Modeling and measuring the non-ideal characteristics of transmission lines

TL;DR

This paper introduces a practical method to experimentally determine the frequency-dependent resistance and conductance of transmission lines, supplementing classic transient response measurements with detailed loss analysis.

Contribution

It presents a simple experimental approach and a physical model to measure and fit the frequency-dependent losses in coaxial transmission lines.

Findings

Measured insertion losses from 1 to 2000 MHz

Developed a distributed circuit model including conductor and dielectric losses

Validated the model with experimental data

Abstract

We describe a simple method to experimentally determine the frequency dependencies of the per-unit-length resistance and conductance of transmission lines. The experiment is intended as a supplement to the classic measurement of the transient response of a transmission line to a voltage step or pulse. In the transient experiment, an ideal (lossless) model of the transmission line is used to determine the characteristic impedance and signal propagation speed. In our experiment, the insertion losses of various coaxial cables are measured as a function of frequency from 1 to 2000 MHz. A full distributed circuit model of the transmission line that includes both conductor and dielectric losses is needed to fit the frequency dependence of the measured insertion losses. Our model assumes physically-sensible frequency dependencies for the per-unit-length resistance and conductance that are determined by the geometry of the coaxial transmission lines used in the measurements.