ece 145b / 218b, notes set 4: methods for circuit noise ......ece 145b / 218b, notes set 4: methods...
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class notes, M. Rodwell, copyrighted 2012
ECE 145B / 218B, notes set 4: Methods for Circuit Noise Analysis
Mark Rodwell
University of California, Santa Barbara
[email protected] 805-893-3244, 805-893-3262 fax
class notes, M. Rodwell, copyrighted 2012
References and Citations:
Theory nInformatio of Elements:Williams andCover
)(! Notes App. Semi. National
design)receiver (optical Personik & Smith noise), (device by Fukui Papers
Kroemer and Kittel Peebles,Jacobs, & Wozencraft Ziel,der Van
study.for references Suggested
circuits. in Noise :Notes nsApplicatio tor LinearSemiconduc National
1982circa Stanford, Hellman, Martin:notes lecturey Probabilit
1982circa Stanford, Cover, Thomas :notes lecture theory nInformatio
Designc ElectroniNoise Low :erMotchenbak
ng. EngineeriionsCommunicat of s Principle:Jacobs & Wozencraft
ory)(introduct s PrincipleSignal RandomVariables, Randomty, Probabili: PeeblesZ. Peyton
ive)comprehens(hard, Variables Randomandity Probabil:Papoulis
DevicesState-Solid in Noise :Zielder Van
PhysicsThermal : Kroemerand Kittel
:Citations / Sources
class notes, M. Rodwell, copyrighted 2012
summary
class notes, M. Rodwell, copyrighted 2012
Goal: Computing Signal/Noise Ratio and Sensitivity
noise. referred-input equivalent theto
magnitude signalinput thecompare toconvenient often isIt
input.circuit decision at the ratio sesignal/noi thefindmust we
y,sensitivitreceiver thecompute To
ReceiverOptical
ReceiverRadio
class notes, M. Rodwell, copyrighted 2012
Goal: Computing Signal/Noise Ratio and Sensitivity
models noise having all devices, passive and active containscircuit -sub Each
subcircuita isreceiver radio theofblock functional Each
class notes, M. Rodwell, copyrighted 2012
Goal: Computing Signal/Noise Ratio and Sensitivity
blockcircuit each withingenerators noise of # largea are There
class notes, M. Rodwell, copyrighted 2012
Goal: Computing Signal/Noise Ratio and Sensitivity
ns.fluctuatio internal from arising noise terminaldevice found Earlier we
:noise referred-inputreceiver total thefind will we thisFrom
:circuit-sub each of noiseinput equivalent thecompute tolearn Next we
found. be thencany sensitivit and SNRReceiver
class notes, M. Rodwell, copyrighted 2012
circuit noise calculations
class notes, M. Rodwell, copyrighted 2012
Circuit noise analysis: Goals
? noise referred-output thecalculate wedoHow
/ where,
:sinput term fictitiousby drepresente be can termsnoise These
load theand amplifier, thegenerator, thefrom arises Noise
noise. and signal both hasoutput circuit The
output noise,input noise,input noise,output noise,
load noise,amplifier noise,generator noise,output noise,
output noise,
