The application of fast adaptive wavelet expansion method in the computation of parameter matrices of multiple lossy transmission lines

The resistance and inductance matrices for multiple lossy transmission lines are evaluated from a two-dimensional field solution. This field solution is obtained by using a wavelet expansion method to solve a set of surface integral equations. The original two-dimensional integral equations are converted into one-dimensional integral equations by mapping the conductor surfaces into a periodic Hilbert space. The new operators are then expanded into wavelets by the modified nonstandard decomposition method. An Nlog(N) algorithm is obtained by employing the fast wavelet transform. The computational complexity of the matrix elements is reduced greatly by utilizing piecewise polynomial decompositions. The computation time is also reduced significantly by increasing the resolution levels of the wavelets; instead of increasing the number of basis functions, in order to accurately represent the behavior of the normal derivative at low frequencies. In addition, a very sparse and well conditioned matrix is obtained. As a result, the frequency range of the integral equation method has been extended at least three orders magnitude toward the lower end, than was feasible using conventional basis functions by Tsuk and Kong (see IEEE Trans. on Microwave Theory and Technique, vol.39, no.8, 1991).<>