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Journal of Electrical and Computer Engineering
Volume 2014, Article ID 198273, 11 pages
Research Article

Steady-State Response of Periodically Switched Linear Circuits via Augmented Time-Invariant Nodal Analysis

Department of Electronics and Telecommunications, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129 Torino, Italy

Received 9 May 2014; Revised 15 July 2014; Accepted 31 July 2014; Published 2 September 2014

Academic Editor: Muhammad Taher Abuelma’atti

Copyright © 2014 Riccardo Trinchero et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We focus on the simulation of periodically switched linear circuits. The basic notation and theoretical framework are presented, with emphasis on the differences between the linear time-invariant and the time-varying cases. For this important class of circuits and sources defined by periodic signals, the computation of their steady-state response is carried out via the solution of an augmented time-invariant MNA equation in the frequency-domain. The proposed method is based on the expansion of the unknown voltages and currents in terms of Fourier series and on the automatic generation of augmented equivalents of the circuit components. The above equivalents along with the information on circuit topology allow creating, via circuit inspection, a time-invariant MNA equation, the solution of which provides the coefficients of both the time- and the frequency-domain responses of the circuit. Analytical and numerical examples are used to stress the generality and benefits of the proposed approach.