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Your Imagination, Our InnovationWireless Semiconductor Division

Stability & LNAs

Microwave UpdateEnfield, CT.

Al WardW5LUA

October 14, 2011


Requirements for an LNA

• Absolute lowest noise figure possible

• Good gain to overcome second stage noise figure• Gain only where we need it• Good large signal handling capabilities

• Must be stable at all frequencies when installed in thesystem between the antenna and/or feed and converter –probably the most difficult task….

• Good indicators of instability are excessive gain, high out-of-band gain and positive return loss


The Process

• Understand what the S Parameters are telling you about adevice

• Make good engineering decisions based on noise figure,gain and stability – both in-band and out-of-band

• Let’s start by taking a look at S Parameters…………


Start with S-parameters?!??!

• A three-terminal two-port, such asthe FET shown, has four S-parameters.

• Snn = voltage reflection coefficient,both amplitude and phase relativeto 50 source impedance

• S21 and S12 are commonly displayedon a polar chart.

• S11 = input displayed on Smith chart

• S22 = output displayed on Smithchart

S21

S12

S11S22

Polar chart Smith chart


ATF-36077 S and Noise Parameters


ATF-36077 S ParametersFreq (GHz) S11 Mag Ang S21 Mag Ang S22 Mag AngS12 Mag Ang

1

1VSWR

2log10RL log20G


ATF-36077 Noise Parameters

Freq (GHz) Fmin (dB)

Gamma Opt (Γo)

Mag Ang Rn


What about Noise Parameters?!??!

• o (Gamma Opt) is the reflectioncoefficient of the sourceimpedance presented to thedevice that allows the device toproduce its’ fmin

• Matching circuit losses often limitthe ability of the amplifier toachieve a noise figure equivalentto device fmin

• o not necessarily equal to S11*

which means noise match is notequivalent to a gain match

• Rn (Noise Resistance) is used tocalculate the device’s sensitivityin noise figure to changes insource impedance, rn isnormalized to 50.

For minimum NF, in = oFor maximum gain, in = S11*

in

Q1

Impedance MatchingNetwork


Input Impedance Match• Match to opt for

minimum noise figure

• Noise degrades incircular contours asmatch moves away fromopt

• Degree of noisedegradation is dependenton Rn, the noiseresistance

• Most amateurapplications aim forminimum noise figure andaccept input VSWR

S11*

opt


Simultaneous Input VSWR and NoiseMatch

new S11*

newopt

• Adding source inductancerotates opt towards S11*

• Source inductance is seriesfeedback which effects gainand stability

• Its’ effect must be analyzedover as a wide a bandwidth asthe device has gain


Output Impedance Match• S22

’* = L is the reflectioncoefficient of the outputmatching network with inputterminated in opt, not 50

• Match to S22’* = L for best

gain/output VSWR• LNA may not be unconditionally

stable when matched for bestoutput VSWR - Some resistiveloading may be required toreduce gain to improve stability

• Best output VSWR does notnecessarily guarantee best P1dBand IP3.

S22*

S22'*

L = S22 + S12 S21 o1 - S11 o

*


ATF-36077 S21, MSG & MAG


Evaluating LNA Stability

• Two factors are typically used to evaluate LNA stability. Thefirst is the Rollett Stability factor K. K > or = 1 forunconditional stability

• The second is mu and mu’This measurement gives the distance from the center of the Smith chart to the nearest output (load) stabilitycircle. This stability factor is given by:mu = {1-|S11|2} / {|S22 - conj(S11)*Delta | + |S12*S21| }where Delta is the determinant of the S-parameter matrix. Having mu > 1 is the single necessary and sufficientcondition for unconditional stability of the 2-port network.

• Both are calculated using LNA S parameters over a widefrequency range for reasons that will be discussed shortly

2112

2222

211

21

SSDSS

K

21122211 SSSSD


ATF-36077 1296 MHz LNA

21

Ref

Adding a 5 pF cap to ground atthe junction of L2 and R1 willlower noise figure

Agilent ADS Simulation


Source Grounding

Ground Plane

LL LL

PCB

FET

Plated Through Holes

Source inductance can be the biggest problem with most LNAs.Usually there are two source leads so the inductance can effectivelybe cut in half. Source inductance is made up from several factorsincluding the length of the source lead, the length of the VIA to thebottom side of the circuit board ground plane and any additionalcircuit trace that connects the source lead to the VIA. If self biasing isused then the equivalent series inductance of the bypass capacitormust be included in the analysis.In a good LNA design, this inductance amounts to a few tenths of anH, but the effects are significant…..


