Compact Microstrip 3-dB Coupled-Line Ring and Branch-Line Hybrids With New Symmetric Equivalent Circuits

New symmetric equivalent circuits are suggested for 90° and 270° transmission-line sections, with which compact coupled-line ring and branch-line hybrids can be designed and fabricated. For this purpose, firstly stepped-impedance transmission-line (SITL) sections, being equivalent to a uniform transmission-line section with arbitrary electrical lengths, are synthesized, and design formulas for the SITL sections are derived. Secondly, three types of equivalent circuits are introduced by combining the SITL sections with coupled-line Π-, modified Π-, or T-type, and are called stepped-impedance coupled-line Π-type (SCΠ ), stepped-impedance modified T-type (SMT), and stepped-impedance modified Π-type (SMΠ). The SCΠs are for 270° transmission-line sections, while both SMTs and SMΠs are for 90° transmission-line sections. Based on the suggested equivalent circuits, compact coupled-line ring and branch-line hybrids designed at 1 GHz are fabricated, and the measured bandwidth of the ring hybrid is 50% with 15-dB return loss. The measured results may be considered as excellent, reflecting their total transmission-line lengths of 183° and 111° for the ring and branch-line hybrids, respectively.