phd defense 2007
DESCRIPTION
ppt presentation of my Phd defense held on February 2007TRANSCRIPT
PhD Final Defense – Claudio Siviero, Feb. 21, 2007
Nonlinear Black-Box Models of
Digital Integrated Circuits
via System Identification
Claudio Siviero
Politecnico di Torino, Italy
http://www.emc.polito.it/
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PhD Final Defense – Claudio Siviero, Feb. 21, 2007
Introduction
System-level simulation of high-performance electronic equipments
prediction of signals propagation on interconnects waveforms distortion immunity radiation
dig LCDdigRF
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PhD Final Defense – Claudio Siviero, Feb. 21, 2007
System-level simulation (i)
nonlineardevices
discontinuities(linear junctions: connectors, vias, packages,…)
transmission lines(linear bus)
Decompose the signal path into a cascade of subsystems
dig LCDdig
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PhD Final Defense – Claudio Siviero, Feb. 21, 2007
dig LCDdig
System-level simulation (ii)
Describe any subsystem by means of suitable numerical models (macromodel)
Interconnect the macromodels to represent the entire structure
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PhD Final Defense – Claudio Siviero, Feb. 21, 2007
Solver(SPICE, VHDL-AMS,…)
System-level simulation (iii)
devices
discontinuities
transmission lines
dBV/m
Frequency
v (t)
t
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PhD Final Defense – Claudio Siviero, Feb. 21, 2007
Motivation
linear interconnects (lumped & distributed) well-developed studies [1,2]
devices
discontinuities transmission lines
Macromodeling resources
many open issues need for a systematic study
nonlinear devices preliminary results [1]
[1] F.G.Canavero, et A., "Linear and Nonlinear Macromodels for System-Level Signal Integrity and EMC Assessment" , IEICE Transactions on Communications , August, 2005[2] R. Achar, M.S. Nakhla, “Simulation of High-Speed Interconnects”, Proceedings of the IEEE, May 2001
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PhD Final Defense – Claudio Siviero, Feb. 21, 2007
Outline
• IC macromodels• Parametric modeling • Model representations• Assessment of models• Application example• Conclusion
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PhD Final Defense – Claudio Siviero, Feb. 21, 2007
Macromodels
A macromodel is a set of equations relating the port variables and describing the subsystem behavior "seen from the outside"
i1 i2
v1 v2 v1 v2
i1 i2
iOUT(t) = F( vIN(t),vOUT(t),d/dt )
Time-domain macromodels needed for nonlinear behavior
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PhD Final Defense – Claudio Siviero, Feb. 21, 2007
Macromodels for active devices
RF devices (e.g. Power Amplifiers) [3]
Digital Integrated Circuits (ICs)
Suitable modeling strategies must be devised to
model different devices
[3] C. Siviero, P.M. Lavrador, J.C. Pedro, "A Frequency Domain Extraction Procedure of Low-Pass Equivalent Behavioral Models of Microwave PAs" , 2006 European Microwave Integrated Circuits Conference (EuMIC2006), Manchester (UK), pp. 253-256, September 10-13, 2006
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PhD Final Defense – Claudio Siviero, Feb. 21, 2007
IC macromodels (i)
OUT1
VDD
IN1
GND
CO
RE
io1
vdd
vo1
idd
vi1ii2
set of equations or circuits describing I/O buffer behavior
nonlinear terminations (buffers, receivers)
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PhD Final Defense – Claudio Siviero, Feb. 21, 2007
IC macromodels (ii)
- IP protection (do not disclose technology details)
- Accuracy (include higher order effects )
- Efficiency (speed-up simulation)
- Implementation (plug models in any commercial tool)
Requirements
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PhD Final Defense – Claudio Siviero, Feb. 21, 2007
Available methodologies
• Physical modeling
• Behavioral modeling
reproduce the internal structure
reproduce the external electrical behavior
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PhD Final Defense – Claudio Siviero, Feb. 21, 2007
Physical modeling
Transistor-level models
- disclose IP
- the most accurate
- lack of efficiency
- not easily portable
v(t)
i(t)
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PhD Final Defense – Claudio Siviero, Feb. 21, 2007
Behavioral modeling (i)
Simplified equivalent circuits from port transient waveformse.g., IBIS [4] (I/O Buffer Information Specification)
- protect IP
- efficient, sometime complicated
- not so accurate
- supported by all commercial simulators
v(t)
i(t)
[4] http://www.eigroup.org/ibis/
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PhD Final Defense – Claudio Siviero, Feb. 21, 2007
Behavioral modeling (ii)
Parametric models & black-box techniques
- protect IP
- efficient
- accurate
- potentially compatible with commercial simulators
i=F(,v,d/dt)
i(t)
nonlinear mathematical relation
v(t)
i(t)
v(t)F()
parameters estimated from port transient waveforms
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PhD Final Defense – Claudio Siviero, Feb. 21, 2007
Parametric models
But...
