Nonlinearity
characterization and
modelling
Giovanni Ghione
Dipartimento di Elettronica
Politecnico di Torino
Microwave & RF electronics group
NEWCOM WPR3 Meeting – 6/9/04
Agenda
 A glimpse on nonlinear models
 Physics-based device-level models
 Equivalent circuit & black-box device-level models
 Vintage behavioral models: power series, Volterra,
envelope
 Advanced models: time-domain, frequency-domain,
envelope
 Characterization techniques (mainly loadpull…)
 Aknowledgements
NEWCOM WPR3 Meeting – 6/9/04
Device models: from physical to behavioral
NEWCOM WPR3 Meeting – 6/9/04
From: D.Root et al.,
IMS2004 WME-4
Physics-based nonlinear modeling
Based on the solution of transport + Poisson
equations on device volume
Mainly single-device, mixed-mode intensive
Often time-domain, Harmonic Balance LS
simulation demonstrated but demanding (>10000
unknowns) order reduction techniques?
Potentially accurate, but NL operation can be a
numerical killer (breakdown, direct junction
conduction…)
NEWCOM WPR3 Meeting – 6/9/04
Example: LDMOS PA simulation
From: Troyanovsky et al, SISPAD 1997
NEWCOM WPR3 Meeting – 6/9/04
Circuit-oriented NL modelling
 Equivalent circuit NL models:
 Extensions of DC + small signal models with NL components
 Ad hoc topologies for device classes: BJT, HBT, MESFETs,
HEMTs, MOS, LDMOS…
 Almost endless variety of topologies and component models
from the shelf, many models proprietary
 Empirical, semi-empirical, physics-based analytical
varieties.
 Pros: numerically efficient, accurate enough for a given
technology after much effort and tweaking
 Cons: not a general-purpose strategy, low-frequency
dispersion (memory) effect modelling difficult
NEWCOM WPR3 Meeting – 6/9/04
NL equivalent circuit examples
Bipolar:
BJT: Ebers-Moll, Gummel-Poon
HBT: Modified GP, MEXTRAM…
FET:
MOS: SPICE models, BSIM models…
MESFET: Curtice, Statz, Materka, TOM…
HEMT: Chalmers, COBRA…
NEWCOM WPR3 Meeting – 6/9/04
Example: the Curtice MESFET model
NEWCOM WPR3 Meeting – 6/9/04
Example: the HBT MEXTRAM model
NEWCOM WPR3 Meeting – 6/9/04
Black-box device-level modelling
Black-box models for circuit NL components:
Look-up-table, interpolatory (e.g. Root)
Static Neural Network based
Global black-box (“grey-box”) device-level (?):
The Nonlinear Integral Model (University of
Bologna)  based on dynamic Volterra expansion +
parasitic extraction
Potentially accurate, but computationally
intensive
NEWCOM WPR3 Meeting – 6/9/04
Non-quasi static effects
Device level: low-frequency dispersion due to:
Trapping effects, surfaces, interfaces
Thermal effects
Amplifier level:
Bias effect (lowpass behavior of bias tees)
Thermal effect
Impact on device modelling  pulsed DC and SS
measurements
NEWCOM WPR3 Meeting – 6/9/04
Pulsed IV characteristics
Investigation of the device behaviour outside the
SOA region
Pulsed measurement for exploiting thermal and
traps effects
Different QP with the same dissipated power
Point out flaws of the fabbrication processes (e.g.
passivation faults, uncompensated deep traps)
Allow the identification of the dispersive model
contributions
NEWCOM WPR3 Meeting – 6/9/04
Pulsed IV: FET example
NEWCOM WPR3 Meeting – 6/9/04
System-level (behavioral) NL models
Classical & textbook results:
Power and Volterra series (wideband) models,
frequency or time-domain
Envelope (narrowband) static models  descriptive
function
A sampler of more innovative techniques:
Dynamic time-domain models
Dynamic neural network models
Dynamic f-domain models  scattering functions
Advanced envelope models
NEWCOM WPR3 Meeting – 6/9/04
Recalling a few basics
PA single-tone test
PA two-tone test
PA modulated signal test
Intermodulation products, ACPR…
NEWCOM WPR3 Meeting – 6/9/04
Single-tone PA test
PA
3rd harmonics
output intercept
1 dB compression
point
Output
saturation
power
NEWCOM WPR3 Meeting – 6/9/04
Two-tone PA test
 Rationale: two-tone operation “simulates” narrowband
operation on a continuous band f1 - f2
PA
CIM
3
NEWCOM WPR3 Meeting – 6/9/04
Two-tone Pin-Pout
IMP3 Input
Intercept Point, IIP3
IMP3 Output
Intercept Point
OIP3
1 dB
Pout(f0), dBm
IMP3, dBm
Pin1=Pin2, dBm
NEWCOM WPR3 Meeting – 6/9/04
Modulated signal test & ACPR
Power spectral density - dBm/Hz
0
Adj. channel
-20
Main channel Adj. channel
Output
signal
Spectral
regrowth
-40
Input
signal
-60
-80
fc-60 kHz
fc-30 kHz
NEWCOM WPR3 Meeting – 6/9/04
fc
fc+30 kHz
fc+60 kHz
Class AABC two-tone test
NEWCOM WPR3 Meeting – 6/9/04
Fager et al, IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 39, NO. 1,
JANUARY 2004, p. 24
Power series (PS) model
 Strictly speaking an IO model for a memoryless NL
system, often cascaded with a linear system with
memory:
U ( )  H ( ) S ( )
s(t)
NEWCOM WPR3 Meeting – 6/9/04
Linear
system
with memory
u(t)
Nonlinear
system
without memory
w(t)
Active device PS cascading
Rg
LG
RG
VDD
VGG
+
iD = f(v*)
v*
eg(t)
RL
CGS
s(t)
u(t)
w(t)
FET transfer
curve
NEWCOM WPR3 Meeting – 6/9/04
PS output with multi-tone excitation
 Assume a multi-tone frequency-domain excitation:
 Output:
NEWCOM WPR3 Meeting – 6/9/04
Single- and two-tone PS test
The PS approach correctly yields the small-signal
harmonic and IMPn slope in small-signal, class
A operation
It also gives an estimate of gain compression
The two-tone output with equal tone power
yields:
Same IMPn power for right & left-hand side lines
IMPn power independent on line spacing ( can be
artificially introduced through H)
NEWCOM WPR3 Meeting – 6/9/04
Single- and two-tone gain compression
 The 2-tone (modulated signal) Pin-Pout is not exactly
the same as the single-tone
 While the AM-AM curve is different, the AM-PM is
almost the same (Leke & Kenney, MTT-S 96, TH2B-8)
 Can be shown already with a PS model, assume:
y b 0 b 1 x b 2 x 2 b 3 x 3
 then the output power is:
 Single-tone
P 0 b 21 P in 3. 0b 1 b 3 P 2in 2. 25b 23 P 3in
 Two-tone
P 1 b 21 P in 4. 5b 1 b 3 P 2in 5. 0625b 23 P 3in
 Two-tone with IMP3 P 2 b 21 P in 4. 5b 1 b 3 P 2in 5. 625b 23 P 3in
NEWCOM WPR3 Meeting – 6/9/04
Example
48
Single-tone test
Two-tone test
Two-tone including IMP3
46
44
Output power, dBm
42
40
38
36
34
b =10, b =-1
1
32
3
30
28
10
12
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14
16
18
20
22
Input power, dBm
24
26
28
30
Volterra series approach
 In frequency domain, generalization of the PS approach:
an Q Q
y (t )   n  
n 1 2 q1  Q q2  Q
N
 H n (q1 , q2 ,
Q

