Upload
nmdg-nv
View
212
Download
0
Tags:
Embed Size (px)
DESCRIPTION
Presented at ESA Microwave Technology and Techniques Workshop 2010 10-12 May 2010
Citation preview
Switching amplifier design with S-functions,
using a ZVA-24 network analyzer
Marc Vanden Bossche
ESA Microwave Technology and Techniques Workshop 201010-12 May 2010
© 2010 - NMDGESA Workshop 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
© 2010 - NMDGESA Workshop May 2010 3
The Switching Amplifier
● Some specifications to optimize● Power gain● PAE● Delivered input and output power● Linearity
● Class A is very inefficient● Improve efficiency
● No signal – no power consumption● Transistor is biased into pinch-off: Class AB, B, C, E, F, ....
● The “ideal switch”● Power dissipation in the harmonics
● Harmonics are an essential part of the “switching amplifier”● Do not waste power in harmonics● Recombine harmonics with fundamental for optimal fundamental behaviour
vdid
vd
id
VD
I DD
VMax
IMax
IMax2
VDDVKnee
VD
Class A
© 2010 - NMDGESA Workshop May 2010 4
Brute Force Method
DUT
Bias
f 0
f 0
2 f 03 f 0
f 02 f 0
3 f 0
PIn
POut
P source
+ +
● Measure● Input and output DC and RF power
● For different values of● Input power● Bias● Load impedances● Source impedances
● Display and analyse collected data● Until “some optimal” point is reached
=Fundamental
AndHarmonic
Source and Load-pull
© 2010 - NMDGESA Workshop May 2010 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????
© 2010 - NMDGESA Workshop May 2010 6
Back to school: S-parameters
● S-parameters do describe a linear component completely● Transfer function● Interaction with other components● Superposition
● The equations
● The extraction● Ideal
● Reality
B1=S11a1S12a2 B2=S 21a1S 22a2
S11S21
S12S22
S11S21
S12S22
© 2010 - NMDGESA Workshop May 2010 7
“Simple” S-functions
f0
f0
3f0
2f0
a1 b2
a2
f0 3f
02f
0b1
f0
VDCv3
i3a1 , a2 and v3Independent variables:b1 , b2 and i3Dependent variables :
a1 f 0 , a2 f 0and vdc
Nonlinear behaviour caused by
B=Table1a1 f 0 , a2 f 0 , vdcI DC=Table0a1 f 0 , a2 f 0 , vdc
Large-Signal Operating Point
Let us increase the input power ...
© 2010 - NMDGESA Workshop May 2010 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
DUT Xa1
b1
a2
b2DUT Y
a3
b3
© 2010 - NMDGESA Workshop May 2010 9
“Naive” S-functions
f0
f0
3f0
2f0
a1 b2
a2
f0 3f
02f
0
b1
f0
VDCv3
i3a1 , a2 and v3Independent variables:b1 , b2 and i3Dependent variables :
a1k f 0 , a2k f 0andvdc
Nonlinear behaviour caused by
B=Table1a1k f 0 , a2k f 0 , vdc I DC=Table0a1k f 0 , a2k f 0 , vdc
Large-Signal Operating Point
3f0
2f0
3f0
2f0
Large amount of data
Infinite measurement time
© 2010 - NMDGESA Workshop May 2010 10
A closer step to S-functionsf0
f0
3f0
2f0
a1 b2
a2
f0 3f
02f
0b1
f0
VDCv3
i3a1 , a2 and v3Independent variables:b1 , b2 and i3Dependent variables :
a1 f 0 , a2 f 0and vdcNonlinear behaviour caused by
2f0 3f
0
2f0 3f
0
Linear perturbation caused bya1k f 0 , a2l f 0with l , k≠0,1
B=H a1 f 0 , a2 f 0 , vdcS k a1 f 0 , a2 f 0 , vdc Ak f 0I DC=F a1 f 0 , a2 f 0 , vdcG k a1 f 0 , a2 f 0 , vdc Ak f 0
S-functions
Linearization
© 2010 - NMDGESA Workshop May 2010 11
The S-functionsf0
f0
3f0
2f0
a1 b2
a2
f0 3f
02f
0b1
f0
VDCv3
i3a1 , a2 and v3Independent variables:b1 , b2 and i3Dependent variables :
a1 f 0 , a2 f 0and vdcNonlinear behaviour caused by
2f0 3f
0
2f0 3f
0
Linear perturbation caused bya1k f 0 , a2l f 0with l , k≠0,1
B=H a1 f 0 , a2 f 0 , vdcS k a1 f 0 , a2 f 0 , vdc Ak f 0
S kc a1 f 0 , a2 f 0 , vdc A
*k f 0
and something special:
I DC=F a1 f 0 , a2 f 0 , vdcG k a1 f 0 , a2 f 0 , vdc Ak f 0
G kc a1 f 0 , a2 f 0 , vdcA
*k f 0
S-functions
© 2010 - NMDGESA Workshop May 2010 12
