Mathematics behind the Fractional-order Smith Chart

摘要

This paper derives the theory for a fractional order Smith chart and provides a comparison between the impedance and admittance fractional order Smith charts. Basic chart features such as boundaries, critical points, peak values, matching (unity) circle, and the central angle are investigated and compared. Mathematical analysis for these basic features and standard Smith chart functions is also described. This Smith chart can be used to study the scattering parameters in fractional-order RF designs. In addition, it may be used for inverse problems whose models depend on fractional-order electrical elements.