qn  Q
X q1
q )e
X qn 
j (q1 q2  qn ) t
n
 Exact representation, but unsuited to true LS regime or
strongly NL system due to the difficulty of characterizing
high-order kernels
 The time-domain version is a generalization of the
impulse response
NEWCOM WPR3 Meeting – 6/9/04
Envelope modeling
 The PS and Volterra models are general and wideband, i.e.
they hold for any excitation  often in analog RF system the
excitation is DC + a narrowband modulated signal
 (Complex) envelope representation of input and output
signals, envelope slowly varying vs. carrier:
x(t )  Re  x(t ) exp( jct )  x(t ) cos ct  x(t ) 
y (t )  Re  y (t ) exp( jct )  y (t ) cos ct  y (t ) 
 Static envelope model (G complex “descriptive function”):
y (t )  G  x(t )  x(t )
NEWCOM WPR3 Meeting – 6/9/04
AM/AM and AM/PM distortion curves
110
14
108
12
106
G
104
102
8
100
6
98
4
96
2
-20
94
-15
10
5
0
-5
-10
Available input power, dBm
NEWCOM WPR3 Meeting – 6/9/04
15
20
arg  G 
10
Static envelope models features
 No information on harmonics and out-of-band spurs 
bandpass filtering implied, unsuited for circuit-level
modeling
 G can be identified from single-tone measurements but
better fitted on two-tone measurements (see caveat on
fitting function  Loyka IEEE Trans. VT49, p.1982)
 IM3 intrinsically symmetrical and independent on tone
spacing  no memory (non quasi-static) effects modeled
 Poor ACPR modeling in many realistic cases,
performances deteriorate increasing channel bandwidth
NEWCOM WPR3 Meeting – 6/9/04
Some “novel” approaches
 Modeling strategies have ups and downs in time, the last
not necessarily the best one
 Recent trends:
 Revival on dynamic state-variable black-box (behavioral)
models based on general system identification techniques
 Steady interest and progress in neural network models
 Progress in exploiting multi-frequency NL measurement
tools
 Search for better system-level envelope models, also on the
basis of classical methods revisited and revamped (e.g.
Volterra)
NEWCOM WPR3 Meeting – 6/9/04
Nonlinear Time Series (NTS) model
 Idea: identify a standard state-variable model on the
basis of measured input and output time series [Root et
al., Agilent]:
State equation x  f ( x, u )
Output equation y  g ( x, u )
"Feedback" model
y  f ( y, y, y,..., u, u, u...)
NEWCOM WPR3 Meeting – 6/9/04
Model identification: how?
 NL model identification amounts to a nonlinear inverse scattering
problem
 Several theoretical methods available from dynamic system theory
(Whitney embedding theorem, Takens’ theorem) which allow in
principle to identify f as a smooth function
 Once f is identified, the implementation in commercial simulators
is straightforward
 Problems:




