Guideline for a UWB waveform robust to the numerical dispersion in FDTD schemes

Research and development of ultra wideband (UWB) systems require model simulations to verify algorithms applied to the systems. In this field, the finite difference time domain (FDTD) method is widely used for simulation of transient wave propagation. The waveforms obtained from FDTD do not perfectly match theoretical ones. Using the assessment of 5 distinctive waveforms, the paper demonstrates that the UWB waveform has a significant bearing on the numerical dispersion. This observation gives a guide for the production of UWB waveforms relatively robust to numerical dispersion in FDTD. The numerical dispersion level proves to be function of the spatial resolution, χ, and the energy distribution of the source in the frequency domain. Although the waveforms with low -3 dB bandwidth tend to have low numerical dispersion, the maximum frequency in the spectrum also holds a significant influence on the numerical dispersion. This suggests the possibility of estimating the level of the numerical dispersion from the whole spectrum with a given χ.