Semi-Symbolic Transient Analysis of Analog Fractional-Order Systems

The concept of algorithmic semi-symbolic transient analysis of analog circuits containing fractional-order elements is described. From the circuit model, the transfer function in symbolic and semi-symbolic form and its w-domain poles are found, the decomposition of the transfer function into partial fractions is performed, and the waveform formula expressed by two-parametric Mittag-Leffler functions and their derivatives are found for each fraction. The formula is then converted into a numerical result. The method is implemented in the SNAP program, and its usefulness is demonstrated on a cascade filter with multiple complex poles.