ppt presentation of my Phd defense held on February 2007

1. Nonlinear Black-Box Models of Digital Integrated Circuits via System Identification Claudio Siviero Politecnico di Torino, Italy [email_address] http://www.emc.polito.it/

3. System-level simulation (i) nonlinear devices discontinuities (linear junctions: connectors, vias, packages,…) transmission lines (linear bus) Decompose the signal path into a cascade of subsystems dig LCD dig

5. Solver (SPICE, VHDL-AMS,…) System-level simulation (iii) devices discontinuities transmission lines dB  V/m Frequency v ( t ) t

8. Macromodels A macromodel is a set of equations relating the port variables and describing the subsystem behavior "seen from the outside" i OUT (t) = F ( v IN (t),v OUT (t),d/dt ) Time-domain macromodels needed for nonlinear behavior i 1 i 2 v 1 v 2 v 1 v 2 i 1 i 2

10. IC macromodels (i) set of equations or circuits describing I/O buffer behavior nonlinear terminations (buffers, receivers) OUT1 VDD IN1 GND CORE i o1 v dd v o1 i dd v i1 i i2

19. (B) Estimation signals Excite the real device with suitable stimuli and record the device output responses Multilevel signals to capture information on both static & dynamic behavior v(t) t VDD i(t) v(t) + -

22. (E) Macromodel implementation 1. Direct equation description/implementation (e.g., VHDL-AMS) 2. Circuit interpretation & SPICE-like Implementation Discrete-time Continuous-time e.g. i ( k ) = 2 exp( -0.1 v ( k ) ) - 0.5 [ v ( k )- v ( k -1) ] i ( t ) = 2 exp( -0.1 v ( t ) ) - 0.5 T d v ( t )/d t F.vhd F.cir v ( t ) 2 exp( -0.1 v ( t ) ) 0.5 T i ( t )

25. Model representations Several parametric representations for i = F (  , v,d/dt ) unknown nonlinear state-space equation [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 ( a T φ ( k ) ) φ ( k ) = [ v ( k ) ,v ( k -1) ,…,i ( k -1),…] T i ( k ) = F ( A z ( k ) + b v ( k ) ) Nonlinear Input-Output [5 ] Nonlinear State-Space [7] regressors vector “ virtual” state vector v ( t ) i ( t )      ) , ( ) , ( v x f i v x g x .

26. I/O vs. SS I/O SS successfully applied to real modeling problems involves input-output measurable variables only well-established estimation methods multiple inputs stability most obvious choice for dynamic systems needs for virtual state variables estimation methods under study multiple inputs stability Literature search

27. Investigated model representations i = F (  , v,d/dt ) Universal approximators of nonlinear dynamical relations [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. 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.

30. Assessment of models (ii) Estimation setup Device response exhibits a slightly different static & dynamic behavior estimation signals For validation , a different v s (t) is employed v s (t) + R s v(t) + - i(t) test device 0.4 0.6 0.8 1 1.2 1.4 v(t), V 0 5 10 15 20 -50 0 50 i(t), mA t ns

32. 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- Δ t),d/dt) + J(t - Δ t ) [v(t)-v(t- Δ t )] + … stable responses oscillating or saturating responses possible eigenvalues outside the 1 circle imaginary real

33. SBF validation Estimation : Levenberg Marquardt-based algorithms (10 runs) dependence on initial guess possible instability ref. best model other models 0 2 4 6 8 10 -60 -40 -20 0 20 40 60 i(t), mA t ns -1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1 imaginary real

34. ESN validation accuracy is independent of initialization, but large size... Estimation : random+heuristic & linear least squares-based algorithm (1 run) Stable a priori 0 2 4 6 8 10 -60 -40 -20 0 20 40 60 i(t), mA t ns ref. model -1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1 real imaginary

35. LLSS validation Good accuracy Unique solution Estimation : Levenberg Marquardt-based algorithm (1 run) Stable a posteriori 0 2 4 6 8 10 -60 -40 -20 0 20 40 60 i(t), mA t ns ref. model 0.85 0.9 0.95 1 -0.2 -0.1 0 0.1 0.2 real imaginary

36. Efficiency comparison Matlab estimation & simulation time Model SBF ESN LLSS Estimation time 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

37. Models comparison LLSS is the best solution for the problem at hand feature/model stability efficiency / size accuracy SBF ESN LLSS

40. Mobile data link DATA = 50 bit pseudo-random, Tbit = 5 ns, rise-time = 500 ps RF-to-Digital interface Courtesy of Nokia Research Center, Helsinki (Finland) Devices : NOKIA single-ended, VDD=1.8V (reference: ELDO transistor-level)

41. Validation: functional signals reference LLSS macromodel 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

42. Validation: power & ground noise reference LLSS macromodel 0 50 100 150 200 250 -40 -20 0 20 40 mV driver ground voltage 0 50 100 150 200 250 1.76 1.78 1.8 1.82 1.84 1.86 t ns V driver power supply voltage

45. 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