time and frequency domain transistor modeling based on ... · issues with compact device models •...

Time and frequency domain transistor modeling based on Nonlinear Vector Network Analyzer databased on Nonlinear Vector Network Analyzer data

D. E. Root, J. Horn, J. Xu, M. Iwamoto, F. Sischka, and Y. Yanagimoto

Agilent Technologies IncAgilent Technologies Inc.

MOS-AK/GSA WorkshopSan Francisco, CADecember 8, 2010

© Copyright Agilent Technologies 2010

Page 1 D. E. RootD. E. RootDecember 8, 2010

MOS-AK/GSA

Three Modeling Flows based on Nonlinear Data

IC-CAP

Measurement, Modeling, & Design Capabilities

parameterextraction fromNVNA data Adv. Dynamic Model

ADSNVNA

DI

Adv. Dynamic Model

IC design21j dsgs φ φ TV V

Measurement-based compact model

X-parameters



NVNA-based devicecharacterization Measurement-based

behavioral modelMOS-AK/GSA

Outline

• Introduction: NVNA Measurements – complex spectra & waveforms

• Compact ModelsCompact model validation and parameter extractionGaAs transistor model identification and validationGaAs transistor model identification and validation

• Load-dependent X-parameter model of packaged GaN transistor & validation with harmonic load-pullp

• Discussion and Comparison

• ConclusionsConclusions



MOS-AK/GSA

Introduction: NVNA measurements complex spectra and waveforms [1]complex spectra and waveforms [1]

2 kA1kA

B 2kB

pkBpkA1kB 2k

Port IndexHarmonic Index

I I Includes:S1I 2I S-paramsWaveformsLoad-linesX-params



time timep

MOS-AK/GSA

Outline


• Compact ModelsCompact model validation and parameter extractionGaAs transistor model identification and validationGaAs transistor model identification and validation






MOS-AK/GSA

Compact Transistor Models: time domain

Thermal Subcircuit (Two-Poles)( )

Standard GaAs FET Model

Model: Coupled nonlinear ordinary differential equations



MOS-AK/GSA

Conventional Empirical Device Modeling Flow

IC CAPIC-CAP

VNA0.09

ADS0.03

0.04

0.05

0.06

0.07

0.08

Cgd

(pF)

CGD vs bias

P t

80

100

120

140

160

180-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

0.01

0.02

Vds

Parameter Analyzer

0 1 2 3 4 5 6 7 8 90

20

40

60

80

Your Compact

Model HereDoes it actually work in NL?

Circuit design

Parameter extraction for std. compact model

NVNA-based devicecharacterization

DC + S-parameter(or C-V data)



p( )

MOS-AK/GSA

Issues with compact device models

• Parameters typically extracted from DC and linear S-pars Ironic for a nonlinear model– Some devices may not be able to be characterized under DC and static

operating conditions (power, temperature)Ad d t b d d l t b id tifi bl f– Advanced measurement-based models may not be identifiable from only DC and S-parameter data.

– No direct evidence that these nonlinear models will reproduce large-i l b h i d t l diti f !signal behavior under actual conditions of use!

• Large-signal data from Nonlinear Vector Network AnalyzerLarge signal data from Nonlinear Vector Network Analyzer (with additional advanced modeling techniques) can solve all these problems



MOS-AK/GSA

Nonlinear Modeling Flow with NVNA data (1)

IC CAPIC-CAPNVNA

ADS

S BiSync. BiasSupply

120

140

160

180

Your Compact

Model Here0 1 2 3 4 5 6 7 8 9

0

20

40

60

80

100

Circuit designParameter extraction for

std. compact model NVNA-based devicecharacterization

Dynamic Load-lineWaveform meas.



pusing NVNA data as targetDC-IV, S-pars

MOS-AK/GSA

Model parameter extraction from Nonlinear Data (1)

NVNA data vs HB simulationusing initial parameter values extracted from DC + CV

Modify parameter values (optimize) to better fit large-signal NVNA data

• Get optimal parameter• Get optimal parameterset for given model

• trade-off DC, SP, fornonlinear performance

• App-dependent tuning



Ref. [10]

• App-dependent tuning• Explore model limits

MOS-AK/GSA

ICCAP comparison of simulated & NVNA measured results

Extract or Tune parameters with this capabilityBased on NVNA data

Large-signal Validation for free!Evaluate model under realistic operationSee where it needs improvement



Based on NVNA dataDetails are model-dependent

p

MOS-AK/GSA

Outline


• Compact Models Compact model validation and parameter extractionGaAs transistor model construction and validationGaAs transistor model construction and validation






MOS-AK/GSA

Nonlinear Modeling Flow with NVNA data (2)[4] J. Xu, M. Iwamoto, J. Horn, D. E. Root, IEEE MTT-S International Microwave Symposium Digest, May, 2010.

