Space and time continuous lumped transmission line model

A lumped transmission line model, based on polynomial approximation and the least squares method, is deduced and investigated. The model enables the line voltage and current to be determined approximately for arbitrary points along the line and at arbitrary times. The model is not restricted to lossless lines, nor to the sinusoidal steady state. Further, some examples are given showing how the transmission line model can be extended to include arbitrary linear terminal dynamics. The model is in the time domain as well as in the frequency domain, and is compared to analytically obtained responses