Analog Behavioral Modeling for High Frequency based on parameter definition (N = number of ports)...
Transcript of Analog Behavioral Modeling for High Frequency based on parameter definition (N = number of ports)...
© Copyright Agilent Technologies 2011
Page 1
David E. RootResearch Fellow
Mihai MarcuSenior Applications Engineer
Agilent Technologies, Inc.
Analog Behavioral Modelingfor High Frequency Components and Systems
Frontiers in Analog Circuits
July 2011
© Copyright Agilent Technologies 2011
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Outline
• Introduction
• Fundamental concepts in behavioral modeling
• Functional block-models– Time domain: nonlinear time-series– Frequency domain: X-parameters– Mixed methods: dynamic X-parameters
• Conclusions
Frontiers in Analog Circuits
July 2011
© Copyright Agilent Technologies 2011
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Behavioral Models and Design Hierarchy
Frontiers in Analog Circuits
July 2011
Equivalent Circuit Model“Compact Model”
Device
Circuit
System
Embedding Variables
( )( ) : ( , , ..., , ..., )ny t i f v v i i
( )v t( )v t( )i t
Multivariate functions for i1, i2 Behavioral Model:
Accurate model of lower level componentfor simulation at next
highest level
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When Are Behavioral Models Needed
• Complex systems– Transistor-level models become too “expensive” (resource-intensive)
• IP-protection is required– Other models reveal the IP
• Other models are simply not available– New technologies, existing HW
Frontiers in Analog Circuits
July 2011
© Copyright Agilent Technologies 2011
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Outline
• Introduction
• Fundamental concepts in behavioral modeling
• Functional block-models– Time domain: nonlinear time-series– Frequency domain: X-parameters– Mixed methods: dynamic X-parameters
• Conclusions
Frontiers in Analog Circuits
July 2011
© Copyright Agilent Technologies 2011
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Some of the Features Needed in Behavioral Models
• … in addition to accurately describing the behavior…
• Cascadability of nonlinear systems arbitrary topology
• Hierarchical modeling
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Some of the Features Needed in Behavioral ModelsCascadability of Models• Predict signals (magnitude and phase), including harmonics
(IMD) through chains of cascaded nonlinear components
• Linear S-parameter theory does not apply– Most previous attempts to generalize are incorrect
(power-dependent S-parameters, hot-S22)
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July 2011
21
Sin(2πf0t)
Freq
Pin
ters
tage
1f0
13f0
12f0
Freq
Pin
f0Freq
Pou
t
2223f02f0f0
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Some of the Features Needed in Behavioral ModelsHierarchical Modeling
• Model the cascade directly, or
• A cascade of many models reduced to one
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July 2011
Dev 1 Dev 2 Dev 1 Dev 2
Mod 1 Mod 2
Mod 1 Mod 2Composite
Model(Higher Level)
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Three Components of Behavioral Modeling
• Model formulation– Time-domain– Frequency-domain– Time-frequency-domain
• Experiment design– Stimulus to excite relevant dynamics
• Model identification– Procedure to determine model parameters
• Briefly reviewed using S-parameters
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July 2011
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S-ParametersPhysical Interpretation
• Based on the traveling waves concept
• A 2-port example (extendable to arbitrary N-port)
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July 2011
Incident Transmitted
Transmitted Incident
DUT
Port 1 Port 2
1 11 1 12 2
2 21 1 22 2
b S a S ab S a S a
11 1S a1b
1a
2a
2b
12 2S a
21 1S a
22 2S a
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S-Parameter Behavioral Model
• Model formulation – frequency domain
• Experiment design– One tone, low-power stimulus applied successively at each port
• Model identification:– based on parameter definition (N = number of ports)
Frontiers in Analog Circuits
July 2011
1 11 1 12 2
2 21 1 22 2
b S a S ab S a S a
0
, , 1,k
iij
ajk j
bS i j Na
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Model Formulation
• Time-domain - nonlinear ODEs– NLTS (Non-Linear Time Series)– Transient simulation and all other simulators
• Frequency-domain - nonlinear spectral map– X-parameters– Harmonic-Balance simulation
