Continued Fraction Expansion of Irrational Transfer Functions for Simulation of Physical Systems

Transfer function of a linear continuous-time system with lumped parameters is a rational function. Transfer function of real systems, however, cannot always be written in the rational function form. It is the case for the systems with distributed parameters, transfer functions for modeling physical properties of materials, and systems for a colored noise generation such as the noise with power spectral density (PSD) falling off at 10 dB per decade of frequency. A time domain simulation of mentioned systems demands an approximation with a finite order system. In this paper, we consider the types of systems, the transfer functions of which are expressed with a square root. An expansion of the transfer function to the continued fraction, a system structure, and state space equations are derived. The stability of the system is shown and an example of the simulation is presented.