i(t)
v(t)F()e.g., i(k)= 2exp(-0.1v(k)) - 0.5[v(k)-v(k-1)]
Typical parametric models are discrete-time relations
Recently applied to ICs: many open research issues
Resources: system identification theory provides methodologies for developing effective parametric models of any unknown nonlinear systems
→ some addressed in this PhD thesis
results from control theory, identification of mechanical systems [5] ,…
[5] L. Ljung, “System Identification: Theory for the User,” Prentice-Hall, 1987.
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PhD Final Defense – Claudio Siviero, Feb. 21, 2007
Outline
• IC macromodels• Parametric modeling • Model representations• Assessment of models• Application example• Conclusion
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PhD Final Defense – Claudio Siviero, Feb. 21, 2007
(A) Model selection
Select a suitable mathematical representation
i(t)
v(t) i(k) = F( , v(k) , v(k-1), … )
Many representations are available to describe any nonlinear dynamics [6]
F =
- neural networks (radial, sigmoidal, splines, wavelet, hyperplane,…)- polynomials (Wiener, Volterra,…) - kernel estimators- fuzzy models- composite local linear models- …
[6] J. Sjoberg et al., “Nonlinear Black-Box Modeling in System Identification: a Unified Overview,” Automatica, Vol. 31, No. 12, pp. 1691-1724, 1995.
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PhD Final Defense – Claudio Siviero, Feb. 21, 2007
(B) Estimation signals
Excite the real device with suitable stimuli and record the device output responses
v(t)
t
VDDMultilevel signals to capture information on both static & dynamic behavior
i(t)
v(t)+-
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PhD Final Defense – Claudio Siviero, Feb. 21, 2007
(C) Parameter estimation
Estimate by minimizing an error function E between the device response and the model response to the excitation
E() = || i – F()||2
= arg min E()
several methods available
i(t)
v(t)+-
F() v(t)+-
i(t)=F()
- gradient-based- genetic- extended Kalman- simulated annealing- …
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PhD Final Defense – Claudio Siviero, Feb. 21, 2007
(D) Model validation
(D) Validate the model by comparing the device and the model responses to different excitations
i(t)
v(t)+-
Accuracy
Stability
Efficiency (small size)
Model selection criteria
F() v(t)+-
i(t)=F()
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PhD Final Defense – Claudio Siviero, Feb. 21, 2007
(E) Macromodel implementation
1. Direct equation description/implementation (e.g., VHDL-AMS)F.vhd
2. Circuit interpretation & SPICE-like Implementation
Discrete-time
Continuous-time
F.cir
e.g. i(k) = 2exp(-0.1v(k)) - 0.5[v(k)-v(k-1)]
i(t) = 2exp(-0.1v(t)) - 0.5T dv(t)/dt
v(t)2exp(-0.1v(t)) 0.5T
i(t)
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PhD Final Defense – Claudio Siviero, Feb. 21, 2007
Specific contributions of this study
(C) Parameter estimation assess the performance of different algorithms
(A) Model selection assess the performance of different representations
first application to IC modeling
(B) Estimation signals multilevel excitations have been proven to be effective
(E) Macromodel implementation well-established procedure
(D) Model validation address stability issue
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PhD Final Defense – Claudio Siviero, Feb. 21, 2007
Outline
• IC macromodels• Parametric modeling• Model representations• Assessment of models• Application example• Conclusion
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PhD Final Defense – Claudio Siviero, Feb. 21, 2007
Model representations
Several parametric representations for i = F(,v,d/dt)
unknown nonlinearstate-space equation
v(t)
i(t)
),(
),(
vxfi
vxgx.
[5] L. Ljung, “System Identification: Theory for the User,” Prentice-Hall, 1987.
