1. Nonlinearity characterization and modelling
Giovanni Ghione
Dipartimento di Elettronica
Politecnico di Torino
Microwave & RF electronics group
NEWCOM WPR3 Meeting – 6/9/04

2. 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

3. Device models: from physical to behavioral
From: D.Root et al., IMS2004 WME-4
NEWCOM WPR3 Meeting – 6/9/04

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

5. Example: LDMOS PA simulation
From: Troyanovsky et al, SISPAD 1997
NEWCOM WPR3 Meeting – 6/9/04

6. 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

7. 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

8. Example: the Curtice MESFET model
NEWCOM WPR3 Meeting – 6/9/04

9. Example: the HBT MEXTRAM model
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10. 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

11. 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

12. 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

13. Pulsed IV: FET example
NEWCOM WPR3 Meeting – 6/9/04

14. 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
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15. Recalling a few basics PA single-tone test PA two-tone test
PA modulated signal test
Intermodulation products, ACPR…
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16. Single-tone PA test PA 3rd harmonics output intercept
1 dB compression point
Output saturation power
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17. Two-tone PA test
Rationale: two-tone operation “simulates” narrowband operation on a continuous band f1 - f2 PA
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18. Two-tone Pin-Pout
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19. Modulated signal test & ACPR
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20. Class AABC two-tone test
Fager et al, IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 39, NO. 1, JANUARY 2004, p. 24
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21. Power series (PS) model
Strictly speaking an IO model for a memoryless NL system, often cascaded with a linear system with memory:
NEWCOM WPR3 Meeting – 6/9/04

22. Active device PS cascading
s(t)
u(t)
w(t)
FET transfer curve
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23. PS output with multi-tone excitation
Assume a multi-tone frequency-domain excitation:
Output:
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24. 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

25. 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:
then the output power is:
Single-tone
Two-tone
Two-tone with IMP3
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26. Example
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27. Volterra series approach
In frequency domain, generalization of the PS approach:
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
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28. 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:
Static envelope model (G complex “descriptive function”):
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29. AM/AM and AM/PM distortion curves
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30. 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

31. 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

32. 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]:
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33. 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

34. 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

35. DNN result example
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36. F-domain dynamic behavioral models
The availability of Large-signal Network Analyzers (LSNA) have fostered the development of generalizations of the scattering parameter approach:
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37. Describing (scattering) functions
NL relationship between power wave harmonics in LS steady state (ij port & harmonics index) [Verspecht, IMS2003]:
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38. Relationship with S parameters
Describing functions reduce to multifrequency S-parameters for a linear device (lowercase used for PW):
however, simplifications can be made (scattering functions model) if a11 is the only “large” component  superposition can be applied to the other terms.
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39. Frequency superposition
Normalization:
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40. Scattering function model
Introducing phase normalized variables one has the relationship [Verspecht, IMS2003]:
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41. 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

42. Envelope LS scattering parameters
Two-port extension of descriptive function concept, same features and limitations:
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43. 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

44. Limitations of static envelope models
IMD simmetry & independence on tone spacing
Both properties are not observed in practice owing to low-frequency dispersion (memory) effects  thermal, trap related, bias related (Pollard et al, MTTS-96, paper TH2B-5):
NEWCOM WPR3 Meeting – 6/9/04

45. 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:
NEWCOM WPR3 Meeting – 6/9/04

46. High-frequency dispersion
While low frequency (long memory) effects arise due to heating etc., also high-frequency (short memory) phenomena can arise leading to high-frequency 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

47. Examples of low- and high-frequency dispersion
LDMOS amplifier, from Ngoya et al., BMAS 2003
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48. More general approaches
In general, the descriptive function can be turned into a descriptive functional:
Volterra-based solutions, with slight variations:
Derivation from Dynamic Volterra Series [Ngoya et al MTT-S 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

