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.

波导定向耦合器是基本的微波器件，通常用于将射频信号路由到波导网络内的不同端口。波导通过它们之间的公共壁上的孔耦合。这些孔径的形状和尺寸可以针对某些耦合因子而变化，并产生特定的方向性图案。本研究应用超级公式从圆形孔径过渡到方形孔径。此外，还讨论了一种使用勒让德多项式确定孔径大小的新方法。切比雪夫和勒让德耦合器的仿真结果比较表明，勒让德耦合器通常在 17.4 dB 的等效耦合因数和以 9 GHz 左右为中心的 4 GHz 带宽下提供更平坦的方向性图。此外，人们发现方形孔径的频率响应明显优于圆形孔径，因为它们在平均超过 50 dB 时保持相似的带宽和更高的方向性，但耦合系数较差，增加了 6 dB。