NVNA Advanced Non-parametricDynamic Model

DI

ANN

)()( tVtI

jT

IG QG IDQD

ADS2_emitC

dsV 2

2_emitR

2_captR1_emitC

gsV 1

1_emitR

1_captR

)()( tVtIthC

thR

0T21j dsgs φ φ TV V

80

100

120

140

160

180

0 1 2 3 4 5 6 7 8 90

20

40

60

80

Circuit designNVNA-based device

characterization

Dynamic Load-lineWaveform meas.DC + Spars

Direct construction of complicated constitutive relations



DC + SparsNot really parameter extraction!

MOS-AK/GSA

Motivations

Modeling modern III-V FETs requires the identification and self-consistent coupling of

(1) slowly varying dynamical variables

e.g., temperature, slow emission of traps

(2) rapidly varying dynamical variables(2) rapidly varying dynamical variables

e.g., the instantaneous intrinsic terminal

lt d f t tvoltages and fast capture processes.


Page 14 D. E. RootD. E. RootDecember 8, 2010 MOS-AK/GSA

Model Formulation [4] J. Xu, M. Iwamoto, J. Horn, D. E. Root, IEEE MTT-S International Microwave Symposium Digest, May, 2010.

IG QG IDQD



Time (ns) Time (ns)

MOS-AK/GSA

NVNA data for identification of constitutive relations

))()()()()(())()()()()(()( t ,t ,tT ,tV ,tVQdtd t ,t ,tT ,tV ,tVItI 21jdsgsD21jdsgsDdrain

Auxiliary Terminal Auxiliary Terminal u a yVariables

e aVoltages

u a yVariables

e aVoltages

NVNA Constitutive Relation Compiled Waveforms Identification / Fit

F(Vgs,Vds, Aux. variables)Terminal Voltages(Vgs,Vds)

pModel in ADS

Auxiliary Variable Generation using Auxiliary variables fixed at their

steady-state large-signal valuesth0j RtV tITT )()(

))(( tVMin gs1

))(( tVMax ds2

AuxiliaryVariables

jT 1 2

steady-state large-signal values established by nonlinear measurements



MOS-AK/GSA

Artificial Neural Networks (ANN)An ANN is a parallel processor made up of simple, interconnectedprocessing units, called neurons, with weighted connections.

sigmoidweights biases

x1

...

baxwsvxxFI

i

K

kikkiiK

1 11 ),...,( xk

• Universal Approximation Theorem: Fit “any” nonlinear function of any # of variables• Infinitely differentiable: good for distortion.• Easy to train (fit) with appropriate SW



• Works well on non-gridded data and data with irregular boundaries (intrinsic FET)

MOS-AK/GSA

NVNA Measurements with Trap State ]1003[][ ,., 21 p ][][ ,, 21

Dynamic Load-lines

200

250

100

150

Ids

50

0

50

-2 0 2 4 6 8 10 12-50

Vds

Red line is one example of the 191 waveforms for this trap state



191 waveforms for this trap state

MOS-AK/GSA

Artificial Neural Network Training Procedure

(t)DI

kEAdjust wID and wQD

waveformthk for (t),measDI

jW

IFFT

j

FFT

QD_ANNID_ANN

th0j RtV tITT )()(

))(())(( tVMax,tVMin ds2gs1 wQDwID

))(())(( , ds2gs1

waveformthk for , (t) (t) 21jdsgs TVV

))()()()()(())()()()()(()( tttTtVtVQdtttTtVtVItI



))()()()()(())()()()()(()( t,t,tT,tV,tVQdt

t,t,tT,tV ,tVItI 21jdsgsD21jdsgsDdrain

MOS-AK/GSA

Intrinsic Model CharacteristicsID @ two different trap state valuesD @

Ids (mA) Ids (mA)

))()()()()(())()()()()(()( t ,t ,tT ,tV ,tVQdtd t ,t ,tT ,tV ,tVItI 21jdsgsD21jdsgsDdrain

120

140

160

180

120

140

160

180

“knee walkout”