Evaluating LNA Stability K versus Frequency

2 4 6 8 10 12 14 160 18

1

2

3

4

5

0

6

freq, GHz

Opt Source Inductance

Zero Source Inductance

Excessive Source Inductance

2112

2222

211

21

SSDSS

K

21122211 SSSSD


Improving Stability with Resistance in the DrainOnce the Optimum Source Inductance has beendetermined

2 4 6 8 10 12 14 160 18

1

2

3

4

0

5

freq, GHz

Sta

bFac

t1

0 Ω

39 Ω

22 Ω

1.30.8 1.8

15

20

25

10

30

freq, GHz

dB(S

(2,1

))dB

(WD

5AG

O_2

3..S

(2,1

))22Ω

39Ω

0 Ω


Noise Figure vs Drain Resistance

0 Ω

39 Ω

22 Ω

1.30.8 1.8

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.0

1.0

freq, GHz

nf(2

)W

D5A

GO

_23_

Hig

h_LL

..nf

(2)


Chip Capacitor Parasitics - A FirstApproximation

• A capacitor shunted across a microstripline exhibits a first order seriesresonance at a frequency where the capacitance C and its’ associatedparasitic lead inductance Lp resonate. The effect is shown as a reductionin S21 at frequency F OR

• Lp can then be easily calculated by = 2 F = 1/ SQRT (L C)


Chip Capacitor Parasitics - A FirstApproximation

• Capacitors are ATC 0.050” square ceramic• Parasitic inductance should be included in circuit designs for best

correlation between simulation and actual bench performance

Capacitor(pF)

AssociatedInductance Lp(nH)

1 0.71

8.2 0.78

27 0.79

1000 1.2

Sample data


Chip Inductor Parasitics - A FirstApproximation

• An inductor inserted in series with a microstripline exhibits a first orderparallel resonance at a frequency where the inductor L and its’ associatedshunt parasitic capacitance Cp resonate. The effect is shown as areduction in S21 at frequency F OR

• Lp can then be easily calculated by = 2 F = 1/ SQRT (L C)


Chip Inductor Parasitics - A FirstApproximation

• Inductors are Coilcraft 1008CS style• Parasitic shunt capacitance should be included in circuit designs for best

correlation between simulation and actual bench performance

Inductor(nH)

Associated shuntcapacitance Cp (pF)

4 0.048

10 0.076

27 0.170

560 0.128

Sample data


Effect of paralleling two capacitors ofdifferent values

LL1L=1.4 nHR=

LL2L=0.7 nHR=

CC1C=1000 pF

CC2C=22 pF

TermTerm1Num=1Z=50 Ohm

LL1L=1.4 nHR=

CC1C=1000 pF


CC1C=1000 pF


Paralleling 22 pF cap with 1000 pFcap may lower Z at 1.2 GHz, however,Z at 0.8 GHz increases dramatically

Paralleling 2 caps of equal Cand L cuts Z in half at all freq


Single Stage ATF-36077 2304 MHz LNA withNominal Source Inductance & 22ΩDrain Resistor

MuPrime

MuPrime1MuPrime1=mu_prime(S)

MuPrime

L_StabCircleL_StabCircle1L_StabCircle1=l_stab_circle(S,51)

LStabCircle

S_StabCircleS_StabCircle1S_StabCircle1=s_stab_circle(S,51)

SStabCircle

S_ParamSP2

CalcNoise=yesStep=0.1 GHzStop=18 GHzStart=16 GHz

S-PARAMETERS

S2PSNP1File="C:\S_DATA\FET\F360772A.S2P"

21

Ref

S2PSNP2File="C:\S_DATA\MGF4919\MGF4919_SPAR.S2P.txt"

21

Ref

MLINTL21

L=125 milW=20.0 milSubst="MSub1"

MLINTL22


RR1R=27 Ohm

WIREWire1

Rho=1.0L=400.0 milD=7.0 mil

MLEFTL19

L=150.0 milW=90.0 milSubst="MSub1"

