Nonlinear Analog Behavioral Modeling of Microwave Devices and … · 2011-03-15 · MEMS switches...

Nonlinear Analog Behavioral Modeling of Microwave Devices and CircuitsMicrowave Devices and Circuits

Dr. David E. Root P i i l R h S i iPrinciple Research Scientist

High Frequency Technology Center Agilent Technologies

Santa Rosa, CA,

IEEE MTT-S DML Lecture #1Bergen NorwayBergen, Norway

May 7, 2010

IEEE DML Norway talk #1 David E. Root

May 7, 2010 Page 1

Acknowledgement Key Contributors

Loren BettsAlex CognataChad Gillease

Norway IEEE MTT/AP ChapterChad GilleaseDaniel GunyanJason HornMasaya Iwamoto

Yngve Thodesen

Karl-Martin GjertsenMasaya IwamotoGreg JueDominique SchreursDavid Sharrit

Marius Ubostad

Jonny LangmyrenNick TufillaroJan VerspechtJianjun Xu

y g y

Peter Myhrberg

Bjorn Birkeland John Wood

Agilent ManagementMany others

Bjorn Birkeland

Riccardo Giacometti

Gi i DIEEE DML Norway talk #1 David E. Root

May 7, 2010 Page 2

yGiovanni Damore

Agilent High Frequency Technology CenterIntegrated Diodes Liquid metal

it h

Measurement and ModelingSciences Internal and

GaNHyperabrupt Diodes

MEMS switches

GaAs

Agilent MeasurementHW & SW IP

external technology

Collaborative Innovation

pHEMT & FET ICsDiodes

InP

InternalCapability

Tech Access

packaging / subsystem

digital & mixed signal ICHBT ICs

Thin Film

Future use PNA2

Agilent ADS

Moment m

HFTC Fabrication & Access p y

microwave nano / microfabrication / MEMS

microwave IC

Modeling and Measurement ScienceThin Film

10M - 13.5 GHz

TC200G=10P1=11

X2

U9TC745

Pin = 15dBmG= - 11

U13TC728

U5TC905G=15P1=17

TC700G=8

P1=18

slopepad

TC728

TC728

ALCModulator

(PIN)

TC700G=8

P1=18

PIN diodespulse

Modulator2-20G

TC700G=8

P1=18

TC724G=7.5P1=26

PINswitche

slopepad

TC702G=7

P1=22

M/ACom

3.2 - 13.5 G Path

13.5 - 26 G Path

SMA

M/ACom TC700

G=8P1=18

ALCModulator(TC709)

TC200G=10P1=11

TC728

DET

SMA

ESD

TC702G=7

P1=22

TC728

TC724G=7.5P1=26

SMA

FL319.5 -26

FL216-21

FL113-16.7

B0

B5 - B7B7

B6

B5

B1 - B4

B1- B7B1 - B6

B0

B2

B

B4 -

B0 - B6

P1

P3

ESD

TC724G=7.5P1=26

TC626

TC626TC674

P4

TC728

TC700G=8

P1=18

Momentum& Access

HFTC Model & Measurement IPanalytical empirical behavioral

semiconductor materialFerromagnetics

Semiconductor

analytical empirical behavioral


May 7, 2010 Page 3

Semiconductor switches

Outline

Introduction: Behavioral Models and NVNA

F ti l Bl k M d lFunctional Block Models• Nonlinear Time Series• X parameters (PHD Model) in the Frequency Domain• X-parameters (PHD Model) in the Frequency Domain• Mixed Time-Frequency Methods

Summary and Conclusionsy


May 7, 2010 Page 4

Introduction: Behavioral Modeling and Design Hierarchy

S tSystem

Circuit( )( ) : ( , , ..., , ..., )ny t i f v v i i=

( )v t( )v t( )i t { Multivariate functions

for i1, i2

Embedding Variables

( )i t {{{

1 2

Behavioral Model:Accurate model of

lower level component

Equivalent Circuit Model“Compact Model”

Device

for simulation at nexthighest level

Compact Model


May 7, 2010 Page 5

Measurement-Based and Simulation-Based ModelsActual Circuit Measurement-Based ModelMeasurement-Based Model

• Ckt. model may not exist• Ckt. models may be inaccurate• Completely protect design IP

Design of Module or Instrument Front EndCompletely protect design IP

GenerateB h i l

Amplifier or Mixer ICDC-20 GHz HBT Agilent HMMC 5200 amp [2]

BehavioralModel

Simulation-Based Model• Simulation speedup

Detailed Circuit Model (SPICE/ADS) f IC

• Simulation speedup• Design system before building/buying IC• Completely protect design IP

Simple for Linear Ckts: S parametersIEEE DML Norway talk #1 David E. Root

May 7, 2010 Page 6

(SPICE/ADS) of IC Simple for Linear Ckts: S-parameters

S-parameters as simplest behavioral model

Easy to measure at high frequenciesmeasure voltage traveling waves with a (linear) vector network analyzer (VNA)don't need shorts/opens which can cause devices to oscillate or self-destruct/ p

Relate to familiar measurements (gain, loss, reflection coefficient ...)Can cascade S-parameters of multiple devices to predict system performanceCan import and use S-parameter files in electronic-simulation tools (e.g. ADS)p p ( g )BUT: No harmonics, No distortion, No nonlinearities, …Invalid for nonlinear devices excited by large signals, despite ad hoc attempts

M d l

Incident TransmittedS 21a 1S parameters

Linear Simulation:Matrix Multiplication

Measure with linear VNA:Small amplitude sinusoids

Model Parameters:Simple algebra

S 11Reflected S 22

Reflectedb 1

a 1b 2

DUT

Port 1 Port 2

S-parametersb1 = S11a1 + S12a2

b2 = S21a1 + S22a20k

iij

ajk j

bSa =

≠

=


May 7, 2010 Page 7

Transmitted Incident

1 a 2S 12

b2 S21a1 + S22a2 k j≠

Three Components of Behavioral Modeling

1. Model FormulationNonlinear ODEs in Time Domain (e g Transient Analysis; all others)– Nonlinear ODEs in Time Domain (e.g. Transient Analysis; all others)

– NL Spectral Map in Freq. Domain (e.g. Harmonic Balance) X-params– Mixed Domains (e.g. ODE-Coupled Envelopes in Circuit Env. Analysis)

2. Experiment Design– Stimulus needed to excite relevant dynamics

3 Model Identification3. Model Identification– Procedure to determine model “parameters”


May 7, 2010 Page 8

Model Formulation: Time & Freq. Domains [1,6]

( ) ( ( ), ( ), ( ), ..., ( ), ...)I t F V t V t V t I t=( ) ( ( ), ( ), ( ), ..., ( ), ...)I t F V t V t V t I tNatural for strongly nonlinear low-order (lumped) systems

,...),,( 321 AAAFB kk =

Freq. Domain natural for low-distortion, high-freq. ICs


May 7, 2010 Page 9

Formulate model eqs. in language native to appropriate simulator

Wanted: Cascadability of Nonlinear Components

21 Pou

t

1 11 222

P di t i l d h i ( it d d h ) th h h i f

Sin(2πf0t)

Freq

1

f0

1

3f0

1

2f0

222

Predict signal and harmonics (magnitude and phase) through chains of cascaded nonlinear components under drive

• Inter-stage mismatch is important to final results– Can not infer these effects from VNA measurements (even “Hot S22”)

• Required for communication circuits and module design• Linear S-parameter theory doesn’t apply!Linear S parameter theory doesn t apply!

Most previous attempts to generalize S-parameters to nonlinear case are wrong!


May 7, 2010 Page 10

Wanted: Hierarchical Modeling Model the cascade directly

Dev 1 Dev 2

Dev 1 Dev 2

Model the cascade directly

Mod 1 Mod 2

Mod 1 Mod 2

CompositeModel

(Higher Level)

A cascade of many models reduced to one

Mod 1 Mod 2


May 7, 2010 Page 11

Experiment Design: Simulation

Detailed Circuit Model Goes here


May 7, 2010 Page 12

Experiment Design: Measurement

Nonlinear Vector Network Analyzer [9,14] (NVNA)

Magnitude and Phase Data Acquisition

RFIC

A1k B1l B AA1k B1l B2m A2nReferenceplanes

Calibrated magnitude & phase of harmonics/IMD

M d li ti l i l ditiMeasures under realistic large-signal conditions

Based on Standard Agilent PNA HardwareAnd custom reference generatorNew phase calibration standard


May 7, 2010 Page 13

New phase calibration standard

Introduction: NVNA measurements complex spectra and waveformscomplex spectra and waveforms

2 kA1kA

B 2kB

pkBpkA1kB 2k

Port IndexHarmonic Index

I 2I1I 2I


May 7, 2010 Page 14

time time

Nonlinear Vector Network Analyzer (NVNA) [14]:

Network Analyzer Phase Reference Meas. Science Algorithms & Software

+ + = NVNA

NVNA = PNA-X + Phase Reference (custom InP IC)+ A li ti SW d lib ti ( d h )+ Application SW and calibration (mag and phase)

two internal sources, internal switches, and an internal broadband combinerNVNA measures Magnitude and Phase of all relevant frequency components


May 7, 2010 Page 15

(cross-frequency coherence) necessary to measure X-parameters!

Nonlinear Vector Network Analyzer (NVNA) [14]

Vector (amplitude/phase) corrected nonlinear measurements from 10 MHz to 50 GHz

Calibrated absolute amplitude and relative phase (cross-p p (frequency relative phase) of measured spectra traceable to standards lab

50 GHz of vector corrected bandwidth for time domain waveforms of voltages and currents of DUTg

Multi-Envelope domain measurements for measurement and analysis of memory effects

X-parameters: Extension of Scattering parameters into the li i idi i i i ht i t linonlinear region providing unique insight into nonlinear

DUT behavior. Efficient measurements with phase control.External instrument control, pulsed, triggered measurements

X t MDIF fil d b ADS X P tX-parameter MDIF file read by ADS XnP component or nonlinear simulation and design.

X-parameter generation from detailed schematics within ADS simulator.


May 7, 2010 Page 16

Standard VNA HW with Nonlinear features & capability

Outline


F ti l Bl k M d lFunctional Block Models• Nonlinear Time Series• X parameters (PHD model) in the Frequency Domain• X-parameters (PHD model) in the Frequency Domain• Mixed Time-Frequency



May 7, 2010 Page 17

Nonlinear Time Series method of Behavioral Modeling [1,6]


May 7, 2010 Page 18

Dynamical Systems & State Space

The dynamics of the nonlinear system can be assumed to be described by a system of nonlinear ODEs

( ) ( 1) ( )( ) ( ,... , , ,... )n n my t f y y x x x−=

O d f ti d i ti

( )( ) ( ), ( )u t f u t x t= Vector of State Equations

Order of time derivative

( )( )

( ) ( ) (

( ) ( ), (

)

)

f

y t h u t x t= Scalar output y(t)

The sampled solution of the ODE, y(t), is a time-series

The solution of the dynamical equations for state variables, (t) i ti t i d t j t i Ph S


May 7, 2010 Page 19

u(t), is a time-parameterized trajectory in Phase Space

Phase Space and Time Series

The multi dimensional space

Lorenz system

The multi-dimensional space spanned by the state variables is known as phase spacephase space

Any measurable output is a projection of this trajectory versus time:a Time SeriesTime Series


May 7, 2010 Page 20

a Time SeriesTime Series

Nonlinear Time Series (NLTS) Phase Space Reconstruction by Embeddingy g

Output y(t)I t (t)

NLTS Behavioral Modeling is “inverse” of solving known ODEsStart from input & output time series and discover dynamics

Output y(t)Input x(t)Unknown Nonlinear

Component

Stimulate System with drive x(t)

Record Time Series output y(t)

timetime

y

Embed drive x(t) & response y(t)

Stop when trajectory single valued

This results in the Nonlinear ODE:

x( )y t y

( ( ), ( ), ( ),...) 0f y t y t x t =

This results in the Nonlinear ODE:

Approximate f with smooth functiony

x


May 7, 2010 Page 21

Attach ODE Model to Circuit Simulator

Excitation DesignsGoal: stimulate all relevant (observable) dynamics

Sweep Power and Frequency to “cover phase space”

Goal: stimulate all relevant (observable) dynamics

‘Two-tone’

f1 f +Δf

‘Three-tone’

Used for modelsf1 f1+Δf

f1 f1+Δff1+Δf

models

‘Modulation’ (CDMA)

f1f1+Δf

f2

‘Multi-tone’ or ‘Multi-sine’

f1+Δf?f1+Δf

fn


May 7, 2010 Page 22

Embedding: Building up phase space to define ODE

i(t)B

i(t)i(t)B

i(t)i(t)BB

BB

AA AA

v(t)v(t)v(t) v(t)v(t)

v’(t)v (t)

( ) ( ( ) ( ))i t i v t v t( ) ( ( ))i t i v t≠IEEE DML Norway talk #1 David E. Root

May 7, 2010 Page 23

( ) ( ( ), ( ))i t i v t v t=( ) ( ( ))

Model Identification: Nonlinear Time Series (NLTS)

X(t) Y(t)Stimulate / Excite SystemSufficiently complex stimulus

( )

( )

( ) [ ( ), ( ),..., ( )]( ) [ ( ), ( ),..., ( )]

m

n

x t x t x t x ty t y t y t y t

→

→

Embed:Create auxiliary variables(represent waveform)( ) [ ( ), ( ), , ( )]y y y y ( p )

( ) ( )1 1 1 1 1 1

( ) ( )

( ) ( ) ... ( ) ( ) ( ) ... ( )( ) ( ) ( ) ( ) ( ) ( )

m n

m n

x t x t x t y t y t y tx t x t x t y t y t y t Sample data:

2 2 2 2 2 2

( ) ( )

( ) ( ) ... ( ) ( ) ( ) ... ( ). . ... . . . ... .