60

80

100

120

60

80

100

120knee walkout

0

20

40

60

0

20

40

60

0 1 2 3 4 5 60

0 1 2 3 4 5 6Vds (V) Vds (V)

fixed Tj and fixed trap state = [-2.0, 8.0] Isothermal DC )080255( TVVI )55( VVTVVI



)080255( .. 21jdsgsD , ,T ,V ,VI )55( ds2gs1jdsgsD V,V,T,V ,VI

MOS-AK/GSA

Model Validation- DC

Model (___ ) Measured data ( o )( )

Vgs=1.2V

Ids (mA)Vgs=0.0V

Vgs=-3.0V



Vds (V)

MOS-AK/GSA

Model Validation- Frequency dispersion of small-signal characteristics

Frequency : 0.5 GHz to 50 GHz

-12 12 -12 1212 12 12 12

-12 12 -12 12

-0.6 0.6 -0.2 0.2

))()()()()(())()()()()(()( tttTtVtVQdtttTtVtVItI

Excellent agreement over the entire bias range



))()()()()(())()()()()(()( t,t,tT,tV,tVQdt

t,t,tT,tV ,tVItI 21jdsgsD21jdsgsDdrain

MOS-AK/GSA

Model Validation- Gain, Bias Current, Harmonic Distortion vs. Power

Simulated (___ ) Measured data (symbols)

Simulated (___ ) Measured data (symbols)Measured data (symbols)



MOS-AK/GSA

Model Validation- Load Line (Freq=2GHz, Bias=[-0.2, 6])

180

200Id (mA) (.): DC

120

140

160

180 (o): MeasuredLine: Simulated

60

80

100

Load

-20

0

20

40

This Load was not usedin the model extraction

0 2 4 6 8 10 1220

Vds (V)

Demonstrates model can go far beyond the range over which ti l DC d li S t b t k



conventional DC and linear S-parameters can be taken

MOS-AK/GSA

Model Validation- Gate Current Contours(4 t f diff t d l d F 4GH )

Ig (A) Symbol: Data

(4 contours for different powers and loads, Freq=4GHz)

Ig (A) Symbol: Data

0.01

0.015

yLine: Simulated

0.01

0.015

g ( ) yLine: Simulated

0

0.005

0

0.005

-0.01

-0.005

-0.01

-0.005

-2 -1.5 -1 -0.5 0 0.5 1-0.015

Vg (V)0 2 4 6 8 10 12

-0.015

Vd (V)



MOS-AK/GSA

Model Validation- Gain vs. Pout @26GHz

Model was extracted using 2GHz and 4GHz dataai

n (d

B)

Ga

Pout (dBm)



( )

MOS-AK/GSA

Outline


• Compact ModelsCompact model validationParameter extractionParameter extractionGaAs transistor model identification and validation

• Load-dependent X-parameter model of packaged GaN p p p gtransistor & validation with harmonic load-pull


• Conclusions



MOS-AK/GSA

S-parameters Solve All Small-Signal ProblemsBut devices must operate linearlyp y

Reflected Transmitted

Incident Freq. Domain ModelB1 S11A1 + S12A2

Measure

Agilent Vector Network AnalyzerS

B1 = S11A1 + S12A2

B2 = S21A1 + S22A2

g y

S-Parameters

ReflectedDesign

What about large-signal

nonlinear problems?

Reflected

Incident

1 2S_ParamSP1

Step=0.1 GHzStop=10.0 GHzStart=1.0 GHz

S-PARAMETERS

freq (1 000GHz to 26 00GHz)

$TC

700.

.S(2

,1)



nonlinear problems?freq (1.000GHz to 26.00GHz)

MOS-AK/GSA

X-parameters Solve Nonlinear Problems [1,8]Same use model as S-parameters, but much more powerfulp , p

Scattered Scattered

Model

Measure

Incident

11

, 11

*

( )

( )

( )

F mpm pm

S m npm qn qn

T m n

B X A P

X A P A

X A P A

Agilent Nonlinear Vector

Network Analyzer X

, 11( )pm qn qnX A P A

Reflected

Design X-Parameters

Reflected

Incident

1 2Agilent ADSEDA Software



MOS-AK/GSA

X-Parameters: Nonlinear Spectral MapsFrom S-Parameters to “Harmonic Time-Domain Load-Pull”

