Design and Simulation of Square Aperture Multi-hole Legendre Waveguide Directional Couplers

Waveguide directional couplers are fundamental microwave devices that are commonly used in routing RF signals to different ports within a waveguide network. Waveguides are coupled through apertures in a common wall between them. The shape and size of these apertures can be varied for certain coupling factors and to produce specific directivity patterns. This research applies the superformula in transitioning from circular apertures to square ones. Additionally, a novel approach to using the Legendre polynomials in sizing the apertures is discussed. Comparisons of the simulation results of Chebyshev and Legendre couplers show that Legendre couplers generally give a flatter directivity pattern for an equivalent coupling factor at 17.4 dB and bandwidth of 4 GHz centered at around 9 GHz. Moreover, square apertures are found to be noticeably superior to circular ones in their frequency response as they maintain a similar bandwidth of and higher directivity at an average of over 50 dB, but suffer poorer coupling factors, which increase by 6 dB.