Stability Analysis of Microwave Circuits
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
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Slide 2
Existing Methods
Linear analysis “small signal”
- K factor
- Normalized Determinant
Non-linear analysis
“large signal”
- Nyquist criterion
- NDF
- Bolcato, Di Paolo & Leuzzi,
low frequency
0
oscillation
-20
-40
-60
-80
-100
-20f0
oscillation
-20
-40
-60
-80
-100
0
2
0
Output power (dBm)
•
Output power (dBm)
-
Function (NDF)
Stability envelope
0
Output power (dBm)
•
200
-40
-60
-80
-100
0
400
200
0
400
200
400
600
600
Frequency (MHz)
Mochizuki, …
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800
1000
600 800 1000 1200 140
Frequency
(MHz) 160
800 Frequency
1000 (MHz)
1200
1400
Slide 3
Existing Methods
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
Limitations:
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 !
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Slide 4
Existing Methods
Linear analysis
• Potentially instable architectures for which K factor is not
enough
OUT
IN
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Gate
Source
Multi-fingers transistor
Multi-stage power amplifier
Drain
Slide 5
Pole-Zero Identification
Principle
dB(Zsond)
|H| (dB)
50
H ( j )
 H (º)
phase(Zsond)
RL
100
f0,
Pin
0
-100
0.0
2.0E9
4.0E9
6.0E9
8.0E9
1.0E10 1.2E10
Node ‘n’
v out
( i in ,fs )
Freq
(GHz)
frequency
Pole-zero plot
6
4
i
 (s   )
j
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Im (GHz)
 (s  z )
j 1
200
-200
n
i 1
p
RG
10
-10
Frequency
domain
Identification
techniques
H ( s) 
30
poles
2
0
zeros
-2
-4
-6
-0.3
-0.2
-0.1
0.0
Re (GHz)
0.1
0.2
0.3
Slide 6
Pole-Zero Identification
Principle
Complex conjugate poles with positive real part -> start-up of an oscillation
Oscillation frequency = Module of the imaginary part
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Slide 7
STAN Tool
• 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.
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Slide 8
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
• Notion of “stability margin”
• Oscillation mode knowledge -> Help to find the suitable
•
•
stabilization strategy
Parametric Analysis implemented
Monte-Carlo Analysis
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Slide 9
STAN Tool
Integration in CAD Environment
GENERATOR
Perturbation
introduction node
in
Var
Eqn
VAR
VAR1
fin=9.65 GHz
Pin=12
Input power
ampli
X1
Meas
Eqn
Term
Term1
Num=1
Z=50 Ohm
I_Probe
I_sond
HARMONIC BALANCE
HarmonicBalance
HB1
Freq[1]=fin
Order[1]=10
SS_MixerMode=yes
SS_Start=f1
SS_Stop=f2
UseAllSS_Freqs=yes
MergeSS_Freqs=yes
LOAD
out
P_1Tone
cmp1198
Num=1
Z=50 Ohm
P=polar(dbmtow(Pin),0)
Freq=fin
Input frequency
CIRCUIT
v_sond
Var
Eqn
I_1Tone
SRC1
I_LSB=polar(0.0001,0)
VAR
VAR3
f1=fstart+fin+0.0001e9
f2=fend+fin
MeasEqn
meas1
Zsond=mix(v_sond,{-1,1})/mix(I_sond.i,{-1,1})
frequency=ssfreq-fin
Var
Eqn
VAR
VAR2
fstart=4.325 GHz
fend=5.325 GHz
n_point=101
Start sweep frequency
Stop sweep frequency
Number of frequency points
Nonlinear stability analysis template
EDA Tool
Templates for ADS
STAN Automation for MWO
AC simulation for linear
HB simulation for non-linear
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STAN tool
integrated in IVCAD software
User-friendly GUIs
Slide 10
STAN Tool
Selecting the node
“All nodes are equal, but some nodes are more equal than others”
SISO transfer function → exact
pole/zero cancellations are
possible
Pole/zero cancellations are
associated with the lack of
controllability and/ or
observability in the system
Slide 11
STAN Tool
Selecting the node - Recommendations
In simple circuits with a clear feedback structure any
node should serve for the analysis
Multistage power amplifiers → At least one analysis per
