S-functions Presentation: The S-parameters for nonlinear components - Measure, Model, Verify,...

March 2011

S-functions“The S-parameters

for nonlinear components”

- Measure, Model, Verify, Simulate -

An application in ICE

© 2011 2

Outline

● Why S-functions? What is the impact?● S-functions, the “S-parameters” for all nonlinear applications?● S-functions: Key Benefits● Theory: from S-parameters to S-functions● Applicability and Assumptions of S-functions● Confidence in S-functions● S-function Extraction and Verification Tool● Deployment of S-functions in ADS and MWO / VSS● Strengths and Key Capabilities● References● Conclusion

© 2011 3

Why S-parameters?

● Complete characterization of a component in linear mode of operation● Derive insertion loss, return loss, gain, …

● S-parameters enable system-level interpretation of behavior of the component● Low – pass filtering, high reflective, ...

● S-parameters enable design in conjunction with other circuits

● S-parameters can be extracted for the designed circuit

● The S-parameters can be measured for the manufactured circuit and can be compared

DESIGN

TEST in Manufacturing

S-parameters close the characterization, design and test loop

© 2011 4

S-parameter Design- and Test-Cycle for Linear Applications

At the Foundry

Semiconductor Manufacturer

PassiveDevices

S-parameters

Design kitDesign library

[S-parameter based]

© 2011 5

S-parameter Design- and Test-Cycle for Linear Applications

At the Semiconductor Manufacturer

Design Houses

S-parameters Design kitDesign library

[S-parameter based]

Design Chips

System Manufacturers

Iterations almost completely eliminated

© 2011 6

Beyond S-parameters???

● S-parameters, the behavioural model for “linear” applications

● Components in linear mode of operation only● Filters● Transistors under small signal of excitation● ...

● Their success is based on its uniform approach for linear RF and microwave problems both to measure and to simulate

● What about components in nonlinear mode of operation?

● No uniform approach for nonlinear RF and microwave problems

● There is a lot of “trial and error” or “measure – tweak”

● S-parameters are used mainly during device modelling in conjunction with a lot of model expertise to go from small-signal to large-signal

© 2011 7

“Trial-Error” Design- and Test-Cycle for “Nonlinear” Applications

At the Foundry



Devices Modelling(6 months)

Small-SignalLarge-SignalLoad-PullMathematics...

© 2011 8

“Trial-Error” Design- and Test-Cycle for “Nonlinear” Applications


Design Houses

InitialDesign

Chips


Trial and Error

DataSheetEval Board

● Models do not meet the needs of application● To time costly to develop own models● Wafer fabs cannot worry about specific problems

© 2011 9

The Magic ...

S-Parameters

S-

S-functionsS-functions

© 2011 10

The S-function Design- and Test-Cycle for Active Devices

At the Foundry


S-Functions


[S-functions based (*)]Devices

(*) S-functions for different applications

© 2011 11

The S-function Design- and Test-Cycle for Active Devices


Design Houses

S-functions Design kitDesign library

[S-functions based]

Design Chips


Reducing the number of iterations

Improving S-functions with application-specific information

© 2011 12

Why S-functions? Adopting the S-parameter paradigm

● “Complete” characterization of a component in nonlinear mode of operation for specific applications under a relevant set of conditions● Derive “insertion loss”, “return loss”, “gain”, “mismatch”, conversion coefficients

● S-functions enable system-level interpretation of behaviour of the component● Power- dependent Low – pass filtering, power conversions, …● Ideal for dividers, multipliers and mixers

● S-functions enable design in conjunction with other circuits● When the signals are limited to the relevant set of conditions

● S-functions can be extracted for the designed circuit

● The S-functions can be measured for the manufactured circuit and can be compared

DESIGN

TEST in Manufacturing

S-functions close the characterization, design and test loop

© 2011 13

S-Functions, the “S-parameters” for nonlinear applications?

● S-Functions, the behavioural model for nonlinear applications

● Deal with a subset of nonlinear RF and microwave phenomena in a uniform way as a natural extension of S-parameters

● Will not solve “all” nonlinear problems

● Can be “measured”

● Can be used for design in simulators

● Can be used for test to compare with realizations in simulator

LinearApplications

NonLinear (*)Applications

AllOther

Applications

(*): Nonlinear behaviour determined by a small number (e.g. 2) of tones

S-parametersS-parameters


How to define the application boundary?

