This document discusses using S-functions to model switching amplifiers. S-functions are similar to S-parameters but can model nonlinear behavior by describing the amplifier's response to both fundamental and harmonic frequencies under different operating conditions. The document outlines how to extract S-functions by applying tickling tones at various harmonic frequencies while varying the large-signal operating point, and solving for the S-function coefficients. It also describes setups using tuners to control harmonic impedances during extraction and validation of the S-function model. An example case study of extracting S-functions for a GaN power amplifier is presented.

1. Switching amplifier design
with S-functions,
using a ZVA-24 network analyzer
Marc Vanden Bossche
ESA Microwave Technology and Techniques Workshop 2010
10-12 May 2010

2. Outline
● The switching amplifier and its optimization
● S-function theory
● Extraction of S-functions
● Setups for S-functions to model switching amplifiers
● A case study
● References
● Conclusion
● Acknowledgement
ESA Workshop May 2010 © 2010 - NMDG 2

3. The Switching Amplifier
● Some specifications to optimize IDD
● Power gain Class A
IMax
● PAE
● Delivered input and output power IMax
● Linearity 2
● Class A is very inefficient
● Improve efficiency VD
● No signal – no power consumption VKne VDD VMax
e
● Transistor is biased into pinch-off: Class AB, B, C, E, F, ....
● The “ideal switch”
● Power dissipation in the harmonics vd vd
id
id
● Harmonics are an essential part of the “switching amplifier”
● Do not waste power in harmonics
● Recombine harmonics with fundamental for optimal fundamental behaviour
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4. Brute Force Method
PIn
f0
f0 DUT
POut
+ +
P source Bias
f0
2f0 2f0
3f0 3f0
● Measure
● Input and output DC and RF power
● For different values of Fundamental
●
●
Input power
Bias
= And
Harmonic
Source and Load-pull
● Load impedances
● Source impedances
● Display and analyse collected data
● Until “some optimal” point is reached
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5. The Behavioural Modelling Approach
● Nothing new under the sun
● Amplifier design using S-parameters
● Advantages
● Use simulation tools for a more automated search in the multi-dimensional space
● Simulate in interaction with other circuits of the system
● Design and test pre-distortion circuits and algorithms in a simulator
● Design rules based on the behavioural model
● BUT S-parameters do not work for switching amplifiers
● What S-parameters are for linear components, are S-functions for nonlinear
components
● Or … not completely????
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6. Back to school: S-parameters
● S-parameters do describe a linear component completely
● Transfer function
● Interaction with other components
● Superposition
● The equations
B1 =S 11 a 1 S 12  a2 
B2 =S 21  a1 S 22  a2  
● The extraction
● Ideal
S 11  S 12 
S 21  S 22 
● Reality
S 11  S 12 
S 21  S 22 
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7. “Simple” S-functions
Let us increase the input power ...
f0 f0 2f
0
3f
0
VDC v 3
a1 i3 b2
Independent variables: a 1 , a 2 and v3
f0 f0 Dependent variables : b1 , b2 and i 3
2f 3f
0 0
b1 a2
Nonlinear behaviour caused by
a 1  f 0 , a 2  f 0 and v dc Large-Signal Operating Point
I DC =Table 0 a 1  f 0 , a 2  f 0  , v dc 
B=Table 1 a 1  f 0 , a 2  f 0  , v dc 
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8. “Simple” S-functions: a useless model
● This model can never be extracted directly
● Imperfect high frequency sources
● Harmonics of reflected waves add up to incident waves due to imperfect match
● Harmonics are essential in cascading circuits
a1 a2 a3
DUT X DUT Y
b1 b2 b3
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9. “Naive” S-functions
f0 f0 2f
0
3f
0
2f 3f
0 0
VDC v 3
a1 i3 b2
Independent variables: a 1 , a 2 and v3
f0 f0 Dependent variables : b1 , b2 and i 3
2f 3f 2f 3f
0 0 0
0
b1 a2
Nonlinear behaviour caused by
a 1 k f 0  , a 2 k f 0 and v dc Large-Signal Operating Point
I DC =Table 0 a 1 k f 0  , a 2 k f 0 , vdc  Large amount of data
B=Table 1 a 1 k f 0  , a 2  k f 0 , vdc  Infinite measurement time
