Pulse Diffusion over Transmission Line

Author：李佾儒

Advisor：江簡富 教授

Consider the distributed equivalent circuit for a loss transmission line.

Apply KCL and KVL to have

Divide both equation by, and let to have

Which are the transmission-line equations in time-domain?

Consider a non-inductive, leakage free cable, which implies in the transmission-line equations.

Equation (1) and (2) reduce to

Taking the partial derivative of (3) with respect to and substituting (4),

Which has the form of diffusion equation?

The solution is

Check：

Where, are constants to be determined from boundary conditions.

Consider an initially quiescent, infinitely long cable extending from to and excited at by a constant voltage source of value , namely,

Substituting (5), we have , . Hence, the particular solution of is