Stability Analysis of Microwave Circuits - · PDF fileStability Analysis of Microwave Circuits...

IMS2011 in Baltimore: A Perfect Match

IMS 2011

Stability Analysis of Microwave Circuits

S. Dellier, PhD


AGENDA

• Introduction

• Existing methods

• STAN tool and application examples

• Q&A

www.amcad-engineering.com


Slide 3

INTRODUCTION

• Stability analysis is a critical step of RF design flow

• Classical methods are either not complete or too

complex…

• Stability analysis need to be efficient (especially in large

signal)

- Rigorous

- Fast

- User-friendly

- Compatible with commercial CAD softwares



EXISTING METHODS

Linear analysis “small signal”- K factor

- Normalized Determinant Function (NDF)

- Stability envelope

- Pole-zero identification

• Non-linear analysis “large signal”- Nyquist criterion

- NDF

- Bolcato, Di Paolo & Leuzzi, Mochizuki, …

- Pole-zero identification

Slide 4www.amcad-engineering.com


Slide 5

Linear analysis• Widely used: K factor (also µ and µ‟ now)

- K>1 & |∆| <1: unconditional stability of two port network

- K<1: conditional stability stability circles

Unconditional stability Conditional stability Unconditional instability

Only indicates that a stable circuit will continue to be stable when loading it with

passive external loads at the input or output

Do not guarantee the internal stability of the circuit !

Limitations:

EXISTING METHODS



INOUT Gate Drain

Sourc

e

Multi-stage power amplifier Multi-fingers transistor

Linear analysis• Potentially instable architectures for which K factor is not

enough

Slide 6

EXISTING METHODS



Slide 7

Node „n‟

in s( i ,f )outv

RG

f0,

Pin

RL

10

30

-10

50

dB

(Zsond)

2.0E9 4.0E9 6.0E9 8.0E9 1.0E100.0 1.2E10

-100

0

100

-200

200

frequencyphase(Z

sond)

Freq (GHz)|H

| (d

B)

H

(º)

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3-6

-4

-2

0

2

4

6

Re (GHz)

Im (

GH

z)

poles zeros

Pole-zero plot

( )H j

1

1

( )

( )

( )

n

i

i

p

j

j

s z

H s

s

Frequency

domain

Identification

techniques

Pole-Zero Identification Principle

EXISTING METHODS

Complex conjugate poles with positive real part -> start-up of an oscillation

Oscillation frequency = Module of the imaginary part



STAN TOOL

Slide 8

• J.M. Collantes et al. “Monte-Carlo Stability Analysis of Microwave Amplifiers”, 12th IEEE

Wireless and Microwave Technology Conference, April 2011, Florida.

• A. Anakabe et al. “Automatic Pole-Zero Identification for Multivariable Large-Signal

Stability Analysis of RF and Microwave Circuits”, European Microwave Conference,

September 2010, Paris.

• J.M. Collantes et al. “Expanding the Capabilities of Pole-Zero Identification Techniques for

Stability Analysis”, IEEE Microwave Theory and Techniques International Symposium, June

2009, Boston.



STAN TOOL

Key Elements

• Suitable for both linear and non-linear stability analysis

• Very easy to use with any CAD tool

• Very easy to analyze results

• Relative stability information delivered

• Oscillation mode knowledge -> Help to find the suitable stabilization strategy

• Parametric Analysis implemented

• Monte-Carlo Analysis

Slide 9www.amcad-engineering.com


STAN TOOL

Input power

Number of frequency points

Stop sweep frequency

Start sweep frequency

Input frequency

v_sond

LOADCIRCUITPerturbation

introduction nodeGENERATOR

Nonlinear stability analysis template

VAR1VAR

Pin=12fin=9.65 GHz

EqnVar

VAR2VAR

n_point=101fend=5.325 GHzfstart=4.325 GHz

EqnVar

meas1MeasEqn

frequency=ssfreq-finZsond=mix(v_sond,{-1,1})/mix(I_sond.i,{-1,1})

EqnMeas

VAR3VAR

f2=fend+finf1=fstart+fin+0.0001e9

EqnVar

HB1

HarmonicBalance

MergeSS_Freqs=yesUseAllSS_Freqs=yesSS_Stop=f2SS_Start=f1SS_MixerMode=yesOrder[1]=10Freq[1]=fin