( ) ( ) ... ( ) ( ) ( ) ... ( )m np p p p p p

x t x t x t y t y t y t

x t x t x t y t y t y t

at high frequency(or envelope; hard if multiple timescales)( ) ( ) ( ) ( ) ( ) ( )p p p p p py y y

( ) ( 1) ( )( ,... , , ,... )n n my f y y x x x−= Fit:Nonlinear function f

p )


May 7, 2010 Page 24

Function approximation Artificial Neural Networks

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: better for distortion than naïve splines or low-order polynomials.•Easy to train (fit) using standard third-party tools (MATLAB)


May 7, 2010 Page 25

•Easy to train on scattered data

Function approximation: Artificial Neural Networks( ) ( 1) ( 2) ( ) ( 1)( ) ( ( ), ( ),..., ( ), ( ), ( ),..., ( ))n n n n n

ANNy t f y t y t y t u t u t u t− − −=

fANN

{ },ki kw a “Dynamic Neural Network”

weights biases

…{ }

{ },ki kw a Obtained by Training

… …Can also define f bypolynomials, radial basis functions, look p tables etc

( 1) ( 2) ( ) ( 1)

lookup tables etc.


May 7, 2010 Page 26

y(n-1)(t) y(n-2)(t) … y(t) u(n)(t) u(n-1)(t) … u(t)

Model Implementation: ODE in circuit simulator(after Zhang and Xu in [6])

xx

x(1)+

-y

v2v1

+

-

( )

( 1) ( )( ,... , , ,... )

n

n m

yf y y x x x−

=

-

(1) (2)

+ v2v3

+

-1v y=

x(1) x(2)-

3 -

+

+ +

vn-1vn -1 2v v=

x(m-1) x(m)- f vn-1

( )( )mnnv v

f− =


May 7, 2010 Page 27

( )1 2( , ,..., , , ,..., )m

n n nv f v v v x xx− −=

NLTSA modeling flow

• MATLAB Toolbox, plus 3rd-party software

Define range of operationChoose DUT Excitation

Design

3 party software

• ‘NLTSfile’ structure

• ADS/NVNA-MATLABinterfacesMATLAB Behavioral

ADSSimulation

NNMSMeasurement

Read data into

NVNAMeasurement

interfaces

• ADS templates for

– simulation

d t di l

Modeling Toolbox

Choosemodel

MATLAB

– data display

– model verification• Model as SDD in ADS

EmbeddingDimension

modelvariables

MultivariateFunction App.

Model Verification

Create Modelin ADS


May 7, 2010 Page 28

A t l Ci itExample: GaAs HBT MMIC

Actual Circuit

DC-20 GHz GaAs HBT (Agilent HMMC 5200 Amp)

Series-Shunt Amplifier

G i 9 5 dB @ 1 5GHGain: 9.5 dB @ 1.5GHz


May 7, 2010 Page 29

Detailed ckt model

Fundamental Phase

Results: NLTS Accuracy and Speed [1,6]NLTS Behavioral model Circuit model data

100

120

140

160

180

od

el[:

:,1

])IC

[::,

1])

Fundamental Phase

11

12

13

14

m(I

n_

mo

de

l[::,

1],

z1[:

:,1

])B

m(I

n_

IC[:

:,1

],z1

ic[:

:,1

])

Fundamental Gain

14

dBm

180

-20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4-22 6

0

20

40

60

80

-20

ph

ase

(Ou

t_m

op

ha

se(O

ut_

-20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4-22 6

7

8

9

10

6

dB

m(O

ut_

mo

de

l[::,

1],

z2[:

:,1

])-d

Bd

Bm

(Ou

t_IC

[::,

1],

z2ic

[::,

1])

-dB

6 -20

1 - 19 GHz

dBm(In_model[::,1],z1[::,1])dBm(In_IC[::,1],z1ic[::,1])

dbm(In_model[::,1],z1[::,1])dbm(In_IC[::,1],z1ic[::,1])-22 6

dBm(2) (2)

1 2 1 2 1 2( ) ( , ( ), ( ), ( ), ( ), ( ), ( ))i i iI t f I V t V t V t V t V t V t=-22 6

dBm

3.5

4.0

4.5

3.5

4.0

4.5

19 neurons

2.0

2.5

3.0

1.5

2.0

2.5

3.0

1 0

229.68 seconds

11315.67 seconds


May 7, 2010 Page 30

Time psec

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.80.0 2.0

1.5

0 200

1.0

Time psecTime Domain Waveforms

Circuit Co-Simulation vs. NLTSA ModelResults 3GPP WCDMA (lower) ACLRResults 3GPP WCDMA (lower) ACLR

3GHz WCDMA

Model generated from

294 sec/pt NLTS

Model generated from only sinusoidal signals

294 sec/pt NLTS

1532 sec/pt Ckt.

40 neuron model

Courtesy Greg Jue


May 7, 2010 Page 31

Circuit Co-Simulation vs. NLTSA Behavioral ModelResults vs. Measured 3GPP WCDMA (lower) ACLRResults vs. Measured 3GPP WCDMA (lower) ACLR

WCDMA Lower ACLR Comparison:Circuit Co-Sim vs. NLTSA Model vs. Measured

3GHz simulated

2 4GH

60

70-15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3

2.4GHz meas

30

40

50

60

CLR

(dB

Circuit Co-Sim 5MHz Lower

10

20

30

AC NLTSA Model 5 MHz Lower

Circuit Co-Sim 10 MHz Lower

NLTSA Model 10 MHz Lower

Measured Data 5 MHz Lower0

Input Power (dBm)Measured Data 10 MHz Lower


May 7, 2010 Page 32

Model is also cascadable Model works in TA, HB, Envelope

Outline





May 7, 2010 Page 33

X-parameters (PHD model): a nonlinear paradigm“Is there an analogue with linear S parameters to help withIs there an analogue with linear S-parameters to help with the nonlinear problem?”

Frequency Domain description is natural for high-frequency, distributed systems

Natural for Harmonic Balance Algorithms and NVNA data


May 7, 2010 Page 34

Arbitrarily Nonlinear; Not limited to Volterra Theory

X-Parameters: The Nonlinear Paradigm

X-parameters are the mathematically correct superset of S-parameters, applicable to both large-signal and small-signal conditions for linear and nonlinear components The math exists!conditions, for linear and nonlinear components.

We can measure, model, & simulate with X-parameters Each part of the puzzle has been created

The math exists!

p pThe pieces now fit together seamlesslyNVNA: Measure X-params X-parameter block

HARM O NIC BALANCE

ADS: Simulate with X-paramsH arm onicBalanceH B2

EquationN am e[3]="Z load"EquationN am e[2]="R Fpower"EquationN am e[1]="R Ffreq"U seKrylov=noO rder[1]=5Freq[1]=R Ffreq

Interoperable Nonlinear Measurement Modeling & Simulation with X params

“X-parameters have the potential to do for characterization, modeling, and design of nonlinear components and systems what

Interoperable Nonlinear Measurement, Modeling & Simulation with X-params


May 7, 2010 Page 35

g, g p ylinear S-parameters do for linear components & systems”

X-Parameters: Why They are Important:Predict performance of cascaded NL componentsPredict performance of cascaded NL components

Cascaded Nonlinear Amplifiers: X-parameters enable nonlinear simulation from pmeasured data in the presence of mismatch

•Unambiguously identifiable from a simple set of measurementsg y p•Extremely accurate for high-frequency, distributed nonlinear systems•Fully nonlinear vector quantities (Magnitude and phase of all harmonics)


May 7, 2010 Page 36

•Cascadable (correct behavior in mismatched environment)

X-parameters come from thePoly-Harmonic Distortion (PHD) Framework [3-6 12]Poly-Harmonic Distortion (PHD) Framework [3-6,12]

2A1A

1B 2B( )B F D C A A A A1 1 11 12 21 22( , , , ..., , , ...)k kB F D C A A A A=

2 2 11 12 21 22( , , , ..., , , ...)k kB F D C A A A A=Port Index Harmonic (or carrier) Index

Spectral map of complex large input phasors to large complex output phasors


May 7, 2010 Page 37

Black-Box description holds for transistors, amplifiers, RF systems, etc.

X-parameters: Simplest Case - driven with single large tone at port 1 [1] (derivation in lecture 2)large tone at port 1 [1] (derivation in lecture 2)

, , 11 12 21 22( , , , ..., , , ...)e f e fB F D C A A A A=

∑ ∑

Concept: simplify general nonlinear spectral mapping by spectral linearization

, ,

( )11

( )( ), 1 1

,,1

*1(| |) (( ) )

ef g gh ef hef

S fF fe f

T f hgh

g

hgh

g h h

B X X A AA P A X P AP − + ⋅= +⋅+∑ ∑

f l h dMismatch terms: Mismatch terms:

11( )j AP e ϕ=

Perfectly matched responses c e s:

linear in ghA linear in *ghA

Not both g and h =1 in sums

Phase terms come from time-invariance:

“Output of delayed input is just the delayed output”


May 7, 2010 Page 38

X-parameter Results: Cascadability of Nonlinear BlocksNonlinear BlocksHMMC 5200 Amp

Sin(2πf0t)P t

dB

Compression

deg

f0 3f02f0

PoutAM/PM

2nd Harmonic PhasedBm deg

Cascaded PHD modelsCascaded Ckt. Models

0 6GH 6 0GH

2nd Harmonic Amplitude 2nd Harmonic PhasedBm deg

Does for distortion of

0.6GHz – 6.0GHz

dBm deg3rd Harmonic Amplitude nonlinear components

what S-parameters do for linear components3rd Harmonic Phase

3rd Harmonic Amplitude


May 7, 2010 Page 39

Improved Asymptotic Behavior

Volterra Theory Constraints Added for

20

Improved asymptotic behavior at low power

-80

-60

-40

-20

0

-40 -35 -30 -25 -20 -15 -10 -5 0 5-45 10

-140

-120

-100

-160


May 7, 2010 Page 40

Pinc

X-parameters: HMMC 5200 Response to Digital Modulation

Circuit Model

Modulation

X-parameters generated from ckt model

f SIEEE DML Norway talk #1 David E. Root

May 7, 2010 Page 41

Excellent Results from Simple Excitations

X-parameter Results: Transportability 27 Ohm validation measurement-based model 50 Ohm data

1 0 1 0

v1

0.0

0.5

1.0

v20.0

0.5

1.0

100 200 300 400 500 6000 700

-0.5

-1.0

100 200 300 400 500 6000 700

-1.0

-0.5

-1.5

100 200 300 400 500 6000 700

time, psec

100 200 300 400 500 6000 700

time, psec

0.005

0.010

i1

0.04

0.05

i2

-0.005

0.000

0.005 1

-0.02

0.00

0.02i2

100 200 300 400 500 6000 700

-0.010

time, psec

100 200 300 400 500 6000 700

-0.04

time, psec

M B d X M d l I d d t NVNA D t


May 7, 2010 Page 42

Measurement-Based X-parameter Model Independent NVNA Data

Rough Comparison of Methods and Applicability

X-Parameters

Frequency Domain natural for highly linear distributed broad band ckts

NLTSA

Works in TA, HB, Envelopelinear, distributed, broad-band ckts

Experiment Design completely solved

Highly automated Model Identification

Excellent for strongly nonlinear, but lumped (low order ODE) systems

T i i l ith i Highly automated Model Identification

Works in HB & Envelope

Very robust for convergence

Training non-algorithmic

Experiment design not fully solved

Not as robust for convergence e y obust o co e ge ce

Always accurate if sampled densely

Complexity increases rapidly for

Not as robust for convergence

Scales well with complexity

Great gains in simulation speedmultiple tones

Great gains in simulation speed


May 7, 2010 Page 43

Outline





May 7, 2010 Page 44

Envelope Domain for Long-Term Memory [7,8]Applies to systems under large-signal modulated drives

Time-varying spectra for all inputs, outputs, & state variables

Perfectly suited for Circuit Envelope Analysis y p y

Well-matched for data from Nonlinear Vector Network AnalyzerTime Domain (envelope)

B2(t)Time-varying spectrum

1 2 3 4DC

02

0

( ) Re ( )H

j h f th

h

x t X t e π

=

⎛ ⎞= ⎜ ⎟⎝ ⎠∑

Xh(t) set of complex (amplitude and phase) waveforms at each harmonic index htime

Freq. (GHz)1 2 3 4DC


May 7, 2010 Page 45

Modeling problem: map input envelopes to output envelopes

Envelope Domain for Long-Term Memory [7,8]

Merge Frequency and Time DomainsSpectral mapping ( ) ( )FB X A A A A=Spectral mapping

a differential equation in the envelope domain

(1) ( ) (1) ( )ˆ ˆ ˆ ˆˆ ˆ ˆ

( )11 12 21 22( , , ..., , , ...)pk pkB X A A A A=

→

(1) ( ) (1) ( )( ( ),..., ( ), ( ), ( ),..., ( ),..., ( ))n mk k k k l l k kB f B t B t A t A t A t A t=

Envelope or carrier indexOrder of time derivative

Envelope or carrier index

21 21 20 11ˆˆ ˆ( ) ( ( ), ( ))

ˆ ( )

B t f B t A t

dB

=Example:2

2011 21

( ) ˆ ˆ( ( ) , ( ))dB t g A t B tdt

=


May 7, 2010 Page 46

Envelope Model: Amplifier with Self-Heating [8]0.4

F d t l I t4

G i R d 0.2

0.3

Fundamental Input

2

3

Fundamental Output

Gain Reduces as device heats up0.1

0.0

1

2

Pulsed RF signal at 1GHz:

10 20 30 400 50time, usec

time, usec10 20 30 400 50

0

0.04 40Third Harmonic Output Mag & Phase

Pulsed RF signal at 1GHz: Thermal Time Const. 10usec

0.02

0.03

20

30

Systematic approach to0.01

0.00

10

0

Systematic approach to identifying “hidden” state variables for long-term


May 7, 2010 Page 47

10 20 30 400 50time, usec memory IMS2007 [13]

Dynamic Long-Term Memory PHD Models Envelope Differential Equations in ADS [7,8,13]

X t ith d i ( d)

Envelope Differential Equations in ADS [7,8,13]Verspecht et al in 2007 International Microwave Symposium Digest [13]

X-parameters with dynamic memory (red)compared to circuit-level model (blue)

2.5

1.5

2.0B21

0.5

1.0

0.2 0.4 0.6 0.8 1.0 1.20.0 1.4

0.0

A11


May 7, 2010 Page 48

A11

ConclusionsPowerful nonlinear device & behavioral modeling approaches inPowerful nonlinear device & behavioral modeling approaches in time, frequency, and mixed domains have been presented• X-parameters are mature. Commercial solutions to measure, model, and

simulate are available supported and expanding (see lecture 2)simulate are available, supported, and expanding (see lecture 2).• Time-domain (NLTSA) techniques could become practical soon.• Envelope domain (dynamic X-parameters) is attractive for memory.

