Synthesis of fractional order immittance matrices

Abstract

Modern life cannot be separated from Smart Devices, the design of Smart Device is inseparable from the study of its circuit properties. Moreover, circuit synthesis is an indispensable way to study its circuit properties. In many cases, fractional order polynomial matrix can describe Smart Device's network characteristics more accurately than integer order polynomial matrix, so how to synthesize these fractional order polynomial matrices gradually becomes the focus of attention. For synthesis of a reactance matrix, a premise is that these reactance matrices have positive-reality. In this paper, fractional immittance order matrix is transformed into a bivariate reactance matrix, then the bivariate reactance matrix is synthesized. The synthesis method in this process is mainly based on Laurent series and spectral factorization of semidefinite Hermite matrices, but also used a traditional univariate synthesis method, then let the obtained bivariate reactance element network transform into a fractional order reactance element network. The synthesis process of the above- mentioned is also illustrated by an example. It is also proved that the method of synthesizing the fractional immittance order matrix is effective.