vinvinvout
invout
AVVVVAVVAV
VVVV
VVAV
class notes, M. Rodwell, copyrighted 2012
Noise model of this circuit
fF4.6cbxC
fF3.7cbiC 49bbR
3.4exR
6500cR
ebmVg 'ebV '
E
B C
diffC
fF182
jeC
fF38
R350
4kTRex
4kTRbb
2kT/gmor2qIc
2kT/Rbbor2qIb
Icbo
2qIcbo
4kT/Rf
Rf
Rgen
4kTRgen
Ree
4kTRee
RL
4kTRL
Vout
Vin
Vgen
circuit. simplea very withnscalculatio illustrate willWe
.techniquesefficient more learn willWe
analysis. handfor hard tooare methods force-Brute
.complexity formidable of is circuits practicalmost of analysis Noise
.generators noise ofnumber largea hascircuit The
class notes, M. Rodwell, copyrighted 2012
Circuit Noise Analysis: 1st Example (a)
densities spectral based- Hzsided,-Single :Notation
model. noise simplified withamplifier, Simple
noise. channel FETfor the 4~
resistors allfor 4~
or 4~
mII
IIVV
gkTS
kTGSkTRS
ndnd
nnnn
G D
EN,Rg
INd
S
Vgen
Vgen
Rgen
RL
Vgen
Rgen g
mV
gsR
g
RL
EN,Rgen
RL
INRLC
gs
Vgs
Vout
Vout
Vin
Vin
class notes, M. Rodwell, copyrighted 2012
Circuit Noise Analysis: 1st Example (b)
noise. channel FETfor the 4)(~
resistors allfor 4)(~
or 4)(~where
21
21
21
21
:tageoutput vol thecalculateNow
1
,gen_noiseout,
,,
1
,iseout,amp_no
1
signalout,
gen_noiseout,iseout,amp_nosignalout,
,,
1
,,
mII
IIVV
LmgenggsRN
LRNdNLmgenggsRN
Lmgenggsgen
LRNdN
LmgenggsRNRNgenout
gkTjfS
kTGjfSkTRjfS
RgRRfCjEV
RIIRgRRfCjEV
RgRRfCjVV
VVV
RII
RgRRfCjEEVV
ndnd
nnnn
gen
Lg
L
ggen
G D
EN,Rg
INd
S
Vgen
Rgen g
mV
gsR
gE
N,RgenR
LI
NRLCgs
Vgs
Vout
Vin
class notes, M. Rodwell, copyrighted 2012
Reminder
)(~
)()(~
and
)()(~
)(~
)(~
)()(~
Then
)()()(
If
2
*
jfSjfHjfS
jfHjfSjfS
jfSjfHjfS
jfVjfHjfV
xxyy
yxyx
xyxy
VVVV
VVVV
VVVV
xy
class notes, M. Rodwell, copyrighted 2012
Circuit Noise Analysis: 1st Example (c)
22
2
,
2
22
2
,
1
signalout,
21
~)(
~
~~
21
~)(
~
21
:So
,
,,,
genggs
LmRNV
LII
genggs
LmRNV
Lmgenggsgen
RRfC
RgSjfS
RSSRRfC
RgSjfS
RgRRfCjVV
genoutgen
LRNdNgoutamp
G D
EN,Rg
INd
S
Vgen
Rgen g
mV
gsR
gE
N,RgenR
LI
NRLCgs
Vgs
Vout
Vin
noise. channel FETfor the 4)(~
resistors allfor 4)(~
or 4)(~where
mII
IIVV
gkTjfS
kTGjfSkTRjfS
ndnd
nnnn
class notes, M. Rodwell, copyrighted 2012
Circuit Noise Analysis: 1st Example (d)
21
4)(~
*generator the todue* noiseoutput The
44
214)(
~
*amplifier the todue* noiseoutput The
)2(
21
signaloutput The
22
2
2
22
2
1
signalout,
,
,
genggs
LmgenV
L
L
m
genggs
LmgV
genv
Lmgenggsgen
RRfC
RgkTRjfS
RR
kTgkT
RRfC
RgkTRjfS
VfjA
RgRRfCjVV
outgen
outamp
G D
EN,Rg
INd
S
Vgen
Rgen g
mV
gsR
gE
N,RgenR
LI
NRLCgs
Vgs
Vout
Vin
class notes, M. Rodwell, copyrighted 2012
Circuit Noise Analysis: 1st Example (e)
4)(~
:is *generator the todue* noiseinput theAnd
21)(
~
||)(||
)(~
)(~
:is noise referred-inputamplifier theSo
)(/ and :simply means This
)(*)(
*)(
*noiseinput equivalent* eNow Defin
,
,
,
, 2
22
2
_,_,,_,
_,_,
_,_,
genV
Lm
genggs
V
v
V
V
vnoiseampoutnoiseampingenNnoisegenin