• Time-frequency-domain – ODE-coupled envelopes– X-parameters with memory effects dynamic X-parameters– Envelope simulation
• Formulate model-equations in forms native to simulatorFrontiers in Analog Circuits
July 2011
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Model FormulationTime-Domain
• Natural for strongly nonlinear low-order (lumped) systems
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July 2011
( ) , , , , ,I t F V t V t V t I t
time time
StimulusResponse
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Model FormulationFrequency-Domain
• Natural for low distortion (sparse spectrum) & high-frequency
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July 2011
,...),,( 321 AAAFB kk
frequency frequency
A1
A2A3 A4
B1
B2B3 B4
B5B6B0
Stimulus (multiple harmonics)Response
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Experiment Design
• Design the experiment such that it exercises the relevant states and dynamics of the system
• Can be achieved in both “worlds”:– Simulation– Measurement
• Conceptually the same (in measurement versus simulation), but… different challenges
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July 2011
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Experiment DesignSimulation
• Exercise all required states and dynamics
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July 2011
System Under Test
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Experiment DesignMeasurement
• Exercise the HW on all required states and dynamics
• Calibrated magnitude and phase for all harmonics/IMD
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July 2011
Magnitude and Phase Data Acquisition
RFIC
A1k B1l B2m A2nReferenceplanes
New phase calibration standard
NVNA
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Nonlinear Vector Network Analyzer (NVNA)combine with previous page• Based on the PNA-X platform
• Measures magnitude and phase of relevant frequency components
• Essential nonlinear measurements for nonlinear models (like NLTS and X-parameters)
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July 2011
PNA-XNetwork Analyzer
+
Phase Reference
+
Meas. Science Algorithms & Software
= NVNA
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Nonlinear Vector Network Analyzer (NVNA)Waveforms and Complex Spectra Measurements
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July 2011
pkBpkA
Port IndexHarmonic Index
2 kA1kA
1kB 2kB
1I 2I
time time
© Copyright Agilent Technologies 2011
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Outline
• Introduction
• Fundamental concepts in behavioral modeling
• Functional block-models– Time domain: nonlinear time-series– Frequency domain: X-parameters– Mixed methods: dynamic X-parameters
• Conclusions
Frontiers in Analog Circuits
July 2011
© Copyright Agilent Technologies 2011
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Dynamical Systems and State-Space
• The dynamics of the nonlinear system can be assumed to be described by a system of nonlinear ODEs
• The sampled solution of the ODE, y(t), is a time-series
• The solution of the dynamical equations for state variables, u(t) is a time-parameterized trajectory in the State-Space
Frontiers in Analog Circuits
July 2011
( ) ( 1) ( )( ) ( ,... , , ,... )n n my t f y y x x x
( ) ( ), ( ) vector of state equ
( ) (
ation
), ( ) sca
s
lar outputy t h u t
u t f u t x t
x t
© Copyright Agilent Technologies 2011
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State-Space and Time-Series
• The multi-dimensional space spanned by the state variables is known as the state-space
• Any measureable output is a projection of this trajectory versus time and it is a time-series
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July 2011
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Model Identification for NLTS
• Stimulate system– Sufficiently complex stimulus
• Embed– Create auxiliary variables to represent the waveform
• Sample data– Data directly or the envelope– Difficult if multiple time-scales
• Fit– Approximate nonlinear function f(.)
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July 2011
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Excitation Design
• Stimulate all relevant (observable) dynamics
• Sweep power and frequency to “cover the state-space”
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July 2011
‘Two-tone’
f1 f1+ff1 f1+f
f1+f
‘Three-tone’
f1+f?
