2022-12-21 09:57 Status: # Even odd mode For odd mode impedance a perfect electric conductor boundary condition (PEC) and a magnetic wall is used. For even mode impedance a Perfect magnetic conductor (PMC) is used and an electric wall.  [^1] ## Equations Example Circuit:  $S_{11}=\frac{\Gamma_e+\Gamma_o}{2}$ $S_{21}=\frac{T_e+T_o}{2}$ $S_{31}=\frac{\Gamma_e-\Gamma_o}{2}$ $S_{41}=\frac{T_e-To}{2}$ [^2] --- # References [^1]: [Ultra-Wideband Compact Millimeter-Wave Printed Ridge Gap Waveguide Directional Couplers for 5G Applications: 10.1109/ACCESS.2022.3201865](https://doi.org/10.1109/ACCESS.2022.3201865) [^2]: [A Wideband Switched-Beam Antenna Array Fed by Compact Single-Layer Butler Matrix: 10.1109/TAP.2021.3060040](https://doi.org/10.1109/TAP.2021.3060040)