A Symbolic Analysis Method to Ideal Soft Switching Circuit System

Soft switching circuits (SSC) are strongly nonlinear system. In their analysis, Ideal switch module (ISM) is often used to improve simulation efficiency and assess the design quality, but Dirac impulse may appear. Conventional numerical circuit simulators have difficulty handling this problem and also have convergence and precision problems. Symbolic analysis method not only overcomes these problems, but also provides avenues to get insight to fundamental circuit behaviors. This paper, based on Matlab/Maple, presents a symbolic method for SSC analysis. This method regards switched elements as linear resistances and obtains the general symbolic circuit solutions expression in s-domain by solving the equations once only. Performing limit computation and inverse Laplace transformation to this expression with appropriate algorithm, the closed-form piecewise to time analytical solutions as well as the SSC' working topology transitions can be obtained. Hence, these results can make the circuit evaluation and auto-design more effectively.