‘Modulation’ (CDMA)
f1f1+f
f2
fn
‘Multi-tone’ or ‘Multi-sine’
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Embedding
• Building-up state-space to define ODE
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July 2011
i(t)
v(t)
A
Bi(t)
v(t)
i(t)
v(t)
A
B
i(t)
v(t)
v’(t)
B
A
i(t)
v(t)
v (t)
B
A( ) ( ( ))i t i v t ( ) ( ( ), ( ))i t i v t v t
X(t) Y(t)
( )
( )
( ) [ ( ), ( ),..., ( )]( ) [ ( ), ( ),..., ( )]
m
n
x t x t x t x ty t y t y t y t
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Sample Data
• Dense enough in all dimensions
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July 2011
X(t) Y(t)
( ) ( )1 1 1 1 1 1
( ) ( )2 2 2 2 2 2
( ) ( )
( ) ( ) ( ) ( ) ( ) ( )( ) ( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( ) ( )
m n
m n
m np p p p p p
x t x t x t y t y t y tx t x t x t y t y t y t
x t x t x t y t y t y t
nth order derivativeStimulus Response
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Function Fit
• For nth derivative of the output
• Many function-types may be used– Polynomials– Radial basis functions– Look-up tables– …– ANNs
• Artificial neural networks (ANNs) a very good option
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July 2011
( ) ( 1) ( )( ,... , , ,... )n n my f y y x x x
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Function FitArtificial Neural Networks (ANNs)
• An ANN is a parallel processor made up of simple, interconnected processing units, called neurons, with weighted connections
Frontiers in Analog Circuits
July 2011
baxwsvxxFI
i
K
kikkiiK
1 11 ),...,(
sigmoidweights biases
x1
...
xk
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Function Fit ANN General Properties
• Fit any nonlinear function of any number of variables (universal approximation theorem)
• Infinitely differentiable better distortion than naïve splines or low-order polynomials
• Easy to train (fit) using standard tools
• Easy to train on scattered data
Frontiers in Analog Circuits
July 2011
baxwsvxxFI
i
K
kikkiiK
1 11 ),...,(
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Function FitANN Training
• wki,ak,b – obtained by training
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July 2011
fANN
…
… …
,ki kw aweightsbiases
y(n-1)(t) y(n-2)(t) … y(t) x(n)(t) x(n-1)(t) … x(t)
y(n)(t)
( ) ( 1) ( 2) ( ) ( 1)( ) , ,..., , , ,...,n n n n nANNy t f y t y t y t x t x t x t
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Model ImplementationAn Example
• ODE in circuit simulator
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July 2011
xx x(1)
+-
x(m-1) x(m)+- f vn
+-
x(1) x(2)+-
yv2v1
+-
v2v3
+-
vn-1vn
+-
( ) ( 1) ( ), , , , ,n n my f y x x x
2
1
( )1
1 2
1
, , , , , , ,n
n n
n
mnv f v v v
v yv v
v v
x x x
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NLTS – ExampleGaAs HBT MMIC
• Agilent HMMC 5200– Series-shunt amplifier– Gain: 9.5 dB @ 1.5 GHz
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July 2011
Actual Circuit Detailed circuit model
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NLTS Accuracy and SpeedSingle-Tone Stimulus
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July 2011
-20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4-22 6
0
20
40
60
80
100
120
140
160
-20
180
dBm(In_model[::,1],z1[::,1])
ph
ase
(Ou
t_m
od
el[:
:,1
])
dBm(In_IC[::,1],z1ic[::,1])
ph
ase
(Ou
t_IC
[::,
1])
Fundamental Phase
Time psec0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.80.0 2.0
2.0
2.5
3.0
3.5
4.0
1.5
4.5
0 200
1.5
2.0
2.5
3.0
3.5
4.0
1.0
4.5
Time psecTime Domain Waveforms
229.68 seconds
11315.67 seconds
-20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4-22 6
7
8
9
10
11
12
13
6
14
dbm(In_model[::,1],z1[::,1])
dB
m(O
ut_
mo
de
l[::,
1],
z2[:
:,1
])-d
Bm
(In
_m
od
el[:
:,1
],z1
[::,
1])
dbm(In_IC[::,1],z1ic[::,1])
dB
m(O
ut_
IC[:
:,1
],z2
ic[:
:,1
])-d
Bm
(In
_IC
[::,
1],
z1ic
[::,
1])
Fundamental Gain
6
14
-22 6
dBm
dBm
180
-20
1 - 19 GHz
(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
19 neurons
-22 6dBm
NLTS modelCkt model
© Copyright Agilent Technologies 2011
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WCDMA Lower ACLR Comparison:Circuit Co-Sim vs. NLTSA Model vs. Measured
0
10
20
30
40
50
60
70-15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3
Input Power (dBm)
AC
LR (d
B
Circuit Co-Sim 5MHz Lower
NLTSA Model 5 MHz Lower
Circuit Co-Sim 10 MHz Lower
NLTSA Model 10 MHz Lower
Measured Data 5 MHz Lower
Measured Data 10 MHz Lower
NLTS Accuracy and SpeedResults 3GPP WCDMA Lower ACLR
Frontiers in Analog Circuits
July 2011
294 sec/pt NLTS
1532 sec/pt Ckt.
