Synthesis of wideband lumped planar directional couplers

A synthesis procedure of wideband lumped directional couplers is presented. The four-port network is separated, using even- and odd-mode excitations, into two pairs of two-port networks with constant phase shift between them. It is shown that to attain wideband matching as well as constant in-band coupling, the two modal two-port networks should not only be matched, but have a constant phase shift between them as well. These restrictions are best met with two ideal linear-phase bandpass filters that are mutually frequency shifted. The lack of detailed lowpass prototype (LPPT) tables for such filters led, in the paper, to an alternative synthesis procedure, which includes recursive optimisation. A design example is given.