Emergence of commercially available Large-Signal HW & SW• e.g. NVNA on modern PNA-X platform [9,14]• e.g. nonlinear simulators with built-in XnP components & X-param analysisg p p y

Great opportunity for applicationsS ifi ti f ti t b X t• Specification of active components by X-parameters

• Device and behavioral modeling applications of NVNA measurements• Stability analysis and matching power amplifiers under drive


May 7, 2010 Page 49

• Active Signal Integrity

References[1] J. Wood, D. E. Root, N. B. Tufillaro, “A behavioral modeling

approach to nonlinear model-order reduction for RF/microwave ICs and systems ” IEEE Transactions on

[9] Blockley et al 2005 IEEE MTT-S International Microwave S i Di t L B h CA USA J 2005RF/microwave ICs and systems, IEEE Transactions on

Microwave Theory and Techniques, Vol. 52, Issue 9, Part 2, Sept. 2004 pp. 2274-2284

[2] Agilent HMMC-5200 DC-20 GHz HBT Series-Shunt Amplifier, Data Sheet, August 2002.

[3] J Verspecht M Vanden Bossche F Verbeyst

Symposium Digest, Long Beach, CA, USA, June 2005.

[10] Jan Verspecht Patent US 7,038,468 B2 (issued May 2, 2006 based on a provisional patent 60/477,349 filed on June 11, 2003)

[11] Soury et al 2005 IEEE International Microwave Symposium Digest pp 975 978[3] J. Verspecht, M. Vanden Bossche, F. Verbeyst,

“Characterizing Components under Large Signal Excitation: Defining Sensible `Large Signal S-Parameters'?!,” in 49th IEEE ARFTG Conference Dig., Denver, CO, USA, June 1997, pp. 109-117.

[4] J. Verspecht, D.E. Root, J. Wood, A. Cognata, “Broad-Band, Multi-Harmonic Frequency Domain Behavioral Models from

Digest pp. 975-978

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

[13] J Verspecht D Gunyan J Horn J Xu A Cognata and D E RootMulti Harmonic Frequency Domain Behavioral Models from Automated Large-Signal Vectorial Network Measurements,” in 2005 IEEE MTT-S International Microwave Symposium Digest, Long Beach, CA, USA, June 2005.

[5] D. E. Root, J. Verspecht, D. Sharrit, J. Wood, and A. Cognata, “Broad-Band Poly-Harmonic Distortion (PHD) Behavioral Models from Fast Automated Simulations and

[13] J. Verspecht, D. Gunyan, J. Horn, J. Xu, A. Cognata, and D.E. Root, “Multi-tone, Multi-Port, and Dynamic Memory Enhancements to PHD Nonlinear Behavioral Models from Large-Signal Measurements and Simulations,” 2007 IEEE MTT-S Int. Microwave Symp. Dig.,Honolulu, HI, USA, June 2007.

[14] Horn et al 2008 Power Amplifier Symposium, Orlando, Jan. 2008

Large-Signal Vectorial Network Measurements”, IEEE Transactions on Microwave Theory and Techniques Vol. 53. No. 11, November, 2005 pp. 3656-3664

[6] J. Wood, D. E. Root, editors, Fundamentals of NonlinearBehavioral Modeling for RF and Microwave Design, 1sted. Norwood, MA, USA, Artech House, 2005.

[7] Root et al US Patent Publication # US2005102124 AA,Published 2005

[8] D. E. Root, D. Sharrit, J. Verspecht, “Nonlinear Behavioral Models with Memory: Formulation, Identification, and Implementation,” 2006 IEEE MTT-S International Microwave S ( S ) ff


May 7, 2010 Page 50

Symposium Workshop (WSL) on Memory Effects in Power Amplifiers

X-parameters*:A new paradigm for measurement modeling andA new paradigm for measurement, modeling, and design of nonlinear microwave & RF components

Dr David E RootDr. David E. RootPrincipal R&D Scientist

High Frequency Technology CenterSanta Rosa, CA USA

IEEE MTT-S DML Lecture #2Bergen, Norway

May 7 2010

* X parameters is a trademark of Agilent Technologies Inc

May 7, 2010

© Copyright Agilent Technologies 2010

Page 1Page 1 D. E. RootD. E. RootX-parameter DML lecture Norway #2

May 7, 2010

* X-parameters is a trademark of Agilent Technologies, Inc.

Key Contributors

• Keith Anderson

• Loren Betts

• Radek Biernacki

• Jack Sifri

• Mary Lou Simmermacher

• Gary Simpson• Radek Biernacki

• Chad Gillease

• Daniel Gunyan

• Gary Simpson

• Franz Sischka

• Darlene Solomon

• John Harmon

• Jason Horn

• Tina Sun

• Yee Ping Teoh

• Yuchen Hu

• Masaya Iwamoto

• Mihai Marcu

• Dan Thomasson

• Jan Verspecht

• Kenn WildnauerMihai Marcu

• Troels Nielson

• Greg Peters

Kenn Wildnauer

• Jianjun Xu

• Yoshiyuki Yanagimoto


Page 2Page 2 D. E. RootD. E. Root

• Mark PierpointX-parameter DML lecture Norway #2

May 7, 2010

Outline

• Introduction: X-parameter Basics

• Survey of X-parameter benefits and applications

• Summary

• References and LinksReferences and Links



May 7, 2010

X-Parameters: Mainstream Nonlinear Interoperable TechnologyElectronic design

automation softwareAgilent Nonlinear Vector

Network Analyzer

Nonlinear Nonlinear

CustomerNonlinear

Simulation & DesignMeasurements

Customer Applications

Nonlinear Modeling



May 7, 2010

*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− += + +

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

Reflected Transmitted

Incident 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)



May 7, 2010

nonlinear problems?freq (1.000GHz to 26.00GHz)

X-parameters Solve Nonlinear ProblemsSame use model as S-parameters, but much more powerfulp , p

Reflected Transmitted

Incident Model

Measure

X

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

−

+

=

+

+Nonlinear Vector Network Analyzer

X-Parameters, 11( )pm qn qnX A P A+

Reflected

Design

Reflected

Incident

1 2EDA Software



May 7, 2010

Capturing the imagination of the industry

Solves real-world problems now

Changing the way the industry worksp

Interoperable characterization, modeling and design

Continuous wave of innovations and award-winning modeling, and design

solutions

Potential to do for

a a d gresearch

nonlinear components and systems what S-parameters do forparameters do for linear components and systems



May 7, 2010

X-parameters: Hierarchical Design and Validation

T D D i S ifi ti ( t t il bl )

ESL

System IntegratorsBottom-up Measurement-based VerificationElectronic System Level Design

Top-Down Design Specifications (not yet available)

Bottom-up Simulation-based Verification

X-parameterSpecs

20092009

X tX-par analysisSimulator

20092009

X-par generator

X-pars X P

2009200920092009

C dNVNA 50 GHz

X-pars XnPcomponent

XnP: nativesimulation

load-dep X-parshi h X



May 7, 2010

Component vendors X-par meassimulationcomponent

high power X-pars

Introduction: NVNA measurements complex spectra and waveformscomplex spectra and waveforms

2 kA1kA

B 2kB

pkBpkA1kB 2k

Port IndexHarmonic Index

I I1I 2I



May 7, 2010

time time

Measurement-Based Modeling & Design Flow“X-parameters enable predictive nonlinear design from NL data”

NVNA ADSSimulation and DesignNonlinear Measurements

X parameters enable predictive nonlinear design from NL data

v2v1

ConnectorX1

MCA_ZX60_2522MCA_ZX60_2522_1fundamental_1=fundamental

MCA_ZFL_11ADMCA_ZFL_11AD_1fundamental_1=fundamental

RR1R=25 Ohm

V_1ToneSRC14

Freq=fundamentalV=polar(2*A11N,0) V

RR11R=50 Ohm DC_Block

DC_Block1DC_BlockDC_Block2

I_Probei2

I_Probei1

X-parameter blocks

Data File25

75

76

20

-15 150

X-parameters enable accurate nonlinear simulation under small to moderate mismatch. (See later for large mismatch)

Drag and drop

-28 -26 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6-30 -4

-30

-20

-10

0

-40

10

.

.

-50

-40

-30

-20

-10

0

10

.

-28 -26 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6-30 -4

5

10

15

20

0

.

.

-28 -26 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6-30 -4

70

71

72

73

74

75

69

.

.

-28 -26 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6-30 -4

-135

-130

-125

-120

-140

-115

2

4

6

8

10

12

14

.

-28 -26 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6-30 -4

-80

-70

-60

-50

-40

-30

-90

-20

.

.

-100

-80

-60

-40

-20

.

-28 -26 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6-30 -4

-40

-35

-30

-25

-20

-45

.

.

130

140

150

160

170

.

-28 -26 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6-30 -4

130

135

140

145

125

.

.

-28 -26 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6-30 -4

120

122

124

126

128

130

132

134

118

136

.

.

-10 -5 0 5 10 15-15 20

-30

-20

-10

0

10

-40

20

.

Drag and drop

-28 -26 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6-30 -4

-60

-70

.

-28 -26 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6-30 -4

0

-2

.

-28 -26 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6-30 -4

-120

.

-28 -26 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6-30 -4

120

.

.

allowing prediction of component behavior in complicated nonlinear circuits. IMD / ACPR exact in narrow-band limit



May 7, 2010

“X-parameters: the same use model as S-parameters but much more powerful”

X-parameter Concept: Linearized Spectral Map around a Large-Signal Operating Point (LSOP)

Incident Port 1 Scattered Port 2Incident Port 1 Scattered Port 22 1 1 1 2 1 3 2 1 2 2 2 3( , , , , . . . , , , . . .)kB D C A A A A A A

Multi-variate NL map

≈

Simpler NL map

( )2 11( , , 0, 0, 0, ...)F

kX DC A

+Linear non analytic map

Simpler NL map

Linear non-analytic map( ) ( ) *2 , 11 2 , 11[ ( , ) ( , ) ]S T

k pj pj k pj pjX D C A A X D C A A+∑X-pars include exact nonlinear mapping to totally linear (S-pars) & everything in between



X pars include exact nonlinear mapping to totally linear (S pars) & everything in between Trade simplicity for accuracy.

May 7, 2010

X-parameter DML lecture Norway #2

X-parameters: What they are & where they come fromDC f

aj2

DC f0 2f0 3f0 4f0 5f0

A11

•Scattering of multiple incident large-amplitude waves.

•Can be simplified according•Can be simplified according to linear or nonlinear dependence on inputs (simplicity vs accuracy)( p y y)

•Measured on NVNA orgenerated in simulator

2

( )3, 2 j

Si jX a

2

( ) *3, 2 j

Ti jX a ( )

3F

iX•Rules for computing the response to general signals

generated in simulator

2j2, jj

0 15 f f− 0 1f f+03 f

, ,

( )11

( )( ), 1 11

*1(| |) (( ) )

ef g gh ef hef

S fF fe f

T f hgh

hghB X X A AA P a X P aP − + ⋅= +⋅+∑ ∑ 11( )j AP e ϕ=

given extracted X-parameters



May 7, 2010

, ,,,

ef g gh ef hefgg h h

Simplest X-parameters for a Power Amplifier( )( ) ( ) 2 *()( ) ( )( ) TF SXB AA A PAP X X A A+ +( )( )

21 11( )21,21

2 *21 11 21 2121 11,21 11()( ) ( )( ) TF SXB AA A PAP X X A A= + +

( )( )11 11

( )11,11

211 11 21 2121 11,21 11()( ) ( )( ) TF SXB AA A PAP X X A A= + +

40dB ( )

21 11FX A

( )F

X-parameters reduce to (linear) S-parameters in the appropriate limit

11

( )11 11 11| | 0

F

AX A s

→→

40

20 ( )21 21

SX11

( )21 11 21| | 0

F

AX A s

→→

( )S 11

( )11,21 11 12| | 0

( )S

AX A s

→→

0

-20

21,21

( )TX 11

( )11,21 11 | | 0

( ) 0T

AX A

→→

11

( )21,21 11 22| | 0

( )S

AX A s

→→11| |

-25 -20 -15 -10 -5 0 5 10-40

20 ( )21,21TX 11| | 0A →

11

( )21,21 11 | | 0

( ) 0T

AX A

→→



May 7, 2010

|A11| (dBm) X-parameters are a superset of S-parameters

X-parameter Experiment Design & Identification [1,14]

Stimulate port 1 with large tone at freq. fStimulate port 2 with small tone at freq. f + ΔMeasure response at three different frequencies

Take limit as D goes to zero

( ) 121 21 1,1( , )FX B f A P−=

Input Spectrum

21 11( )21 21

( , )S B f AX

+ Δ= Output Spectrum

f+Δf21,21

21( )A f + Δ

11 2121 11 2 ( )( ) ( , ) j A AT B f AX e φ −− Δ

Optimal and orthogonalf f+Δ

11 21( )( )21,21

21( )jX e

A fφ=

+ ΔSimilarly for harmonics

Optimal and orthogonalexperiment design and model identification



May 7, 2010

X-Parameters and the Harmonic Jacobian [1]X t th “ d li l ” f HB l i

From 1-tone HB analysis ( )11( )F m

pm pmX A B P−=

X-parameters are the “modeling analog” of HB analysisWrite model equations in language native to simulator algorithms

y 11( )pm pm

( ) ( ) pmS m n BX A P− + ∂

=( )

11 *( ) pmT m npm qn

BX A P

A− − ∂

=∂

11 12 21

, 11

, 0,... 0,...

