Analysis of Coupled or Single Nonuniform Transmission Lines Using Step-by-Step Numerical Integration

Abstract

Abstract-A method is proposed for analysis of arbitrarily loaded lossy and dispersive nonuniform single or coupled transmission lines. In this method, the transmission lines are subdivided to several uniform sections, at first. Then the voltage and current distributions are obtained using second order step-by-step numerical integration (second order finite difference method). The accuracy of the method is studied using analysis of some special types of single and coupled transmission lines.

Closed Form Solutions for Nonuniform Transmission Lines

“…The differential equations describing NTLs have nonconstant coefficients, so except for a few special cases, no analytical solution exists for them. There are some methods to analyze NTLs such as cascading many short sections [6,7], finite difference [8], Taylor's series expansion [9], Fourier series expansion [10], the equivalent sources method [11] and the method of Moments [12]. These methods are numerical and do not yield an analytic closed form solutions.…”

Wideband Differential Phase Shifter Using Microstrip Nonuniform Transmission Lines

“…There are some methods to analyze the NTLs such as finite difference [10], Taylor's series expansion [11], Fourier series expansion [12], the equivalent sources method [13] and the method of Moments [14]. Of course, the most straightforward method is subdividing NTLs into many uniform or linear electrically short sections [15,16] with length ∆z, which…”

Utilizing Nonuniform Coupled Transmission Lines to Compact Microstrip Circuits Such as Edge-Coupled Bandpass Filters

“…Also, there are some methods to obtain the ABCD parameters of NCTLs such as cascading many short sections [8,9], finite difference [10], Taylor's series expansion [11], Fourier series expansion [12], the equivalent sources method [13], the method of Moments [14] and an approximate closed form solution [15]. Of course, the most straightforward to determine the ABCD parameters of NCTLs is dividing them into K uniform segments and then to use the following relation [8]…”