noise notes set13.ppt - UCSBECE594I notes, M. Rodwell, copyrighted ECE594I Notes set 13: Two-port...

ECE594I notes, M. Rodwell, copyrighted

ECE594I Notes set 13:Two-port Noise Parametersp

Mark RodwellUniversity of California, Santa Barbara y

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


References and Citations:

DevicesState-Solid in Noise :Zielder Van PhysicsThermal : Kroemerand Kittel

:Citations / Sources

ng.EngineeriionsCommunicatofsPrinciple:Jacobs&Wozencraftory)(introduct s PrincipleSignal RandomVariables, Randomty, Probabili: PeeblesZ. Peyton

ive)comprehens(hard, Variables Randomandity Probabil:Papoulis

1982circaStanfordHellmanMartin:noteslectureyProbabilit1982circa Stanford, Cover, Thomas :notes lecture theory nInformatio

Designc ElectroniNoise Low :erMotchenbakng.EngineeriionsCommunicatofs Principle:Jacobs & Wozencraft

t dffS t d

circuits. in Noise :Notes nsApplicatio tor LinearSemiconduc National1982circa Stanford,Hellman, Martin:notes lecturey Probabilit

design)receiver (optical Personik & Smith noise), (device by Fukui Papers Kroemer and Kittel Peebles,Jacobs, & Wozencraft Ziel,der Van

study.for references Suggested

Theory nInformatio of Elements:Williams andCover )(!Notes App. Semi. National


Two-Port Noise Description

bdtddbcircuita of generators noise internal the

analysis,circuit of methods theThrough

. and generators noise twobydrepresente and summed be can

nn IE

ifi ddl l t dbltd itt lThspecified. and calculated bemust and of densities spectral The nn IE

specified. andcalculatedbealsomust density spectral cross The


Calculating Total Noise

genE kTRSgenN

4~noise, thermalhasjust generator theIf

,=

sourcesingleabynoisecurrentandvoltageamplifier of ncombinatio theRepresent

genNNTotal ZIEE ⋅+=sourcesinglea by noisecurrent and voltage

:noise total thisofdensity spectral thecalculatenow can We

{ }( ){ }gengenIEIg

gIEIgE

jXRSSZ

ZSSZS

nnn

nnnamplifiertotaln

−+=

+=~Re2~||||

~Re2~|||| ~ 2

*2,,

{ }ggg nnn


Signal / Noise Ratio of Generator

EEV i dl dthdiid EEV genntotalnsignal

powers.noiseaviableheconsider tThereforeload. theupon dependnot willby these delivered powers of ratios The

impedance.loadsametheseeandseriesinare and , ,,

RVP genRMSsignalavailablesignal = 4/ isgenerator thefrom availablepower signal The

powers.noiseaviableheconsider t Therefore

2,,

Effff signalsignal Δ+Δ−

ifiil blhh ),2/( and )2/(between bandwidthnarrow a consider weIf

RfjfSEEP

E

gengenngeneratoravailablenoise

genN

Δ⋅== 4/)(~][

isfrompower noise available thethen2,,,

,

RVRVP genRMSsignalgenRMSsignalavailablesignal 4/4/SNR

thenisgenerator theof ratio sesignal/noi The22

fkTRfjfSPgenRMSsignal

genE

genRMSsignal

generatoravailablenoise

availablesignal

gennΔ⋅

=Δ⋅

==4/)(~SNR ,,

,,

,

,


Signal / Noise Ratio of Generator+Amplifier

genRMSsignalavailablesignal RVP 4/ :generator thefrom availablepower Signal 2,, =

fkTRfSP genVgenavnoise Δ⋅=Δ⋅= 4/~ :generator from availablepower Noise ,, gg

genEAmpavnoise RfSPamplifiertotaln

4/~ :amplifier from availablepower Noise,,,, Δ⋅=

RVP genRMSsignalavailablesignal 4/ : noiseamplifier including ratio seSignal/noi

2

RV

RfSRfSPPSNR

genRMSsignal

genEgenE

genRMSsignal

ampavailnoisegenavailnoise

availablesignal

genntotalΔ⋅+Δ⋅

=+

=

4/

4/~4/~

2,

,

,,,,

,

,

fkTRfS genE

gg

totalΔ⋅+Δ⋅

=4/~ ,


Noise Figure: Signal / Noise Ratio Degradation

amplifier adding before ratio sesignal/noiamplifieraddingbeforeratiosesignal/noi figure Noise =

