This article presents a modal analysis based on the reciprocity theorem to calculate the coupled/penetrated fields into an open-ended waveguide mounted on a finite flange. Although there is no limitation on the geometry and type of the external source, an infinitesimal dipole is chosen to produce a plane wave incident to the waveguide aperture. The proposed method relates the amplitude of each penetrated mode into the waveguide to the far-field radiation components of that mode from the waveguide aperture. The accuracy of the final result depends on the accuracy of the calculated radiated fields. The radiated field components are calculated considering the reflected fields due to the aperture and the diffracted fields due to the flange edges. For the first time, the impact of a finite flange on the penetrated fields into a waveguide is discussed comprehensively. The geometry of a rectangular waveguide mounted on a thick square flange is selected to be evaluated. The effects of changing the main parameters of the geometry on the penetrated fields are discussed rigorously in various examples. Our results are compared with 3-D full-wave simulations, and an excellent agreement was found between the results while our analytical approach showing a 60 times faster performance. In addition, we compared our results with the measurement reported in a previous study.

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