[7] I.Rivals and L.Personnaz, “Black-Box Modeling with State-Space Neural Networks”, in Neural and Adaptive Control Technology,1996
i(k) = F ( aTφ(k) )
φ(k) = [ v(k),v(k-1),…,i(k-1),…]T
i(k) = F (Az(k) + bv(k) )
Nonlinear Input-Output [5]
Nonlinear State-Space [7]
regressors vector
“virtual” state vector
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PhD Final Defense – Claudio Siviero, Feb. 21, 2007
I/O vs. SS
I/O SS
successfully applied to real modeling problems
involves input-outputmeasurable variables only
well-established estimation methods
multiple inputs
stability
most obvious choice fordynamic systems
needs for virtual statevariables
estimation methods under study
multiple inputs
stability
Literature search
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PhD Final Defense – Claudio Siviero, Feb. 21, 2007
Investigated model representations
i = F(,v,d/dt)
Universal approximators of nonlinear dynamical relations
representation
Echo State Networks (ESN) [8]
Local Linear State-Space (LLSS) [9]
Sigmoidal Basis Functions (SBF) [6]
F structure
large size SS
weighted composition of LTI models
I/0 e.g., Σ tanh
estimation
random + heuristic & linear least squares-based
iterative gradient-based, pseudo-random init.
iterative gradient-based, deterministic init.
[6] J. Sjoberg et al., “Nonlinear Black-Box Modeling in System Identification: a Unified Overview,” Automatica, 1995.[8] H. Jaeger, “The Echo State Approach to Analyzing and Training Recurrent Neural Networks,” GMD Report, 2001.
[9] V.Verdult, “Nonlinear Systems Identification: A State-Space Approach”, Ph.D. Thesis, 2002.
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PhD Final Defense – Claudio Siviero, Feb. 21, 2007
Outline
• IC macromodels• Parametric modeling • Model representations• Assessment of models• Application example• Conclusion
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PhD Final Defense – Claudio Siviero, Feb. 21, 2007
Assessment of models (i)Synthetic nonlinear dynamic one-port test device
reference responses: Matlab ODE implementation
representative of IC buffers
f1 = 0 → receiver operationf1 ≠ 0 → driver operation @ fixed state
nonlinear dynamic behavior defined by f2 (“clamp”) and L
v(t)
i(t)
f1(v)
f2(v2)+
-
+ v2(t) -
+VDD
L
C
→ tuned to have a stiff example (BENCHMARK)
f1(v) = a1+a2exp(a3v)+a4vf2(v2) = b1exp(b2(v2-VDD))
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PhD Final Defense – Claudio Siviero, Feb. 21, 2007
Assessment of models (ii)Estimation setup
Device response exhibits a slightly different static & dynamic behavior
vs(t)+
Rs
v(t)+
-
i(t)
test device
estimation signals
0.40.60.8
11.21.4 v(t), V
0 5 10 15 20-50
0
50
i(t), mA
t ns
For validation, a different vs(t)is employed
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PhD Final Defense – Claudio Siviero, Feb. 21, 2007
Stability
What do we mean for stability?
Non trivial issue for nonlinear systems [10]
How can we formulate / implement the stability requirement?
Global stability (complicate, probably too restrictive)
Stability for a certain class of excitations / load conditions
(would be ok, but how can we validate exhaustively a model?)
Local stability (simplest, readily extended from the linear case)
[10] Hassan K.Kalihl, “Nonlinear Systems”, Prentice Hall, 2004.
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PhD Final Defense – Claudio Siviero, Feb. 21, 2007
Local stability
@ each time step :
compute the eigenvalues of the linearized model equation [11]
[11] C.Alippi, V.Piuri, “Neural Modeling of Dynamic Systems with Nonmeasurable State Variables”, TI&M 1999.
F (v(t),d/dt) ≈ F (v(t- Δt),d/dt) + J(t-Δt) [v(t)-v(t-Δt)] + …
stable responses
oscillating or saturating responses
possible eigenvaluesoutside the 1 circle
imag
inar
y
real
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PhD Final Defense – Claudio Siviero, Feb. 21, 2007
SBF validationEstimation : Levenberg Marquardt-based algorithms (10 runs)
ref. best model other models
dependence oninitial guess
0 2 4 6 8 10-60
-40
-20
0
20
40
60i(t), mA
t ns -1 -0.5 0 0.5 1
-1
-0.5
0
0.5
1
imag
inar
y
realpossible
instability
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PhD Final Defense – Claudio Siviero, Feb. 21, 2007
ESN validation
accuracy is independent of initialization, but large size...