2 kA1kA 1 1 1 1 1 2 2 1 2 2( , , , . . . , , , . . . )k kB F D C A A A A

2 2 1 1 1 2 2 1 2 2( , , , . . . , , , . . . )k kB F D C A A A A

Port IndexHarmonic (or carrier) Index

1kB 2kB magnitude & cross-frequency phase

Port Index

X-parameters allow us to simplify the general B(A) relations:Trade efficiency, practicality, for generality & accuracyPowerful correct and practical; Native Freq Domain ModelPowerful, correct, and practical; Native Freq. Domain Model

1 1 2 2( )) (i i iB S DC A S DC A The simplest X-parameters are just linear S-parameters

,,

( ) *1

( )11

,1

( ), 1

,1( ,| |) ), ( ,( )

ef gef gh hef

S f hgh

g h

T f hg

F fe

g hf hB X DC A X DP C A DC A P AP A X

, ,

( )11 21

( ), 11

( ) *11 2112 ( , ,| |,( ,| ( , ,| |,|,| ) )| ),

ef ghghf efe

F fe f

S f h T f hggh hB X DC A A X DC A X DC AA A AP AP P



, ,hg h g

MOS-AK/GSA

NVNA+Load-Pull = Instant Large-Signal Model

• Drag and drop measured X-parameters into ADS for immediate nonlinear circuit design based on measured X-pars

NVNA +Load-Pull



MOS-AK/GSA

Load-Dependent X-Parameters of a FETWJ FP2189 1W HFET

G. Simpson et al IEEE ARFTG Conference, December, 2008

15

20

0.25

0.30

Me

ag

eg

e Sim

Measured and Simulated Voltage and Current Waveforms

Measurements X-par Simulation

Pout Contour (dBm)

WJ FP2189 1W HFET

0

5

10

0.10

0.15

0.20

ea

sure

dC

urre

ntM

ea

sure

dV

olta

Sim

ula

ted

Vo

lta

mu

late

dC

urre

nt

0.2 0.4 0.6 0.80.0 1.0

-5 0.05

time, nsec

Measured and Simulated Voltage and Current Waveforms0 30

Measured and Simulated Dynamic Load Line

8

10

12

14

16

0.2

0.3

0.4

0.5

Me

asu

red

Cu

sure

dV

olta

ge

late

dV

olta

ge S

imu

late

dC

u0.15

0.20

0.25

0.30

asu

red

Cur

ren

tm

ula

ted

Cu

rre

nt

0.2 0.4 0.6 0.80.0 1.0

4

6

2

0.1

0.0

time, nsec

urre

ntM

ea

sS

imu

urre

nt

0 2 4 6 8 10 12 14 16-2 18

0.10

0.05

MeasuredVoltage

Me

SimulatedVoltage

Sim

E i t l H i B l X t if S t d l d ll



Experimental Harmonic Balance X-parameters unify S-parameters and load-pull

MOS-AK/GSA

Load-Dependent X-Parameter Model for GaN HEMT:C[12] J Horn G Simpson D E Root

GPIB

Bias

Cree CGH40010 GaN HEMT

[12] J. Horn, G. Simpson, D. E. Root IEEE CSIC Symposium Oct. 4, 2010

NVNA

MDC S l

Bias Tees

NVNA

10 W packaged transistor

900 MHzMaury Software

U

DC Supply NVNA Firmware

• 900 MHz• Measure Load-dependent X-parameters vs power at 9 impedances

DUT Maury Tuner

USB

Maury Tuner

vs power at 9 impedances• 4 harmonics measured• probe tones at 2nd and 3rd

harmonicsTunerTuner

9 load states at f1

harmonics• harmonic impedancesuncontrolled

X parameters > ADS for independent validation© Copyright Agilent Technologies 2010


X-parameters -> ADS for independent validation

MOS-AK/GSA

Harmonic Load-pull Setup: For Validation Only[12] J. Horn, G. Simpson, D. E. Root IEEE CSIC Symposium Oct. 4, 2010

•Waveforms measured

NVNA

GPIB

Bias Tees

•Waveforms measured versus power at each set of 729 harmonic loads as controlled independently

Maury Software

DC Supply NVNA Firmware

by the tuners.•Fundamental, second, and third complex impedances setSoftware

USB

Firmware impedances set independently

DUT Maury Tuner Z1

Maury Tuner

Maury Tuner Z2

Maury Tuner Z3



9 states 9 states 9 states

MOS-AK/GSA

Load-Dependent X-Parameters versus Harmonic Load-Pull

Load-dependent X-pars• One output tuner to vary load at

Harmonic load-pull validation• Three output tuners to vary• One output tuner to vary load at

fundamental frequency. At each load inject small tones at 2nd and 3rd

harmonic freqs

• Three output tuners to vary loads at fundamental, second, and third harmonics independentlyharmonic freqs

