Practical expression for frequency deviation due to insertion hole in cylindrical cavity

One of the most widely used techniques for dielectric material characterisation is the partially filled circular cavity. To make these measurements the dielectric material is introduced into the cavity through a circular hole whose effects in the resonant frequency are traditionally neglected. A very simple expression is introduced to model this frequency deviation that improves the classical one. It takes into account the saturation effect that appears when materials with high permittivities are measured. The expression is obtained using circuital analysis and monomode approximation.