Impedance of a narrow longitudinal shunt slot in a slotted waveguide array

A variational solution is derived for computing the impedance of a radiating longitudinal shunt slot of rectangular shape in the broad face of a rectangular waveguide. This solution, an extension of Oliner's deviation, yields the slot resonant length, accounting for the displacement of the slot from the center of the waveguide. Taking advantage of the results reported in the existent literature, the computation of impedance can be extended to that for a slot in a large array environment, with or without a dielectric sheath covering. Under some reasonable assumptions and comparing the experimental data with theoretical values, a semi-empirical equation is obtained for the resonant length of a slot with round ends in practical applications. The computational method presented in this paper is experimentally assessed to be valuable for the design of slotted waveguide arrays.