Transmission Lines

The following analysis requires making two assumptions which limit the analysis to frequencies up to the low MHz region:

 

  • A transmission line can be simplified into small, distributed passive electrical elements (R, L, C, and G).
  • These elements are independent of frequency (their reactance may be a function of frequency).

 

The second assumption is because of the skin effect. The resistance of a wire increases with frequency because the electrons migrate towards the skin (outside of the wire), thus reducing the conduction cross-section.

Equivalent Circuit

The purpose behind the math is to find an expression that defines the voltage (or current) at any time on any part of the transmission line.

Voltage and current are functions of time (t) and distance (x) along the wire.