noisegeninnoiseampingenV
noisegenoutnoiseampoutgenvout
kTRjfS
Rg
RRfCjfS
jfA
jfSjfS
jfAVVEV
VVVjfA
VVVjfAV
ingen
outamp
outamp
inamp
G D
EN,Rg
INd
S
Vgen
Rgen g
mV
gsR
gE
N,RgenR
LI
NRLCgs
Vgs
Vout
Vin
class notes, M. Rodwell, copyrighted 2012
Circuit Noise Analysis: 1st Example (f)
4)(~
*generator thefrom* noiseInput
noiseresistor load referred-input
2114
noise channel referredinput
211
4
from noise referred-input 4)(~
,
,
22
2
2
22
2
2
genV
genggs
mL
genggs
m
m
ggV
kTRjfS
RRfCgR
kT
RRfCg
gkT
RkTRjfS
ingen
inamp
G D
EN,Rg
INd
S
Vgen
Rgen g
mV
gsR
gE
N,RgenR
LI
NRLCgs
Vgs
Vout
Vin
class notes, M. Rodwell, copyrighted 2012
Circuit Noise Analysis: 1st Example (g)
density spectralpower ssignal'input theis )(~
Where
)(~
)(~
SNR
:ratio seSignal/Noi
4)(~
can write which weFrom
)(~
)(~
)(~
:definition Figure Noise
_,
_,
,
,,
jfS
jfS
jfS
FkTRjfS
jfS
jfSjfSF
signal
noisetotalin
signal
noisetotalin
ingen
inampingen
V
V
V
genV
V
VV
G D
EN,Rg
INd
S
Vgen
Rgen g
mV
gsR
gE
N,RgenR
LI
NRLCgs
Vgs
Vout
Vin
class notes, M. Rodwell, copyrighted 2012
Circuit Noise Analysis: 1st Example: Summary
t.inefficien bemust methodour then,Clearly,
answer. final thefound weone cancelled weresteps
ncalculatioour ofmany noise, referred-input computing in that,Note
circuit. smalla for even tedious,extremely is method The
these.calculatemight computer a how is This
figure. noise and SNR, noise, referred-output
noise, referred-input of ncalculatiofor stepsexact theare These
G D
EN,Rg
INd
S
Vgen
Rgen g
mV
gsR
gE
N,RgenR
LI
NRLCgs
Vgs
Vout
Vin
class notes, M. Rodwell, copyrighted 2012
Circuit Noise Analysis: 1st Example: Summary
***input near the are sources noiseimportant most The***
becauset inefficienly particular isIt
.extra work---steps cancelled involves This
input. theback to thempropagated ...then
output,circuit the togenerators noisecircuit thegated.....propa
webecause hard wasAnalysis
class notes, M. Rodwell, copyrighted 2012
Circuit Noise Analysis: Source Transposition Method
output. andinput betweennetwork theof ticscharactersoutput -inputport -2
thechangenot do whichations transform toourselvesrestrict must We
input.circuit the togenerators noisecircuit theall move useLet
box red insideonly ations transformmake means, This
G D
EN,Rg
INd
S
Vgen
Rgen g
mV
gsR
gE
N,RgenR
LI
NRLCgs
Vgs
Vout
Vin
class notes, M. Rodwell, copyrighted 2012
Circuit Noise Analysis: Source Transposition Method
ortonN-Thevenin
R
EN=I
NR
IN
R
Input-Output
gm
Iout
=gm(V+-V-)
gmI
N
EN=I
N/g
m
EN/A
vE
N
Av A
v
IN
IN
IN
BranchA AcrossCurrent Moving
Node A Through Voltage Moving
EN
EN
EN
class notes, M. Rodwell, copyrighted 2012
Circuit Noise Analysis: Source Transposition Method
input the to Walk"" NRLI
G D
S
Vgen
Rgen g
mV
gsR
gR
LI
NRLCgs
Vgs
Vout
Vin
G
S
Vgen
Rgen g
mV
gsR
g
INRL
/gm
Cgs
Vgs
Vin
G
