Transient solution for lossy transmission line by means of orthogonal projection method

A novel electromagnetic transient analysis technique by means of the orthogonal projection method for lossy transmission line is proposed. By employing the proposed method, the traveling waves propagating from one terminal to another can be quickly obtained with less amount of computation at considerably large steps. First of all, the differential function to variable time can be approximated to be the convolution with a fixed vector relates to a certain set of orthogonal basis, e.g., Daubechies' basis. The partial differential telegraph equations related to both variable time t and distance x are then transformed to be differential equations only related to x. The solution of such equations can be obtained accordingly. The discrete coefficients of propagation function for lossy line are obtained as well, by which the propagating traveling waves can be calculated precisely at considerably large sampling periods with less amount of computation.