Reduced-order modelling of linear time-varying systems

We present a theory for reduced order modelling of linear time varying systems, together with efficient numerical methods for application to large systems. The technique, called TVP (Time-Varying Pade), is applicable to deterministic as well as noise analysis of many types of communication subsystems, such as mixers and switched capacitor filters, for which existing model reduction techniques cannot be used. TVP is therefore suitable for hierarchical verification of entire communication systems. We present practical applications in which TVP generates macromodels which are more than two orders of magnitude smaller but still replicate the input-output behaviour of the original systems accurately. The size reduction results in a speedup of more than 500.

[1]  Roland W. Freund,et al.  Circuit noise evaluation by Pade approximation based model-reduction techniques , 1997, 1997 Proceedings of IEEE International Conference on Computer Aided Design (ICCAD).

[2]  Jaijeet Roychowdhury,et al.  Cyclostationary noise analysis of large RF circuits with multitone excitations , 1998 .

[3]  Jacob K. White,et al.  Efficient AC and noise analysis of two-tone RF circuits , 1996, DAC '96.

[4]  G. Golub,et al.  Iterative solution of linear systems , 1991, Acta Numerica.

[5]  Jaijeet S. Roychowdhury.  Efficient methods for simulating highly nonlinear multi-rate circuits , 1997, DAC.

[6]  Roland W. Freund,et al.  Efficient linear circuit analysis by Pade´ approximation via the Lanczos process , 1994, EURO-DAC '94.

[7]  R. Freund,et al.  Computing minimal partial realizations via a Lanczos-type algorithm for multiple starting vectors , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[8]  Michel Nakhla,et al.  Asymptotic waveform Evaluation , 1994 .

[9]  Lawrence T. Pileggi,et al.  Asymptotic waveform evaluation for timing analysis , 1990, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[10]  H. G. Brachtendorf,et al.  Numerical steady state analysis of electronic circuits driven by multi-tone signals , 1996 .

[11]  Lawrence T. Pileggi,et al.  PRIMA: passive reduced-order interconnect macromodeling algorithm , 1997, ICCAD 1997.

[12]  Jacob K. White,et al.  Efficient Steady-State Analysis Based on Matrix-Free Krylov-Subspace Methods , 1995, 32nd Design Automation Conference.

[13]  K. J. Antreich,et al.  Schnelle stationäre simulation nichlinearer Schaltungen im Frequenzbereich , 1992 .

[14]  Leon O. Chua,et al.  Computer-Aided Analysis Of Electronic Circuits , 1975 .

[15]  M.L. Liou,et al.  Computer-aided analysis of electronic circuits: Algorithms and computational techniques , 1977, Proceedings of the IEEE.

[16]  M. Nakhla,et al.  Asymptotic Waveform Evaluation: And Moment Matching for Interconnect Analysis , 1993 .

[17]  David E. Long,et al.  Efficient frequency domain analysis of large nonlinear analog circuits , 1996, Proceedings of Custom Integrated Circuits Conference.

[18]  Roland W. Freund,et al.  Reduced-Order Modeling of Large Linear Subcircuits via a Block Lanczos Algorithm , 1995, 32nd Design Automation Conference.

[19]  Jaijeet Roychowdhury,et al.  Efficient multi-tone distortion analysis of analog integrated circuits , 1995, Proceedings of the IEEE 1995 Custom Integrated Circuits Conference.

[20]  Andreas C. Cangellaris,et al.  Simulation of multiconductor transmission lines using Krylov subspace order-reduction techniques , 1997, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[21]  D. Jordan,et al.  Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers , 1979 .

[22]  R. Freund.  Reduced-Order Modeling Techniques Based on Krylov Subspaces and Their Use in Circuit Simulation , 1999 .

[23]  Lawrence T. Pileggi,et al.  PRIMA: passive reduced-order interconnect macromodeling algorithm , 1998, 1997 Proceedings of IEEE International Conference on Computer Aided Design (ICCAD).