HARMONIC BALANCE

X1ampli

outin

SRC1I_1Tone

I_LSB=polar(0.0001,0)

I_sondI_Probe

cmp1198P_1Tone

Freq=finP=polar(dbmtow(Pin),0)Z=50 OhmNum=1

Term1Term

Z=50 OhmNum=1

Input power




Input frequency

v_sond




VAR1VAR

Pin=12fin=9.65 GHz

EqnVar

VAR2VAR


EqnVar

meas1MeasEqn


EqnMeas

VAR3VAR


EqnVar

Input power




Input frequency

v_sond




VAR1VAR

Pin=12fin=9.65 GHz

EqnVar

VAR2VAR


EqnVar

meas1MeasEqn


EqnMeas

VAR3VAR


EqnVar

HB1

HarmonicBalance


HARMONIC BALANCE

X1ampli

outin

SRC1I_1Tone


I_sondI_Probe

cmp1198P_1Tone


HB1

HarmonicBalance


HARMONIC BALANCE

X1ampli

outin

SRC1I_1Tone


I_sondI_Probe

cmp1198P_1Tone


Term1Term

Z=50 OhmNum=1

Integration in CAD Environment

EDA Tool

Templates for ADS, MWO…

AC simulation for linear

HB simulation for non-linear

Slide 10

STAN tool

integrated in IVCAD software

User-friendly GUIs



STAN TOOL

Automatic mode

ˆ ( )H s• The order of is a priori unknown 1

1

( )

( )

( )

n

i

i

p

j

j

s z

H s

s

• Automatic algorithm for pole-zero identification in the

context of stability analysis is integrated in STAN tool

Freq (GHz)

Phase(H

0)

(º)

Mag(H

0)

(dB

) ( )

( )

H j

H s

Slide 11

• This routine eases the use of pole-zero identification for multivariable stability

analysis



STAN TOOL

Multi-nodes

Slide 12

FET2

FET1

FET3

FET4

FET5

FET6

Node „n‟

in s( i ,f )outv

AB

A- No oscillation

detected in the

common node

B- Oscillation

detected in the

transistor node

Odd mode (parametric frequency division)

will determine the stabilization strategy



STAN TOOL

Slide 13

Multi-parameters

• Analysis with swept parameter(s)

• Verification for various conditions (Pin, Zload, …)

• Optimization of stabilization networks

in s( i ,f )outv

RG

f0, Zload

PIN

Rstab



Example: 3-stage LDMOS DPA

for SDR applications

• Multivariable large-signal

stability analysis versus input

frequency, input power and real

and imaginary parts of load

termination ZL.

Stable and unstable regions in

the L plane for fin=500 MHz

and Pin=17.1 dBm

Stable

loads

Unstable

loads

• Application requires absence

of spurious for a wide range of

operating conditions

Frequency division (fin/2) detected

Multi-parameters

STAN TOOL

Slide 14

freq (1.000GHz to 1.000GHz)

S(1

,1)

mod (0.693 to 0.990)

pola

r(in

esta

ble

s_H

B1..

mod,inesta

ble

s_H

B1..

phase)

A. Anakabe et al. “Automatic Pole-Zero Identification for Multivariable

Large-Signal Stability Analysis of RF and Microwave Circuits”, 2010

European Microwaev Conference, Paris, September 2010.


STAN TOOL

Monte-Carlo

Slide 15

Example: L-Band medium power FET amplifier

• Low frequency instability related to the input bias network

• Stabilization by the inclusion of a gate-bias resistor RSTAB

• Monte Carlo sensitivity analysis for different RSTAB (5 %

dispersion in all circuit parameters)

-0.2 -0.1 0 0.1-40

-20

0

20

40

Real Axis (MHz)

Ima

gin

ary

Axis

(M

Hz)

-0.2 -0.1 0 0.1-40

-20

0

20

40

Real Axis (MHz)

Ima

gin

ary

Axis

(M

Hz)

RSTAB = 44 RSTAB = 70


Q & A

Contact

Stéphane Dellier

E-mail: [email protected]

Phone: +33 555 040 531


mailto:[email protected]



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