S-functions Paper Presentation: Switching Amplifier Design With S-functions

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


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


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


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????


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


“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 ...


“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


“Naive” S-functions

f0

f0

3f0

2f0

a1 b2

a2

f0 3f

02f

0

b1

f0

VDCv3


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


A closer step to S-functionsf0

f0

3f0

2f0

a1 b2

a2

f0 3f

02f

0b1

f0

VDCv3


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


The S-functionsf0

f0

3f0

2f0

a1 b2

a2

f0 3f

02f

0b1

f0

VDCv3


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


The Extraction of S-functionsf0

f0

3f0

2f0

a1 b2

a2

f0 3f

02f

0b1

f0

VDCv3


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


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


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


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


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


Class B mode of operation

Gate DrainV g=−0.93V V d=6.3V


Class B mode of operation

S-functions, predicting behaviour for small and large harmonic reflection factorsto deal with different typesof “switching” amplifiers


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


S-functions


Verification of Interpolation Capability on B2


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


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)


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.


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


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


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]


Thank you for your patience ...

Want to try S-functions and ICE?Request a Free Trial here:

http://www.nmdg.be/register_freeICEsoftware.php

http://www.nmdg.be/register_freeICEsoftware.php

S-functions Paper Presentation: Switching Amplifier Design With S-functions

Technology

Transcript of S-functions Paper Presentation: Switching Amplifier Design With S-functions