Introduction

When dealing with fast changing signals or long transmission distances the signal propogation time becomes very important. In these cases we must use a transmission line model for signal wires. The basic loss-less model is a 4-terminal model with a distributed capacitance and inductance along the line. This model can be described with the Telegrapher's Equation. Basically this describes the propogation of signals using a 1D wave equation, who's general solution describes the superposition of two waves traveling in opposite directions. To visualize this effect I thought I would try to solve the Telegrapher's Equation using a lumped/finite element method. The basic idea is to divide the transmission line into a network of series inductors and parallel capacitors. The voltages and currents through the transmission line can be solved for using a transient circuit simulator.

I know that there exists a simplified SPICE model which can be used to easily and quickly solved for the currents/voltages at the ends of the transmission line. However, this model does not accurately model what happens inside the transmission line. There are also methods for solving the type of Partial Differential Equation described by the Telegrapher's Equation numerically. I chose the finite element method mainly because I wanted to learn more about how SPICE solvers work internally. This circuit should allow me to do that with a semi-complicated circuit. I also wanted to visualize the signal propogation of a pulse which can't be done using the SPICE transmission line model.