© 2011 14

S-Functions – Key Benefits

● Simplify the use of HF components and circuits● Complement limited data sheets with more complete system-level models ● Complement evaluation boards, enabling upfront more realistic simulations

● Improve and speed up the design and test process● Adequate replacement when classic models fail● Simulate with a behavioural model, optimized for your design problem● Same Look and Feel as S-parameters: measure, model, verify and simulate● Verify the realized circuit with S-functions against the simulation during test

● Shorter time to market for component manufacturers and buyers

S-Functions are for nonlinear applications ...... what S-parameters are for linear applications

© 2011 15

From S-parameters to S-functions

S-parameters measured at different DC bias points

S-parameters measured at fixed DC bias point

ff

f

S f

I DC V DC

S V DC ; f Linear

Nonlinear

VDC

Remark: for the sake of intuitive explanation, mathematics is not 100% correct

IDC

Keep signal small to stay in a linear mode of operation

© 2011 16


Nonlinear

Nonlinear

f0

f0

f0

3f0

2f0

VDC

Bm n f 0=F mnV DC , f 0 ,∣a1 f 0∣

A1 f 0A1 f 0B2 k f 0

50

f0 3f

02f

0

B1k f 0

Simple model and “easy” to measure

I DC=H V DC , f 0 ,∣a1 f 0∣

A2=0

k : 1... 3 ...

k : 1... 3 ...

© 2011 17


Bm n f 0=F mnV DC , f 0 ,∣a1 f 0∣

Simple model and “easy” to measure

I DC=H V DC , f 0 ,∣a1 f 0∣

But not useful in the real world

● AM-AM● AM-PM● Harmonic Distortion

● S-functions should be able to predict cascades

● “Easy” to measure .... not in reality

Input contains harmonics !!

● Harmonic distortion of source● Imperfect match at input and output

f0 3f

02f

0A1k f 0

A2l f 0

© 2011 18


f0

f0f

03f

02f

0

VDC

Bm n f 0=F mnV DC , f 0 ,∣a1 f 0∣

A1k f 0 B2 k f 0

Z Lf0 3f

02f

0

B1k f 0

“Simple” model extension

I DC=H V DC , f 0 ,∣a1 f 0∣

3f0

2f0

A2k f 0

f0

3f0

2f0

Bm n f 0=F mnV DC , f 0 ,∣a i j f 0∣,all phase comb of ai j f 0

I DC=H V DC , f 0 ,∣a i j f 0∣,all phase comb of ai j f 0

k : 1... 3 ...

© 2011 19




Huge number of combinations with sweeps in amplitude and phase

© 2011 20


What now ???

