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For the first time the eigenoscillation problem of composite cylindrical metal-dielectric resonators was solved using the specific mode matching technique. A method for the calculation of the resonant characteristics of the resonator was developed. The impact of the geometrical and electrical parameters of the resonator on the resonant characteristics in case of a very thin dielectric gap was considered.

Also, for the first time the high sensitivity of the resonant frequencies of the lower TM and HE modes of tunable cylindrical metal-dielectric resonators to an alteration of the air gap thickness was demonstrated. It allows a resonant frequency tuning of tens of percents by moving the metal plate by a few percents of the dielectric cylinder height. It was also established that the Q-factor and the coupling coefficient of the lowest mode of the tunable shielded cylindrical metal-dielectric resonator do not decrease with increasing air gap thickness. This allows creating tunable resonant elements without additional electromagnetic energy losses. Finally, for the first time the dependencies of resonant frequency and Q-factor of the lowest mode of the tunable shielded cylindrical metal-dielectric resonator on its geometrical and electrical parameters were obtained. This allows the optimization of the characteristics of the resonant element.