Nonuniform transmission line simulation with circuit simulator

In the present article a method of lossless nonuniform transmission line (NUTL) analysis is proposed. The method reduces analysis of the NUTL to the analysis of cascaded sections of linear varied transmission line (LNTL). Frequency response of each section is described by Bessel functions. Therefore direct implementation of the method in circuit simulator is usually impossible. LNTL input-output relations can be approximated by rational function in frequency domain. It is a form of Padé approximation. The model can be implemented in circuit simulator as an active circuit. Unfortunately circuit input reflection coefficient is distorted in unacceptable manner. Input reflection coefficient is equal for DC to one irrespectively of order of Padé approximation. Author proposed a method which deforms rational approximation residua slightly so frequency response of the model is disturbed minimally and passivity of the circuit is preserved. Synthesis of the passive modeling circuit was conducted for broad range of LNTL slope parameter. The circuit was a cascade connection of Darlington C-type sections. Parameters of the sections were approximated by polynomial regression functions. The specific insensitivity of cascaded circuits on parameter changes assures high accuracy of the model despite inevitable errors in process of parameter regression.