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
ECE594I notes, M. Rodwell, copyrighted
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
ECE594I notes, M. Rodwell, copyrighted
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
ECE594I notes, M. Rodwell, copyrighted
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
ECE594I notes, M. Rodwell, copyrighted
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 ,,
,,
,
,
ECE594I notes, M. Rodwell, copyrighted
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/~ ,
ECE594I notes, M. Rodwell, copyrighted
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 +=+=
ECE594I notes, M. Rodwell, copyrighted
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 ⋅++
+=
ECE594I notes, M. Rodwell, copyrighted
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
ECE594I notes, M. Rodwell, copyrighted
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
ECE594I notes, M. Rodwell, copyrighted
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
ECE594I notes, M. Rodwell, copyrighted
Example LNA Design: 60 GHz, 130 nm SiGe BJT
gain & noise circles after input matchingnote compromise between gain & noise tuning
ECE594I notes, M. Rodwell, copyrighted
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
ECE594I notes, M. Rodwell, copyrighted
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