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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
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
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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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IMS2011 in Baltimore: A Perfect Match
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
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IMS2011 in Baltimore: A Perfect Match
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
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IMS2011 in Baltimore: A Perfect Match
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
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IMS2011 in Baltimore: A Perfect Match
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.
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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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IMS2011 in Baltimore: A Perfect Match
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
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
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
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
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
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IMS2011 in Baltimore: A Perfect Match
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
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IMS2011 in Baltimore: A Perfect Match
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
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IMS2011 in Baltimore: A Perfect Match
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
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IMS2011 in Baltimore: A Perfect Match
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.
IMS2011 in Baltimore: A Perfect Match
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
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