( )pm qnqn A A A

X A PA

= =

=∂

from known Jacobian of 1-tone HB analysis.

11 12 21

, 11 *

, 0,... 0,..

( )pm qnqn A A A

A= =

∂

yJacobian comes from I-V and Gij, Cij from element constitutive relations

Never need 2-tone HB analysis. Faster, guaranteed spectrally linearMost of the terms in the required Jacobian are know ahead of time

( ) *( )11

)11

(11(| | ( ) )) (S f T f h

hh

hF f

fB X A P X A P AX A P A− += + +∑ ∑© Copyright Agilent Technologies 2010


May 7, 2010

, ,11,

1111,

, (| | ( ) )) (ef ghe ef ghf ghgh

gh hge fB X A P X A P AX A P A+ +∑ ∑

X-Parameter: How they are measured: Experiment Design & Identification (2): Ideal CaseExperiment Design & Identification (2): Ideal Case

E.g. functions for Bpm (port p, harmonic m) given small extraction tones Aqn (port q, harmonic n)

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

pm pm pm qn qn pm qn qnB X A P X A P A X A P A− += + +

Perform 3 independent experiments with fixed A11input Aqn output Bpm

( ) ( ) ( )(1) ( ) ( ) (1) ( ) (1)11 11 11

F m S m n T m npm pm pm qn qn pm qn qnB X A P X A P A X A P A− += + +

p qn pm

ImIm ( )(0) ( )

11F m

pm pmB X A P=

( ) ( ) ( )11 , 11 , 11pm pm pm qn qn pm qn qn

( ) ( ) ( )(2) ( ) ( ) (2) ( ) (2)*11 , 11 , 11

F m S m n T m npm pm pm qn qn pm qn qnB X A P X A P A X A P A− += + +Re

Re



May 7, 2010

X-parameter properties and benefitsStatic nonlinearity (AM-AM) at any/all CW frequenciesStatic nonlinearity (AM-AM) at any/all CW frequencies

High-frequency memory (AM-PM)

Large-signal output match (correct “Hot S22”)

Harmonics (even and odd) at input and output ports

PAE and DC currents / voltages at supply ports

Cascadable: distortion through chains of components Does for driven nonlinear systems what S-parameters do for linear systems

Hierarchical: apply to one component or multiple (e.g. multi-stage amp)pp y p p ( g g p)

Transportable: mismatch at fundamental and harmonics taken into account

Can be used to simulate some long-term memory affects g y

Can be generated from Simulation and Measurement

Highly automated experiment design & model identification



May 7, 2010

g y p g

Outline

• Introduction: X-parameter Basics

• Survey of X-parameter benefits and applications– Cascading nonlinear blocks– Integrating handset amplifier into cell phone (customer example)

Load dependent X parameters and their harmonic tuning capability– Load-dependent X-parameters and their harmonic tuning capability– High power X-parameter measurements– X-parameter generation from detailed schematics in ADS– X-parameter simulation component (XNP) built-in to ADS– Dynamic X-parameters: Long-term memory research

• Summaryy

• References and Links



May 7, 2010

Measurement-based nonlinear design with X-parameters

ZFL-AD11+11dB gain, 3dBmmax output power

SourceConnector

80 psdelay

ZX60-2522M-S+23.5dB gain, 18dBm

max output powerLoad

v2v1

ConnectorX1

MCA_ZX60_2522MCA_ZX60_2522_1fundamental 1=fundamental

MCA_ZFL_11ADMCA_ZFL_11AD_1fundamental 1=fundamental

RR1R=25 Ohm

RR11R=50 Ohm DC_Block

DC_Block1DC_BlockDC_Block2

I_Probei2

I_Probei1

fundamental_1 fundamentalfundamental_1 fundamental

V_1ToneSRC14

Freq=fundamentalV=polar(2*A11N,0) V Amplifier Component Models from individual X-parameter measurements



May 7, 2010

ResultsCascaded Simulation vs. MeasurementCascaded Simulation vs. Measurement

Red: Cascade MeasurementBlue: Cascaded X-parameter SimulationLight Green: Cascaded Simulation No X(T) termsLight Green: Cascaded Simulation, No X(T) termsDark Green: Cascaded Models, No X(S) or X(T) terms

34

36

1])

::,1]

)T

[::,1

])

Fundamental Gain

74

76

]))1]))

,1])

):,1

]))

Fundamental Phase

30

32

34

dB(b

2[::,

1]/a

1[::,

1])

B(b

2ref

[::,1

]/a1r

ef[::

,b2

NoT

[::,1

]/a1N

oT[:

2NoS

T[::

,1]/a

1NoS

T

70

72

74

wra

p(ph

ase(

b2[::

,1]

wra

p(ph

ase(

b2re

f[::,

rap(

phas

e(b2

NoT

[::ap

(pha

se(b

2NoS

T[:

-28 -26 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6-30 -4

28

26

Pinc

dBdB

(bdB

(b2

-28 -26 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6-30 -4

68

66

Pinc

unw

Pincref

unw

unw

run

wra



May 7, 2010

ResultsCascaded Simulation vs. MeasurementCascaded Simulation vs. Measurement

Red: Cascade MeasurementBlue: Cascaded X-parameter SimulationLight Green: Cascaded Simulation, No X(T) termsgDark Green: Cascaded Models, No X(S) or X(T) terms

Fundamental % Error Second Harmonic % Error

0*2]

6

8

10

12

::,1

])/b

2ref

[::,

1]*1

00ef

[::,

1])/

b2re

f[::

,1]*

1re

f[::

,1])

/b2r

ef[:

:,1]

*

60

80

100

[::,

2])/

b2re

f[::

,2]*

10re

f[::

,2])

/b2r

ef[:

:,2]

2ref

[::,

2])/

b2re

f[::

,2

28 26 24 22 20 18 16 14 12 10 8 630 4

2

4

6

0

(b2[

::,1

]-b2

ref[

:(b

2NoT

[::,

1]-b

2re

(b2N

oST

[::,

1]-b

2r

28 26 24 22 20 18 16 14 12 10 8 630 4

20

40

0(b

2[::

,2]-

b2re

f[(b

2NoT

[::,

2]-b

2r(b

2NoS

T[:

:,2]

-b2

-28 -26 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6-30 -4

Pinc

-28 -26 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6-30 -4

Pinc

“X-parameters enable predictive nonlinear design from NL data”



May 7, 2010

X-parameters solve key, real customer problems Example: GSM amp. and cell phone integrationH l IEEE E Mi C f A d O b 2008Horn et al IEEE European Microwave Conference, Amsterdam, October 2008

F d t l b t t 2

Red Elliptical shape: X-parameter predictionBlue circular shape Hot S22 prediction

Fundamental b-wave at port 2

-1 2

-1.1

-1

Measurementssmall colored crossesSkyworks amp

-1.5

-1.4

-1.3

-1.2

Imag

0 0.2 0.4Real

-1.7

-1.6

“X-parameters predict output match under large input drive Hot S does not”

Allowed Sony-Ericsson to take into account second-harmonic mismatch on amp in system integration



May 7, 2010

input drive Hot S22 does not

Complete X-parameter Model of GSM Amplifier“We didn’t think this was possible”“We didn’t think this was possible” – Sony-Ericsson engineer Joakim Eriksson, Ph.D

Unprecedented capability

1015

Output Voltage

Unprecedented capabilityData acquisition 30x faster

.

-10-505

10

-15

Volts

02

-2

4

Volts

TX_Enable

VAPC

1 2 3 4 5 6 7 8 9 10 11 12 13 14 150 16

0.51.01.5

0.0

2.0

Time (ms)

Volts



May 7, 2010

( )

“X-parameters provide a nonlinear electronic interactive datasheet based on data”

Load-dependence of another GSM commercial Amp from X-parameters measured at only 50 ohms 900 MHz Vbatt=3.7, Vapc = 1.4

System Integrator wants to use X-parameters to compareperformance among vendor parts within their system

Pout, 1dBm contour spacingm7IndexPout2=$LPData ZPout2=0 010 / 40 002

28.000m8indep(m8)=Pdel contours p 0 040 / 137 001

12 Red: LoadPull measurementsBl Si l ti i X

p g p y

$LPData..ZPout2=0.010 / -40.002Pout2=34.364350impedance = Z0 * (1.015 - j0.012)

Pdel_contours_p=0.040 / -137.001level=34.364350, number=1impedance = Z0 * (0.942 - j0.051)

Blue: Simulations using X-parameters extracted in 50 ohms

m7m8 50 ohm X-parameters, predict performance well over a wide range of impedance

But what if we want even more accuracy?



May 7, 2010

X-parameters with load-dependence

1 1 11 12 21 22( , , , ..., , , ...)k kB F DC A A A A=

2 2 11 12 21 22( , , , ..., , , ...)k kB F DC A A A A=

2kA1kA

Port IndexHarmonic (or carrier) Index

1kB 2kBX-parameters allow us to simplify the general B(A) relations:Trade efficiency, practicality, for generality & accuracyPowerful, correct, and practical

,,

( ) *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 +− ⋅= + +⋅∑ ∑

, , p

, ,

( )11 21

( ), 11

( ) *11 21

,1

,2 ( , ,| |,( ,| ( , ,| |,|,| ) )| ),

ef ghghf efe

F fe f

S f h T f hg

hgh

g hh

g

B X DC A A X DC A X DC AA A AP AP Pθθθ − += + + ⋅⋅∑ ∑

,,

( )11 2

,

( ) *( ), 1 2 1

,1 1 2( , , ) (( ,| , ,|, ) )

ef ef f ghg eh

S f hgh

g

T f hgh

gh

F f

he f X DC XAB X DC A AP DP C AA P− += Γ + + Γ ⋅Γ ⋅∑ ∑


Page 25Page 25 D. E. RootD. E. RootMay 7, 2010

“X-parameters unify S-parameters and Load-Pull”X-parameter DML lecture Norway #2

NVNA+Load-Pull = Instant Large-Signal Model

• Drag and drop measured X-parameters for immediate ADS simulation “This is a breakthrough for the industry.”

– Gary Simpson Maury Microwavey p y

NVNA +Load-Pull



May 7, 2010

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


Harmonic Load-Tuning Predictions from X-parametersHorn et al, IEEE Power Amplifier Symposium, September, 2009

Fundamental Output Magnitude Second Harmonic Output Magnitude

, p y p , p ,

Cree CGH40010 10 W RF Power GaN HEMT

Contours vs. 2nd Harmonic Load (Fixed input power and fundamental load)

X-Parameter Prediction: Blue

)

Measured with Harmonic LP System: RedKey Agilent IP calibrates out uncontrolled harmonic impedances presented by tuner &re-grids impedance data for accuracy and interpolation in ADS



May 7, 2010

Harmonic load-pull may be unnecessary! Simpler, cheaper, faster alternatives exist

Simple SetupFast, automated measurementsTime-domain waveforms

Load-dependent X-parameters as a measurement-based device model“The data is the model”The data is the model

Useful for:• High-power device characterization• X-parameter transistor modelsp• multi-stage amps w. large mismatch

Control power, frequency, bias and load at fundamental frequency: faster, fewer d t i l t th h i L Pdata, simpler setup than harmonic L-P

• Get sensitivity to harmonic loads at output and input ports without having to control harmonic impedances

• Estimate the effects of source-pull on device performance in ADS without having



May 7, 2010

to control source impedance

Load-dependent X-parameters versus harmonic load-pull Root et al INMMiC Conference, April, 2010versus harmonic load pull

Load-dependent X-pars Harmonic load-pull validation

Root et al INMMiC Conference, April, 2010Horn et al submitted to IEEE CSICS2010

• One output tuner to vary load at fundamental frequency. At each load inject small tones at 2nd and

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

3rd harmonic freqs(9x(1+2x2) = 45 measurements,actually ~99 measurements)

independently (9x9x9 = 729 measurements)

actually ~99 measurements)

• Measured DC – 4th harmonic • Measured DC - 4th harmonic

• Take into ADS. Present 729 independent loads to model



May 7, 2010

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

Load-dependent X-parameter model for GaN HEMT:

GPIB

Bias

Cree CGH40010 G N HEMTPNA‐X

MDC S l

Bias Tees

NVNA

GaN HEMT10 W packaged

transistor Maury Software

U

DC Supply NVNA Firmware

• 900 MHz• Measure Load-dependent

DUT Maury Tuner

USB

Maury Tuner

X-parametersvs power at 9 impedances

• 4 harmonics measured2 d 3 dTunerTuner

9 load states x 3 x 2• probe tones at 2nd and 3rd

harmonics• harmonic impedancesuncontrolledX-parameter file taken into ADS



May 7, 2010

uncontrolledpfor independent validation

Harmonic Load-pull Setup: For Validation Only

J. Horn et al Submitted to CSICS2010

•Waveforms measured

PNA‐X

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 Z2



May 7, 2010

9 states 9 states 9 states

Load-dependent X-parameters versus harmonic load-pullversus harmonic load pull

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

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

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

and 3rd harmonic freqs(9x(1+2x2) = 45 measurements,actually ~125 measurements)

independently (9x9x9 = 729 measurements)

actually ~125 measurements)

• Measured DC – 4th harmonic • Measured DC - 4th harmonic

• Take into ADS. Present 729 independent loads to model



May 7, 2010

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

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

60

70

80

PAE

Courtesy of J. Horn J. Horn et al, submitted to CSICS2010

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 t d l

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)


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



0 10 20 30 40 50 60-10 70

May 7, 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)

70

PAE vs. Available Input Power


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

May 7, 2010


Vd [V] Time (nanoseconds)


50

60

70

PAE

20

30

40

_Z1Z2 Z3

Cree CGH40010

Harmonic loads

6 8 10 12 14 16 184 20

10

70 2.0

2.0

GaN HEMT

Id Vd VdId

Pin (available)

30

40

50

60

0 5

1.0

1.5

1.0

1.5

Id [A] Vd IdVdId

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

0.0

0.5

-0.5



0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.20.0 2.410 20 30 40 50 600 70

0.5

May 7, 2010


Vd [V] Time (nanoseconds)

Summary: Fundamental-only load-dependent X-parametersFundamental only load dependent X parameters• Full two-port nonlinear functional block model for simulation

A t f l d t i d d f d i f– Accounts for load-tuning dependence of device performance without the requirement of independently controlling harmonic loads

– Use to design matching networks, multi-stage amps, Doherty amps., …

• Large data / time reduction compared to harmonic load-pullX t d l l li l i b f l d N• X-parameter model scales linearly in number of loads N

• Harmonic L-P scales as H = no. of controlled harmonic loads

• Harmonic load pull may be unnecessary

HN• Harmonic load-pull may be unnecessary

– Validates “principle of harmonic superposition” (Verspecht et al 1997) – Source-pull unnecessary (Horn et al submitted to CSISC 2010])



May 7, 2010

Source pull unnecessary (Horn et al submitted to CSISC 2010]) except for power transfer

X-parameters at 100W(courtesy K. Anderson) Gain Compression at fundamental

Mini-Circuits ZHL-100W-52

51.0

51.5

100 MHzParameter Description

P t N b ZHL 100W 52

50.0

50.5

/a1

[::,1

])

Part Number ZHL-100W-52

Pout max(@1dB compression)

45dBm (min, 50M-500MHz)47dBm (typ, 50M-500MHz)

49.0

49.5

dB

(b2[

::,1]

/

Pout max(@3dB compression)

46.5dBm (min, 50M-500MHz)48.5dBm (typ, 50M-500MHz)

48.0

48.5

47 5

Pin max (no damage)

+3dBm

Gain 48dB (min)50dB (typ)

-18 -16 -14 -12 -10 -8 -6 -4 -2-20 0

47.5

pinInput VSWR 1.45:1 (typ)

Output VSWR 2.5:1 (typ)X-parameters have been

d t 250 W© Copyright Agilent Technologies 2010


May 7, 2010

measured at 250 W

X-parameters at 100W

XS21,21

5 harmonics magnitude and phase:XT21,21

5 harmonics, magnitude and phase: fund=150 MHz

200 4

XS23,21

50

100

150

200

1

2

3

4

x,re

al_i

ndex

,::])

ts(Iload.i[imag_in

XT23,21

-150

-100

-50

0

-3

-2

-1

0

ts(v

load

[imag

_ind

ex

ndex,real_index,::])



May 7, 2010

2 4 6 8 10 12 14 16 180 20

-200 -4

time, nsec

t

Generate an IP-Protected X-parameter model

Slid t f J Sif i



Slide courtesy of J. Sifri


Single Tone Amp model with 50 ohm loadIP protected model; Fast X parameter simulation component (20x faster)IP-protected model; Fast X-parameter simulation component (20x faster)

X-pars Vs ckt-level PA Results

Test the PA circuit




Soon: Two-tone X-parameter NVNA measurements

•Magnitude and Phase of intermod products and sensitivity to mismatch•Measure and simulate freq-dependence & asymmetry of complex intermodsD i li i it th t l di t ti•Design nonlinear circuits that cancel distortion

•ADS X-parameter generator and XnP component can do this already

Red = 2‐Tone X‐parameters predictionBl I d d t d d t

Courtesy J. Horn

-22

-21

-20

(dB

m)

-22

-21

-20

(d

Bm

)

Blue = Independent measured data

26

-25

-24

-23

IM3

_L

ow

-25

-24

-23

-22

IM3

_H

igh

1.0

E6

2.0

E6

3.0

E6

4.0

E6

5.0

E6

6.0

E6

7.0

E6

8.0

E6

9.0

E6

0.0

1.0

E7

-26

-27 1.0

E6

2.0

E6

3.0

E6

4.0

E6

5.0

E6

6.0

E6

7.0

E6

8.0

E6

9.0

E6

0.0

1.0

E7

-25

-26



May 7, 2010

Tone Spacing Tone Spacing

3-Port X-parameter Measurements

For characterization and measurement-based simulation of three-port components (mixers, converters, switches)

Note: ADS can already generate and simulate with multi-port, multi-tone X t

V4

4GND I4

X-parameters

Here A and B

1 2A1

B1

A2

B2

waves include multiple spectral components

3

A3B3



May 7, 2010

33

Multi-tone, Multi-port X-parameters: Two large signals at different frequencies at different portssignals at different frequencies at different portsLess restrictive approximation to the general theory:Linearization around the multi-tone nonlinear responses

1A1

2BTerms linear in the

remaining components( )

, , 1,10 2 ,01( , , 0, 0, ...)Fi kl i klB X A A= +



May 7, 2010

Mixers: X-parameters extracted from an Agilent DC-50 GHz InP-based Mixer 1GC1-8068: Mismatched (10 Ohms) at IFAccurate fast IP protectedAccurate, fast, IP-protected

Gain (dB) Phase (deg)Down

Conversion

UpCConversion

LO: 45 GHz RF: 45.1 GHz LO power = 3.5 dBmSi l ti b d



May 7, 2010

LO: 45 GHz RF: 45.1 GHz LO power 3.5 dBmCircuit Model (solid blue) X-parameter Model (red points)Simulation-based

Mixers: X-parameters extracted from an Agilent DC-50 GHz InP-based Mixer 1GC1-8068: Mismatched (10 Ohms) at IFAccurate, fast, IP-protected

Gain (dB) Phase (deg)Down

Conversion

UpUpConversion




May 7, 2010

LO: 45 GHz RF: 45.1 GHz LO power 3.5 dBmCircuit Model (solid blue) X-parameters (red points)Simulation-based

Two Fundamentals: 50 GHz Integrated Mixer Mismatched load (10 Ohms) at IFMismatched load (10 Ohms) at IF

Gain (dB) Phase (deg)LO

Leakageg

RFRFLeakage




May 7, 2010

LO: 45 GHz RF: 45.1 GHz LO power 3.5 dBmCircuit Model (solid blue) X-parameter Model (red points)Simulation-based

Agilent MMICs: Available for purchase

50 GHz InP-based Mixer Part number: 1GC1-8068Part number: 1GC1-8068

See: http://www.agilent.com/find/mmic

X-parameters available



May 7, 2010

Design Nonlinear RF Systems

Antenna

LTCC LPF

RFICMMIC PA

Simulation speedup of 20x to 100x



Simulation speedup of 20x to 100x


X-Parameter technology available in commercial EDA SW

Available Today

Available Soon Available



May 7, 2010

TodaySoon

Extending X-parameters to long-term memoryOriginal X-parameters are Static Spectral Mappings

Static transmission

NVNA

Original X parameters are Static Spectral Mappings

Can be measured under

Slides courtesy J. Verspecht

Static transmission X-parameter: XF21

Can be measured under True CW, pulsed DC orPulsed RF conditions

A1 B2

time

1 2

B2

XF21

F D i

A1( ) ( )1

1212AjeAXFB ϕ=

Frequency Domain:



May 7, 2010

1

Modulation Simulated in Envelope Domain:

A1(t) B2(t)ADS envelope simulator

t tt t

XF2121B2

( ) ( ))(1212

1)()( tAjetAXFtB ϕ=Envelope Domain:

A

( )1212 )()(X-parameters determine Quasi-Static Response

No “BW” effects



May 7, 2010

A1Symmetric intermods independent of envelope rate (or history)

Memory Effects: Beyond Static X-parametersMemory Effects:

When output depends not only in instantaneous input but also on past input values

• Response to fast input envelope variations may violate quasi-static assumption for useResponse to fast input envelope variations may violate quasi static assumption for use in envelope domain for estimation of response to modulated signals

• Physical causes of memory: Dynamic self-heating, bias-line interaction, trapping effects caused by additional dynamic variables – multiple time-scale problem

Hysteresis in compression plotIM3 products asymetricDepend on tone spacing

HBT IM3 [dB ] t ti [H ] GHBT IM3 [dBm] versus tone separation [Hz] Gain-compression



May 7, 2010

Dynamic X-parameters: Long-Term MemoryF d t l “hidd i bl ” th Anadigics AWT6282

ain

Fundamental “hidden variable” theoryVerspecht et al “Extension of X-parameters to include long-term dynamic memory effects,” IEEE MTT-S Int’l Microwave Symposium Digest, 2009. pp 741-744

Anadigics AWT6282

Vol

tage

Ga

( ) ( ) ( )( )tAjeduuutAtAGtAXFtB ϕ

⎭⎬⎫

⎩⎨⎧

−+= ∫∞

021 ,)(,)()()(

A1 (V)

3.2

3.3

V)

3.0

3.1

B2

Am

plitu

de (V

17

-14

184 186 188 190 192 194 196 198182 200

2.9

Time (µs)Measured Data: RedMemory model prediction: Blue

-23

-20

-17

Sim

IM3

Mea

sIM

3



May 7, 2010

Memory model prediction: BlueStatic X-parameter prediction: Magenta-4.0E6 0.0 4.0E6-8.0E6 8.0E6

-26

Offset Frequency

Dynamic X-parameters Beyond Quasi-Static

|B (t)|

comparison• Pulsed Envelope NVNA extraction• Prototyped in ADS• Not yet commercialized

B (t)|A(t)|

|Bmeas (t)|Not yet commercialized

A(t)Bmeas(t)

t |Bsim(t)|B i (t)B2 t | sim( )|Bsim(t)

t

( ) ( ) ( )( )tAjeduuutAtAGtAXFtB ϕ⎬⎫

⎨⎧

−+= ∫∞

21 ,)(,)()()(ADS envelope simulatorA1



( ) ( ) eduuutAtAGtAXFtB⎭⎬

⎩⎨ + ∫

021 ,)(,)()()(

May 7, 2010

Dynamic X-parameters Predict Memory Effects0.5|B|

0.4

0.5|B|Vpeak 60kHz Tone Spacing

Courtesy

ZFL11AD AmpF0= 1.75GHz

0.2

0.3

yJ. Verspecht

0.0

0.1

30kHz Tone Spacing

0.00 0.05 0.10 0.15

|A| (Vpeak)Measurement 60kHz Tone Spacing Measurement 30kHz Tone SpacingModel 60kHz Tone Spacing Model 30kHz Tone Spacing

See Latest Research Results on Dynamic X-parametersJ. Verspecht, J. Horn, D. E. Root “A Simplified Extension of X-parameters to Describe Memory Effects for Wideband Modulated Signals”



May 7, 2010

to Describe Memory Effects for Wideband Modulated Signals ARFTG Conference Session 2-1 Friday, May 28, 2010 10:20AM (Hilton)

X-parameter universe is expanding rapidlyPowerful, practical interoperable solutions for nonlinear

Summary:characterization, modeling, and design of microwave and RF

X-parameters: “doing for nonlinear components and systems what S-parametersdo for linear components and systems”

• X-parameters for GSM amp.• Load-dependent X-parameters

Applications

• 50 GHz Agilent NVNA• High-Power X-parameter meas.• X-parameter generator in ADS• XnP component in ADS• Two-tone measured X-pars• Three-port measured X-pars

Memory: Dynamic X params• Memory: Dynamic X-params• Device modeling• Education, training, app. notes• Industry is adopting paradigm



May 7, 2010

Industry is adopting paradigm

X-Parameters: Agilent Completes the Nonlinear Puzzle!Electronic design

automation softwareAgilent Nonlinear Vector

Network Analyzer

Nonlinear Nonlinear

CustomerNonlinear

Simulation & DesignMeasurements

Customer Applications

Nonlinear Modeling



May 7, 2010

*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− += + +

Selected References and Links1 D E Root J Horn L Betts C Gillease J Verspecht “X-parameters: The new paradigm for measurement modeling and design1. D. E. Root, J. Horn, L. Betts, C. Gillease, 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. http://www.nxtbook.com/nxtbooks/cmp/mwee1208/#/16

2. D. E. Root, “X-parameters: Commercial implementations of the latest technology enable mainstream applications” Microwave Journal, Sept. 2009, http://www.mwjournal.com/search/ExpertAdvice.asp?HH_ID=RES_200&SearchWord=root

3. J. Verspecht and D. E. Root, “Poly-Harmonic Distortion Modeling,” in IEEE Microwave Theory and Techniques Microwave Magazine June 2006Magazine, June, 2006.

