Wave Propagation on Nonuniform Lines

The conventional traveling-wave technique is extended to nonuniform lines by attributing distributed reflection and refraction coefficients to each point on the line. Analytical expressions are derived giving the variations in voltage and current wave fronts as they travel along a nonuniform line as well as variations in the voltage and current and their respective ratio Z(t) = E/I at a fixed position of the line caused by the continuous generation of reflections along the line. It is shown that the ratio Z(t), representing the so-called transient surge impedance of a given position of a nonuniform line, depends not only on time and the function expressing the conventional surge impedance of the line but also on the shape of the current wave, a fact which considerably reduces the usefulness of Z(t) in solving nonuniform line problems.