system identification in the presence of noisy data
identification when the state space is large
building suitable sets of I/O data
providing a suitable numerical approximation to f
 See D.Root et al, IMS2003, paper WE2B-2 and references
NEWCOM WPR3 Meeting – 6/9/04
Dynamic Neural Network (DNN) model
 Neural networks can provide an alternative to identify
the NL dynamical system
 In DNNs (see Ku et al, MTT Trans. Dec. 2002, p. 2769)
the NN is trained with data sequences including the
input / output and their time derivatives
 Once trained the NN defines a “feedback” dynamic
model and simply “is” the dynamic system
 Very promising technique in terms of accuracy, CPU
effectiveness and generality; easy implementation in
circuit simulators.
NEWCOM WPR3 Meeting – 6/9/04
DNN result example
NEWCOM WPR3 Meeting – 6/9/04
F-domain dynamic behavioral models
 The availability of Large-signal Network Analyzers (LSNA) have
fostered the development of generalizations of the scattering
parameter approach:
NEWCOM WPR3 Meeting – 6/9/04
Describing (scattering) functions
 NL relationship between power wave harmonics in LS
steady state (ij port & harmonics index) [Verspecht,
IMS2003]:
NEWCOM WPR3 Meeting – 6/9/04
Relationship with S parameters
 Describing functions reduce to multifrequency Sparameters for a linear device (lowercase used for PW):
b 11 F 11 
a 11 , a 21 ,  a 1N , a 2N 
b 11 S 11 
1 a 11 S 12 1 a 21
b 21 F 21 
a 11 , a 21 ,  a 1N , a 2N 
b 21 S 21 
1 a 11 S 22 1 a 21