Measured
Model: - 40 neurons, cascadable
- generated from sinusoidal signals only
- works in Transient, HB, Envelope
Simulation: 3 GHz (courtesy Greg Jue)Measured: 2.4 GHz
© Copyright Agilent Technologies 2011
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Outline
• Introduction
• Fundamental concepts in behavioral modeling
• Functional block-models– Time domain: nonlinear time-series– Frequency domain: X-parameters– Mixed methods: dynamic X-parameters
• Conclusions
Frontiers in Analog Circuits
July 2011
© Copyright Agilent Technologies 2011
Page 36
X-Parameters
• Similar to S-parameters, but for nonlinear behavior
• The mathematically correct superset of S-parameters
• Applicable to:– Both large- and small-signal– Both linear and nonlinear systems
• All pieces of the puzzle work together:– Measure– Model– Simulate
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July 2011
© Copyright Agilent Technologies 2011
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X-Parameters
• Cascadable models – correctly account for mismatch
• Model identification from a simple set of measurements
• Very accurate
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July 2011
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X-ParametersFundamental Concepts
• Spectral map of complex large input phasors to large complex output phasors
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July 2011
2A1A
1B 2B1 1 11 12 21 22
2 2 11 12 21 22
( , , , ..., , , ...)( , , , ..., , , ...)
k k
k k
B F D C A A A AB F D C A A A A
Port Index Harmonic Index
© Copyright Agilent Technologies 2011
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X-Parameters for Multi-Harmonic StimulusHarmonics Are Large-Signals
• Response is a nonlinear function of stimulus
• Behavior can be described by X-parameters
• Phase-coefficient comes from time-invariance:– Output of delayed input is the delayed output
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July 2011
, , 11 12 21 22, , , . , ,p k p kB F D C A A A A
( )
( ), ,
1,1 1, 2,
1,1 1, 2,
, 1, , , , 2, , , 1,
, 1, , , , 2, , , 1,
1, , 1,
k kq k k
k kq k k
FDCRp p
FB kp k p k
DCR X
B
DCS q N A A P k K A P k K
DCS q N A A P k K A P k K
p N k K
X P
1,1 j phase AP e
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• If all stimuli are small except for the fundamental simplify the general nonlinear spectral mapping by spectral linearization
• X(S) and X(T) terms synthetic load-pull
X-Parameters for Single-Tone StimulusHarmonics Are Small-Signals
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July 2011
( )1,1 ,, ; ,
11
, 1
( ), 1,1.
( ) *1,1 ,, ; ,
11
, 1 1,1 ,
q Nl K
S k lq lp k q l
ql
q
FB kp k p k
q Nl K
T k lq lp k q
l
lql
q l
X A P AB X A P X A P A
Mismatch terms linear in Aq,l
Perfectly matched response
Mismatch terms linear in A*q,l
© Copyright Agilent Technologies 2011
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Practical Applications of X-Parameters
• Black-box description holds for arbitrary systems (amplifiers, mixers, receivers, transmitters, etc.)
• Supports multi-variable swept conditions:– bias– RF-power– frequency– load-pull– additional user-defined variables
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July 2011
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Single-Tone Amplifier
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July 2011
CktXpar
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Mismatch Effects in a Nonlinear Cascade
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July 2011
CascadedX-parameter models
Cascaded PA circuits
Mismatch
Mismatch
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Mismatch Effects in a Nonlinear CascadeResults
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July 2011
Fundamental
2nd Harmonic
3rd Harmonic
Overlaid Results
Model (Red)Vs.