MLINTL8


MLINTL4


C

C2C=.03 pF

CC3C=.03 pF

CC1C=.03 pF

VIA2V2

W=20.0 milRho=1.0T=1.4 milH=31.0 milD=15.0 mil

VIA2V1


MSUBMSub1

Rough=0 milTanD=.01T=1.4 milHu=3.9e+034 milCond=1.0E+50Mur=1Er=2.2H=31.0 mil

MSub

VIA2V5


VIA2V4

W=100 milRho=1.0T=1.4 milH=31.0 milD=15.0 mil

VIA2V3


StabFactStabFact1StabFact1=stab_fact(S)

StabFact

MuMu1

Mu1=mu(S)

Mu

MLINTL11


SRLCSRLC3

C=1000 pFL=.4 nHR=.3 Ohm

MLINTL12


MLINTL10


MLINTL9


MSTEPStep1

W2=20.0 milW1=100.0 milSubst="MSub1"

MLINTL13


MLINTL7


MCROSOCros1

W4=90.0 milW3=90.0 milW2=20.0 milW1=70.0 milSubst="MSub1"

MLINTL6


MTAPERTaper1

L=50.0 milW2=70.0 milW1=20.0 milSubst="MSub1"

MLINTL5


MLINTL15


SRLCSRLC5


MLINTL14


MLEFTL20


MSTEPStep2


MLINTL18


MLINTL3


MTEE_ADSTee1

W3=20.0 milW2=90.0 milW1=90.0 milSubst="MSub1"

R

R3R=50 Ohm

TermTerm2

Noise=yesZ=50 OhmNum=2

SRLCSRLC4


RR2R=50 Ohm

SRLCSRLC2


MLINTL2


SRLCSRLC1


OptionsOptions2

MaxWarnings=10GiveAllWarnings=yesI_RelTol=1e-6V_RelTol=1e-6TopologyCheck=yesTnom=25Temp=16.85

OPTIONS

MLINTL1


TermTerm1


m2freq=dB(S(2,1))=17.137

2.300GHz

2 4 6 8 10 12 14 160 18

-40

-30

-20

-10

0

10

-50

20

freq, GHz

dB(S

(2,1

))

m2

m2freq=dB(S(2,1))=17.137

2.300GHz

2 4 6 8 10 12 14 160 18

-20

-10

0

-30

10

freq, GHz

dB

(S(1

,1))

dB

(S(2

,2))

2 4 6 8 10 12 14 160 18

1

2

3

4

0

5

freq, GHz

Sta

bFa

ct1

Mu

1M

uP

rime

1

m4freq=nf(2)=0.447

2.300GHz

2 4 6 8 10 12 14 160 18

1

2

3

4

0

5

freq, GHz

nf(2

)

m4

m4freq=nf(2)=0.447

2.300GHz

indep(S_StabCircle1) (0.000 to 51.000)

S_St

abC

ircle

1

indep(L_StabCircle1) (0.000 to 51.000)

L_St

abC

ircle

1


Single Stage ATF-36077 2304 MHz LNA withNominal Source Inductance & no Drain Resistor

MuPrime


MuPrime


LStabCircle


SStabCircle

S_ParamSP2


S-PARAMETERS


21

Ref


21

Ref

MLINTL21


MLINTL22


RR1R=27 Ohm

WIREWire1


MLEFTL19


MLINTL8


MLINTL4


C

C2C=.03 pF

CC3C=.03 pF

CC1C=.03 pF

VIA2V2


VIA2V1


MSUBMSub1


MSub

VIA2V5


VIA2V4


VIA2V3



StabFact

MuMu1

Mu1=mu(S)

Mu

MLINTL11


SRLCSRLC3


MLINTL12


MLINTL10


MLINTL9


MSTEPStep1


MLINTL13


MLINTL7


MCROSOCros1


MLINTL6


MTAPERTaper1


MLINTL5


MLINTL15


SRLCSRLC5


MLINTL14


MLEFTL20


MSTEPStep2


MLINTL18


MLINTL3


MTEE_ADSTee1


R

R3R=50 Ohm

TermTerm2


SRLCSRLC4


RR2R=50 Ohm

SRLCSRLC2


MLINTL2


SRLCSRLC1


OptionsOptions2


OPTIONS

MLINTL1


TermTerm1


m2freq=dB(S(2,1))=18.638

2.300GHz

2 4 6 8 10 12 14 160 18

-40

-30

-20

-10

0

10

-50

20

freq, GHz

dB(S

(2,1

))

m2

m2freq=dB(S(2,1))=18.638

2.300GHz

2 4 6 8 10 12 14 160 18

-20

-10

0

-30

10

freq, GHz

dB

(S(1

,1))

dB

(S(2

,2))