f0

f0

f0

3f0

2f0

VDC

A1k f 0 B2k f 0

Z Lf0 3f

02f

0

B1k f 0

3f0

2f0

A2k f 0f0

3f0

2f0

© 2011 21


f0

f0

f0

3f0

2f0

VDC

A1k f 0 B2k f 0

Z Lf0 3f

02f

0

B1k f 0

3f0

2f0

A2k f 0f0

3f0

2f0

In many cases : A1k f 0 , A2k f 0with k1 SMALL

Linearize equations in A1k f 0 , A2k f 0with k1

© 2011 22


f0

f0

f0

3f0

2f0

VDC

A1 f 0 B2k f 0

Z Lf0 3f

02f

0

B1k f 0 A2 f 0f0

The intuitive approach

© 2011 23


f0

f0

f0

3f0

2f0

VDC

A1k f 0 B2k f 0

Z Lf0 3f

02f

0

B1k f 0

2f0

A2 f 0f0

© 2011 24


f0

f0

f0

3f0

2f0

VDC

A1k f 0 B2k f 0

Z Lf0 3f

02f

0

B1k f 0

2f0

A2 f 0f0

x2

x2

x2

LINEARBut with frequency conversion, like a mixer

© 2011 25


f0

f0

f0

3f0

2f0

VDC

A1k f 0 B2k f 0

Z Lf0 3f

02f

0

B1k f 0

2f0

A2 f 0f0

3f0

LINEAR Superposition

© 2011 26


f0

f0

f0

3f0

2f0

VDC

A1k f 0 B2k f 0

Z Lf0 3f

02f

0

B1k f 0

2f0

A2k f 0f0

2f0

3f0

© 2011 27


f0

f0

f0

3f0

2f0

VDC

A1k f 0 B2k f 0

Z Lf0 3f

02f

0

B1k f 0

2f0

A2k f 0f0

3f0

2f0

3f0

© 2011 28




Bmn=Sf mn01 V DC , A11 , A21Sf mnij V DC , A11 , A21 AijSfcmnijV DC , A11 , A21 Aij*

with j1

I DC=Sf 0001V DC , A11 , A21Sf 00ijV DC , A11 , A21 AijSfc00ijV DC , A11 , A21 Aij*

Linearization

with Bmn≡Bmn f 0with Aij≡Ai j f 0

Sf mnij“LSOP”

m: output portn: frequency at output port mi: input portj: frequency at input port i

LSOP: large-signal operating point Sweep in strongly reduced LSOP

The S-functions

“Tickle tone”

The Mathematical Approach

© 2011 29

Sfc ???

f0

f0

f0

3f0

2f0

VDC

A1k f 0 B2k f 0

Z Lf0 3f

02f

0

B1k f 0

2f0

A2 f 0f0

© 2011 30

Sfc ???

f0

f0

f0

3f0

2f0

VDC

A1k f 0 B2k f 0

Z Lf0 3f

02f

0

B1k f 0

2f0 + df

A2 f 0f0

df

df

© 2011 31

Sfc ???

f0

f0

f0

3f0

2f0

VDC

A1k f 0 B2k f 0

Z Lf0 3f

02f

0

B1k f 0

2f0 + df

A2 f 0f0

df

df

Akl*

© 2011 32

How to extract S-functions?

Bmn=Sf mn01 V DC , A11 , A21Sf mnij V DC , A11 , A21 AijSfcmnijV DC , A11 , A21 Aij*

Select a LSOP and keep it constant

constant constant constant

Change the tickle tones

Measure each time Aij ,Bmn

Solve for the S-functions : Sf mnij LSOP , SfcmnijLSOP

Select a new LSOP and repeat

© 2011 33

Extract S-functions for a real deviceDC

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

Large-SignalSource

DC Bias

TicklingSource

© 2011 34

S-functions for Real Devices with ZVxPlus

Large-SignalSource

TicklingSource

Bias

ZVxPlus

© 2011 35

Extract S-functions for a simulated device

Large-SignalSource

TicklingSource

Bias Bias

Bias Settings Large-Signal Source Settings

Tickling Source Settings

© 2011 36

Assumptions of S-functions

DUTa1

b1

a2

b2

Is causing only a LINEAR perturbation on the NONINEAR behaviour

a1k f 0 , a2l f 0with l , k≠0,1

v3 i3

`

VDC

a1 f 0 , a2 f 0and vdcLarge-Signal Operating Point (LSOP) Tickle or probing tones

a1k f 0 , a2l f 0with l , k≠0,1

© 2011 37

The crucial question for S-functions

LinearApplications

SomeNonLinear

Applications

AllOther

Applications

S-parametersS-parameters


Mathematically well-defined To what applications does it apply?

a1k f 0 , a2l f 0with l , k1 SMALL

20 dBc down from main tone

BUT

© 2011 38

Applicability of S-functions

DUT Xa1

b1

a2

b2

● Transistors● Amplifiers● Dividers● Multipliers

Components Prediction● Harmonic distortion● AM – AM and AM – PM● Source-pull● Load-pull● Modulation behaviour (*)● Intermodulation

(*): The component is assumed to be pseudo-static

DUT Ya3

b3

© 2011 39

S-functions in ICE(*)

● Sweepable Large-Signal Operating Point (LSOP)● Auto or user-defined tickle signal level● From simple push-the-button solution to access to expert-level details● Visualization of component behaviour during data collection● Easy model verification (no EDA tool required)● Sanity checks included● Easy export to and integration in Agilent™ ADS and AWR™ MWO