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10. A closer step to S-functions
f0 f0 2f
0
3f
0
2f0 3f
VDC v 3
a1 0 i3 b2
Independent variables: a 1 , a 2 and v3
f0 f0 Dependent variables : b1 , b2 and i 3
2f 3f
0 0 2f0 3f a
b1 0 2
Nonlinear behaviour caused by Linear perturbation caused by
a 1  f 0 , a 2  f 0 and v dc a 1 k f 0  , a 2 l f 0  with l , k ≠0,1
I DC =F a 1  f 0 , a2  f 0  , v dc G k a 1  f 0  , a 2  f 0 , v dc  A k f 0
S-functions
B=H  a1  f 0  , a 2  f 0 , v dc S k  a1  f 0  , a 2  f 0 , v dc  Ak f 0 
Linearization
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11. The S-functions
f0 f0 2f
0
3f
0
2f0 3f
VDC v 3
a1 0 i3 b2
Independent variables: a 1 , a 2 and v3
f0 f0 Dependent variables : b1 , b2 and i 3
2f 3f
0 0 2f0 3f a
b1 0 2
Nonlinear behaviour caused by Linear perturbation caused by
a 1  f 0 , a 2  f 0 and v dc a 1 k f 0  , a 2 l f 0  with l , k ≠0,1
I DC =F a 1  f 0 , a2  f 0  , v dc G k a 1  f 0  , a 2  f 0 , v dc  A k f 0
S-functions
B=H  a1  f 0  , a 2  f 0 , v dc S k  a1  f 0  , a 2  f 0 , v dc  Ak f 0 
c *
and something special: G k  a1  f 0  , a 2  f 0 , v dc  A k f 0
S c a 1  f 0 , a 2  f 0 , v dc  A* k f 0 
k
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12. The Extraction of S-functions
f0 f0 2f
0
3f
0
2f0 3f
VDC v 3
a1 0 i3 b2
Independent variables: a 1 , a 2 and v3
f0 f0 Dependent variables : b1 , b2 and i 3
2f 3f
0 0 2f0 3f a
b1 0 2
Constant Large-Signal Operation Point
Adequate variation in harmonic tones
(LSOP)
a 1  f 0 , a 2  f 0 and v dc a 1 k f 0  , a 2 l f 0  with l , k ≠0,1
Solve (overdetermined) set of equations for the coefficients
c c
F  LSOP  , Gk  LSOP , H  LSOP , S k  LSOP ,G k  LSOP  , S k  LSOP 
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13. Assumptions of S-functions
VDC
v3
i3
a1 a2
DUT
b1 b2
`
Linear perturbation of nonlinear behavior caused by
a 1 k f 0  , a 2 l f 0  with l , k ≠0,1
Constant(*) Large-Signal Operating Point (LSOP) Tickle or probing tones
a 1  f 0 , a 2  f 0 and v dc a 1 k f 0  , a 2 l f 0  with l , k ≠0,1
(*)
the equations can be adapted to deal with small variations
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14. Extract S-functions
DC Bias f0
f0 or
Large-Signal Tickling
Source k f0 ZL
Source
● Repeat the following for all LSOPs of interest
● Select tickle tones
● Large enough to be detectable
● Small enough not to violate linearity assumption
● Measure incident and reflected waves for different tickle tones
● Model by solving for all Sf and Sfc
● Resulting into S-functions
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15. Non-50 Ohm Setup for S-function extraction
f0 DUT f0
f0
Variable loss Variable loss
k f0
● Fundamental load-tuner (realistic termination)
● Fundamental source-tuner for high reflective devices
● Continuous de-embedding of the tuners
● S-function extraction software compensates for tuner losses
● Harmonic terminations are being measured but change in an uncontrolled
way
● Impossible to verify the S-function model for switching amplifiers
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16. Non-50 Ohm Setup for S-function extraction + validation
f0 DUT k f0
f0
k f0
● Harmonic load-tuner (realistic termination)
● Controlled impedances at harmonics while stepping the fundamental load during
S-function extraction simplifies the tickling
● Controlled impedances has advantage in case of instabilities
● Creating high harmonic reflection factor for S-function verification
● Low-loss coupler structure between DUT and harmonic tuner
● S-function extraction software compensates for tuner losses
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17. Case Study: EPA120B-100P
 EPA120B-100P
• high efficiency heterojunction power FET
• power output: + 29.0dBm typ.
• power gain: 11.5dB typ. @ 12 GHz
NMDG:
ZVxPlus Add-on kit
Rohde&Scwarz:
ZVA and NGMO (Bias)
EPA
Focus Microwaves: CCMT Fixture Low-loss VIProbing MPT
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18. Class B mode of operation
Gate V g =−0.93 V Drain V d =6.3V
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19. Class B mode of operation
S-functions, predicting behaviour
for small and large
harmonic reflection factors
to deal with different types
of “switching” amplifiers
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20. Level of tickle tone
