Efficient model reduction of linear periodically time-varying systems via compressed transient system function

This paper presents a new algorithm to obtain reduced-order model of linear periodically time-varying (LPTV) systems. The proposed algorithm introduces the approach of projection-based reduction algorithms, which have been used for reduction of linear time-invariant (LTI) systems, to the domain of LPTV systems. The key idea in the proposed approach is the utilization of integrated congruence transform to project the original LPTV system matrices onto the Hilbert subspace spanned by the time-dependent derivatives (or moments) of the transfer function. We prove that the transfer function of the resulting reduced-order model has the same derivatives as that of the original system in the Laplace-domain. The new approach presents a computationally efficient method to generate the orthogonal transformation operator (used in the integrated congruence transform) through expanding the time-varying transfer function in the right-half plane of the Laplace-domain. This enables using numerical time-domain integration for a very short transient period to generate the orthogonal transformation operator.

[1]  L. Zadeh,et al.  Frequency Analysis of Variable Networks , 1950, Proceedings of the IRE.

[2]  W. Arnoldi.  The principle of minimized iterations in the solution of the matrix eigenvalue problem , 1951 .

[3]  Albert E. Ruehli,et al.  The modified nodal approach to network analysis , 1975 .

[4]  Jiri Vlach,et al.  A piecewise harmonic balance technique for determination of periodic response of nonlinear systems , 1976 .

[5]  Gene H. Golub,et al.  Matrix computations , 1983 .

[6]  Kishore Singhal,et al.  Computer Methods for Circuit Analysis and Design , 1983 .

[7]  P. Mikusinski,et al.  Introduction to Hilbert spaces with applications , 1990 .

[8]  Alberto L. Sangiovanni-Vincentelli,et al.  Steady-state methods for simulating analog and microwave circuits , 1990, The Kluwer international series in engineering and computer science.

[9]  Tetsuro Itakura,et al.  Numerical noise analysis for nonlinear circuits with a periodic large signal excitation including cyclostationary noise sources , 1993 .

[10]  K. S. Kundert,et al.  Accurate Fourier analysis for circuit simulators , 1994, Proceedings of IEEE Custom Integrated Circuits Conference - CICC '94.

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

[12]  Michel S. Nakhla,et al.  Analysis of interconnect networks using complex frequency hopping (CFH) , 1995, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[13]  Imad M. Jaimoukha,et al.  Oblique Production Methods for Large Scale Model Reduction , 1995, SIAM J. Matrix Anal. Appl..

[14]  Jose E. Schutt-Aine,et al.  Optimal transient simulation of transmission lines , 1996 .

[15]  A. Sangiovanni-Vincentelli,et al.  Simulation and modeling of phase noise in open-loop oscillators , 1996, Proceedings of Custom Integrated Circuits Conference.

[16]  L. M. Silveira,et al.  Coordinate-Transformed Arnoldi Algorithm for GeneratingGuaranteed Stable Reduced-Order Models of Arbitrary RLC Circuits , 1996 .

[17]  Jacob K. White,et al.  A coordinate-transformed Arnoldi algorithm for generating guaranteed stable reduced-order models of RLC circuits , 1996, ICCAD 1996.

[18]  Alper Demir,et al.  Analysis and Simulation of Noise in Nonlinear Electronic Circuits and Systems , 1997 .

[19]  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..

[20]  I. Elfadel,et al.  A block rational Arnoldi algorithm for multipoint passive model-order reduction of multiport RLC networks , 1997, ICCAD 1997.

[21]  I. Elfadel,et al.  Zeros And Passivity Of Arnoldi-reduced-order Models For Interconnect Networks , 1997, Proceedings of the 34th Design Automation Conference.

[22]  P. Feldmann,et al.  The SyMPVL algorithm and its applications to interconnect simulation , 1997, SISPAD '97. 1997 International Conference on Simulation of Semiconductor Processes and Devices. Technical Digest.

[23]  R. Winkler,et al.  How Floquet Theory Applies to Index 1 Differential Algebraic Equations , 1998 .

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

[25]  J. Phillips,et al.  Model reduction of time-varying linear systems using approximate multipoint Krylov-subspace projectors , 1998, 1998 IEEE/ACM International Conference on Computer-Aided Design. Digest of Technical Papers (IEEE Cat. No.98CB36287).

[26]  Franco Mastri,et al.  A rigorous frequency-domain approach to large-signal noise in nonlinear microwave circuits , 1998 .

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

[28]  Lawrence T. Pileggi,et al.  Practical considerations for passive reduction of RLC circuits , 1999, 1999 IEEE/ACM International Conference on Computer-Aided Design. Digest of Technical Papers (Cat. No.99CH37051).

[29]  Zhaojun Bai,et al.  Error bound for reduced system model by Pade approximation via the Lanczos process , 1999, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[30]  Jaijeet S. Roychowdhury.  Reduced-order modelling of time-varying systems , 1999, Proceedings of the ASP-DAC '99 Asia and South Pacific Design Automation Conference 1999 (Cat. No.99EX198).

[31]  Ernest S. Kuh,et al.  Passive multipoint moment matching model order reduction algorithm on multiport distributed interconnect networks , 1999 .

[32]  Jaijeet Roychowdhury,et al.  Reduced-order modeling of time-varying systems , 1999 .

[33]  Michel S. Nakhla,et al.  Simulation of high-speed distributed interconnects using Krylov-space techniques , 2000, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[34]  Albert E. Ruehli,et al.  Model order reduction techniques applied to electromagnetic problems , 2000, IEEE 9th Topical Meeting on Electrical Performance of Electronic Packaging (Cat. No.00TH8524).

[35]  Anestis Dounavis,et al.  Passive model reduction of multiport distributed interconnects , 2000 .

[36]  Michel Nakhla,et al.  A circuit reduction technique for finding the steady-state solution of nonlinear circuits , 2000, IMS 2000.

[37]  Ramachandra Achar,et al.  Simulation of high-speed interconnects , 2001, Proc. IEEE.

[38]  Yousef Saad,et al.  Iterative methods for sparse linear systems , 2003 .