● Support for mismatched environments● Harmonics generated by RF sources don't cause any problem● Simple output prediction does not require EDA tool● Export to and integration in other EDA tools on request● Possible to extend the LSOP variables, e.g. temperature

(*) Integrated Component Characterisation Environment

© 2011 40

Confidence in S-functions

● Constantness of LSOP● All Sf, and Sfc are assumed to be extracted at fixed LSOP

● e.g. variation in DC drain voltage due to changing current violates this assumption

● Interpolation capability of all Sf, and Sfc● LSOP interleaving verification measurements

● Linearity assumption of tickle tones● Model verification for different amplitude and phases of tickle tones

Measure ExtractS-functions

Confidencethrough

VerificationSimulate

© 2011 41

Confidence in S-functions through Verification

ADSMWO

ADS: Agilent Technologies Advanced Design Systems design softwareMWO: AWR Corporation's Microwave Office design software

© 2011 42

S-functions for Real and Simulated Components / Circuits

Data CollectionMeasurements

on Real Devicesusing ICE (*)

SimulationsOn Virtual Devices

in Simulation Tool (ADS - MWO)

S-functions Deployment Simulators(ADS - MWO)

S-functions

S-functions Verifications

Extraction

© 2011 43

S-functions Verification – Constantness of LSOP

Select LSOP variable

Filter for a LSOP variableand value

Variation on fixed input power

Variation ondrain bias voltage

© 2011 44

S-functions Verification – Interpolation Capability

verify interpolation of b2 using independent set of measurements

© 2011 45

S-functions Verification – Linearity Assumption of Tickle TonesDC

k f0

f0

f0

or

ZL

Large-SignalSource

TicklingSource

Bias

DC Bias

Large-Signal

Small-Signalfor harmonics

Switching Amplifier design

DC Bias a2k f 0

Lk f 0 L2 f 0 L3 f 0

a22 f 0 Still small signal?a23 f 0

© 2011 46

ICEBreaker – Option S-function Verification Tool

ICEBreakerDataset

● Measured Data

● Realistic Sweep Plan

● Under multi-harmonic Load-Pull

PredictedICEBreakerDataset

CompareDatasets

● Using S-function ● Derived Quantities

● Incident / Reflected Waves

● Voltage and Current

● Absolute Error

● Relative Error

© 2011 47

Generation of “S-function Predicted Dataset” in ICEBreaker

GenerateS-function basedDataset

CompareDatasetandS-function basedDataset

© 2011 48

Absolute Comparisons with S-function Predictions

Quantity forwhich to comparemeasurement andprediction

Measurements

S-functionPrediction

Absolute Error

● Derived quantities➢ Idc_out➢ Gain➢ Pdel_in➢ Pdel_out➢ PAE➢ ..➢ Frequency selection

● Basic quantities➢ Incident waves➢ Reflected waves➢ Voltages / Currents➢ Frequency selection

Idc_out

© 2011 49

Relative Comparisons with S-function Predictions

b_out(3f0)

● Versus➢ Harmonic index➢ Harmonic refl

Relative Error (dB)

50© 2009 - NMDG NV© 2011

Case Study(*): EPA120B-100P

EPA120B-100P• high efficiency heterojunction power FET• power output: + 29.0dBm typ.• power gain: 11.5dB typ. @ 12 GHz

Real Device Virtual Device

(*): all results in this slide set are based on S-function extraction and deployment for this device

© 2011 51

Data Collection with ZVxPlus

LSOPsweep

detailedfeedbackof LSOPfor actual

measurement

“tickle”settings

detailedfeedbackon ticklefor actual

measurement

© 2011 52

Expert Details If Desired @ Data Collection

Observewhat happens

at the DUT

MonitorRF and DC

sourcesettings

Summary

© 2011 54

S-functions Verifications – Residual Error

amplitude of complex error for measured and predicted b2 using extraction data

zoom inon result

Number of measurementsrequired to extractS-functions

zoom inontickling

© 2011 55

S-functions Verification – Interpolation Capability

verify interpolation of b2 using independent set of measurements

© 2011 56

S-functions Verifications – Constantness LSOP

Select LSOP variable

Filter for a LSOP variableand value

Variation on fixed input power

Variation ondrain bias voltage

© 2011 58

S-functions Useage in Agilent ADS

EPAClassAMediumPower.aelEPAClassAMediumPower.dsn

Set of equations using FDD

Values of all Sf, Sfc

© 2011 59

S-functions Verification in ADS - Schematic

● Example: Harmonic Balance simulation with measured a1 and a2 spectra● Excitation: Sweeping through a subset of LSOP points + tickle tones