(9x(1+2x2) = 45 measurements,actually ~125 measurements)

• Measured DC 4th harmonic

independently (9x9x9 = 729 measurements)

• Measured DC – 4th harmonic

• Take into ADS. Present 729 independent loads to model

• Measured DC - 4th harmonic

Compare waveforms PAE dynamic load lines etcADS



Compare waveforms, PAE, dynamic load-lines, etc.

MOS-AK/GSA

Prediction of GaN HEMT Harmonic-Load Dependencefrom Fundamental-Only Load-Dependent X-Parameters

60

70

80

PAE

30

40

50Z1Z2 Z3 Cree

Harmonic loads

6 8 10 12 14 16 184 20

20

10

CGH40010 GaN HEMT

Pin (available)2.0

y

Id [A] 70 2.0

Vd VdId

0.5

1.0

1.5

Id [A]

30

40

50

60

0 5

1.0

1.5

Vd IdVdId

10 20 30 40 50 600 70

0.0

-0.5

Vd [V]X parameter model

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.20.0 2.4

10

20

30

0

0.0

0.5

-0.5

Time (nanoseconds)



X-parameter model Harmonic time-domain load-pull measurements

Time (nanoseconds)

MOS-AK/GSA

Prediction of GaN HEMT Harmonic-Load Dependencefrom Fundamental-Only Load-Dependent X-Parameters

50

60

70

ZCree

CGH40010

PAE

20

30

40Z1Z2 Z3

CGH40010 GaN HEMT Harmonic loads

6 8 10 12 14 16 184 20

10

2.0

y a c oad e

Pin (available)70 2.0

VdId

VdId

1.0

1.5Id [A]

30

40

50

60

1.0

1.5

Vd

0.0

0.5

0.5

0

10

20

-10

0.0

0.5

-0.5


Page 37 D. E. RootD. E. Root

0 10 20 30 40 50 60-10 70

December 8, 2010

Vd [V] 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.20.0 2.4

Time (nanoseconds)

MOS-AK/GSA

70

PAE vs. Available Input Power

Prediction of GaN HEMT harmonic-load dependencefrom fundamental-only load-dependent X-pars

50

60

70

Cree CGH40010

PAE

20

30

40Z1Z2 Z3

CGH40010 GaN HEMT Harmonic loads

6 8 10 12 14 16 184 20

10

y 60

70

1 5

2.0

Vd IdVdId

Pin (available)

0 5

1.0

1.5

2.0

30

40

50

60

0.5

1.0

1.5

Id [A]

-0.5

0.0

0.5

-1.0

10

20

0

-0.5

0.0

-1.0



10 20 30 40 50 600 70 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.20.0 2.4

December 8, 2010

Vd [V] Time (nanoseconds)

MOS-AK/GSA

10W GaN Device Model Comparisonp

Harmonic Loads 75

50(%)Z1

0

25PAE

Z2

0 100 200 300Phase of Γ2 (degrees)

45

Z3

40

el(d

Bm

)

35

Pde

0 100 200 300Ph f Γ (d )



Phase of Γ2 (degrees) MOS-AK/GSA

10W GaN Device Model Comparisonp

Harmonic Loads 75

50

E(%

)

Z1

0

25PAE

Z2

0 100 200 300Phase of Γ2 (degrees)

45)Z3

40

el(d

Bm

)

35

Pde

0 100 200 300Phase of Γ (degrees)



Phase of Γ2 (degrees) MOS-AK/GSA

Fundamental-only load-dependent X-parameters

• Full two-port nonlinear functional block model for simulationAccounts for load tuning dependence of device performance without the– Accounts for load-tuning dependence of device performance without the requirement of independently controlling harmonic loads

– Use to design matching networks, multi-stage amps, Dougherty amps.– Accurate model of GaN device demonstrated

• Large reduction of data / time compared to harmonic load-pull

• Harmonic load-pull may be unnecessary– Source-pull unnecessary (see [12]) except for power transfer



MOS-AK/GSA

Comparison of approaches presented hereApproach Advantages DisadvantagesApproach Advantages Disadvantages

