ABSTRACT
This chapter derives the general traveling-wave transforms, a closed-form approximate operational propagation function, and the corresponding operational characteristic impedance. It examines the responses to three sets of boundary conditions: a semi-infinite line connected directly to an ideal voltage source; a semi-infinite line connected to an ideal voltage source through a resistor RG; and a line of finite length, connected to an ideal voltage source through a resistor RGc and terminated with a resistor RT. The partial differential equations for the lossless line will be converted to Laplace transforms with respect to time, and the parameters modified to accommodate frequency-dependent loss. The transform equations may then be solved as ordinary differential equations in z. The propagation of voltage on a skin-effect-lossy line caused by a step-function voltage source connected directly to the line was first analyzed by Pleijel in 1918, and the same result was independently derived by other investigators during succeeding years.
