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.

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.