S-function to be verified

Measurements for model verification

Measured incident waves

Access to measured datausing DAC

Sweeping through subsetof LSOP and tickle tones

© 2011 60

S-functions Verification in ADS - Frequency Domain

Frequency = 2 GHz, VDC1= -1.3 V, VDC2= +2.0 V

circles – measurementssolid lines - simulations

Measurements at different input powers than those

which were used for S-functions model extraction!

© 2011 61

S-functions Verification in ADS - Time Domain

Frequency = 2 GHz, VDC1= -1.3 V, VDC2= +2.0 V, Pa1 = +10.0 dBm circles – measurementssolid lines - simulations

Pinch-off

Saturation

© 2011 62

S-functions in ADS – Modulation Prediction - Schematic

Frequency = 2 GHz, VDC1= -1.37 V, VDC2= +4.0 V, Pa1 = +0.0 dBm – Class C

© 2011 63

S-functions in ADS – Modulation Prediction - Display

Frequency = 2 GHz, VDC1= -1.37 V, VDC2= +4.0 V, Pa1 = +0.0 dBm – Class C

© 2011 64

S-functions in ADS – Source-Pull - Schematic

Frequency = 2 GHz, VDC1= -1.37 V, VDC2= +4.0 V, Pav = +1.0 dBm – Class C

Reflection : -0.27

© 2011 65

S-functions in ADS – Source-Pull - Schematic

Frequency = 2 GHz, VDC1= -1.37 V, VDC2= +4.0 V, Pav = +1.0 dBm – Class C

Measured Input Impedance

Complex Conjugate

© 2011 67

S-functions Usage in AWR MWO

DCRFRF&DC

1 2

3

BIASTEEID=X2

DCRF RF&DC

12

3

BIASTEEID=X1

DCVSID=V1V=-1.8 V

DCVSID=V2V=6 V

1

2

SUBCKTID=S1NET="SFUNC_Model"

PORTP=2Z=50 Ohm

PORT_PS1P=1Z=50 OhmPStart=PinMin dBmPStop=PinMax dBmPStep=PinStep dB

..

..1.16226472890446E-16,-1.35308431126191E-16-3.15025783237388E-15,4.72191730160887E-159.71445146547012E-17,-2.37310171513627E-151.51267887105178E-15,1.07899800205757E-15-2.98198965520413E-15,1.59594559789866E-15-5.759281940243E-16,-1.97758476261356E-16-1.83880688453542E-15,1.92901250528621E-15-5.06539254985228E-16,2.94209101525666E-15-2.50494069931051E-15,-6.73072708679001E-16-8.60422844084496E-16,2.65412691824451E-16-2.019218126037E-15,2.7373936450914E-15-2.28289609438548E-15,1.70870262383715E-151.08246744900953E-15,-6.78276879106932E-16-1.02955838299224E-15,-1.31578775652841E-155.45570533194706E-16,3.99333344169861E-15-3.62904151174348E-15,-1.74860126378462E-15-2.00100352953925E-15,-5.68989300120393E-162.14975606760426E-15,-5.53376788836601E-16-1.16226472890446E-15,-2.44942954807925E-152.08166817117217E-16,2.4980018054066E-151.04372118124342E-05,-1.36061371223614E-052.85882428840978E-15,3.11556336285435E-15-2.15105711021124E-16,1.37390099297363E-159.71445146547012E-16,9.95731275210687E-16-1.69309011255336E-15,2.33146835171283E-154.27435864480685E-15,3.3584246494911E-15-1.08246744900953E-15,-8.60422844084496E-16…