Vgen
Rgen R
g
INRL
/gm
Cgs
Vin
class notes, M. Rodwell, copyrighted 2012
Circuit Noise Analysis: Source Transposition Method
Vgen
Rgen
INRL
*j2fCgs
/gm
INRL
*(1/gm)(1+
j2fC
gsR
g)
Vgen
Rgen
INRL
*j2fCgs
/gm
INRL
*(1/gm)(1+
j2fC
gsR
g)
INRL
*[(1/gm)(1+
j2fC
gsR
g)+(1/g
m)
j2fC
gsR
gen)]
=INRL
*[1/gm+
j2fC
gs(R
g+R
gen)/g
m]
class notes, M. Rodwell, copyrighted 2012
Circuit Noise Analysis: Source Transposition Method
214)(
~
so, of that withparallel in isgenerator current noise channel The
make. toncalculatiohardest single theit was
input, thefromfar is becausebut n,calculatioeasy annot certainly wasThis
214)(
~
2
22
2_;
2
22
2;
m
genggs
m
mnoisechannelV
L
L
m
genggs
mL
noiseRV
g
RRfC
ggkTjfS
R
R
g
RRfC
gR
kTjfS
input
Linput
class notes, M. Rodwell, copyrighted 2012
Circuit Noise Analysis: Source Transposition Method
G D
EN,Rg
INd
S
Vgen
Rgen g
mV
gsR
gE
N,RgenR
LI
NRLCgs
Vgs
Vout
Vin
21441
1~
~
1
hence
21444)(
~
so
4)(~
4)(~
thatsee alsocan weexample,easy ly particular In this
22
2
;
;
2
22
2;
;;
genggs
Lmmgengen
g
generatorV
amplifierV
m
genggs
mL
mgamplifierV
gengeneratorVgRV
RRfCRg
kT
g
kT
RR
R
S
SF
g
RRfC
gR
kTgkTkTRjfS
kTRjfSkTRjfS
input
input
input
inputginput
class notes, M. Rodwell, copyrighted 2012
Input Noise Voltage / Input Noise Current Model
this.allows tionrepresenta The
dunspecifie and unknown impedancegenerator thewith
circuitor devicea of noisespecify to wishfrequently We
nn IE
G D
EN,Rg
INd
S
Vgen
Vgen
RL
Vgen
Rgen g
mV
gsR
g
RL
EN,Rgen
RL
INRLC
gs
Vgs
Vout
Vout
Vin
Vin
Zgen
jXgen
Zgen
class notes, M. Rodwell, copyrighted 2012
En-In Model: Source Transposition Again
only. noiseresistor load of onillustrati
generator theintonot -but -input tosources walk"" again, Once
G D
S
gmV
gsR
gR
LI
NRLCgs
Vgs
Vout
Vin
G
S
gmV
gsR
g
INRL
/gm
Cgs
Vgs
Vin
GR
g
INRL
/gm
Cgs
Vin
class notes, M. Rodwell, copyrighted 2012
En-In Model: Source Transposition Again
GR
g
Cgs
Vin
INRL
/gm
INRL
*j2fCgs
/gm
Rg
INRL
/gm I
NRL*j2fC
gs/g
m
Rg
INRL
/gm I
NRL*j2fC
gs/g
m
INRL
*Rg j2fC
gs/g
m
Vin
Vin
INRL
*j2fCgs
/gm
INRL
*(1/gm)(1+
j2fC
gsR
g)V
in
.correlated 100% are they , to
1:1 related both are they As
source.current a and source voltage
a of ncombinatioa by Vat
drepresente is noiseoutput The
in
NRLI
class notes, M. Rodwell, copyrighted 2012
En-In Model: With All Sources
(INRL
+INd
)*j2fCgs
/gm
(INRL
+INd
)*(1/gm)(1+
j2fC
gsR
g)+E
NRGV
in
density. spectral cross theparticular in Note
2211
44
)(~
/244
)(~
4211
44
)(~
4)(~
/4)(~
4)(~
BecauseAnd
/2/2
211
211
Because
*
2
2
2
,
,
,,
,,
,,
gsggs
m
m
L
IE
mgsm
L
II
gggs
m
m
L
EE
mILIgE
mgsndmgsNRLtotaln
NRGggs
m
ndggs
m
NRLtotaln
fCjRfCjg
gkTR
kTjfS
gfCgkTR
kTjfS
kTRRfCg
gkTR
kTjfS
gkTjfSRkTjfSkTRjfS
gfCjIgfCjII
ERfCjg
IRfCjg
IE
totalntotaln
totalntotaln
totalntotaln
NdNRLNRG
class notes, M. Rodwell, copyrighted 2012