2 4 6 8 10 12 14 160 18

1

2

3

4

0

5

freq, GHz

Sta

bF

act

1M

u1

Mu

Pri

me1

m4freq=nf(2)=0.422

2.300GHz

2 4 6 8 10 12 14 160 18

1

2

3

4

0

5

freq, GHz

nf(2

)

m4

m4freq=nf(2)=0.422

2.300GHz


S_

Sta

bC

ircl

e1


L_S

tab

Cir

cle1

Source and Load Stability Circles

ADS Schematic


Single Stage ATF-36077 2304 MHz LNA withExcessive Source Inductance

m2freq=dB(S(2,1))=15.716

2.300GHz

2 4 6 8 10 12 14 160 18

-50

-40

-30

-20

-10

0

10

-60

20

freq, GHz

dB

(S(2

,1))

m2

m2freq=dB(S(2,1))=15.716

2.300GHz

2 4 6 8 10 12 14 160 18

-20

-10

0

-30

10

freq, GHz

dB(S

(1,1

))dB

(S(2

,2))

2 4 6 8 10 12 14 160 18

1

2

3

4

0

5

freq, GHz

Sta

bF

act

1M

u1

MuP

rim

e1

m4freq=nf(2)=0.417

2.300GHz

2 4 6 8 10 12 14 160 18

1

2

3

4

0

5

freq, GHz

nf(2

)

m4

m4freq=nf(2)=0.417

2.300GHz


S_S

tab

Circ

le1


L_S

tabC

ircle

1

MuPrime


MuPrime


LStabCircle


SStabCircle

S_ParamSP2


S-PARAMETERS


21

Ref


21

Ref

MLINTL21


MLINTL22


RR1R=27 Ohm

WIREWire1


MLEFTL19


MLINTL8


MLINTL4


C

C2C=.03 pF

CC3C=.03 pF

CC1C=.03 pF

VIA2V2


VIA2V1


MSUBMSub1


MSub

VIA2V5


VIA2V4


VIA2V3



StabFact

MuMu1

Mu1=mu(S)

Mu

MLINTL11


SRLCSRLC3


MLINTL12


MLINTL10


MLINTL9


MSTEPStep1


MLINTL13


MLINTL7


MCROSOCros1


MLINTL6


MTAPERTaper1


MLINTL5


MLINTL15


SRLCSRLC5


MLINTL14


MLEFTL20


MSTEPStep2


MLINTL18


MLINTL3


MTEE_ADSTee1


R

R3R=50 Ohm

TermTerm2


SRLCSRLC4


RR2R=50 Ohm

SRLCSRLC2


MLINTL2


SRLCSRLC1


OptionsOptions2


OPTIONS

MLINTL1


TermTerm1


ADS Schematic

Source and Load Stability Circles


Single Stage LNA Designs

• Easy to obtain low noise figure but difficult to obtain goodstability mainly because of either gain peaking above orbelow the desired frequency of operation.

• Picking the right combination of source inductance anddrain resistance can be difficult

• Best solution is a multi-stage LNA


2 Stage LNA Designs

• The noise figure of a properly designed 2 stage LNA willonly increase the noise figure of the LNA by the secondstage contribution based on the gain of the first stage.

• Gain at the frequency of operation will normally be up totwice the gain of one stage with the exception at lowerfrequencies where 30 or 31 dB for a 2 stage may be thedesired maximum based on stability.

• Provide a band-pass type response at the frequency ofoperation by rolling off the gain at lower frequencies andminimizing gain peaks especially at higher frequencies.

• Input return loss can often be optimized with the interstagenetwork.


