This paper presents analysis, design and simulation of a novel sub-wavelength metamaterial resonator and its application in designing miniaturized filters. The presented sub-wavelength resonator is a coaxial cylindrical cavity in which a combination of an ordinary dielectric material and a metamaterial layer has been inserted. The general dispersion relation for such a resonator is formulated. Using this general formula and considering the sub-wavelength scenario, the approximate dispersion relation is extracted. Based on this approximate dispersion relation and through the use of an anisotropic μ negative (MNG) layer, it is shown that this configuration may in principal exhibit an arbitrary low resonant frequency for a fixed dimension. In comparison with miniaturized rectangular cavities and also miniaturized one-dimensional resonators, the above mentioned resonator provides the possibility of selecting a distinct mode of operation and also a further degree of freedom in the approximate dispersion relation which brings more flexibility in designing miniaturized resonators. As an example design and simulation of a miniaturized coaxial cavity resonator together with the complete design of the anisotropic MNG layer are presented. The resultant cavity diameter is shortened by approximately 69% in comparison with theoretical minimum dimensions of a cylindrical cavity resonator of the same height. Finally based on the designed miniaturized resonator a miniaturized filter with the center frequency of 5.85GHz and the bandwidth of 20MHz is designed and simulated.
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