IMS2011 in Baltimore: A Perfect Match
IMS 2011
Stability Analysis of Microwave Circuits
S. Dellier, PhD
IMS2011 in Baltimore: A Perfect Match
AGENDA
•
•
•
•
Introduction
Existing methods
STAN tool and application examples
Q&A
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IMS2011 in Baltimore: A Perfect Match
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 3
IMS2011 in Baltimore: A Perfect Match
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
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Slide 4
IMS2011 in Baltimore: A Perfect Match
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 5
IMS2011 in Baltimore: A Perfect Match
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 6
IMS2011 in Baltimore: A Perfect Match
EXISTING METHODS
Pole-Zero Identification Principle
50
dB(Zsond)
|H| (dB)
H ( j )
30
RG
10
 H (º)
phase(Zsond)
-10
200
Frequency
domain
Identification
techniques
RL
100
f0,
Pin
0
-100
-200
0.0
2.0E9
4.0E9
6.0E9
8.0E9
1.0E10 1.2E10
Complex conjugate
poles with positive
real part -> start-up
of an oscillation
Oscillation frequency =
Module of the
imaginary part
i 1
p
 (s   )
j 1
j
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4
Im (GHz)
H ( s) 
( i in ,fs )
Pole-zero plot
n
i
v out
Freq
(GHz)
frequency
6
 (s  z )
Node „n‟
2
0
-2
-4
-6
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
Re (GHz)
poles
zeros
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IMS2011 in Baltimore: A Perfect Match
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.
www.amcad-engineering.com
Slide 8
IMS2011 in Baltimore: A Perfect Match
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
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Slide 9
IMS2011 in Baltimore: A Perfect Match
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, MWO…
AC simulation for linear
HB simulation for non-linear
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STAN tool
integrated in IVCAD software
User-friendly GUIs
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IMS2011 in Baltimore: A Perfect Match
STAN TOOL
Automatic mode
• The order of Hˆ ( s) is a priori unknown
• Automatic algorithm for pole-zero identification in the
context of stability analysis is integrated in STAN tool
n
H ( s) 
 (s  z )
i 1
p
i
 (s   )
j 1
j
Mag(H0) (dB)
H ( j )
Phase(H0) (º)
H ( s)
Freq (GHz)
• This routine eases the use of pole-zero identification for multivariable stability
analysis
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Slide 11
IMS2011 in Baltimore: A Perfect Match
STAN TOOL
Multi-nodes
Node „n‟
v out
( i in ,fs )
A
B
FET2
A- No oscillation
detected in the
common node
FET1
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 12
IMS2011 in Baltimore: A Perfect Match
STAN TOOL
Multi-parameters
• Analysis with swept parameter(s)
• Verification for various conditions (Pin, Zload, …)
• Optimization of stabilization networks
RG
PIN
f0,
v out
( i in ,fs )
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Zload
Rstab
Slide 13
IMS2011 in Baltimore: A Perfect Match
STAN TOOL
Multi-parameters
• Application requires absence
of spurious for a wide range of
operating conditions
polar(inestables_HB1..mod,inestables_HB1..phase)
S(1,1)
Example: 3-stage LDMOS DPA
for SDR applications
• Multivariable large-signal
stability analysis versus input
frequency, input power and real
Unstable
and imaginary parts of load
loads
termination ZL.
Frequency division (fin/2) detected
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.
Stable
loads
freq (1.000GHz to 1.000GHz)
to 0.990)regions in
Stablemod
and(0.693
unstable
the L plane for fin=500 MHz
and Pin=17.1 dBm
Slide 14
IMS2011 in Baltimore: A Perfect Match
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 15
IMS2011 in Baltimore: A Perfect Match
Q&A
Contact
Stéphane Dellier
E-mail: dellier@amcad-engineering.com
Phone: +33 555 040 531
www.amcad-engineering.com