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Microsystems, Electronics and Acoustics
ISSN 2523-4447 · e‑ISSN 2523-4455 Open Access · CC BY-SA 4.0
Vol. 25 · Issue 1 · 2020 Jul 6, 2020 Electronic Systems and Signals

Improving Efficiency of the Periodic Steady-State Analysis of Electronic Circuits Using Spectral Analysis

AM
Artem Olehovych Moskovko Corresponding Національний технічний університет України «Київський політехнічний інститут імені Ігоря Сікорського» Ukraine
OV
Oleh Oleksiiovych Vytiaz Національний технічний університет України «Київський політехнічний інститут імені Ігоря Сікорського» Ukraine
GV
Guy Vandenbosch Католицький університет Льовену Belgium
Pages33-40 PublishedJul 6, 2020
PDF (Ukrainian)
VOL 25 · ISS 1 · 2020 View issue

Abstract

A key problem in the periodic steady-state analysis of electronic circuits is that the duration of transient processes in a circuit might be much larger than the period of a steady-state response. Thus, application of traditional transient methods becomes ineffective due to a huge amount of redundant computations, and special periodic-steady state methods should be used. The method for periodic steady-state analysis using the Kotelnikov-Shannon series is a time-domain method that has proved to be effective for a such type of circuits. In this method the unknown signals are expanded in the Kotelnikov-Shannon series and the derivatives of these signals are calculated as the derivatives of the series. A matrix form of the derivatives approximation leads to simple matrix expressions in a mathematical model. When using the method for periodic steady-state analysis of non-linear circuits using the Kotelnikov-Shannon series to find the steady-state response of a circuit, a time discretization step is chosen based on the spectral characteristics of the signals. As far as the goal of the method is to calculate the unknown signals in a circuit, a vicious circle occurs: to calculate the signals, the time discretization step has to be chosen, and to choose the time discretization step, the spectral characteristics of the signals have to be known, namely the upper frequency in these characteristics. In order to choose the time discretization step, we propose to calculate a partial transient response of a circuit for an input signal of the form of the Heaviside step function, which is usually used to obtain a step response of a linear circuit. The response is calculated with any method, suitable for solving a system of non-linear ordinary differential equations, which usually represents the mathematical model of a circuit. The upper frequency in the spectral characteristic of the partial transient response depends on the duration of the computational domain. The upper frequency versus the duration of the computational domain dependency can be approximated with a hyperbolic function. Thus, calculating few values of the upper frequency at different durations of the computational domain, the value of the upper frequency when the duration of the computational domain is equal to the period of a steady-state response can be forecasted using the hyperbolic approximation.

Keywords

#periodic steady-state #discrete singular convolution #non-linear circuit #Kotelnikov-Shannon series

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