Compact Works in all simulation modes (TA, D l i lCompact

Device model

( ,HB, CE)

More scalable Simple statistics Noise models;

Development time long Extraction difficult Technology-dependent

Noise models; dynamic self-heating common

What-if scenarios possible

X-parameter Device model

Technology independent Extremely accurate within

characterization range Complete IP protection

Limited by NVNA BW Large file size, especially

for multi-tone models Complete IP protection Works for packaged parts Automated extraction Often converge better than compact

Limited memory effects in products (but demonstrated in [15])



models in circuits

MOS-AK/GSA

Conclusions

• NVNA is a powerful, valuable tool for device modeling1 NVNA data (“HB data”) can be used to validate tune extract optimal1. NVNA data ( HB data ) can be used to validate, tune, extract optimal

parameters, explore compact model limitations & suggest improvements2. NVNA data can be used to identify complicated constitutive relations for

advanced compact models not possible using conventional dataadvanced compact models - not possible using conventional data.3. Load-dependent X-parameters, measured on an NVNA, is a powerful,

efficient, and accurate way to model important, new devices for PA and i it d i C l t h t t d licircuit design. Complementary approach to compact modeling.

• Compact models & X-parameters compared for device modeling applicationsg pp

• Every nonlinear modeling station should use an NVNA instead of a conventional linear VNA.



MOS-AK/GSA

NVNA, ANNs, and X-parameters fill in nonlinear puzzleElectronic design

automation softwareAgilent Nonlinear Vector

Network Analyzer

Nonlinear Nonlinear

CustomerNonlinear

Simulation & DesignMeasurements

Customer Applications

Nonlinear Modeling



*11 , 11 , 11( ) ( ) ( )F S m n T m n

pm pm pm qn qn pm qn qnB X A X A P A X A P A

MOS-AK/GSA

References[1] http://www.agilent.com/find/nvna[1] http://www.agilent.com/find/nvna

[2] Chiu et al “Characterization of annular-structure RF LDMOS transistors using Polyharmonic Distortion Model,” IEEE MTT-S International Microwave Symposium Digest, June, 2009, pp 977-980

[3] D. Gunyan et al, “Nonlinear validation of arbitrary load X-parameter and measurement-based device models,” IEEE MTT-S ARFTG Conference, Boston, MA, June 2009

[4] J. Xu, M. M. Iwamoto, J. Horn, D. E. Root, “Large-signal FET model with multiple time scale dynamics from nonlinear vector network analyzer data,” IEEE MTT-S International Microwave Symposium Digest, May, 2010.

[5] J. Horn, “Harmonic load-tuning predictions from X-parameters,” IEEE PA Symposium, San Diego, Sept. 2009

[6] G. Simpson et al, “Load-pull + NVNA = Enhanced X-parameters for PA designs with high mismatch and technology-independent large-signal device models,” IEEE ARFTG Conference, Portland, OR December 2008.g

[7] J. Verspecht and D. E. Root, “Poly-Harmonic Distortion modeling,” in IEEE Microwave Theory and Techniques Microwave Magazine, June, 2006

[8] D. E. Root et al “X-parameters: The new paradigm for measurement, modeling, and design of nonlinear RF and microwave components,” Microwave Engineering Europe, Dec. 2008 pp 16-21.

[9] A il t Ad d D i S t d t ti N li D i[9] Agilent Advanced Design System documentation: Nonlinear Devices

[10] E. Vandamme et al, “Large-signal network analyzer measurements and their use in device modeling,” MIXDES 2002, Wroclaw, Poland.

[11] http://www.cree.com/products/pdf/CGH40010.pdf

[12] J. Horn, G. Simpson, and D. E. Root IEEE MTT-S CSIC Symposium , Monterey, CA 2010.

[13] O. Jardel et al, “An electrothermal model for AlGaN/GaN power HEMTs including trapping effects to improve large-signal simulation results on high VSWR,” IEEE Transactions on MTT., vol. 55, Dec., 2007.

[14] J Verspecht, "Black box modelling of power transistors in the frequency domain," INMMiC'96 Conference Record, Duisburg, 1996

[15] J. Verspecht et al, “Extension of X-parameters to include long-term dynamic memory effects,” IEEE MTT-S International Microwave Symposium Digest, 2009. pp 741-744, June, 2009.



y g

December 8, 2010

MOS-AK/GSA

time and frequency domain transistor modeling based on ... · issues with compact device models •...

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