Circuit (Blue)
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Systems with Frequency ConversionMixer (2-Tone: RF, LO)
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July 2011
1.0E9
2.0E9
3.0E9
4.0E9
5.0E9
6.0E9
7.0E9
8.0E9
9.0E9
1.0E10
0.0
1.1E10
-160
-140
-120
-100
-80
-60
-40
-180
-20
freq, Hz
dB
m(v
ou
t_ck
t)
m3
freq+(0.05 GHz)
dB
m(v
ou
t_m
dl)
m4
m3indep(m3)=plot_vs(dBm(vout_ckt), freq)=-38.914
2.500E8
m4indep(m4)=plot_vs(dBm(vout_mdl), freq+(0.05 GHz))=-38.914
3.000E8
1.0E9
2.0E9
3.0E9
4.0E9
5.0E9
6.0E9
7.0E9
8.0E9
9.0E9
1.0E10
0.0
1.1E10
-150
-100
-50
0
50
100
150
-200
200
freq, Hz
ph
ase
(vo
ut_
ckt)
m1
freq+(0.05 GHz)
ph
ase
(vo
ut_
md
l)
m2
m1indep(m1)=plot_vs(phase(vout_ckt), freq)=-50.105
2.500E8
m2indep(m2)=plot_vs(phase(vout_mdl), freq+(0.05 GHz))=-50.105
3.000E8
CktXpar
v out_mdlv out_ckt
HarmonicBalanceHB1
Order[2]=5Order[1]=5Freq[2]=2 GHzFreq[1]=1.75 GHzMaxOrder=5
HARMONIC BALANCE
P_1TonePORT3
Freq=2 GHzP=polar(dbmtow(-50),0)Z=50 OhmNum=3 P_1Tone
PORT4
Freq=1.75 GHzP=polar(dbmtow(-5),0)Z=50 OhmNum=4
V_DCSRC2Vdc=5 V
X4PXNP1File="a0_Mixer.ds"
4
1 2
3 Ref
RR2R=50 Ohm
RR1R=50 Ohm
P_1TonePORT1
Freq=2 GHzP=polar(dbmtow(-50),0)Z=50 OhmNum=1 P_1Tone
PORT2
Freq=1.75 GHzP=polar(dbmtow(-5),0)Z=50 OhmNum=2
V_DCSRC1Vdc=5 V
x_2_GilCellMixX1
IF_portRF_port
LO_port
Bias_port
© Copyright Agilent Technologies 2011
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Systems with Frequency Conversion Mixer Sub-System - Spectrum Measurement Setup
• RFpwr = -50
• LOpwr = -5 dBm
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July 2011
v out_mdl
v out_ckt
X4PXNP1File="d0_MixerBPF.ds"
4
1 2
3 Ref
RR2R=50 Ohm
RR1R=50 Ohm
BPF_Cheby shevBPF1
N=15Ripple=0.5 dBBWpass=100 MHzFcenter=250 MHz
V_DCSRC2Vdc=5 V
HarmonicBalanceHB1
Order[2]=5Order[1]=5Freq[2]=2 GHzFreq[1]=1.75 GHzMaxOrder=5
HARMONIC BALANCE
P_1TonePORT1
Freq=2 GHzP=polar(dbmtow(-50),0)Z=50 OhmNum=1 P_1Tone
PORT2
Freq=1.75 GHzP=polar(dbmtow(-5),0)Z=50 OhmNum=2
V_DCSRC1Vdc=5 V
x_2_GilCellMixX1
IF_portRF_port
LO_port
Bias_port
P_1TonePORT4
Freq=1.75 GHzP=polar(dbmtow(-5),0)Z=50 OhmNum=4
P_1TonePORT3
Freq=2 GHzP=polar(dbmtow(-50),0)Z=50 OhmNum=3
© Copyright Agilent Technologies 2011
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Systems with Frequency ConversionMixer Sub-System – Results: Output Spectrum
• small intentional display offset – to distinguish traces
Frontiers in Analog Circuits
July 2011
1.0E9
2.0E9
3.0E9
4.0E9
5.0E9
6.0E9
7.0E9
8.0E9
9.0E9
1.0E10
0.0
1.1E10
-800
-600
-400
-200
-1000
0
freq, Hz
dB
m(v
ou
t_ck
t)
freq+(0.05 GHz)
dB
m(v
ou
t_m
dl)
1.0E9
2.0E9
3.0E9
4.0E9
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0.0
1.1E10
-100
0
100
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200
freq, Hz
ph
ase
(vo
ut_
ckt)
freq+(0.05 GHz)
ph
ase
(vo
ut_
md
l)
Mag
Phase
CktXpar
© Copyright Agilent Technologies 2011
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Amplifier Load-Pull
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July 2011
Pd
el_
ckt_
con
tou
rs_
pP
de
l_m
dl_
con
tou
rs_
p
Pdel_dBm
PA
E_
ckt_
con
tou
rs_
pP
AE
_m
dl_
con
tou
rs_
p
PAE
PA
E_
ckt_
con
tou
rs_
pP
AE
_m
dl_
con
tou
rs_
p
PAE
Pd
el_
ckt_
con
tou
rs_
pP
de
l_m
dl_
con
tou
rs_
p
Pdel_dBm
CktXpar
50 Ω X-parameters
Load-dependent X-parameters