4. D . E. Root, J. Verspecht, D. Sharrit, J. Wood, and A. Cognata, “Broad-Band, Poly-Harmonic Distortion (PHD) Behavioral Models from Fast Automated Simulations and Large-Signal Vectorial Network Measurements,” IEEE Transactions on Microwave Theory and Techniques Vol. 53. No. 11, November, 2005 pp. 3656-3664

5. Verspecht, J.; Horn, J.; Betts, L.; Gunyan, D.; Pollard, R.; Gillease, C.; Root, D.E.; “Extension of X-parameters to include long-term dynamic memory effects,” IEEE MTT-S International Microwave Symposium Digest, 2009. pp 741-744, June, 2009

6. J. Verspecht, J. Horn, D. E. Root “A Simplified Extension of X-parameters to Describe Memory Effects for Wideband Modulated p , , p p ySignals,” Proceedings of the 75th IEEE MTT-S ARFTG Conference, May, 2010

7. J. Xu, J. Horn, M. Iwamoto, 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.

8. J. Horn, S. Woodington, R. Saini, J. Benedikt, P. J. Tasker, and D. E. Root; “Harmonic Load-Tuning Predictions from X-parameters,” IEEE PA Symposium, San Diego, Sept. 2009

9. D. Gunyan , J. Horn, J Xu, and D.E.Root, “Nonlinear Validation of Arbitrary Load X-parameter and Measurement-Based Device y y pModels,” IEEE MTT-S ARFTG Conference, Boston, MA, June 2009

10. G. Simpson, J. Horn, D. Gunyan, and D.E. Root, “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.

11. J. Horn, J. Verspecht, D. Gunyan , L. Betts, D. E. Root, and Joakim Eriksson, “X-Parameter Measurement and Simulation of a GSM Handset Amplifier,” 2008 European Microwave Conference Digest Amsterdam, October, 2008

12. J. Verspecht, D. Gunyan, J. Horn, J. Xu, A. Cognata, and D.E. Root, “Multi-tone, Multi-Port, and Dynamic Memory Enhancements to PHD Nonlinear Behavioral Models from Large-Signal Measurements and Simulations,” 2007 IEEE MTT-S Int. Microwave Symp. Dig., Honolulu, HI, USA, June 2007.

13. http://www.agilent.com/find/x-parameters for X-parameters14. http://www.agilent.com/find/nvna for NVNA15. http://www.agilent.com/find/mmic for Agilent MMICs16. http://www.agilent.com/find/x-parameters-info for information about X-parameter open standards



May 7, 2010

Survey and Trends in Nonlinear T i t M d li M th d l iTransistor Modeling Methodologies

Dr. David E. RootPrincipal R&D Scientistp

High Frequency Technology CenterSanta Rosa, CA USA

IEEE MTT-S Lecture #3Bergen, Norway

May 7 2010May 7, 2010


Page 1Page 1 D. E. RootD. E. RootNorway #3 Transistor Modeling

May 7, 2010

Key Contributors

• Alex Cognata

• Daniel Gunyan

• Jason Horn• Jason Horn

• Masaya Iwamoto

• Alexander Pekker

• Dominique Schreurs

• Jonathan Scott

• Gary Simpson

• Franz Sischka

• Paul TaskerPaul Tasker

• John Wood

• Jianjun Xu



May 7, 2010

Presentation Outline

• Introduction• I-V modeling• Nonlinear Charge Modeling• Non Quasi-Static Effects & Dispersion Modeling• Electro-Thermal Modeling• Advanced Measurements

NVNA d t d d d d i l FET d li• NVNA data and advanced dynamical FET modeling• Symmetry Considerations • Summary & Conclusions• Summary & Conclusions



Norway #3 Transistor Modeling

Introduction

All models are wrong, but some are useful.“

t ti ti i G B- statistician George Box

“All models are approximations. Some models are useful ”Some models are useful.

- attributed to Mike Golio and others



May 7, 2010

Compact Transistor Models (AgilentHBT model) [48, 49, 10][48, 49, 10]

Thermal Subcircuit (Two-Poles)( )

Complete Circuit Model(Intrinsic Model in Red)

Coupled nonlinear ordinary differential equations in the time

IqI

Icr

cf −⎟⎟⎠

⎞⎜⎜⎝

⎛3 ⎟

⎠⎞

⎜⎝⎛ −

−=VKDC

VJCVIKDCIcrit BCi131

equations in the time domain

Equivalent Circuit with d

ICE⎠⎝=

( ) ( )IKDCIKDCIcritIcf

IKDCIKDCIKDCIcritIcf

IKDC 211

21

211

21 22

⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛−⎟

⎠⎞

⎜⎝⎛ −+⎟

⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛ −

⎠⎝ VKDCnonlinear elements



May 7, 2010

oqIKDCIKDCIKDCIKDC

q 312

22223 −+⎦⎣ ⎠⎝⎠⎝⎠⎝⎠⎝=

Agilent HBT Model Parameters (over 100)

AgilentHBT_ModelHBTM1HBTM1

Xth2=0.0Cth2=0.0Rth2=0.0Xth1=0.0Cth1=5.0e-10Rth1=1000.0

Eaa=0.0 VXtik3=0.0Xtirh=4.0Xtic=3.0Xtir=3.0Egc=1.5 V

Tvje=0.0Xre=0.0Xrc=0.0Xrb=0.0Lpe=0.0 HLpc=0.0 H

Vkrk2Inv=0.2Vkrk=3.0 VIkrktr=1.0e-06 AIkrk=0.025 ATkrk=1.0e-12 secFextc=0.8

Itc=0.006 ATcmin=5.0e-13 secTfc0=2.0e-12 secFextb=0.2Tfb=1.0e-12 secAbcx=0.75

Cemax=1.0e-13 FMje=0.3Vje=1.3 VCje=4.0e-14 FIk=1.0 AGkdc=0.0

Var=1000.0 VVaf=500.0 VAbel=0.0Nc=2.0Isc=1.0e-13 ANrh=2.0

Rbx=5.0 OhmRbi=15.0 OhmRcx=5.0 OhmRci=1.0 OhmRe=2.0 OhmTnom=25.0

Fb=1.0 HzAb=1.0Kb=0.0Ffe=1.0Af=1.0Kf=0.0Xth2 0.0

Xitc2=0.0Xitc=0.0Xtfc0=0.0Xtcmin=0.0Xtfb=0.0Eab=0.0 VEaa 0.0 V

Ege=1.55 VTnr=0.0Tnf=0.0Tvpc=0.0Tvjc=0.0Tvpe=0.0Tvje 0.0

Cpce=1.0e-15 FTr=1.0e-09 secFexke=0.2Vkmx=1.0 VVktr=1.0 VGkrk=4.0Vkrk2Inv 0.2

Vtrmin=1.0 VVtcminInv=0.5Vmx0=2.0 VVtr0=2.0 VVtc0Inv=0.3Itc2=0.008 AItc 0.006 A

Mjc=0.3Vjc=1.1 VCjc=5.0e-14 FAbex=0.0Mjer=0.05Vpte=1.0 VCemax 1.0e 13 F

Ikdc2Inv=0.0Ikdc1=1.0 ANb=1.0Isb=1.0e+10 ANa=1.0Isa=1.0e+10 AVar 1000.0 V

Nh=1.0Ish=1.0e-27 ANr=2.0Isr=1.0e-15 ANf=1.0Is=1.0e-25 ARbx 5.0 Ohm

AllParams=Imax=10.0 A

Xvkrk=0.0Xikrk=0.0Xtkrk=0.0

Xtie=3.0Xtih=4.0Xtis=3.0

g

Lpb=0.0 HCpbc=1.0e-15 FCpbe=1.0e-15 F

p

Vtc2Inv=0.1VtcInv=0.1Vmxmin=1.0 V

Mjcr=0.03Vptc=3.0 VCcmax=9.0e-14 F

j

Nkdc=3.0VkdcInv=0.1Ikdc3=1.0 A

Isrh=1.0e-15 ANe=2.0Ise=1.0e-18 A

Resistances: 5 Parasitics: 6Resistances: 5DC Currents: 26Depletion Charge: 14Delay Charge: 25

Parasitics: 6Temp., DC & R’s: 22Temp., Charges: 12Noise: 6



May 7, 2010

Delay Charge: 25 Noise: 6

Transistor Modeling

• Compact Models: Equivalent circuit models for IC design formulated in the time-domain. Examples are BSIM models for MOSFET Angelov model for GaAs FETs Gummel PoonMOSFET, Angelov model for GaAs FETs, Gummel-Poonmodels for bipolars, AgilentHBT model for III-V HBTs

• “Compact” models can be complex (> 100 parameter values)• Compact models can be complex (> 100 parameter values)

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

operating conditions (power, temperature)– Advanced models may not be identifiable from only DC and

S-parameter data.– No direct evidence that these nonlinear models will reproduce large-



p gsignal behavior


May 7, 2010

Device Requirements and Modeling Implications• Linearity: Harmonic & Intermod. Distortion; ACPR; AM-AM; AM-PM• Efficiency: PAE; Fundamental Output Power; Self-biasing

M Sl th l ff t l t i h• Memory: Slow thermal effects, slow trapping phenomena• Modeling Challenges from • Device physics (III V transport trapping dynamics)• Device physics (III-V transport, trapping dynamics)

Complex signals, multiple time-scale dynamicsAmplifier, switch, and mixer applicationsWide variety of device designs in many material systemsy g y y

• Accuracy required over • Bias, frequency, and temperature; power; • Different types of models may be required at different stages in the

development of a technology




Physical Models to Circuit (compact) Models [16,17]

Q(VGS) Q(VGD)

( ( ))( ) ( ( ) ( ))DC GDdQ V tI t I V t V t ( ( ))( ) ( ( ), ( ))DC GDD D GS DS

QI t I V t V tdt

= −( ( )) ( ( ))( ) GS GD

GdQ V t dQ V tI t

dt dt= +

dt dt

( )( )3 32 2

2

2 2( , ) ( )3

DC DD GS DS DS DS GS GS

D

W qN aI V V V V V VL qN a

μ ε φ φε

⎛ ⎞⎡ ⎤= − + − − −⎜ ⎟⎢ ⎥⎜ ⎟⎣ ⎦⎝ ⎠



( ) 2 ( ) (up to a constant)DQ V WL q N Vε φ= − −

May 7, 2010


Typical characteristics of real devices not ideal120 90

80

100

120

A)

50

60

70

80 Vgs=1.4V

(0.2V steps)

I d(m

A)

20

40

60

Ids

(mA

20

30

40

50

Vgs=-1.2V

2 4 6 80 10

20

0

Vds (Volts)

1 2 3 4 5 6 7 8 9 10 110 12

10

0

Vgs=-1.6VVgs=-2.0V

Vds (V)Vds (Volts)

pHEMTMESFET 3 temperatures

Typical Features of real device often not captured by

ds ( )

simple physics-based models

Non-zero, and sometimes negative, output conductanceDrain-voltage dependent “pinch-off voltage”



Drain voltage dependent pinch off voltageHigher drain current at lower ambient temperature (near Vp)

May 7, 2010


Measurement-Based (Empirical) Modeling “The Device Knows Best”The Device Knows BestElectrons know where to go, even if the modelers don’t!

Use device data as much as possible in the modelUse device data as much as possible in the modelUseful for circuit design when good measurements are available, and when no good (fast, robust, extractable) physical models are available•Empirical models (fitting closed-form functions to data) •Table-based models with spline interpolation•Neural-network based modelsExperiment Design:

measure the device I-V (and Q-V) Model Identification

fit the empirical expressions to data (parameter extraction)fit the empirical expressions to data (parameter extraction)or store data and interpolate




Empirical Models

The same dynamics (equivalent circuit topology) G( ( ))dQ V t ( )GS GSQ V ( )GD GDQ V( ( ))( ) ( ( ), ( ))DC GD GD

D D GS DSdQ V tI t I V t V t

dt= −

( ( )) ( ( ))( ) GS GS GD GDG

dQ V t dQ V tI t = +DS

( , )dcD GS DSI V V

Large Signal Equivalent Circuit

( )G dt dt

Large-Signal Equivalent Circuit

Modified Constitutive Relations for easy fitting (Curtice Cubic[7])

( )2 30 1 1 2 1 3 1( , ) ( )DC

D GS DS DSI V V A AV A V A V tanh Vγ= + + +

0( )GD GDQ V C V=1

0( ) 11

jGS

C VQ Vηφ

η φ

+⎛ ⎞

= − −⎜ ⎟+ ⎝ ⎠



η φ⎝ ⎠

May 7, 2010


Experiment Design: Measure DC I-V curves

IDDC Vgs Vds,( ) A0 A1V1 A2V1

2 A3V13+ + +

⎝ ⎠⎛ ⎞ γVds( )tanh⋅=

Model Identification (1): minimize error

Guess Initial Coefficient Values in Fixed Constitutive Relations

D g( ) 0 1 1 2 1 3 1⎝ ⎠ γ ds( )

Simulate Circuit

Compare Simulation with MeasurementsCompare Simulation with Measurements

Good Fit?ModifyCoefficientGood Fit?

