Effects of the sample insertion holes of the TM010 mode cylindrical cavity are analyzed on the basis of rigorous analysis by the Ritz-Galerkin method. The measurement accuracy of complex permittivity is examined by comparing the values by the perturbation method with ones by the rigorous analysis. Charts of relative errors Δ ε/εp and Δ tan δ/tan δp are presented, which are useful to measure the complex permittivity accurately by the perturbation method. The present analysis extends the validity of the conventional perturbation method.

A rigorous analysis for a TM010 mode cylindrical cavity with insertion holes is presented on the basis of the Ritz-Galerkin method to realize accurate measurements of the complex permittivity of liquid. The effects of sample insertion holes, a dielectric tube, and air-gaps between a dielectric tube and sample insertion holes are taken into account in this analysis. The validity of this method is verified from measured results of some kinds of liquid.