Design of compact branch-line couplers using π-equivalent artificial transmission lines

Compact branch-line couplers (BLCs) are developed using π-equivalent shunt-stub-based artificial transmission lines (SSB ATLs). A conventional quarter-wave microstrip can be equivalent to a π-equivalent SSB ATL which is realised by a series high-impedance microstrip with two bilateral low-impedance shunt stubs. The SSB ATLs are then applied to implement a BLC. The low-impedance shunt stubs of the adjacent SSB ATLs are merged and replaced by the shunt branch-type structures. The folding technique is used to optimally miniaturise the coupler circuit size. Distributed-capacitor structures are employed to improve the operating bandwidth. At the design frequency 0.9πGHz, the developed 3- and 6-dB BLCs using shunt branch-type structures occupy about 8 and 8.2π of the circuit sizes of the conventional structures, respectively. In addition, the circuit size of the 3-dB BLC using shunt distributed-capacitor structures reduces to a 13.9π of the conventional one.