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class notes, M. Rodwell, copyrighted 2009
ECE145a / 218a Resistive Feedback Amplifiersp
Mark RodwellUniversity of California, Santa Barbara y
rodwell@ece.ucsb.edu 805-893-3244, 805-893-3262 fax
class notes, M. Rodwell, copyrighted 2009
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
class notes, M. Rodwell, copyrighted 2009
World's Simplest Amplifier
lines.-nsmissionoutput tra andinput toconnected tees,bias andr transistoof consistsAmplifier
dlitlfamplifier; toexternal are lines-onTransmissi
ends.lineat areplanes reference
class notes, M. Rodwell, copyrighted 2009
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
class notes, M. Rodwell, copyrighted 2009
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
class notes, M. Rodwell, copyrighted 2009
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
class notes, M. Rodwell, copyrighted 2009
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
class notes, M. Rodwell, copyrighted 2009
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
→
class notes, M. Rodwell, copyrighted 2009
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
class notes, M. Rodwell, copyrighted 2009
Analysis
implicit) (biasCircuit
d ld ii lifi d( ) modeldevice simplified-(over)
0pick willWeelCiruit Mod
ZRR Lds =
class notes, M. Rodwell, copyrighted 2009
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
class notes, M. Rodwell, copyrighted 2009
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
class notes, M. Rodwell, copyrighted 2009
Input Impedance
:ionApproximat Miller theUsing
circleG-constanta follows (almost) that thisNote
pole-singletheNotechart. Smith theon
circle G-constanta . ofbehavior
polesingle theNote
11S
class notes, M. Rodwell, copyrighted 2009
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
class notes, M. Rodwell, copyrighted 2009
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
class notes, M. Rodwell, copyrighted 2009
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 =
class notes, M. Rodwell, copyrighted 2009
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 +=→
class notes, M. Rodwell, copyrighted 2009
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( +=→
class notes, M. Rodwell, copyrighted 2009
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
class notes, M. Rodwell, copyrighted 2009
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 ==
class notes, M. Rodwell, copyrighted 2009
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
class notes, M. Rodwell, copyrighted 2009
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
→
class notes, M. Rodwell, copyrighted 2009
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
class notes, M. Rodwell, copyrighted 2009
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
class notes, M. Rodwell, copyrighted 2009
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
class notes, M. Rodwell, copyrighted 2009
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
+++
+=
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