b 1N F 1N 
a 11 , a 21 ,  a 1N , a 2N 
b 1N S 11 
N a 1N S 12 N a 2N
b 2N F 2N 
a 11 , a 21 ,  a 1N , a 2N 
b 2N S 21 
N a 1N S 22 N a 2N
 however, simplifications can be made (scattering
functions model) if a11 is the only “large” component 
superposition can be applied to the other terms.
NEWCOM WPR3 Meeting – 6/9/04
Frequency superposition
a Nj,k a Nj,k exp
ik arg
a 1,1 

Normalization:
b Nj,k b Nj,k exp
ik arg
a 1,1 

a N1,1 |a 1,1 |
NEWCOM WPR3 Meeting – 6/9/04
Scattering function model
 Introducing phase normalized variables one has the
relationship [Verspecht, IMS2003]:
b N1,1 S 11,11 
a N1,1 
a N1,1 S 12,11 
a N1,1 
a N2,1 S 
a N1,1 
a N
a N1,1 
a Nj,k S 
a N1,1 
a N
12,11 
2,1  S 1j,1k 
1j,1k 
j,k
j1,2
k1
b N2,1 S 21,11 
a N1,1 
a N1,1 S 22,11 
a N1,1 
a N2,1 S 
a N1,1 
a N
a N1,1 
a Nj,k S 
a N1,1 
a N
22,11 
2,1  S 2j,1k 
2j,1k 
j,k
j1,2
k1

b N1,N S 11,N1 
a N1,1 
a N1,1 S 12,N1 
a N1,1 
a N2,1 S 
a N1,1 
a N
a N1,1 
a Nj,k S 
a N1,1 
a N
12,N1 
2,1  S 1j,Nk 
1j,Nk 
j,k
j1,2
k1
b N2,N S 21,N1 
a N1,1 
a N1,1 S 22,N1 
a N1,1 
a N2,1 S 
a N1,1 
a N
a N1,1 
a Nj,k S 
a N1,1 
a N
22,N1 
2,1  S 2j,Nk 
2j,Nk 
j,k
j1,2
k1
NEWCOM WPR3 Meeting – 6/9/04
Scattering functions features
Also called large-signal scattering parameters
Directly measurable through a VNA
Effective in providing a model for a HB
environment and for strongly nonlinear
components
Can be used at a circuit level, providing
interaction with higher harmonics; not an
envelope model
NEWCOM WPR3 Meeting – 6/9/04
Envelope LS scattering parameters
Two-port extension of descriptive function
concept, same features and limitations:


ai (t )   ai (t ) exp( jct ) , bi (t )   bi (t ) exp( jct )
b1 (t )  S11 ( a1 , a2 )a1 (t )  S12 ( a1 , a2 )a2 (t )
b2 (t )  S21 ( a1 , a2 )a1 (t )  S 22 ( a1 , a2 )a2 (t )
NEWCOM WPR3 Meeting – 6/9/04
Envelope models
 Envelope models consider (narrowband) modulated
signal  “time varying spectrum” signals
 Model purpose: relating input and output signal
envelopes
 Well suited to envelope circuit simulation techniques
NEWCOM WPR3 Meeting – 6/9/04
Limitations of static envelope models
 IMD simmetry & independence on tone spacing
 Both properties are not observed in practice owing to lowfrequency dispersion (memory) effects  thermal, trap related,
bias related (Pollard et al, MTTS-96, paper TH2B-5):
NEWCOM WPR3 Meeting – 6/9/04
Improving static models: simple solutions
 Add a state-variable Z
dependence (temperature, bias)
[Asbeck IMS2002, p.135]; Z in
turn depends (linearly or not) on
the input variable:
y (t )  G  x(t ) , Z (t )  x(t )
NEWCOM WPR3 Meeting – 6/9/04
High-frequency dispersion
While low frequency (long memory) effects arise
due to heating etc., also high-frequency (short
memory) phenomena can arise leading to highfrequency dispersion
This amount to an output sensitivity when the
modulation bandwidth increases  e.g. in next
generation systems
General (usually, but not only) Volterra-based
approaches have been suggested to overcome the
static limitation
NEWCOM WPR3 Meeting – 6/9/04
Examples of low- and high-frequency dispersion
LDMOS amplifier, from Ngoya et al., BMAS 2003
NEWCOM WPR3 Meeting – 6/9/04
More general approaches
 In general, the descriptive function can be turned into a
descriptive functional:
y(t )    x(t ) 
 Volterra-based solutions, with slight variations:
 Derivation from Dynamic Volterra Series [Ngoya et al MTTS Digest 2000]
 Nonlinear Impulse Response Transient (NIRT) envelope
model [Soury et al. MTT-S Digest 2002 paper WE2E-1]
 Extracting memory effects from modified Volterra series
[Filicori et al., IEEE CAS-49, p.1118 and IEEE Instr. & Meas.
V.53 p.341]
NEWCOM WPR3 Meeting – 6/9/04
DC response
DC (LF) regime
Dynamic Volterra
linearity
 1st step: from the
conventional Volterra series
extract a modified series in
the instantaneous deviations
x(t)-x(t-t); truncate the
series to the first term; one
has:
amplitude
Dynamic Volterra in a nutshell
Volterra
ss regime
memory
frequency
1  ˆ
y (t )  yDC ( x(t )) 
H ( x(t ),  ) X ( ) exp( jt ) d 


2
Hˆ ( x(t ),  )  H ( x(t ),  )  H ( x(t ), 0)
small-signal response
NEWCOM WPR3 Meeting – 6/9/04
Dynamic Volterra – cntd.
 2nd step: introduce an envelope representation of input
and output into the dynamic Volterra series; one has:
1 BW / 2 ˆ
*
(t ), ) X () exp( jt ) d 
x
,
)
t
(
x
(
H
y (t )  yDC ( x(t ), x (t )) 
1

2
/
BW

2
1 BW / 2 ˆ
*
*
() exp( jt )d 
X
)

,
)
t
(
x
,
)
t
(
x
(
H

2

2
/
BW

2
*
AM/AM – AM/PM
1 BW / 2 ˆ
H1 ( x(t ) , ) X () exp( jt )d 
 G  x(t )  x(t )  

2
/
BW

2
1 BW / 2 ˆ
*
() exp( jt  2x (t ) )d 
X
)