0 2 4 6 8 10-60
-40
-20
0
20
40
60i(t), mA
t ns
ref. model
Estimation : random+heuristic & linear least squares-based algorithm (1 run)
-1 -0.5 0 0.5 1
-1
-0.5
0
0.5
1
real
imag
inar
y
Stable a priori
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PhD Final Defense – Claudio Siviero, Feb. 21, 2007
LLSS validation
Good accuracyUnique solution
0 2 4 6 8 10-60
-40
-20
0
20
40
60i(t), mA
t ns
Estimation : Levenberg Marquardt-based algorithm (1 run)
ref. model
0.85 0.9 0.95 1
-0.2
-0.1
0
0.1
0.2
real
imag
inar
y
Stable a posteriori
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PhD Final Defense – Claudio Siviero, Feb. 21, 2007
Efficiency comparison
Model
SBF
ESN
LLSS
Estimationtime
Simulation time
reference
10 ÷ 60 s
1 s
60 s
-
0.2 s
16 s
0.8 s
40 s
Speed-up
x200
x2.5
x50
x1
Matlab estimation & simulation time
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PhD Final Defense – Claudio Siviero, Feb. 21, 2007
Models comparison
feature/model
stability
efficiency / size
accuracy
SBF ESN LLSS
LLSS is the best solution for the problem at hand
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PhD Final Defense – Claudio Siviero, Feb. 21, 2007
Outline
• IC macromodels• Parametric modeling• Model representations• Assessment of models• Application example• Conclusion
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PhD Final Defense – Claudio Siviero, Feb. 21, 2007
Application example
TASK : evaluate the performance of LLSS macromodels for the simulation of a real NOKIA mobile data link
waveforms distortion ← immunity radiation
dig LCDdigRF
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PhD Final Defense – Claudio Siviero, Feb. 21, 2007
Mobile data link
DATA = 50 bit pseudo-random, Tbit = 5 ns, rise-time = 500 ps
RF-to-Digital interfaceCourtesy of Nokia Research Center, Helsinki (Finland)
Devices: NOKIA single-ended, VDD=1.8V (reference: ELDO transistor-level)
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PhD Final Defense – Claudio Siviero, Feb. 21, 2007
Validation: functional signals
0 50 100 150 200 250-0.5
0
0.5
1
1.5
2
V
driver output voltage
0 50 100 150 200 250-1
0
1
2
3
t ns
V
receiver input voltage
referenceLLSS macromodel
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PhD Final Defense – Claudio Siviero, Feb. 21, 2007
Validation: power & ground noise referenceLLSS macromodel
0 50 100 150 200 250-40
-20
0
20
40
mV
driver ground voltage
0 50 100 150 200 2501.76
1.78
1.8
1.82
1.84
1.86
t ns
V
driver power supply voltage
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PhD Final Defense – Claudio Siviero, Feb. 21, 2007
Remarks
Model (ELDO)
transistor-level
LLSS macromodel
simulation time
36 min. 26 sec.
1 min. 45 sec.
LLSS macromodels can be effectively used for real applications
Good accuracy
Include power & ground fluctuations
Speed up ~ 30x
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PhD Final Defense – Claudio Siviero, Feb. 21, 2007
Outline
• IC macromodels• Parametric modeling• Model representations• Assessment of models• Application examples• Conclusion
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PhD Final Defense – Claudio Siviero, Feb. 21, 2007
Conclusion: summary
System-level simulation of complex high-performance systems (e.g., high-end digital devices)
Accurate and efficient behavioral models (macromodels) of active components play a key role
→ Systematic study of the application of parametric models and system identification techniques for the behavioral modeling of digital ICs
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PhD Final Defense – Claudio Siviero, Feb. 21, 2007
Conclusion: results
Performance assessment of the performance of different representations (first time applied to IC macromodeling)
→ Local-Linear State-Space (LLSS) models provide the best results
good accuracy unique solution local stability verified a posteriori
Application of LLSS models for the system-level simulation of a real data link
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PhD Final Defense – Claudio Siviero, Feb. 21, 2007
Conclusion: future work
Formulate a tighter criteria to enforce / analyze the stability of a generic nonlinear parametric model.
Further explore LLSS features and capabilities.
Extend the device modeling methodology to account for the enhanced features of devices / applications
overclocked device operation
current models do not include incomplete state-transitions
include additional inputs/effects
e.g., to account for the RF immunity effects of digital ICs