Complex hybrid symbolic analysis of nonlinear analog circuits driven by multi-tone signals

Lucia Dumitriu, Mihai Iordache, Ilie Luican,
“Politehnica” University of Bucharest, Electrical Engineering Department, Bucharest, Romania

DOI: 10.36724/2664-066X-2022-8-2-2-7

SYNCHROINFO JOURNAL. Volume 8, Number 2 (2022). P. 2-7.


The paper presents a general symbolic method for generating the complex hybrid matrix necessary for computing the periodic or nonperiodic steady-state response of a nonlinear analog circuit driven by multitone signals. This method is remarkable by its great efficiency and generality, and it is very useful in frequency-domain approach based on harmonic balance and least square approximation. For the general case of the nonperiodic steady-state response there are three basic methods: frequency-domain approach based on Voltera series; time-domain approach and a frequency-domain approach based on harmonic balance and least square approximation. The last one is significantly more efficient when the total number of nonlinear resistors, inductors and capacitors is significantly less than the total number of linear inductors and capacitors in the circuit, as is often the case in practice.

Keywords: Symbolic analysis, hybrid analysis, nonlinear analog circuits, multi-tone signals.


[1] B. J. Leon, D. J. Shaefer, “Voltera series and Picard iteration for nonlinear circuits and systems”, IEEE Trans. on Circuits and Systems, CAS-25, Sept. 1978, pp. 789-793.

[2] L. O. Chua, A. Ushida, “Algorithms for computing almost periodic steady-state response of nonlinear systems to multiple input frequencies”, IEEE Trans. on Circuits and Systems, CAS-28, Oct. 1981, pp. 953-971.

[3] A. Ushida, L. O. Chua, “Frequency-domain analysis of nonlinear circuits driven by multi-tone signals”, IEEE Trans. on Circuits and Systems, CAS-31, Sept. 1984, pp. 766-778.

[4] M. Iordache, S. Chira, “A new determination method of the order of complexity for a nonreciprocal electric circuit”, Rev. Roum. Sci. Techn. – Électrotechn. et Énerg., 8, nr. 1, Bucarest, 1983, pp. 37-43.

[5] M. Iordache, “Generalization of the topological formulas with homogeneous parameters”, Rev. Roum. Sci. Techn. – Électrotechn. et Énerg. nr.4, Bucarest, 1980, p. 501- 513.

[6] M. Iordache, D. Dornescu, “On the hybrid method for nonlinear resistive network analysis”, Rev. Roum. Sci. Techn. – Électrotechn. et Énerg., nr.4, Bucarest, 1982, pp. 399-410.

[7] P. R. Bryant, The order of complexity of electrical networks, Proc. IEE (GB), Part C, 1959, pp. 174-188.

[8] P. M. Lin, Symbolic Network Analysis, Elsevier, 1991.

[9] L., O., Chua, and P., M., Lin, Computer-Aided Analysis of Electronic Circuits: Algorithms and Computational Techniques, Englewood cliffs, NJ:Prentice-Hall, 1975.

[10] M. Iordache, Lucia Dumitriu, I.Matei, ECSAP – Electronic Circuit Symbolic Analysis Program, Using Guide, Electrical Department Library, Bucharest, 2000.

[11] P. Wambacq, G. Gielen, J. Gerrits, Low – Power Design Techniques and CAD Tools for Analog and RF Integrated Circuits, Kluwer Academic Publishers, Boston/Dordrecht/London, 2001.

[12] A. Brambilla, P. Maffezoni, “Envelope-following method to compute steady-state solutions of electric circuits”, IEEE Trans. on Circuits and Systems – Fundamental Theory and Applications, Vol. 50, N0. 3, March 2003, pp. 404-417.

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