En-In Model: With All Sources
*
2
2
2
2211
44
)(~
/244
)(~
4211
44
)(~
,,
,,
,,
gsggs
m
m
L
IE
mgsm
L
II
gggs
m
m
L
EE
fCjRfCjg
gkTR
kTjfS
gfCgkTR
kTjfS
kTRRfCg
gkTR
kTjfS
totalntotaln
totalntotaln
totalntotaln
input. itsat generators noise correlated ofpair a by
drepresente is present,or specifiednot generator the withamplifier, An
:done have hat weConsider w
power). availableor current, (voltage, noiseinput total thecalculate to
used be can~
and ,~
,~
specified, is impedancegenerator a whenLater,nnnn IEIE SSS
class notes, M. Rodwell, copyrighted 2012
Using the En-In Model to Compute total Noise
IN
EN
Vin
Vgen
Rgen
EN,Rgen
jXgen
EN+I
NZ
genV
inV
gen
Rgen
EN,Rgen
jXgen
gengenIEIgE
gIEIgEE
gNnamplifiertotaln
gengengen
IEIIEE
jXRSSZS
ZSSZSS
ZIEE
jXRZ
jfSjfSjfS
nnnn
nnnnamplifiertotaln
totalntotalntotalntotalntotalntotaln
~Re2
~||||
~
~Re2
~||||
~
~
So
impedancegenerator specifieda given and
),(~
and ),(~
, )(~
specified thcircuit wia Given
2
*2
,,
,,
,,,,,,
class notes, M. Rodwell, copyrighted 2012
Using the En-In Model--Conclusion
.expression figure noise FET Fukuithe
calculate can wei.e. this,provides whichimpedance source optimum theand
figure noise minimun device thefind can we,(calculus) by varying Then
2211
44
)(~
/244
)(~
4211
44
)(~
ipsrelationsh device theand
~Re2
~||||
~
~Re2
~||||
~
~
iprelationshcircuit theuse weIf
*
2
2
2
2
*2
,,
,,
,,
,,
g
gsggs
m
m
L
IE
mgsm
L
II
gggs
m
m
L
EE
gengenIEIgE
gIEIgEE
Z
fCjRfCjg
gkTR
kTjfS
gfCgkTR
kTjfS
kTRRfCg
gkTR
kTjfS
jXRSSZS
ZSSZSS
totalntotaln
totalntotaln
totalntotaln
nnnn
nnnnamplifiertotaln
class notes, M. Rodwell, copyrighted 2012
Supplementary slides follow
class notes, M. Rodwell, copyrighted 2012
Example Problem (1a): FET with Source Degeneration
Circuit Circuit EquivalentCircuit Equivalent
Simplified
error. no ion,approximat ...no
. and together lumped have We
error. some introducesmation ...approxi
. neglected have We
ig
gd
RR
C
class notes, M. Rodwell, copyrighted 2012
Example Problem (1b): FET with Source Degeneration
input. theto
and with associated generators noise themoved have We gs RR
alone. on econcentrat---slideNext ndI
class notes, M. Rodwell, copyrighted 2012
Example Problem (1c): FET with Source Degeneration
.generators noise and replacelater must we:Recall si RR
class notes, M. Rodwell, copyrighted 2012
Example Problem (1d): FET with Source Degeneration
.generators noise and replacelater must we:Recall si RR
class notes, M. Rodwell, copyrighted 2012
Example Problem (1f): FET with Source Degeneration
mI
sE
iE
gkTS
kTRS
kTRS
nd
ns
ni
4~
4~
4~
: thatRecall
answer finalour is This
class notes, M. Rodwell, copyrighted 2012
Example Problem (1g): FET with Source Degeneration
.current noise referred-input
stage-2nd thefrom resulting noise referred-input the
find topage previous theofresult theuse nowcan We
2stI