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The SPRIM Algorithm for Structure-Preserving Order Reduction of General RCL Circuits

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Model Reduction for Circuit Simulation

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 74))

Abstract

In recent years, order-reduction techniques based on Krylov subspaces have become the methods of choice for generating macromodels of large-scale multi-port RCL networks that arise in VLSI circuit simulation. A popular method of this type is PRIMA. Its main features are provably passive reduced-order models and a Padé-type approximation property. On the other hand, PRIMA does not preserve other structures inherent to RCL circuits, which makes it harder to synthesize the PRIMA models as actual circuits. For the special case of RCL circuits without voltage sources, SPRIM was introduced as a structure-preserving variant of PRIMA that overcomes many of the shortcomings of PRIMA and at the same time, is more accurate than PRIMA. The purpose of this paper is twofold. First, we review the formulation of the equations characterizing general RCL circuits as descriptor systems. Second, we describe an extension of SPRIM to the case of general RCL circuits with voltage and current sources. We present some properties of the general SPRIM algorithm and report results of numerical experiments.

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Notes

  1. 1.

    See Chap. 3 for recent progress in the adaptation of control-theoretic methods to large-scale descriptor systems.

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Acknowledgements

This work was supported in part by the National Science Foundation through Grant DMS-0613032. The author is grateful to the two anonymous referees for their careful reading of the original manuscript and their constructive comments that helped to improve the presentation of the paper.

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Authors and Affiliations

  1. Department of Mathematics, University of California at Davis, One Shields Avenue, Davis, CA, 95616, USA

    Roland W. Freund

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  1. Roland W. Freund
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Correspondence to Roland W. Freund .

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Editors and Affiliations

  1. Inst. Dynamics of Complex Techn. Systems, Max Planck Institute, Sandtorstrasse 1, Magdeburg, 39106, Germany

    Peter Benner

  2. , Fachbereich Mathematik, Universität Hamburg, Bundesstr. 55, Hamburg, 20146, Germany

    Michael Hinze

  3. , Dept. Mathematics & Comp. Sci., Eindhoven University of Technology, P.O.Box 513, Den Dolech 2, HG 8.02, Eindhoven, 5600 MB, Netherlands

    E. Jan W. ter Maten

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Freund, R. (2011). The SPRIM Algorithm for Structure-Preserving Order Reduction of General RCL Circuits. In: Benner, P., Hinze, M., ter Maten, E. (eds) Model Reduction for Circuit Simulation. Lecture Notes in Electrical Engineering, vol 74. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0089-5_2

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  • DOI: https://doi.org/10.1007/978-94-007-0089-5_2

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