ECE 145B / 218B, notes set 4: Methods for Circuit Noise ......ECE 145B / 218B, notes set 4: Methods for Circuit Noise Analysis Mark Rodwell University of California, Santa Barbara

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


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


summary


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



models noise having all devices, passive and active containscircuit -sub Each

subcircuita isreceiver radio theofblock functional Each



blockcircuit each withingenerators noise of # largea are There



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


circuit noise calculations


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


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


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


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


Reminder

)(~

)()(~

and

)()(~

)(~

)(~

)()(~

Then

)()()(

If

2

*

jfSjfHjfS

jfHjfSjfS

jfSjfHjfS

jfVjfHjfV

xxyy

yxyx

xyxy

VVVV

VVVV

VVVV

xy


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


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


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


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


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


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


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


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



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



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



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]



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



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


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


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


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


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


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


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

,,

,,

,,,,,,


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


Supplementary slides follow


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


Example Problem (1b): FET with Source Degeneration

input. theto

and with associated generators noise themoved have We gs RR

alone. on econcentrat---slideNext ndI


Example Problem (1c): FET with Source Degeneration

.generators noise and replacelater must we:Recall si RR


Example Problem (1d): FET with Source Degeneration

.generators noise and replacelater must we:Recall si RR


Example Problem (1f): FET with Source Degeneration

mI

sE

iE

gkTS

kTRS

kTRS

nd

ns

ni

4~

4~

4~

: thatRecall

answer finalour is This


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

Documents

ECE 145B / 218B, notes set 4: Methods for Circuit Noise ......ECE 145B / 218B, notes set 4: Methods for Circuit Noise Analysis Mark Rodwell University of California, Santa Barbara