,
)
t
(
x
(
H

2

2
/
BW

2
NEWCOM WPR3 Meeting – 6/9/04
Dynamic Volterra – cntd.
 3rd step: identify the AM/AM and AM/PM response from
two-tone (one-tone?) measurements; identify the two
transfer functions with two-tone measurements vs. tone
spacing  and tone amplitude
 Comments: the Dynamic Volterra Envelope approach
still has problems when long-memory effects with highly
nonlinear features are present; further modifications
are suggested in Soury et al. MTT-S 2003 p.795
NEWCOM WPR3 Meeting – 6/9/04
Example
from Ngoya et al., BMAS 2003
NEWCOM WPR3 Meeting – 6/9/04
Nonlinear Dynamic Measurements
Amplifiers and two port devices
50 Ohm fixed impedance systems
Spectrum Analyzer based
Power Meter based
Load Pull systems
Fundamental Load Pull
Harmonic Load Pull
Waveform Load Pull
NEWCOM WPR3 Meeting – 6/9/04
Spectrum Analyzer and PWM Based
1- Pout measurement
2- IM3, ACPR
measurement
3- Gain
measurement
NEWCOM WPR3 Meeting – 6/9/04
Load pull – Source pull
Load-pull procedure  characterization of a
device performance as a function of the load
reflection coefficient, in particular the output
power
Source pull  same when changing the source
reflection coefficient
NEWCOM WPR3 Meeting – 6/9/04
Class A Load-Pull theory (Cripps)
Im(L)
0.8
PRF,M
0.6
0.4
-1 dB
-2 dB
0.2
0
-3 dB
-0.2
-4 dB
-5 dB
-0.4
-0.6
|Z'L|<RLo
-0.8
|Z'L|>RLo
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 Re(L)
NEWCOM WPR3 Meeting – 6/9/04
Basics of Load Pull
Example of Load Pull data
Output Power [dBm]
@ 1dB gain compression
NEWCOM WPR3 Meeting – 6/9/04
Power Added Efficiency (PAE) [%]
@ 2dB gain compression
Comments on load pull contours
 Ideally the loadpull
measurement indicates the
“maximum power” or
“saturation power” for each
load
 In practice the power sweep is
stopped up to a certain
compression value (e.g. 1 or 2
dB compression point)
 Points having the same output
power (curves in red) do not
usually have the same gain
NEWCOM WPR3 Meeting – 6/9/04
Constant power
curves
Measured
loads
2 dB gain compression
constant output power curves
Load Pull Systems
Power meter or scalar analyzer-based
only scalar information on DUT performances
economic
Vector receiver (VNA)
vector and more complete information on DUT
performances
high accuracy, thanks to vector calibration
expensive
Time Domain Receiver (MTA)
Waveform capabilities
Complexity, high cost
NEWCOM WPR3 Meeting – 6/9/04
Passive Load Pull Systems I
Passive loads
Mechanical tuners
Electronic tuners (PIN diode-based)
Passive tuners
Power
Meter
Power
Sensor
S
NEWCOM WPR3 Meeting – 6/9/04
L
Power
Sensor
Passive Load Pull Systems II
Features
Single or double slug tuners
High repeatability of tuner positions
Pre-characterization with a network
analyzer, no real time load measurements
High power handling
NEWCOM WPR3 Meeting – 6/9/04
Passive Load Pull Systems III
Motors
DUT
Tuners
NEWCOM WPR3 Meeting – 6/9/04
Slab Line
Passive Load Pull Limits
Drawbacks
Load reflection coefficient limited in magnitude
by tuner and test-set losses
This is true especially for harmonic tuning
 higher frequency
 optimum load on the edge of the Smith Chart
Pre-Matching using tuners or networks
To reach higher gamma while characterizing
highly mismatched transistors
NEWCOM WPR3 Meeting – 6/9/04
Pre-Matching
Tuners
LOSS
L
L
Networks
LOSS
NEWCOM WPR3 Meeting – 6/9/04
L
Real Time VNA based Load Pull
Vector network analyzer-based system
VECTOR INFO
TUNABLE
LOADS
TUNABLE
LOADS
NORMAL VNA CAL
LOSSES
