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This paper presents a new waveguide shunt-slot feed for a microstrip patch antenna that is analyzed using a formulation based on the method-of-moments (MoM). Starting from a generalized formulation, expressions are obtained for a rectangular patch radiator excited by a rectangular slot using entire-domain basis functions with a Galerkin procedure to obtain the moment matrix. Expressions for the dielectric region are derived using Green's function in Fourier transform domain. The developed analysis is used on a prototype C-band radiator presenting details. Subsequently, parametric studies are performed on the key design variables of the configuration, i.e., slot dimensions, axial offset of slot and patch position w.r.t. slot center. A slot length of 0.08λ is found a good initial design estimate to obtain resonance. The variation of coupled power with axial slot offset is reported while showing little effect on resonant frequency. This can be a useful design aid for linear arrays to control amplitude excitations. Patch offset from slot center is found to be noncritical in regard to alignment tolerances. However, changes in coupling factor and resonant frequency are reported. The proposed technique is validated through a commercial e.m. simulator, prototype hardware measurements and comparison to an earlier reported antenna. The paper thus establishes the proposed feeding technique using a developed MoM based analysis and presents useful parametric studies to serve as design aids.