Causal models of electrically large and lossy dielectric bodies

This paper presents a novel formula for the complex permittivity of lossy dielectrics, which is valid in a broad frequency range and is ensuring a causal impulse response in the time domain. The application of this formula is demonstrated through the analysis of wet soil, where the coefficients of the formula are tuned to match the measured data from the literature. Additionally, an analytical expression for the impulse response of the relative permittivity is derived. The influence of the frequency dependence of the complex permittivity on the causality of responses is illustrated through the analysis of 1-D, 2-D, and 3-D electromagnetic systems. Being the most complex, the 3-D system is also used as a test bed for comparing the computational limitations of two commercially available solvers, CST and WIPL-D.