  It is widely thought that small time steps lead to small numerical errors in
the finite-difference time-domain (FDTD) simulations. In this paper, we
investigated how time steps impact on numerical dispersion of two FDTD methods
including the FDTD(2,2) method and the FDTD(2,4) method. Through rigorously
analytical and numerical analysis, it is found that small time steps of the
FDTD methods do not always have small numerical errors. Our findings reveal
that these two FDTD methods present different behaviors with respect to time
steps: (1) for the FDTD(2,2) method, smaller time steps limited by the
Courant-Friedrichs-Lewy (CFL) condition increase numerical dispersion and lead
to larger simulation errors; (2) for the FDTD(2,4) method, as time step
increases, numerical dispersion errors first decrease and then increase. Our
findings are also comprehensively validated from one- to three-dimensional
cases through several numerical examples including wave propagation, resonant
frequencies of cavities and a practical electromagnetic compatibility (EMC)
problem.