-18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4-20 6
0
5
10
15
-5
20
Power in (dBm)
Pow
er o
ut (
dBm
)
© Copyright Agilent Technologies 2011
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Load-Dependent Waveforms27 Ω Validation of Measurement-Based 50 Ω Model
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July 2011
v1
100 200 300 400 500 6000 700
-0.5
0.0
0.5
-1.0
1.0
time, psec
v2
100 200 300 400 500 6000 700
-1.0
-0.5
0.0
0.5
-1.5
1.0
time, psec
100 200 300 400 500 6000 700
-0.005
0.000
0.005
-0.010
0.010
time, psec
i1
100 200 300 400 500 6000 700
-0.02
0.00
0.02
0.04
-0.04
0.05
time, psec
i2
Measurement-Based X-parameter Model Independent NVNA Data
© Copyright Agilent Technologies 2011
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Rough Comparison of Methods and Applicability
NLTS• Works in TA, HB, Envelope
• Excellent for strongly nonlinear, but lumped (low-order ODE) systems
• Training non-algorithmic
• Experiment design not fully solved
• Not as robust for convergence
• Scales well with complexity
• Great gains in simulation speed
X-Parameters• Frequency-domain natural for highly
nonlinear, distributed, broad-band circuits
• Experiment design completely solved
• Highly automated model identification
• Works in HB and Envelope
• Very robust for convergence
• Always accurate if sampled densely
• Complexity increases rapidly for multiple tones
Frontiers in Analog Circuits
July 2011
© Copyright Agilent Technologies 2011
Page 51
Outline
• Introduction
• Fundamental concepts in behavioral modeling
• Functional block-models– Time domain: nonlinear time-series– Frequency domain: X-parameters– Mixed methods: dynamic X-parameters
• Conclusions
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July 2011
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Why Mixed-Methods
• Applies to systems under large-signal modulated drive
• Long-term memory effects are present
• Time-varying spectra for all inputs, outputs and state-variables
• Perfectly suited for Envelope simulations
• Well matched for data from NVNA
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July 2011
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Envelope Domain for Long-Term Memory
• Xh(t) – a set of time-varying complex-waveforms (amplitude and phase) at each harmonic-index, h
• Modeling problem: map input envelopes to output envelopes
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July 2011
Freq. (GHz)1 2 3 4DC
Time-varying spectrum
02
0
( ) Re ( )H
j h f th
h
x t X t e
B2[1](t) – time-domain envelope
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Merging Frequency and Time Domains
• The static spectral mapping becomes a differential equation in envelope domain
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July 2011
11 12 21 22( , , ..., , , ...)pk pkB f A A A A
1 1 110 10 11 11 20 21 2,..., , , ,..., , ,..., ,..., ,...,n m
pk pk pk pk kB f B t B t A t A t A t A t A t A t A t
Envelope index
Order of time derivative
21 21 20 11
22011 21
,
,
B t f B t A t
dB tg A t B t
dt
Example:
Port index
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Envelope Model: Amplifier with Self-Heating
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July 2011
Pulsed RF signal at 1GHz: Thermal Time Const. 10usec
10 20 30 400 50