NEWCOM WPR3 Meeting – 6/9/04
Real Time MTA based Load Pull
Transition Analyzer based system
VECTOR
AND TD INFO
REF SIGNAL
TUNABLE
LOADS
TUNABLE
LOADS
TD CAL REQUIRED
NEWCOM WPR3 Meeting – 6/9/04
Active Load
Active loop technique
exp(j)
A
C
G
a
b = a·C·A·exp(j)·G
NEWCOM WPR3 Meeting – 6/9/04
Harmonic Load Pull
Controlling the Load/Source condition at
harmonic frequencies
Wave-shaping techniques at microwave
frequencies
Great complexity of the system but
potential improvement of the performance
NEWCOM WPR3 Meeting – 6/9/04
Passive harmonic Load Pull
A Tuner for each harmonic
Complex
Easy to change frequency
More harmonic load control
Harmonic Resonators within the
slug
Only Phase control of the load
Difficult to change frequency
NEWCOM WPR3 Meeting – 6/9/04
f0
2f0
Fundamental
Harmonic
Active Harmonic Load Pull
Politecnico di Torino implementation
NEWCOM WPR3 Meeting – 6/9/04
Four Loop Harmonic System
Amplifier
VNA
Loop Unit
Switching
Unit
Couplers
DUT
and Probe
NEWCOM WPR3 Meeting – 6/9/04
RF & BB Load Pull System
Exploit BB Load Pull: wide band analysis
Sweeper
Switc h C
Bias T Couplers
Source Pull
RF Frequency
Test Set
Switch B
TRIPLEXER
Load Pull
Couplers Bias T
DUT
TRIPLEXER
Switch A
2nd 3rd
2nd 3rd
Ch2
Phase
Align
Ch1
MTA
Bias T
Couplers
D.C.
BB Frequency
Test Set
NEWCOM WPR3 Meeting – 6/9/04
IF Switch B
IF Switch A
Source
Switch
ESG
Source Pull
Source
Ch2
Ch1
Scope
ESG ESG
F1 F2
Bias T
D.C.
Couplers
ESG
F1, F2
Load
Switch
ESG
Load Pull
Source
Low Freq Source
Load Pull and PA Design
Classical PA design information like:
Power Sweep
Optimum Loads
Load/Source Map based design
Active Real Time System Additional info
Gamma In
AM/PM conversion
Harmonic Load conditions
Time Domain Info
NEWCOM WPR3 Meeting – 6/9/04
Load Pull and PA Design
Data set example
NEWCOM WPR3 Meeting – 6/9/04
Power Sweep and More
GammaL= 0.41 , 167
Frequency= 18 GHz
60.00
30.00
58.00
20.00
56.00
10.00
54.00
0.00
52.00
-10.00
50.00
-20.00
48.00
-30.00
46.00
-40.00
44.00
-50.00
42.00
-60.00
40.00
12.74
14.31
15.96
17.71
19.58
Pav (dBm)
NEWCOM WPR3 Meeting – 6/9/04
21.60
23.60
1dB Compression
25.44
26.75
-70.00
27.55
1dB compression Point
Pout=26.29 dBm
Gain= 9.72 dB
IM3R= -18.34 dBc
IM3L=-18.50 dBc
Eff=48.07%
dB / dBm
Power Sweep @ Best Load for Pout
Pout
Gain
IM3L
IM3R
AM/PM
Eff
Load Pull and PA Design
COMBINING LP MAP INFORMATION
TO OPTIMIZE POWER PERFORMANCES
12 dB
OUTPUT POWER
@ 1 dB GAIN
COMPRESSION
NEWCOM WPR3 Meeting – 6/9/04
26dBm
POWER GAIN
@ 1 dB GAIN
COMPRESSION
Load Pull and PA Design
COMBINING LP MAP INFORMATION
TO OPTIMIZE LINEARITY PERFORMANCES
PAE
@ 1 dB GAIN
COMPRESSION
NEWCOM WPR3 Meeting – 6/9/04
50%
C/I 3 LEFT
@ POUT = 24 dBm
-28 dBm
Harmonic LP Example
2nd Harmonic
Load Plane
PAE
f: 3.6 GHz
NEWCOM WPR3 Meeting – 6/9/04
TD Harmonic Source Pull
Ids, A
Instantaneous working point for different harmonic Gamma S
0.2
PAE=65%
0.18
PAE =55%
0.16
PAE =51%
0.14
Fundamental
0.12
Freq: 1 GHz
0.1
Gamma L fixed at
0.08
1 GHz and at 2 GHz
SII harm
0.06 mag
phase
0.04 0.21 149
88 
0.02 0.65
0.54 65
0
0
2
4
6 8 10 12 14
Vds, V
NEWCOM WPR3 Meeting – 6/9/04
TD Harmonic Source Pull
PAE=65%
0.2
0.16
10
0.12
8
6
0.08
4
0.04
2
0
0
2
0
0.4
NEWCOM WPR3 Meeting – 6/9/04
0.8
1.2
time, ns
1.6
Vds, V
Ids, A
12
Acknowledgements
The presentation includes work from many
colleagues from the Microwave & RF
Group:
Prof. Andrea Ferrero
Prof. Marco Pirola
Dr. Simona Donati
Dr. Laura Teppati
Dr. Vittorio Camarchia
NEWCOM WPR3 Meeting – 6/9/04