fkTRV

SNR genRMSsignal

Δ⋅=

4/ :amplifier adding before ratio seSignal/noi

2,

fkTRfSRV

SNRgenE

genRMSsignal

totalΔ⋅+Δ⋅

=4/~

4/ :amplifier addingafter ratio seSignal/noi

2,

fkTfkTRfS

F genEtotal

Δ⋅Δ⋅+Δ⋅

==4/~

figure Noise

RS genEtotal powernoiseinput availableamplifier 14/~

1figureNoise ++kTkT

gtotal ppp11 figure Noise +=+=


Calculating Noise Figure~

kTRS genEtotal

4/1 figure Noise +=

{ }*2 ~Re2~|||| ~

:know that also We

,, gIEIgE ZSSZSnnnamplifiertotaln

+=

:figure noisefor expression an thisfrom calculate can We

( )gen

IEsIsE

kTRSZSZS

F nnnn

4Re2

1*2 ⋅++

+=


Minimum Noise Figure

:offunctiona as variesfigure Noise gengengen jXRZ +=

( )IEsIsE SZSZSF

~Re2~~1

*2 ⋅++ ( )gen

IEsIsE

kTRF nnnn

41+=

figurenoisemimimuma findcan wecalculus, someAfter :minimum thisus gives whichimpedancegenerator a and

g,

[ ]( ) [ ]SSSSF ~R2~I~~2112 ⎤⎡ [ ]( ) [ ]

[ ] [ ]nnnnn

nnnnnn

IEIEE

IEIEIE

Sj

SSjXRZ

SSSSkT

F

~Im~Im~

Re2Im24

1

2

min

⎟⎞

⎜⎛

+

⎥⎦⎤

⎢⎣⎡ +−+=

[ ] [ ]n

nn

n

nn

n

n

IIIoptoptopt S

jSS

jXRZ ~~~ −⎟⎟⎠

⎜⎜⎝

−=+=

tiithh(b)ithi( )btP i t ZZF. (c) minimuma gives which

optimuman istherehence (b) ,withvaries(a) :remember toPointsF

ZZF gengen


Noise Figure in Wave Notation

[ ]2

4

,parameters waveof termsin instead Written

optsnrFFΓ−Γ⋅

+ [ ] [ ]22min 11 opts

pFFΓ−⋅Γ−

+=

circles"figurenoise":figurenoiseconstantof plane thein contous describe These s −Γ

t.coefficienreflection source withfigure noise of variation theof ndescriptioa i.e.

,circlesfigurenoise:figure noiseconstant


Low-Noise Amplifier Design

Design steps areDesign steps are 1) in-band stabilization: this is best done at output port to avoid degrading noise2) input tuning for Fmin3) output tuning (match)4) out of band stabilization4) out-of-band stabilization

Note that tuning for minimum noise figure requires a *mismatch* on the amplifier input;amplifier gain therefore must lie below the transistor MAG/MSG.

Note that tuning for minimum noise figure implies that amplifierinput is mismatched: input reflection coefficient is therefore not zero !

Z

Discrepancy in input noise-match & gain-matchcan be reduced by adding source inductance

Zs=Zonoisematch

Zs

Vgen


Example LNA Design: 60 GHz, 130 nm SiGe BJT

gain & noise circles after input matchingnote compromise between gain & noise tuning


Friis Formula for Noise Figure

hfil bloutput amplifier thefrom availablepower

loadthetomatched*output* thewithamplifier thenofgainpower :gain Available

== AVAA P

PG

amplifiers of cascadea of figure Noise

generatorthefromavailablepower AVGA P

using given calculated areamplifier each of gains available and figures noise theHere

...11

21

3

1

21 +

−+

−+=

AAAtotal GG

FG

FFF

limits. time todue here proven benot willexpression FriisThe

stage.prior theof impedanceoutput the toequal impedance sourcea


Noise Measure

signal. the torelative noise increased ofcost at the comes that and it, use tosignala amplify toneed We output. andinput connecting wiresimplea than

figure noisepoorer has device activeany that is figure noise ofy peculiarit One

:amplifiersidentical ofcascadeinfiniteanoffigure noise theas Define

!amplfier noise-lowa for merit -of-figurebest a thenot is Clearly

F

F

∞

...111pg

32 GF

GF

GFFF

AAA

+−

+−

+−

+=∞

∞

1:so as defined thenis *measure noise* The

FM −= ∞

d idt/iFETfthith tparticular in implies This network. reciprocal losslessa in device theembedding

respect to withinvariant is i.e. invariant,network a is that proves Mason

M

M

ions.configuratdrain-commonandgate-common/ source-commonina FETfor same theis that M

noise notes set13.ppt - UCSBECE594I notes, M. Rodwell, copyrighted ECE594I Notes set 13: Two-port...

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