0.1
0.2
0.3
0.0
0.4
Fundamental Input
time, usec time, usec10 20 30 400 50
1
2
3
0
4
Fundamental Output
10 20 30 400 50
0.01
0.02
0.03
0.00
0.04
10
20
30
0
40
Third Harmonic Output Mag & Phase
time, usec
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Frontiers in Analog Circuits
July 2011
Dynamic X-parameterPNA-X NVNA
Dynamic Compression Characteristic
Out
put (
Vp)
Input (Vp)
Dynamic X-Parameters - Memory Effects [12]
Power Sweep @ 19.2 kHz Tone Spacing
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Conclusions
• Time, frequency and mixed domain methods:– NLTS could become practical soon– X-parameters are mature, both measurement and simulation– Dynamic X-parameters proven for memory
• Commercial availability– NVNA – based on PNA-X HW platform– X-parameters available in circuit and system simulators (ADS, Genesys,
SystemVue)
• Great opportunities for applications– Specifications of active components by X-parameters– Better understanding of nonlinear behavior new design practices– Nonlinear stability, matching, etc.
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© Copyright Agilent Technologies 2011
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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 Microwave Theory and Techniques, Vol. 52, Issue 9, Part 2, Sept. 2004 pp. 2274-2284
[2] D. E. Root, J. Wood, and N. Tufillaro, “New Techniques for Non-Linear Behavioral Modeling of Microwave/RF ICs from Simulation and Nonlinear Microwave Measurements,” in 40th ACM/IEEE Design Automation Conference Proceedings, Anaheim, CA, USA, June 2003, pp. 85-90 (videotaped)
[3] D. E. Root, “Nonlinear Analog Behavioral Modeling of Microwave Devices and Circuits,” IEEE Microwave Theory and Techniques Distinguished Microwave Lecture (now available from MTT-S Speaker’s Bureau)
[4] Agilent HMMC-5200 DC-20 GHz HBT Series-Shunt Amplifier, Data Sheet, August 2002.
[5] 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.
[6] 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
[7] J. Wood, D. E. Root, editors, Fundamentals of Nonlinear Behavioral Modeling for RF and Microwave Design, 1st ed. Norwood, MA, USA, Artech House, 2005.
[8] D. E. Root, D. Sharrit, J. Verspecht, “Nonlinear Behavioral Models with Memory: Formulation, Identification, and Implementation,” 2006 IEEE MTT-S International Microwave Symposium Workshop (WSL) on Memory Effects in Power Amplifiers
[9] Blockley et al 2005 IEEE MTT-S International Microwave Symposium Digest, Long Beach, CA, USA, June 2005.
[10] Soury et al 2005 IEEE International Microwave Symposium Digest pp. 975-978
[11] J. Verspecht and D. E. Root, “Poly-Harmonic Distortion Modeling,” in IEEE Microwave Theory and Techniques Microwave Magazine, June, 2006.
[12] J. Verspecht, J. Horn, L. Betts, D. Gunyan, R. Pollard, C. Gillease, and D. E. Root, “Extension of X-parameters to include long-term dynamic memory effects,” IEEE MTT-S International Microwave Symposium Digest, 2009. pp 741-744, June, 2009
[13] J. Horn, L. Betts, C. Gillease, D. Gunyan, J. Xu, J. Verspecht, and D. E. Root, “X-Parameters: Extending S-parameters for Measurement, Modeling, and Simulation of Nonlinear Components,” 2008 IEEE Power Amplifier Symposium, Orlando, FL
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July 2011