Numerical Solution of Transmission Line PDEs Using Finite Difference

Abstract

Transmission lines refer to a variety of electrical structures that transfer information or energy typically in the form of carrying electromagnetic waves. Examples of transmission lines include coaxial cables, telephone wires, microstrips, and optical fibers. Understanding the transmission and distribution of the electromagnetic waves across the line is critical for matching the load with the generator to deliver the energy or information with minimum losses. The flow of electromagnetic waves across the line is described based on the voltage and current using Partial Differential Equations (PDEs). In this paper we apply the Central Space Central Time (CSCT) finite difference numerical method to solve the transmission line PDEs. We present the numerical solution of the waveforms and compare it with the analytical solution to evaluate the accuracy of this numerical method in solving the transmission line problem. It is found that the numerical solution of the voltage waveform is very near the analytical result with small error margin. However, while the numerical solution of the current shows the same waveform as the analytical one, there is some quite significant error in the magnitude. The error is found to result from the fact that the waveform of the numerical solution has some phase shift from that of the analytical solution. Adjusting the phase shift of the current waveform results in having good agreement between numerical and analytical results.