49. Dynamic Volterra in a nutshell
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:
DC (LF) regime
amplitude
Dynamic Volterra
linearity
Volterra
ss regime
memory
frequency
DC response
small-signal response
NEWCOM WPR3 Meeting – 6/9/04

50. Dynamic Volterra – cntd.
2nd step: introduce an envelope representation of input and output into the dynamic Volterra series; one has:
AM/AM – AM/PM
NEWCOM WPR3 Meeting – 6/9/04

51. 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 W 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

52. Example
from Ngoya et al., BMAS 2003
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53. 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

54. Spectrum Analyzer and PWM Based
1- Pout measurement
2- IM3, ACPR
measurement
3- Gain measurement
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55. 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
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56. Class A Load-Pull theory (Cripps)
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57. Basics of Load Pull Example of Load Pull data
Output Power [dBm] @ 1dB gain compression
Power Added Efficiency (PAE) [%] @ 2dB gain compression
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58. 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
Constant power curves
Measured loads
2 dB gain compression constant output power curves
NEWCOM WPR3 Meeting – 6/9/04

59. 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

60. Passive Load Pull Systems I
Passive loads
Mechanical tuners
Electronic tuners (PIN diode-based)
Power
Meter
Sensor
Passive tuners G S L
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61. 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
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62. Passive Load Pull Systems III
Motors
Slab Line
DUT
Tuners
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63. 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
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64. Pre-Matching G L
LOSS
Tuners
Networks
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65. Real Time VNA based Load Pull
Vector network analyzer-based system
VECTOR INFO
TUNABLE
LOADS
NORMAL VNA CAL
LOSSES
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66. Real Time MTA based Load Pull
Transition Analyzer based system
VECTOR AND TD INFO
REF SIGNAL
TUNABLE
LOADS
TD CAL REQUIRED
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67. Active Load Active loop technique A exp(j) C G a b = a·C·A·exp(j)·G
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68. 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
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69. 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 G f0
2f0
Fundamental
Harmonic
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70. Active Harmonic Load Pull
Politecnico di Torino implementation
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71. Four Loop Harmonic System
Amplifier
VNA
Loop Unit
Switching
Unit
Couplers
DUT
and Probe
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72. RF & BB Load Pull System Exploit BB Load Pull: wide band analysis
RF Frequency Test Set
BB Frequency Test Set
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73. 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
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74. Load Pull and PA Design
Data set example
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75. Power Sweep and More 1dB compression Point
Pout=26.29 dBm Gain= 9.72 dB IM3R= dBc
IM3L= dBc Eff=48.07%
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76. Load Pull and PA Design COMBINING LP MAP INFORMATION
TO OPTIMIZE POWER PERFORMANCES
12 dB
OUTPUT POWER @ 1 dB GAIN COMPRESSION
POWER 1 dB GAIN COMPRESSION
26dBm
NEWCOM WPR3 Meeting – 6/9/04

77. PAE @ 1 dB GAIN COMPRESSION
Load Pull and PA Design
COMBINING LP MAP INFORMATION
TO OPTIMIZE LINEARITY PERFORMANCES
PAE @ 1 dB GAIN COMPRESSION
50%
-28 dBm
C/I 3 LEFT @ POUT = 24 dBm
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78. Harmonic LP Example 2nd Harmonic Load Plane PAE f: 3.6 GHz
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79. TD Harmonic Source Pull
Instantaneous working point for different harmonic Gamma S 2 4 6 8 10 12 14
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Vds, V
Ids, A
PAE=65%
PAE =55%
PAE =51%   
SII harm
mag
phase
Fundamental Freq: 1 GHz Gamma L fixed at 1 GHz and at 2 GHz
NEWCOM WPR3 Meeting – 6/9/04

80. TD Harmonic Source Pull
0.04
0.08
0.12
0.16
0.2
0.4
0.8
1.2
1.6 2 4 6 8 10 12
time, ns
Ids, A
Vds, V
PAE=65%
NEWCOM WPR3 Meeting – 6/9/04

81. 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