2304 MHz 2 Stage ATF-36077 LNA

2 4 6 8 10 12 14 160 18

1

2

3

4

0

5

freq, GHz

nf(2

)

m2

m2freq=nf(2)=0.388

2.300GHz

2 4 6 8 10 12 14 160 18

-60

-40

-20

0

20

-80

40

freq, GHz

dB(S

(2,1

))m3

m3freq=dB(S(2,1))=30.105

2.340GHz

2 4 6 8 10 12 14 160 18

1

2

3

4

0

5

freq, GHz

Mu1

Sta

bFac

t1

2 4 6 8 10 12 14 160 18

-30

-20

-10

-40

0

freq, GHz

dB(S

(1,1

))dB

(S(2

,2))



2 4 6 8 10 12 14 160 18

-40

-20

0

20

-60

40

freq, GHz

dB

(S(2

,1))

m2

m2freq=dB(S(2,1))=29.864

3.440GHz

2 4 6 8 10 12 14 160 18

-20

-15

-10

-5

-25

0

freq, GHz

dB

(S(1

,1))

dB

(S(2

,2))

m4

m4freq=dB(S(2,2))=-16.531

3.450GHz

2 4 6 8 10 12 14 160 18

1

2

3

4

0

5

freq, GHz

nf(2

)

m3

m3freq=nf(2)=0.410

3.520GHz

2 4 6 8 10 12 14 160 18

1

2

3

4

0

5

freq, GHz

Sta

bFa

ct1

Mu

1



2 4 6 8 10 12 14 160 18

1

2

3

4

0

5

freq, GHz

nf(2

)

m3

m3freq=nf(2)=0.493

5.760GHz

2 4 6 8 10 12 14 160 18

-150

-100

-50

0

-200

50

freq, GHz

dB(S

(2,1

))

m2

dB(S

(1,2

))

m2freq=dB(S(2,1))=29.878

5.760GHz

2 4 6 8 10 12 14 160 18

1

2

3

4

0

5

freq, GHz

Mu1

Sta

bFa

ct1

2 4 6 8 10 12 14 160 18

-25

-20

-15

-10

-5

-30

0

freq, GHz

dB(S

(1,1

))dB

(S(2

,2))

m4m4freq=dB(S(2,2))=-24.599

5.760GHz



2 4 6 8 10 12 14 16 180 20

-80

-60

-40

-20

0

20

-100

40

freq, GHz

dB(S

(2,1

))

m2

m2freq=dB(S(2,1))=25.215

10.37GHz

2 4 6 8 10 12 14 16 180 20

1

2

3

4

0

5

freq, GHz

nf(2

)

m3

m3freq=nf(2)=0.539

10.37GHz

2 4 6 8 10 12 14 16 180 20

1

2

3

4

0

5

freq, GHz

Sta

bFa

ct1

Mu1

2 4 6 8 10 12 14 16 180 20

-30

-25

-20

-15

-10

-5

-35

0

freq, GHz

dB(S

(1,1

))dB

(S(2

,2))

m4

m4freq=dB(S(2,2))=-17.017

10.37GHz


10368 MHz Single Stage ATF-36077 LNA

F_lim1freq=3.600GHzdB(S(2,1))=2.527

F_lim2freq=10.40GHzdB(S(2,1))=12.988

F_lim1freq=3.600GHzdB(S(2,1))=2.527

F_lim2freq=10.40GHzdB(S(2,1))=12.988

2 4 6 8 10 12 14 16 180 20

-40

-30

-20

-10

0

10

-50

20

freq, GHz

dB

(S(2

,1))

F_lim1

F_lim2

Gain peaking at 3.5 and 16 GHz can contribute to problems when cascading stages



2 4 6 8 10 12 14 160 18

-80

-60

-40

-20

0

20

-100

40

freq, GHz

dB(S

(2,1

))

m2

m2freq=dB(S(2,1))=28.246optIter=5

8.310GHz

2 4 6 8 10 12 14 160 18

1

2

3

4

0

5

freq, GHz

nf(2

)

m3

m3freq=nf(2)=0.554optIter=5

8.450GHz

2 4 6 8 10 12 14 160 18

1

2

3

4

0

5

freq, GHz

Sta

bFac

t1M

u1

2 4 6 8 10 12 14 160 18

-30

-20

-10

-40

0

freq, GHz

dB(S

(1,1

))dB

(S(2

,2))

m4m4freq=dB(S(2,2))=-33.568optIter=5

8.360GHz


Summary

• New 2 stage LNA designs should offer a major improvementin stability over cascading individual stages.

• My presentation will be uploaded to www.ntms.org after theconference

• Any questions?• Thanks and 73 de W5LUA

stability & lnas - · pdf filewireless semiconductor division your imagination, our...

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