Abstract
The mathematical problem of the perfectly conducting cylindrical cavity resonator containing two and three dielectrics is set up, and solved in terms of the electric and magnetic Hertzian vector potentials. The relations between the various natural frequencies and resonant lengths are determined and discussed, in particular for a cylindrical resonator containing a movable slab of dielectric. It is shown that modes of the form ${E}_{\mathrm{np}0}$ and ${H}_{\mathrm{np}0}$ are not excitable if there is more than one dielectric present in the resonator. The band transmission characteristics of such resonators are considered briefly, and a simple and convenient absolute method for the measurement of dielectric constant at microwave frequencies is suggested. Experimental measurements were made at 3070 megacycles per sec., for the ${H}_{111}$ mode, and the results were found to agree well with the theory. Experimental and theoretical curves illustrating various points of the discussion are included.
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