Time-Domain Simulation of Nonlinear Circuits Through Implicit Runge–Kutta Methods

This paper presents a novel approach to the accurate time-domain simulation of nonlinear circuits that employs a class of high-order implicit Runge-Kutta (RK) formulas. The RK methods that are here considered are selected among the wide family of known RK methods as being particularly suited to the task of analog simulation. The properties of stability and accuracy of these RK methods are briefly reviewed while the implementation in the flow of an analog simulator is described in detail. When compared to standard multistep methods, the considered RK techniques reveal to be much more reliable and thus particularly suited to the analysis of those circuits, such as circuits for RF applications or sharply nonlinear switched circuits, that are critical for conventional integration methods

[1]  A. Opal,et al.  Modern CAD methods for analysis of switched networks , 1997 .

[2]  Alper Demir,et al.  CAD for RF circuits , 2001, Proceedings Design, Automation and Test in Europe. Conference and Exhibition 2001.

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

[4]  E. Hairer,et al.  Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems , 2010 .

[5]  Tore Undeland,et al.  Power Electronics: Converters, Applications and Design , 1989 .

[6]  D. Bedrosian,et al.  Time-domain analysis of networks with internally controlled switches , 1991, 1991., IEEE International Sympoisum on Circuits and Systems.

[7]  Lawrence F. Shampine,et al.  The Art of Writing a Runge-Kutta Code, Part I , 1977 .

[8]  Randall W. Rhea,et al.  Oscillator design and computer simulation , 1990 .

[9]  Behzad Razavi,et al.  Challenges in portable RF transceiver design , 1996 .

[10]  Karlheinz Ochs,et al.  Passive Integration Methods: Fundamental Theory , 2001 .

[11]  G. Dahlquist.  A special stability problem for linear multistep methods , 1963 .

[12]  U. Ascher,et al.  Numerical Methods for Differential-Algebraic Equations , 1998 .

[13]  L.O. Chua,et al.  INSITE—A software toolkit for the analysis of nonlinear dynamical systems , 1987, Proceedings of the IEEE.

[14]  A. Opal,et al.  Computer methods for switched circuits , 2003 .

[15]  J. Lambert.  Numerical Methods for Ordinary Differential Systems: The Initial Value Problem , 1991 .

[16]  Uri M. Ascher,et al.  Computer methods for ordinary differential equations and differential-algebraic equations , 1998 .

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

[18]  Ernst Hairer,et al.  Solving Ordinary Differential Equations I: Nonstiff Problems , 2009 .

[19]  Mark Zwolinski,et al.  Overview of SPICE-like circuit simulation algorithms , 1994 .

[20]  Karlheinz Ochs,et al.  Synthesis and Design of Passive Runge-Kutta Methods , 2001 .

[21]  Kartikeya Mayaram,et al.  Computer-aided circuit analysis tools for RFIC simulation: algorithms, features, and limitations , 2000 .

[22]  C. W. Gear,et al.  Numerical initial value problem~ in ordinary differential eqttations , 1971 .

[23]  D. Bedrosian,et al.  Time-domain analysis of networks with internally controlled switches , 1992 .

[24]  A. Demir,et al.  Phase noise in oscillators: a unifying theory and numerical methods for characterization , 2000 .

[25]  G.R. Walker,et al.  Cascaded DC-DC converter connection of photovoltaic modules , 2004, 2002 IEEE 33rd Annual IEEE Power Electronics Specialists Conference. Proceedings (Cat. No.02CH37289).

[26]  E. Kuh,et al.  The state-variable approach to network analysis , 1965 .