2D and 3D package data

Model data

MDF file

© 2011 68

S-functions Verification in MWO - Frequency Domain

DCVSID=V1V=DC2val V

DCRF RF&DC

12

3

BIAST EEID=X2

DCVSID=V2V=DC 1val V

3:Bias

1 2

HBT UNER2ID=X1Mag1=0Ang1=0 DegMag2=0Ang2=0 DegMag3=0Ang3=0 DegFo=2 GHzZo=50 Ohm

1

2

SUBCKTID=S1NET ="EPA_120_B"

PORTP=2Z=50 Ohm

PORT_PS1P=1Z=50 OhmPStart=-20 dBmPStop=8 dBmPStep=1 dB

-20 -15 -10 -5 0 5 10Power (dBm)

Gain and Phase with swept Pin

-50

0

50

100

15017

17.518

18.519

19.520

DB(|LSSnm(PORT_2,PORT_1,1,1)|)[1,X]Swept Power.AP_HB

Ang(LSSnm(PORT_2,PORT_1,2,1))[1,X] (Deg)Swept Power.AP_HB

-20 -15 -10 -5 0 5 10Power (dBm)

Po with swept Pin

-80

-60

-40

-20

0

20

40

DB(|Pcomp(PORT_2,1)|)[1,X] (dBm)Swept Power.AP_HB



F0

2F0

3F0

© 2011 69

S-functions Verification in MWO - Time Domain

DCVSID=V1V=DC2val V

DCRF RF&DC

12

3

BIASTEEID=X2

DCVSID=V2V=DC1val V

3:Bias

1 2

HBTUNER2ID=X1Mag1=0Ang1=0 DegMag2=0Ang2=0 DegMag3=0Ang3=0 DegFo=2 GHzZo=50 Ohm

I_METERID=AMP1

V_METERID=VM1

1

2

SUBCKTID=S1NET="EPA_120_B"

PORTP=2Z=50 Ohm

PORT_PS1P=1Z=50 OhmPStart=-20 dBmPStop=8 dBmPStep=1 dB

0 0.2 0.4 0.6 0.8 1Time (ns)

IV

0

5

10

150

50

100

150

200

250

Vtime(V_METER.VM1,1)[*,T] (V)Waveform Tests.AP_HB

Itime(I_METER.AMP1,1)[*,T] (mA)Waveform Tests.AP_HB

-20 -10 0 8Power (dBm)

Harmonics

-80

-60

-40

-20

0

20

40

DB(|Pcomp(PORT_2,1)|)[1,X] (dBm)Waveform Tests.AP_HB

DB(|Pcomp(PORT_2,2)| )[1,X] (dBm)Waveform Tests.AP_HB

DB(|Pcomp(PORT_2,3)|)[1,X] (dBm)Waveform Tests.AP_HB

© 2011 70

S-functions in MWO – Modulation Prediction - Schematic

TPID=RX Cons tellation

QAM_SRCID=A1MOD=16-QAM (Gray)OUT LVL=-0.2OLVLTYP=Avg. Power (dBm)RAT E=_DRATECTRFRQ=2 GHzPLSTYP=Root Raised CosineALPHA=0.35PLSLN=

R D

IQ

1 2

3

45

QAM_RXID=A2

BER

BERID=5VARNAME="PBASE"VALUES=stepped(-76,-40,2)OUT FL=""

AWGNID=A3PWR=-170PWRTYP=Avg. Po wer, Symbol (dBW)LOSS=0 dB

SRC MEAS

VSAID=M1VARNA ME=""VALUE S=0NAVG=

NL_ SID=S 1NET ="AMAM AMPM.AP_HB"SIMTYP=Harmonic BalanceNOI SE=RF Budget onlyRFIFRQ=

TPID=AMP In

TPID=AMP Out

PBASE = -76

1 6 Q A M ( G r a y ) S y s t e m

1 6 Q A M S o u r c e

V e c t o rS i g n a l

C i r c u i tB a s e d A m p l i f i e r

A n a l y z e r

C h a n n e l N o i s e

G e n e r a l R e c e i v e r

B E R D e t e c t o r

S w e p t v a r i a b l e

1.92 1.94 1.96 1.98 2 2.02 2.04 2.06 2.08Frequency (GHz)

