Novel Compact Dual-Band Rat-Race Coupler Combining Fractal Geometry and CRLH TLs

A super compact fractal-shaped composite right/left handed (CRLH) rat-race coupler (RRC) is proposed for the first time by skillfully combining two circuit schematics of the RRC operating at two arbitrary frequencies. For dual-band (DB) purpose, novel circuit schematics of RRC are deducted, and close-form formula and design procedures are derived in detail. The CRLH transmission line (TL) consists of lumped elements for the left handed part and Koch-shaped microstrip lines (MLs) for the right handed part. Since conventional RRC exhibits two types of unique branches, the DB design often suffers a tedious process. By employing the CRLH TL, the realization of a DB RRC becomes much easier. Moreover, constructing the microstrip lines as Koch curves enables the compactness of the circuit. For verification, a coupler operating at 0.75 and 1.8? GHz is fabricated and measured. Consistent results between simulation and measurement have confirmed the design and shown that the RRC with an area of 10.2% of its conventional counterpart owns excellent in-band performances.