The method of lines for the analysis of lossy planar waveguides

The method of lines is extended to calculate the losses of waveguide structures. Ohmic losses in metallizations (with frequency-dependent, extremely high dielectric constants) and dielectric losses are simultaneously considered. Despite the high ratios of the dielectric constants of the metallizations and the dielectrics, the analysis and numerical treatment are carried out accurately. Using nonequidistant discretizations the results are computed efficiently, and an approximate value of the propagation constant close to the exact value is found by extrapolation. The phase constant deviates less than 0.5%. The attenuation may deviate up to 2%. The advantages of the method of lines are a small computation time and, due to the analytical solutions of the fields in one direction, a very good approach to the fields inside the strip as well as to the strong fields directly adjacent at the edges. The results for a single microstrip line are shown and compared with those of other authors