Resonant frequency of a circular microstrip antenna in a parallel-plate waveguide

In this study, to simplify a problem, a circular microstrip antenna (MSA) in a narrow parallel-plate waveguide is considered as a model of a typical installation situation and a representative antenna. So far, we have formulated an analytical expression for the input impedance and have confirmed its validity through comparisons with measurement [2]. In addition to the input impedance, the resonant frequency must be predicted accurately because a MSA has a narrow bandwidth and is usually operated in the vicinity of the resonant frequency. Though, in [2], we have also shown the resonant frequencies, they have been calculated indirectly from the calculation results of the input impedance and their dependence on the parallel-plate waveguide has been not clear. From the antenna designer´s point of view, a design formula to calculate the resonant frequency directly is needed. In this paper, we therefore formulate an analytical expression for the resonant frequency and validate it through the comparison with measurement.