No

Yes

Done

CoefficientValues



Done

May 7, 2010


Issues with parameter extraction

Optimization-based parameter extraction can be:

• Slow (simulate circuit and update parameters hundreds of times)• Sensitive to initial parameter values• Non-repeatablep• Can get stuck in local minima of optimizer cost function•Require user interaction• Good parameter values depend on good datap p g

•May never achieve good fit (constitutive relations may not be flexible enough)( y g )Changes to constitutive relations -> changes to extraction routines




Parameter Extraction: What can go wrong

(Curtice Cubic example also see [30])

( )2 3( ) ( )DCI V V A AV A V A V tanh Vγ= + + +( )1 2 0 1 1 2 1 3 1 2( , ) ( )DI V V A AV A V A V tanh Vγ= + + +

I XX

VVp Vmax

X

XX

XX

V1Vp Vmax




Table-Based Models: Accurate and General [3,17,21]

Vertical Power Si MOSFET GaAs pHEMT

Measure, transform data, tabulate, interpolate, scale

[A][A]

0.3

ID

0.15

ID[A][A]

0.00 0 10 0VDS 0 0 5 0VDS

0.0



Process and Technology Independent0.0 10.0VDS 0.0 5.0VDS

May 7, 2010


Table Models

C tit ti R l ti i t l t d f d tConstitutive Relations are interpolated from dataTable 1 Table 2

d gs ds d_dcI t Interpolate{Table1, [V t ,V t ,I ]}=( ) ( ) ( )

gs ds dInterpolate{Table2, [V t ,V t ,Q ]}ddt

+ ( ) ( )

Works well for dc S versus bias & freq med-high power signals



Works well for dc, S versus bias & freq., med-high power signals

May 7, 2010


Warning: Interpolation algorithms may limit table models! [43]models! [43]

Original HPFET Model with ADS splines vs Measured25

Two-tone Intermodulation

-25

0

-75

-50

ower

(dB

m)

Fund

R h d

-125

-100

Out

put P

o

IM3

IM5

IM7

Fund

Spline-based Root Model

Rough and unphysical behavior

200

-175

-150Fund

IM3

IM5

IM7Measured



-200-50 -40 -30 -20 -10 0 10

Input Power (dBm)

May 7, 2010


Vgs 2 @ 100MH ( 1MH )

Naïve Splines Limit Distortion Accuracy [17, 8]

IP3(dBM)

0.2V

P=-10dBmVgs

-0.6 Si NJFET2-tones @ 100MHz (+1MHz)

Table Model

Vd

(a) Vg=-1V Power=-10dBmVds

-1.4

-1.0

IP3(dBM)

P=-20dBm

Voltage Swing

Vgs

-0.6

VdDataHPFET table modelCurtice analytic model

-1.4

-1.0

Voltage Swing

Vds0.06V(b) Vg=-1V Power=-20dBm

VdSimple Cubic Splines

•Third order derivative vanishes at symmetry points•Low order polynomial can’t predict high-order distortion at low amplitudes



p y p g pinterpolation model is better when signal size ~ data spacing

May 7, 2010


OutputsSpline Alternatives: Artificial Neural Networks

( )y F x x x=y1 y2

Outputs

yyjj = = Σ Σ VVjkjk Zkk

1 1 3( , , )i iy F x x x=

VjkHidden Neuron Output

k

Z1 Z2 Z3 Z4

Wki

Σ Σ WWki ki xiZk = tanh( = tanh( )

Wki

Parameters w = [WWkiki, V, Vjkjk]x1 x2 x3 Inputs

• Universal Approx. Thm: Can fit any nonlinear function of many variables• Infinitely differentiable: better for distortion than naïve splines



y p• Easy to train (identify) using standard third-party tools (MATLAB)

May 7, 2010


NeuroFET: FET Model using ANNs [43]Constitutive Relations are ANNs!

80

90Vgs=1.4V ANN-based FET model (___ ) dcI

Constitutive Relations are ANNs!

50

60

70

(0.2V steps)

Measured device test data ( o ) dIANN

30

40

50

I d(m

A)

V =-1 2V

10

20

0

Vgs=-1.6VVgs=-2.0V

Vgs=-1.2V

Vgs Vds

1 2 3 4 5 6 7 8 9 10 110 12

Vds (V)




NeuroFET Distortion Validation (2-tone) [43]ANN-Based FET vs Measured

-25

0

25

-75

-50

-25

wer

(dB

m)

Fund

-125

-100

Out

put P

ow

Fund

IM3

IM5

IM7

Physically

correct behavior-175

-150Fund

IM3

IM5

IM7-200

-50 -40 -30 -20 -10 0 10Input Power (dBm)

IM7

Alternatives to ANNs are “Smoothing Splines” [5]



gbut they don’t have all the advantages

May 7, 2010


Global Domains for Measurement-based Models

ANNs inside, Intelligent Extrapolation outside [44]Enables nonlinear simulation from discrete, bounded, measured data

Two orders of continuity at boundary Asymptotically ~ exponential

+ simpler algorithmx robust algorithm



Required for robust convergenceMay 7, 2010


Guided Extrapolation Algorithm Compiled into Model

Improves DC convergence, HB, TA range of use [45]

Training Domain Training Domain





• Introduction• I-V modeling• Nonlinear Charge Modeling and Related Issues• Non Quasi-Static Effects & Dispersion Modeling• Electro-Thermal Modeling• Advanced Measurements for

Experiment Design & Model IdentificationExperiment Design & Model Identification• Symmetry Considerations • Summary & ConclusionsSummary & Conclusions

Artificial Neural Network applications given throughout© Copyright Agilent Technologies 2010


Artificial Neural Network applications given throughout

May 7, 2010


Charge Modeling: Key to Distortion at high frequencies [4]

M d l A Sh kl M d l B St t ] M d l C HP/A il tFET ]

Gain/Phase vs. Pin IM3 vs. Pin

•All three models use the same DC analytical equations

Model A= Shockley Model B = Statz[32] Model C =HP/AgilentFET [33]

[4] J. Staudinger, M.C. De Baca, R. Vaitkus, “An examination of several large signal capacitance



g , , , g gmodels to predict GaAs HEMT linear power amplifier performance,” Radio and Wireless Conference, Aug. 1998 pp343-346.

May 7, 2010


Good Charge Model Required to Predict ACPR [4][ ]

M d l A Sh klModel A= Shockleyjunction capacitances

Model B = Statz/Raytheon gate terminal chargegate terminal charge conserving but not terminal charge conserving at drain

Model C =HPFETModel C =HPFET (Root model) terminal charge conserving model at both gate and drain by direct integration of measured admittances and spline interpolation




Adjoint Neural Network Training for Qg

ωYIm

bias11 )(ω

YImbias12 )(Train Adjoint network on partial

derivative data derived from ω ω

Q E

derivative data derived from S (Y) parameters

Qg

gQf

)( w,V,Vf Q dsgsgQ

ANNg =bias

gs

QANNV

f g

∂∂

biasds

QANNV

f g

∂∂

Adjust wgQE

gdQ( )

gANN

f

ww

gQI (t)= g dt

V VV V

1Adjoint Neural

NetworkJianjun Xu, M.C.E. Yagoub, Runtao Dingand Q.J. Zhang,“Exact adjoint sensitivity analysis for neuralbased microwave modeling and design,”IEEE Transactions on Microwave Theory and



Vgs VdsVgs VdsIEEE Transactions on Microwave Theory andTechniques, vol. 51, pp.226-237, 2003.

May 7, 2010


Adjoint Neural Network Approach to Charge ModelingCharge Q obtained by Adjoint Training Methods [27 43]

Im(Y11)/ω and ∂Qg/∂Vgsx 10-12(F)Q ( C)

Charge Qg obtained by Adjoint Training Methods [27,43](Generate an ANN function given partial derivative data)

0 15

0.2

0.25

Vgs

Qg (pC)

0

0.1

0.2

0 2 4 6 8 10 12

0.1

0.15

x 10-12(F)-0.3

-0.2

-0.1

0.1

0.15 -Im(Y12)/ω and -∂Qg/∂Vdsx 10(F)

-0 7

-0.6

-0.5

-0.4

NeuroFET model ( __ ) Measured device data ( o )

0 2 4 6 8 10 120

0.05 Vgs -2 0 2 4 6 8 10 12-0.8

-0.7

Vds (V)

Measured device data ( o )

Another experimental validation of terminal



0 2 4 6 8 10 12

Vds (V) charge conservation at the gate for GaAs pHEMT

May 7, 2010


Advantages of Adjoint ANN over contour Integration

• More uniform approximation of terminal charges than implementations of contour integration

• Applies to scattered data. No gridding necessary.

• Results in infinitely differentiable charge function rather than finite-order spline representation

• More easily deals with complicated boundary of data domain

• More easily generalizes to higher number of terminals










May 7, 2010


Dynamic electro-thermal (self-heating) model

( ) ( ( ) ( ), ( ), )d d dI t I V t V T tt=( ) ( ( ) ( ), ( ), )d d ds gsI t I V t V T tt( ) ( ( ) ( ), ( ), )g g ds gsQ t Q V t V T tt=

( )( ) ( ) ( ) ( )dT T R I t V t I t V tτ + Δ +

Temperature evolution equation based on dissipated power

( )( ) ( ) ( ) ( )TH D DS G GST R I t V t I t V tdt

τ + Δ = +

This example is a simplified to 1st order ODEp pHeat propagates via diffusion Eqn. (PDE)

. Alternatively estimate T(t) as linear filter in frequency domain [34]



Trade off “fractional pole” response for nonlinearity

May 7, 2010


Dynamic electro-thermal (self-heating) model

Currents, Voltages, and Temperature calculated by the simulator self-consistently using coupled electrical and thermal equivalent circuits

G D

T T deltaT= +Thermal Equivalent CircuitS S

ambT T deltaT= +

( ( ), ( ), ( ))G GS DSQ V t V t T t( ( ), ( ), ( ))D GS DSI V t V t T t( ( ), ( ), ( ))D GS DSQ V t V t T t

( ( ), ( ), ( ))G GS DSI V t V t T tCan approximate distributednature of heat propagation

T=device junction temperatureT =device ambient (backside) temperature

Electrical Equivalent Circuit

atu e o eat p opagat oby many sections

External node allows coupling



Tamb=device ambient (backside) temperature to other heat sources

May 7, 2010


ANN T-dependent constitutive relations

0 07

Ids

Blue: T =25 constant ambient temp

Given measured non-isothermal ambient temp. (T0 – dependence), one constructs isothermal (T – dependent) constitutive relations

0.06

0.07 Blue: T0=25 constant ambient tempRed: T=70 constant junction tempNeuroFET

T-dependent

0.04

0.05

Ids

dc I-V curves

0.02

0.03

0

0.01



0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5Vds

May 7, 2010


NeuroFET dynamic self-heating resultsFixed Vg

-2

0

2Ig

4

5

6Vd

-10

-8

-6

-4

-2

Ig.i,

uA

0

1

2

3

Vd,

V

1 2 3 40 5

-12

time, usec

1 2 3 40 5

-1

time, usec

Id 140

30

40

50

60

i, m

A

Id

80

100

120

140

T, V

1 2 3 40 5

0

10

20

-10

Id.i

1 2 3 40 5

40

60

20

T



time, usec1 2 3 40 5

time, usec

May 7, 2010


NeuroFET static self-heatingIds

0 06

0.07

O : Data __ : Model

pHEMT

0.05

0.06 T0: -65T0: -25T0: -5T0: 25

0 03

0.04

Ids

T0: 25T0: 55T0: 85T0: 115

0.02

0.03

0

0.01



0 1 2 3 4 5

0

Vds

May 7, 2010








May 7, 2010


Need for Advanced Characterization for empirical Modeling [21]Modeling [21]

True for neural network model too if built from dc + S-paramdatadata




GaN Devices

1 mm 10 fingers

GaN on SiGaN on Si

fT ~ 30GHz

Pulse width 2usPulse width 2us

Slide courtesy J. Scott

Pulsed measurements provide much more datathan can be measured under static (DC) conditions



than can be measured under static (DC) conditions

May 7, 2010


Pulsed I-V characteristics at different quiescent points vs DC [1 21]points vs DC [1,21]

pHEMT device




Nonlinear Vector Network Analyzer (NVNA) Measurements for Transistor Modeling:Measurements for Transistor Modeling:

• These measurements will compliment and eventually totally replace small-signal measurements for large-signal device model experiment design and model identification [36-38].Such systems are also useful for model validation.Such systems are also useful for model validation.• Stimulates device with more realistic signals• Reduce degradation of device characteristics from static

measurements• Less reliance on inferring large-signal dynamic behavior from

linear small- signal measurementsg• Some device properties may very different (breakdown, Ig, …)• Use to identify parametric (empirical) models or even train (generate)

data based models directly



data-based models directly

May 7, 2010


(1a) NVNA data for compact model validation

measuredsimulated

measuredsimulated

BSIM3 2 modelBSIM3.2 model

•Parameters extracted from DC and S-parameters (or CV)•BSIM3 model simulated in Harmonic balance (HB) analysis



May 7, 2010

Slide courtesy of Franz Sischka, data from [51]•Results compared with NVNA data

(1b) Model parameter extraction from NVNA Data [51]

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



May 7, 2010

• App-dependent tuning• Explore model limits

Parameter extraction from NVNA data



May 7, 2010

Slide courtesy Franz Sischka

Examples of measured dynamic load-lines using NVNA for advanced FET model constructionNVNA for advanced FET model construction

Root et al INMMiC2010 [52]Xu et al IMS2010 [53]

• Entire operating range coveredp g g• Can measure into limiting operating regions• Get data under realistic operating conditions



May 7, 2010

Model I-V characteristics at different trap-statesI V t V t T ϕ ϕ( ( ) ( ) )

Ids (mA)

D gs ds j 1 2I V t , V t , T , , ϕ ϕ( ( ) ( ) )

Ids (mA) Ids (mA)

Xu et al IMS2010 [53]

120

140

160

180

120

140

160

180Ids (mA)

Ids

40

60

80

100

120

40

60

80

100

120(mA)

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

0

20

40

0 1 2 3 4 5 60

20

40

Vds (V)

Corresponds to drain-lag (knee walk-out) (intrinsic)Trap state

Static “Iso-thermal” intrinsic I-V

Measured and simulated extrinsic DC - IV

1 2 2 8ϕ ϕ= − = 1 2 65jVgs Vds Tϕ ϕ= = =



May 7, 2010

Bias-dependent small-signal admittances fit better everywhere

Nonlinear validation of advanced GaAs FET model(using NVNA data) X t l IMS2010 [53](using NVNA data) Xu et al IMS2010 [53]

Simulated (___ ) Measured data (symbols)

With NVNA, Nonlinear validation comes for free



May 7, 2010

Tradeoffs

Physical I i htInsight

Physics based

Physical TCADDevice Model

Abilit t

TableM d l

Physics-basedCircuit Model

Ability toGeneralize

ModelX-parameterBehavioral

Ease of Use / extraction

Accuracy



May 7, 2010

Conclusions

• Physical, Empirical, Table-based, and Behavioral models (e.g. X-parameters) of transistors all have their place in device p ) pmodeling

• Advanced characterization techniques and instruments (e.g. NVNA) will change the paradigm for nonlinear device modeling and validation. This is a key industry trend.