stage
Slide 12
STAN Tool
Multi-nodes
→ Relevant information about the nature of the oscillation and the place
in which it is being generated can be extracted → extremely useful for
circuit stabilization
6
6
4
4
4
2
2
2
0
clear
-2
-2
-4
-6
-0.3
0
quasi-cancellation
-4
-0.2
-0.1
0.0
Re (GHz)
0.1
0.2
0.3
-6
-0.3
Im (GHz)
6
Im (GHz)
Im (GHz)
Vbias _ n
Vbias _ m
Vbias_1
0
not observable
-2
-4
-0.2
-0.1
0.0
Re (GHz)
0.1
0.2
0.3
-6
-0.3
-0.2
-0.1
0.0
Re (GHz)
0.1
0.2
0.3
Slide 13
STAN Tool
Multi-nodes
Node ‘n’
v out
( i in ,fs )
B
A
FET2
FET1
A- No oscillation
detected in the
common node
FET3
FET5
FET4
FET6
BOscillation
detected in the
transistor node
 Odd mode (parametric frequency division)
 will determine the stabilization strategy
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Slide 14
STAN Tool
Parametric
Re (GHz)
• Analysis with swept parameter(s)
• Verification for various conditions (Pin, Zload, …)
• Checking of critical resonances
• Optimization of stabilization networks
RG
PIN
f0,
v out
( i in ,fs )
Zload
Pin (dBm)
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Slide 15
STAN Tool
Monte-Carlo
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)
40
20
 RSTAB = 44 
0
-20
-40
-0.2 -0.1
0
Real Axis (MHz)
0.1
Imaginary Axis (MHz)
Imaginary Axis (MHz)
40
20
 RSTAB = 70 
0
-20
-40
-0.2 -0.1
0
Real Axis (MHz)
0.1
Slide 16
STAN Tool
Performances optimization
Example: Ku-Band MMIC PA for active space antenna
• Stable original circuit
Inter-branch
stabilization resistances
RF in
RC stabilization
networks
RF out
Natanael
Ayllón
Rozas
“Développement des méthodes de
stabilisation pour la conception des
circuits hyperfréquences : Application
à l’optimisation d’un amplificateur de
puissance spatial.”, PhD Thesis,
February 2011.
STAN Tool
Performances optimization
Example: Ku-Band MMIC PA for active space antenna
• All stabilization networks removed
resistances maintained
for topological reasons
RF in
RF out
Parametric frequency
division /2 instability
Slide 18
STAN Tool
Performances optimization
Example: Ku-Band MMIC PA for active space antenna
• Optimized version
resistances maintained
for topological reasons
RF in
Stabilization
resistances
RF out
No oscillation detected,
especially around F0/2
Slide 19
STAN Tool
Performances optimization
Example: Ku-Band MMIC PA for active space antenna
• Results comparison
Original
Optimized
STAN Tool
Some recommendations
• Always do first a small signal stability analysis (AC) from low
frequencies (LF) to the max gain of the devices.
• Do the LF part separately or use a log sweep to avoid losing
information at LF if the sweep covers several decades.
• Do the identification in sub-bandwidths if the sweep covers
several decades.
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Slide 21
STAN Tool
Some recommendations
• In large-signal stab analysis use [f1, f1 + f0 + δ] but keep in
mind at least two things:
- Survey the evolution of the critical poles found in the AC
analysis as input drive is increased. Focus the analysis on
those bands.
- Focus the analysis also in instabilities that are very common
as f0/2
Note: In the sweep, avoid the precise case where the frequency
fs of the frequency generator coincides exactly with a
harmonic (not sub-harmonic) of the large signal operating
frequency f0 of the circuit
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Slide 22
STAN Tool
Some recommendations
• If in your circuit simulation you have
some measurement files ([S] blocks)
or EM-simulated block files, relax the
phase tolerance (1°) to avoid overmodeling
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Slide 23
Q&A
Contact
Stéphane Dellier
E-mail: dellier@amcad-engineering.com
Phone: +33 555 040 531
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