Radio frequency numerical simulation techniques based on multirate Runge-Kutta schemes. (English) Zbl 1235.94009

Oliveira, Jorge F.; Pedro, José C.

J. Appl. Math. 2012, Article ID 528045, 21 p. (2012).

Summary: Electronic circuit simulation, especially for radio frequency (RF) and microwave telecommunications, is being challenged by increasingly complex applications presenting signals of very different nature and evolving on widely separated time scales. In this paper, we will briefly review some recently developed ways to address these challenges, by describing some advanced numerical simulation techniques based on multirate Runge-Kutta schemes, which operate in the one-dimensional time and also within multidimensional frameworks.

MSC:

94-04	Software, source code, etc. for problems pertaining to information and communication theory
65N06	Finite difference methods for boundary value problems involving PDEs
94C05	Analytic circuit theory

Software:

SPICE

References:

[1]	S. A. Maas, Nonlinear Microwave and RF Circuits, Artech House, Norwood, Mass, USA, 2nd edition, 2003. · Zbl 1084.93010
[2]	P. J. Rodrigues, Computer-Aided Analysis of Nonlinear Microwave Circuits, Artech House, Norwood, Mass, USA, 1998. · Zbl 1127.62415
[3]	E. Hairer, S. P. Nørsett, and G. Wanner, Solving Ordinary Differential Equations. I, vol. 8 of Springer Series in Computational Mathematics, Springer, Berlin, Germany, 1987. · Zbl 0638.65058
[4]	E. Hairer and G. Wanner, Solving Ordinary Differential Equations. II, vol. 14 of Springer Series in Computational Mathematics, Springer, Berlin, Germany, 1991. · Zbl 0731.65062
[5]	J. D. Lambert, Numerical Methods for Ordinary Differential Systems, John Wiley & Sons Ltd., Chichester, UK, 1991. · Zbl 0825.93391
[6]	L. Nagel, SPICE2: A Computer Program to Simulate Semiconductor Circuits, Electronics Research Laboratory, University of California, Berkeley, Calif, USA, 1975. · Zbl 0323.68002
[7]	K. Kundert, J. White, and A. Sangiovanni-Vincentelli, Steady-State Methods for Simulating Analog and Microwave Circuits, Kluwer Academic, Norwell, Mass, USA, 1990. · Zbl 0723.94009
[8]	J. C. Pedro and N. B. Carvalho, Intermodulation Distortion in Microwave and Wireless Circuits, Artech House, Norwood, Mass, USA, 2003. · Zbl 1221.28020
[9]	M. Günther and P. Rentrop, “Multirate ROW methods and latency of electric circuits,” Applied Numerical Mathematics, vol. 13, no. 1-3, pp. 83-102, 1993. · Zbl 0787.65045
[10]	M. Günther and P. Rentrop, “Partitioning and multirate strategies in latent electric circuits,” International Series of Numerical Mathematics, vol. 117, pp. 33-60, 1994. · Zbl 0805.65070
[11]	A. Kværnø and P. Rentrop, Low Order Multirate Runge-Kutta Methods in Electric Circuit Simulation, IWRMM Universität Karlsruhe, 1999.
[12]	A. Kværnø, “Stability of multirate Runge-Kutta schemes,” International Journal of Differential Equations and Applications, vol. 1A, no. 1, pp. 97-105, 2000. · Zbl 0955.65052
[13]	M. Günther, A. Kværnø, and P. Rentrop, “Multirate partitioned Runge-Kutta methods,” BIT, vol. 41, no. 3, pp. 504-514, 2001. · Zbl 0990.65081
[14]	A. Bartel, M. Günther, and A. Kværnø, “Multirate methods in electrical circuit simulation,” in Progress in Industrial Mathematics at ECMI 2000, pp. 258-265, Springer, 2002.
[15]	J. Oliveira and A. Araújo, “Envelope transient simulation of nonlinear electronic circuits using multi-rate Runge-Kutta algorithms,” WSEAS Transactions on Electronics, vol. 3, no. 2, pp. 77-84, 2006.
[16]	J. F. Oliveira and J. C. Pedro, “An efficient time-domain simulation method for multirate RF nonlinear circuits,” IEEE Transactions on Microwave Theory and Techniques, vol. 55, no. 11, pp. 2384-2392, 2007.
[17]	J. Roychowdhury, “Analyzing circuits with widely separated time scales using numerical PDE methods,” IEEE Transactions on Circuits and Systems, vol. 48, no. 5, pp. 578-594, 2001. · Zbl 1001.94060
[18]	T. Mei, J. Roychowdhury, T. S. Coffey, S. A. Hutchinson, and D. M. Day, “Robust, stable time-domain methods for solving MPDEs of fast/slow systems,” IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 24, no. 2, pp. 226-238, 2005. · Zbl 05448977
[19]	J. F. Oliveira and J. C. Pedro, “A new time-domain simulation method for highly heterogeneous RF circuits,” Proceedings of the 37th European Microwave Conference (EUMC ’07), pp. 1161-1164, 2007.
[20]	J. F. Oliveira and J. C. Pedro, “An innovative time-domain simulation technique for strongly nonlinear heterogeneous RF circuits operating in diverse time-Scales,” in Proceedings of the 38th European Microwave Conference (EuMC ’08), pp. 1557-1560, Amsterdam, The Netherlands, October 2008.
[21]	J. F. Oliveira and J. C. Pedro, “A multiple-line double multirate shooting technique for the simulation of heterogeneous RF circuits,” IEEE Transactions on Microwave Theory and Techniques, vol. 57, no. 2, pp. 421-429, 2009.
[22]	J. F. Oliveira and J. C. Pedro, “Advanced time-domain techniques for strongly nonlinear RF circuit simulation: recent developments and remaining challenges,” in Proceedings of the International Conference on Computer as a Tool (EUROCON ’11), Lisbon, Portugal, April 2011.
[23]	C. E. Christoffersen and J. Alexander, “An adaptive time step control algorithm for nonlinear time domain envelope transient,” in Proceedings of the Canadian Conference on Electrical and Computer Engineering, vol. 2, pp. 883-886, Ontario, Canada, May 2004.
[24]	A. Brambilla and P. Maffezzoni, “Envelope-following method to compute steady-state solutions of electrical circuits,” IEEE Transactions on Circuits and Systems, vol. 50, no. 3, pp. 407-417, 2003. · Zbl 1368.94176
[25]	E. Ngoya and R. Larcheveque, “Envelop transient analysis: a new method for the transient and steady state analysis of microwave communication circuits and systems,” in IEEE MTT-S International Microwave Symposium Digest, vol. 3, pp. 1365-1368, San Francisco, Calif, USA, June 1996.
[26]	P. Bogacki and L. F. Shampine, “A 3(2) pair of Runge-Kutta formulas,” Applied Mathematics Letters, vol. 2, no. 4, pp. 321-325, 1989. · Zbl 0705.65055