M d li i i d l G d lt• Modeling is a rigorous and complex process. Good results take time, expertise, good measurements, and care.



May 7, 2010

References

[1] A.E.Paker and D.E.Root “Pulse Measurements Quantify Dispersion in PHEMTs,” 1998 IRSI Symposium on Signals, Systems, and Electronics, Pisa, Italy, Sept. 29 - Oct. 2, 1998, URSI and IEEE, pp. 444-449.[2] Pirola,M., Root,D.E., Ghione,G., “Large-signal performance of measurement-based diode models for nonlinear circuit simulation: a comparison, 1995 European Microwave Conf. Technical Digest, Italy,[3] Root, D.E., Fan, S., Meyer, J. “Technology Independent Non Quasi-Static FET Models by Direct Construction from Automatically Characterized Device Data” 21st European Microwave Conf.Proceedings, Stuttgart,

Germany, Sept 1991, pp 927-932.[4] J. Staudinger, M.C. De Baca, R. Vaitkus, “An examination of several large signal capacitance models to predict GaAs HEMT linear power amplifier performance,” Radio and Wireless Conference, Aug. 1998 pp343-

346346.[5] V. Cuoco, M.P. van den Heijden, L.C.N de Vreede, “The ‘Smoothie’ data base model for the correct modeling of non-linear distortion in FET devices,” International Microwave Symposium Digest, 2002, Vol. 3, pp2149

– 2152[6] HP NMDG Group[7] Aarts, A.C.T.; van der Hout, R.; Paasschens, J.C.J.; Scholten, A.J.; Willemsen, M.; Klaassen, D.B.M.; “Capacitance modeling of laterally non-uniform MOS devices,” 2004 IEEE IEDM Technical Digest, 13-15 Dec. 2004

Page(s):751 - 754 [8] D.J.McGinty and D.E.Root, and J.Perdomo, “A Production FET Modeling and Library Generation System,” in IEEE GaAs MANTECH Conference Technical Digest, San Francisco, CA, July, 1997 pp. 145-148[9] Root, D.E. and Fan, S., “Experimental Evaluation of Large-Signal Modeling Assumptions Based On Vector Analysis of Bias-Dependent S-Parameter Data from MESFETs and HEMTs”, 1992 IEEE MTT-S International [9] Root, D.E. and Fan, S., Experimental Evaluation of Large Signal Modeling Assumptions Based On Vector Analysis of Bias Dependent S Parameter Data from MESFETs and HEMTs , 1992 IEEE MTT S International

Microwave Symposium Technical Digest, pp.255-259 [10] Agilent ADS manual[11] Parker & Rathmell IEEE Intl. Microwave Symp. Dig. 2004[12] Curtice, W.R.; Ettenberg, M.; “A Nonlinear GaAs FET Model for Use in the Design of Output Circuits for Power Amplifiers” IEEE Transactions on Microwave Theory and Techniques, Volume 33, Issue 12, Dec 1985

Page(s):1383 - 1394[13] Agilent ADS manual [14] S. Maas, “Ill conditioning in self-heating FET models,” IEEE Microwave & Wireless Comp. Let. 12, 3 Mar. 02 pp 88-89[15] A. Parker, Comments on" ill conditioning in self-heating FET models"., IEEE Microwave and Wireless Components Letters 12:99, 351-352, 2002[16] D.E.Root, “Nonlinear Charge Modeling for FET Large-signal Simulation and its Importance for IP3 and ACPR in Communication Circuits,” Proc. of the 44th IEEE Midwest Symposium on Circuits and Systems, Dayton

OH, August, 2001, pp 768 - 772 (contact author for corrected version)[17] D.E. Root “Overview of Microwave FET Modeling for MMIC Design, Charge Modeling and Conservation Laws, and Advanced Topics,” 1999 Asia Pacific Microwave Conference Workshop Short Course on Modeling

and Characterization of Microwave Devices and Packages, Singapore, November, 1999[18] AE Parker and JG Rathmell, “Bias and Frequency Dependence of FET Characteristics, IEEE Transactions on Microwave Theory and Techniques vol. 51, no. 2, pp. 588--592, Feb. 2003. [19] Ouarch, Z.; Collantes, J.M.; Teyssier, J.P.; Quere, R.;

Measurement based nonlinear electro thermal modeling of GaAs FET with dynamical trapping effects 1998 IEEE MTT S International Microwave Symposium Digest Volume 2 7 12 June 1998 pp :599 602Measurement- based nonlinear electro-thermal modeling of GaAs FET with dynamical trapping effects, 1998 IEEE MTT-S International Microwave Symposium Digest Volume 2, 7-12 June 1998 pp :599 - 602[20] Webster, D.; Darvishzadeh, M.; Haigh, D.;“Total charge capacitor model for short-channel MESFETs,” IEEE Microwave and Guided Wave Letters, Volume 6, Issue 10, Oct. 1996 Page(s):351 - 353 [21] D.E.Root, 2001International Symposium on Circuits and Systems Tutorial/Short-Course and Special Session on High-Speed Devices and Modeling, Sydney, Australia, May, 2001, pp 2.3_1 - 2.3_7 and 2.7_1 - 2.7_8 [22] Schreurs, D.; Verspecht, J.; Vandenberghe, S.; Carchon, G.; van der Zanden, K.; Nauwelaers, B.; Easy and accurate empirical transistor model parameter estimation from vectorial large-signal measurements,” IEEE Intl

Microwave Symp. Digest, Volume 2, 13-19 June 1999 Page(s):753 - 756 vol.2 [23] Schreurs et al “Direct Extraction Of The Non-linear Model For Two-port Devices From Vectorial Non-linear Network Analyzer Measurements,” 27th European Microwave Conf. Sept ’97 921-926

[24] Curras Francos M C ; Tasker P J ; Fernandez Barciela M ; Campos Roca Y ; Sanchez E ; “Direct extraction of nonlinear FET Q V functions from time domain large signal



[24] Curras-Francos, M.C.; Tasker, P.J.; Fernandez-Barciela, M.; Campos-Roca, Y.; Sanchez, E.; “Direct extraction of nonlinear FET Q-V functions from time domain large signal measurements,” IEEE Microwave and Guided Wave Letters Volume 10, Issue 12, Dec. 2000 Page(s):531 - 533


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2003 Page(s):226 – 237[28] J. Verspecht & D. Schreurs, “Measuring transistor dynamic loadlines and breakdown currents under large-signal high-frequency operating conditions,” in IEEE Microwave Symposium

Digest, 1998 Vol 3, 7-12 June 1998 pages 1495-1498 vol. 3[29] Aarts, A.C.T.; van der Hout, R.; Paasschens, J.C.J.; Scholten, A.J.; Willemsen, M.B.; Klaassen, D.B.M.; “New fundamental insights into capacitance modeling of laterally nonuniform MOS

devices,”IEEE Transactions on Electron Devices, Volume 53, Issue 2, Feb. 2006 Page(s):270 - 278

[30] S. Maas, “Fixing the Curtice FET Model” Microwave Journal, March 2001[31] Parker, A.E.; Skellern, D.J.; “A realistic large-signal MESFET model for SPICE,” IEEE Transactions on Microwave Theory and Techniques Volume 45, Issue 9, Sept. 1997 Page(s):1563 -

1571 [32] D.E.Root, in 1999 Asia-Pacific Microwave Conference Workshop (WS2) Modeling and Characterization of Microwave Devices and Packages, Singapore, 1999[33] D.E.Root “Elements of Measurement-Based Large-Signal Device Modeling,” in 1998 IEEE Radio and Wireless Conference (RAWCON) Workshop on Modeling and Simulation of Devices

and Circuits for Wireless Communication Systems, Colorado Springs, August, 1998[34] AE Parker and JG Rathmell, “Broad-band Characterization of FET Self-Heating” IEEE Transactions on

Microwave Theory and Techniques, vol. 53, no. 7, pp. 2424--2429, Jul. 2005. [35] Filicori, F.; Vannini, G.; Monaco, V.A.; “A nonlinear integral model of electron devices for HB circuit analysis,” IEEE Transactions on Microwave Theory and Techniques, Volume 40, Issue [ ] , ; , ; , ; g y , y q , ,

7, July 1992 Page(s):1456 - 1465 [36] HPNMDG group[37] D.Schreurs, J.Verspecht, B.Nauwelaers, A.Van de Capelle, and M. Van Rossum, “Procedure to extract the nonlinear HEMT model from vectorial non-linear network analyzer

measurements,” International IEEE Workshop on Experimentally Based FET Device Modeling and Related Nonlinear Circuit Design, Kassel, Germany, pp. 20.1 - 20.7, July, 1997.[38] Martín-Guerrero et al “Frequency domain-based approach for nonlinear quasi-static FET model extraction from large-signal waveform measurements,” EuMICC Conf. 2006[39] V. Cuoco, “ Smoothie – A Model for Linearity Optimization of FET Devices in RF Applications,” Ph.D. Thesis Technical University of Delft, 2006[40] Lingquan Wang, “Investigation on High Frequency Terminal Current Non-conservation and its Physical Implications,” University of California at San Diego Class EE283 Final Project, 2005[41] Trew, R.J.; Yueying Liu; Bilbro, L.; Weiwei Kuang; Vetury, R.; Shealy, J.B.; “Nonlinear source resistance in high-voltage microwave AlGaN/GaN HFETs,” IEEE Transactions on Microwave

Theory and Techniques Volume 54, Issue 5, May 2006 Page(s):2061 - 2067 [42] A. Conway and P. Asbeck, To be published at IEEE 2007 International Microwave Symposium[43] Xu, J.; Gunyan, D.; Iwamoto, M.; Cognata, A.; Root, D.E.; “Measurement-Based Non-Quasi-Static Large-Signal FET Model Using Artificial Neural Networks,” IEEE MTT-S International

Microwave Symposium Digest June 2006 Page(s):469 - 472 [44] D.Root and J. Wood, “Simulator Requirements for Measurement and Simulation-based Black-Box Nonlinear Models,” 2004 IEEE International Microwave Symposium Workshop[45] Xu, J.; Gunyan, D.; Iwamoto, M, Horm, J,, Cognata, A.; Root, D.E.; “Drain-Source Symmetric Artificial Neural Network-Based FET Model with Robust Extrapolation Beyond Training Data,”

IEEE MTT-S International Microwave Symposium Digest June 2007IEEE MTT S International Microwave Symposium Digest June 2007 [46] Li, E.X.; Scheinberg, N.; Stofman, D.; Tompkins, W.; “An independently matched parameter SPICE model for GaAs MESFET's,” IEEE Journal of Solid-State Circuits, Volume 30, Issue

8, Aug. 1995 Page(s):872 - 880 [47] F.Filicori et al “Empirical Modeling of Low-Frequency Dispersive Effects Due to Traps and Thermal Phenomena in III-V FETs,” IEEE Trans. Microwave Theory Tech. Vol 43, No. 12, Dec.,

1995, pp.2972-2981[48] M. Iwamoto et al “Large-signal HBT model with improved collector transit time formulation for GaAs and InP technologies,” in 2003 IEEE MTT-S Int. Microwave Symp. Dig., Philadelphia,

PA, June 2003 pp.635-638[49] M. Iwamoto, D.E. Root, “Large-Signal III-V HBT Model with Improved Collector Transit Time Formulations, Dynamic Self-Heating, and Thermal Coupling,” 2004 International Workshop on

Nonlinear Microwave and Millimeter Wave Integrated Circuits (INMMIC) Rome Nov 2004



Nonlinear Microwave and Millimeter Wave Integrated Circuits (INMMIC), Rome, Nov. 2004[50] Blockley et al 2005 IEEE MTT-S International Microwave Symposium Digest, Long Beach, CA, USA, June 2005.


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

[52] D. E. Root et al “Device Modeling with NVNAs and X-parameters,” IEEE INMMiC Conference, Gotenborg, Sweden, April, 2010

[53] J. Xu et al “Large-signal FET model with multiple time scale dynamics from nonlinear vector network analyzer data,” IEEE MTT-S International Microwave Symposium Digest, May, 2010



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