ACPR

-150

-100

-50

0

50

DB(PWR_SPEC(TP.AMP Out,1000,0,10,0,-1,0,-1,1,0,4,0,1,0)) (dBm)16QAM System

DB(PWR_SPEC(TP.AMP In,1000,0,10,0,-1,0,-1,1,0,4,0,1,0)) (dBm)16QAM System

DCRF RF&DC

12

3

BIASTEEID=X1 3:Bias

1 2

HBTUNER2ID=DCBlock2Mag1=0Ang1=0 DegMag2=0Ang2=0 DegMag3=0Ang3=0 DegFo=2000 GHzZo=50 Ohm

ISOL8RID=U1R=50 OhmLOSS=0 dBISOL=30 dB

DCVSID=V1V=DC1val V

DCVSID=V3V=DC2val V

1

2

SUBCKTID=S1NET="EPA_120_B"

PORT_PS1P=1Z=50 OhmPStart=-20 dBmPStop=8 dBmPStep=0.5 dB

PORTP=2Z=50 Ohm

© 2011 71

S-functions in MWO – Load-Pull

DCRF RF&DC

12

3BIASTEEID=X1

DCVSID=V1V=-0.6 V

DCVSID=V2V=7 V

3:Bias

1 2

HBTUNER2ID=DCBlock2Mag1=0.8Ang1=40 DegMag2=0Ang2=0 DegMag3=0Ang3=0 DegFo=2 GHzZo=50 Ohm

1

2

SUBCKTID=S1NET="SFUNC_Model"

PORTP=2Z=50 Ohm

PORT1P=1Z=50 OhmPwr=10 dBm

Load Tuner (and bias)

0 1.0

1.0

-1.0

10.0

1 0. 0

-10.0

5.0

5 .0

-5.0

2.0

2 .0

-2.0

3.0

3 .0

-3.0

4.0

4 .0

-4.0

0.2

0.2

- 0.2

0.4

0.4

- 0. 4

0.6

0.6

-0.

6

0.8

0.8

-0.

8

LP_Data_High_PowerSwp Max

25.93

Swp Min21.93

p11

p10p9 p8 p7 p6 p5p4

p3p2

p1

p1: Pcomp_PORT_2_1_M_DB = 21.93











0 1.0

1.0

-1.0

10.0

1 0 . 0

-10.0

5.0

5 . 0

-5.0

2.0

2 .0

-2.0

3.0

3 .0

-3.0

4.0

4 .0

-4.0

0.2

0.2

- 0 .2

0.4

0.4

- 0.4

0.6

0.6

-0.6

0.8

0.8

-0.8

LP_Data_Low_PowerSwp Max

-0.89

Swp Min-2.87

p10

p9

p8p7

p6

p5

p4

p3

p2

p1

p1: Pcomp_PORT_2_1_M_DB = -2.87










© 2011 72

S-functions Strengths

● S-functions are completely public

● S-functions are transparent

● S-functions are connected into ADS and MWO and can be connected in other tools on request, e.g. Matlab

● S-functions are closely integrated with load-pull in general and especially with tuners from Focus Microwave

● S-functions extraction tool has a verification capability for LSOP constantness and interpolation capability, investigating quality of model, without needing a simulation tool

● The source- and load-pull software ICEBreaker from NMDG allows S-function verification, related to the linearity assumption

● Customers can explore the capabilities of S-functions via NMDG services

© 2011 73

S-Functions - Key Capabilities

● Natural extension of S-parameters● Reduce to S-parameters for small-signal excitation● S-parameters are cascadeable, S-Functions are cascadeable too● e.g. Transistors, amplifiers, dividers, multipliers

● Predict harmonic behaviour of components under different impedances● Source – Pull● Load – Pull● Harmonic distortion, Waveforms

● Predict modulation behaviour of components under different impedances● When no long-term memory effects

● Valid for multi-ports, applicable to differential components

© 2011 74

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.

© 2011 75

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

● S-function extraction is supported on R&S network analysers

● S-functions can be coupled into ADS and MWO

● S-functions can be used to compress or hide specifics of nonlinear circuits in ADS and MWO

For more information [email protected]

www.nmdg.be

© 2011 76

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S-functions Presentation: The S-parameters for nonlinear components - Measure, Model, Verify,...

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