The Extraction of S-functionsf0
f0
3f0
2f0
a1 b2
a2
f0 3f
02f
0b1
f0
VDCv3
i3a1 , a2 and v3Independent variables:b1 , b2 and i3Dependent variables :
a1 f 0 , a2 f 0and vdc
Constant Large-Signal Operation Point(LSOP)
2f0 3f
0
2f0 3f
0
Adequate variation in harmonic tones
a1k f 0 , a2l f 0with l , k≠0,1
F LSOP ,Gk LSOP , H LSOP , S k LSOP ,G kc LSOP , S k
c LSOP Solve (overdetermined) set of equations for the coefficients
© 2010 - NMDGESA Workshop May 2010 13
Assumptions of S-functions
DUTa1
b1
a2
b2
Linear perturbation of nonlinear behavior caused by
a1k f 0 , a2l f 0with l , k≠0,1
v3 i3
`
VDC
a1 f 0 , a2 f 0and vdcConstant(*) Large-Signal Operating Point (LSOP) Tickle or probing tones
a1k f 0 , a2l f 0with l , k≠0,1(*) the equations can be adapted to deal with small variations
© 2010 - NMDGESA Workshop May 2010 14
Extract S-functionsDC
k f0
f0
f0
or
ZL
● 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
Large-SignalSource
TicklingSource
Bias
© 2010 - NMDGESA Workshop May 2010 15
Non-50 Ohm Setup for S-function extractionDUT
Variable loss Variable lossf 0
k f 0
f 0 f 0
● 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
© 2010 - NMDGESA Workshop May 2010 16
Non-50 Ohm Setup for S-function extraction + validation
● 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
DUT
f 0
k f 0
f 0 k f 0
17© 2010 - NMDGESA Workshop May 2010
Case Study: EPA120B-100P
EPA120B-100P• high efficiency heterojunction power FET• power output: + 29.0dBm typ.• power gain: 11.5dB typ. @ 12 GHz
Focus Microwaves: CCMT Fixture Low-loss VIProbing MPT
EPA
Rohde&Scwarz:ZVA and NGMO (Bias)
NMDG:ZVxPlus Add-on kit
18© 2010 - NMDGESA Workshop May 2010
Class B mode of operation
Gate DrainV g=−0.93V V d=6.3V
19© 2010 - NMDGESA Workshop May 2010
Class B mode of operation
S-functions, predicting behaviour for small and large harmonic reflection factorsto deal with different typesof “switching” amplifiers
© 2010 - NMDGESA Workshop May 2010 20
Level of tickle tone
● 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)
DUT
f 0
k f 0
f 0 k f 0
fPin
© 2010 - NMDGESA Workshop May 2010 21
S-functions
© 2010 - NMDGESA Workshop May 2010 22
Verification of Interpolation Capability on B2
© 2010 - NMDGESA Workshop May 2010 23
Verification under high reflections
0.75 0.5 0.25 0.25 0.5 0.75
0.75
0.5
0.25
0.25
0.5
0.752 f 0
3 f 0=0
2 4 6 8 10 12 14 16
40
30
20
10
10
20
dBm b2 f0 and complex error
Complex error
dBm b2 f 0
dBm b2 f 0−b2Sfunc f 0
R0
R0.5
R1.0
R2.0
X2.0
X1.0
X0.5
X0
X2.0
X1.0
X0.5
R0
R0.5
R1.0
R2.0
X2.0
X1.0
X0.5
X0
X2.0
X1.0
X0.5R0
R0.5
R1.0
R2.0
X2.0
X1.0
X0.5
X0
X2.0
X1.0
X0.5
-45
-5
-50 -50
-15-10
dBm b2k f 0−b2Sfunc k f 0
Oscillation
© 2010 - NMDGESA Workshop May 2010 24
50 100 150 200 250
2
2
4
High reflection factor of second and third harmonic
∣2 f 0∣=1 and phase rotating 360 degrees
∣3 f 0∣=1 and fixed phase
4 6 8 10 12 14 16
10
5
5
10
15
20
dBm b2f0 and prediction error
2 f 0
Complex error
dBm b2 f 0
dBm b2 f 0−b2Sfunc f 0
Oscillation
50 100 150 200 250
2
2
4
50 100 150 200 250
2
2
4
(2)
(2)
(8)
(12)(8)
(12)
© 2010 - NMDGESA Workshop May 2010 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.
© 2010 - NMDGESA Workshop May 2010 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 [email protected]
www.nmdg.be
© 2010 - NMDGESA Workshop May 2010 27
Acknowledgement
● The use of the S-function models in ADS™ was made possible thanks to the support from Agilent Technologies
For more information [email protected]
www.nmdg.be
© 2010 - NMDGESA Workshop May 2010 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 [email protected]
© 2010 - NMDGESA Workshop May 2010 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