If a four-port network is terminated by arbitrary impedances, the conventional methods for even- and/or odd-mode excitation analyses are not available because no symmetry planes exist. Under these conditions, two types of new design equations for asymmetric 3-dB branch-line hybrids are reported. To make sure that the derived design equations are correct and adaptable, simulations were performed under assumed ideal conditions for one type of asymmetric 3-dB branch-line hybrid and a uniplanar branch-line hybrid terminated by 50 Ω, 41.6 Ω, 55.6 Ω and 62.5 Ω was fabricated and measured for another type of asymmetric 3-dB branch-line hybrid.