cable


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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

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Analysis

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Analysis

2

:always As

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VVS =

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:or MOTC analysis nodalBy

221

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sbZgS m +++

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

12

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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


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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 ===

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Simple Resistive-Terminated Amplifier: General Form

sgeneralize stage Thisblock. any withuse to mg

isondegenerati urceemitter/so or witha transist

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,, )/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

+++

+=

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

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