This paper presents the dispersion characteristics of the FD-TD algorithm by showing the numerical phase and group velocities of the TEM, T E or TM modal solutions. For the TEM wave propagation, there exist three fundamental directions to which phase and group velocities can be expressed by only a single variable (wave number k or frequency 0 ) . Those special directions were chosen to show the dispersive nature of the FD-TD algorithm of which the group and phase velocities depend explicitly on frequencies.
In view of similarities between the TLM and FD-TD algorithms, a comparison of phase velocity characteristics of both methods was made. Under the special condition where the stability factor s is larger than 1/2, the FD-TD algorithm is found less dispersive than that of the original TLM. However, newly developed symmetrical TLM method appears less dispersive than the FD-TD algorithm.
In the numerical simulation of waveguide modal solutions, it was found that there exists an optimum frequency which provide least numerical error in the FD-TD application. A procedure, which determines the stability factor s and the maximum allowed frequency F,,, for the best numerical results, is proposed in this paper.