f0 DUT k f0
f0
Pin
k f 0  f
● Offset frequency for tickle tone
● Small offset for transistor
● Large enough to be out of resolution bandwidth of network analyzer
● Measurement system only measures the harmonic behaviour and DC
● Increase tickle tone power until
● Harmonic behaviour changes
● DC bias shifts
● Case study: at input: -20 dBm, at output: -5 dBm (no changes observed)
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21. S-functions
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22. Verification of Interpolation Capability on B2
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23. Verification under high reflections
b2 f0  and complex error
dBm
 2 f 0  20
0.75
0.5
dBm b2  f 0 
10 Oscillation
0.25
0.75 0.5 0.25 0.25 0.5 0.75
0.25 2 4 6 8 10 12 14 16
0.5
10
0.75
 3 f 0=0 20
30
Complex error
dBm b2  f 0 −b 2Sfunc  f 0
dBm b2  k f 0 −b2Sfunc k f 0  40
X1.0 X1.0
R0 R0 X1.0
R0
X0.5 X2.0 X0.5 X2.0
X0.5 X2.0
R0.5 R0.5
R0.5
R1.0 R1.0
R1.0
R2.0 R2.0
R2.0
X0
-45 X0
-50 X0 -50
X0.5
-5 X2.0 X0.5
-10 X2.0 X0.5
-15 X2.0
X1.0 X1.0
X1.0
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24. High reflection factor of second and third harmonic
∣ 2 f 0 ∣=1 and phase rotating 360 degrees 4 (2)
2
∣3 f 0 ∣=1 and fixed phase
50 100 150 200 250
2
dBm b2f0  and prediction error
20 (8)
dBm b2  f 0  4
15
2
10
Oscillation
(12) 50 100 150 200 250
5
2
4 6 8 10 12 14 16
  2 f 0
5
(8) 4 (12)
10
(2) Complex error 2
dBm b2  f 0 −b 2Sfunc  f 0
50 100 150 200 250
2
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25. References
● F. Verbeyst and M. Vanden Bossche, “VIOMAP, the S-parameter equivalent for
weakly nonlinear RF and microwave devices”, published in the Microwave
Symposium Digest of IEEE 1994 MTT-S International and published in the 1994
Special Symposium Issue of the MTT Transactions, vol. 42, no. 12, pp. 2531 – 2535.
● F. Verbeyst and M. Vanden Bossche, “VIOMAP, 16QAM and Spectral Regrowth:
Enhanced Prediction and Predistortion based on Two-Tone Black-Box Model
Extraction”, published in the Proceedings of the 45th ARFTG Conference, Orlando,
June 1995 and winner of the “Best Conference Paper Award”.
● J. Verspecht and P. Van Esch, “Accurately characterizating of hard nonlinear
behaviour of microwave components by the Nonlinear Network Measurement
System: introducing the nonlinear scattering function,” Proc. International Workshop
on Integrated Nonlinear Microwave and Millimiterwave Circuits (INMMiC), October
1998, pp.17-26.
● J. Verspecht, “Scattering functions for nonlinear behavioral modeling in the frequency
domain,” IEEE MTT-S Int. Microwave Symp. Workshop, June 2003.
● J. Verspecht and D.E. Root “Polyharmonic Distortion Modeling,” IEEE Microwave
Magazine, vol.7 no.3, June 2006, pp.44-57.
● D.E. Root, J. Horn, L. Betts, C. Gillease, and J. Verspecht, ”X-Parameters: The new
paradigm for measurement, modeling, and design of nonlinear RF and microwave
components,” Microwave Engineering Europe, December 2008, pp. 16-21.
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26. Conclusion
● S-functions are a natural extension to S-parameters for nonlinear behaviour
● S-functions aren't much more complex than S-parameters
● S-functions are accurate when assumptions are not violated
● Linearity assumption
● Constantness of LSOP
● S-function extraction is supported on R&S network analysers
● For switching amplifier modelling and design
● S-functions need to be used with care
● S-functions require proper verification with realistic signals, at the expense of
more complicated equipment
For more information info@nmdg.be
www.nmdg.be
ESA Workshop May 2010 © 2010 - NMDG 26

27. Acknowledgement
● The use of the S-function models in ADS™ was made possible thanks to the
support from Agilent Technologies
For more information info@nmdg.be
www.nmdg.be
ESA Workshop May 2010 © 2010 - NMDG 27

28. Explore the power of S-functions
Send your device or circuit to NMDG ...
`
… and NMDG sends you the S-functions
Please contact NMDG at info@nmdg.be
ESA Workshop May 2010 © 2010 - NMDG 28

29. Thank you for your patience ...
Want to try S-functions and ICE?
Request a Free Trial here:
http://www.nmdg.be/register_freeICEsoftware.php
ESA Workshop May 2010 © 2010 - NMDG 29