Multiple dielectric slabs in waveguide cell

The transverse resonance method is used to evaluate the effective dielectric constant of a material present in the form of multiple slabs that partially fill a waveguide cell. It is shown that the commonly-used linear relationship for the effective dielectric constant of a mixture of dielectrics holds good to better than 1% accuracy only when the slabs are, in general, of a width each less than 5% of the wavelength in the dielectric. Alternative mixture equations with empirical terms are also presented.