Miniaturized D-Band CMOS Rat-Race Coupler With Slow-Wave Transmission Line and Phase Inverter

A miniaturized D-band CMOS rat-race coupler is proposed in this brief. Different with conventional 3
$\lambda $
/2-ring rat-race coupler in microstrip line, the proposed structure origins from compact 7
$\lambda $
/6-ring structure, and further reduces the size by using slow-wave transmission line and phase inverter simultaneously. The slow-wave transmission line efficiently uses multilayered back-end-of-lines in standard CMOS process, to confine the electromagnetic waves and reduce the physical length of
$\lambda $
/6 sections. Moreover, a 180° phase inverter with two parallel striplines is designed to further shorten the 2
$\lambda $
/3 Section to
$\lambda $
/6. The proposed on-chip rat-race coupler features a compact size of
$0.0032{\lambda }_{0}^{2}$
and a measured impedance bandwidth of 42.9%.