Dual-band CRLH branch-line coupler in LTCC by lump elements with parasite control

The capacitance of a rectangle MIM capacitor is mainly controlled by its over-lapping area, while its aspect ratio can control the amount of parasitic inductance. With these two parameters, we can achieve both capacitance and parasitic inductance simultaneously. To achieve inductance and parasitic capacitance of a shunt spiral inductor at the same time, we add slot at ground plane to control the amount of shunt capacitance with spiral inductor size to control inductance. With these layout strategies, we can realize CRLH transmission lines in LTCC for dual band branch-line coupler with only series MIM capacitor and shunt spiral inductor in layout. Measurement results show dual-band coupling responses at 2.4 GHz and 5.2 GHz and agree well with simulation.