high speed mixed signal ic design notes set 8 noise in ... · goal: computing signal/noise ratio...

ECE145C /218C notes, M. Rodwell, copyrighted 2007

High Speed Mixed Signal IC Design notes set 8 Noise in Electrical Circuits: circuit noise analysis

Mark Rodwell

University of California, Santa Barbara

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


Noise in electrical circuits: topics

Math: distributions, random variables, expectations, pairs of RV,

joint distributions, mean, variance, covariance and correlations.

Random processes, description, stationarity, ergodicity,

correlation functions, autocorrelation function, power spectral

density.

Noise models of devices: thermal and "shot" noise. Models of

resistors, diodes, transitors, antennas.

Circuit noise analysis: network representation. Solution. Total

output noise. Total input noise. 2 generator model. En/In model.

Noise figure, noise temperature. Signal / noise ratio.


Noise in electrical circuits: Strategy

shown.simply all here are stepskey but the

detail, more much provide notes noise ece594 The

problem.any toextend thencan one n,imaginatio much oWithout to

s.definition and methods analytical develop to thisUse

problem. meaningful possiblesimplest Work the

limited. is here our time Again,


Goal: Computing Signal/Noise Ratio and Sensitivity

sin

cos

clock anddatarecovery

clock anddatarecovery

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


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)(~ 22

mndnd

nIInVV

gkTdfIId

kTGdfIdjfSkTRdfVdjfSnnnn

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)



or 4)(~where

21

21

21

21

:tageoutput vol thecalculateNow

22

1

,gen_noiseout,

,,

1

,iseout,amp_no

1

signalout,

gen_noiseout,iseout,amp_nosignalout,

,,

1

,,

mndnd

nIInVV

LmgenggsRN

LRNdNLmgenggsRN

Lmgenggsgen

LRNdN

LmgenggsRNRNgenout

gkTdfIId

kTGdfIdjfSkTRdfVdjfS

RgRRfCjEV

RIIRgRRfCjEV

RgRRfCjVV

VVV

RII

RgRRfCjEEVV

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)



or 4)(~

21

~)(

~

~~

21

~)(

~

21

:So

22

22

2

,

2

22

2

,

1

signalout,

,

,,,

mndnd

nIInVV

genggs

LmRNV

LII

genggs

LmRNV

Lmgenggsgen

gkTdfIId

kTGdfIdjfSkTRdfVdjfS

RRfC

RgSjfS

RSSRRfC

RgSjfS

RgRRfCjVV

nnnn

genoutgen

LRNdNgoutamp

G D

EN,Rg

INd

S

Vgen

Rgen g

mV

gsR

gE

N,RgenR

LI

NRLCgs

Vgs

Vout

Vin


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)(~

BecuaseAnd

/2/2

211

211

Becuase

*

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


Using the En-In Model

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

high speed mixed signal ic design notes set 8 noise in ... · goal: computing signal/noise ratio...

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