Exact design of novel miniaturised fractal-shaped branch-line couplers using phase-equalising method

Although miniaturised and fractal-shaped branch-line couplers have been reported by many researchers, their operating bandwidth are narrowed and shifted because the phase-shifting properties of the fractal-shaped microstriplines with different iteration orders are different to each other; thus the application of these techniques were limited. In this paper, an exact design technique is presented to obtain compact and fractal-shaped branch-line couplers for a given frequency. By using the length reduction formulae of the chamfered bend and equalising the transmission phase of the fractal-shaped microstriplines of the proposed fractal-shaped branch-line couplers to their counterparts of the conventional branch-line coupler, the phase-shifting phenomenon of the fractal branch-line couplers can be compensated. As an example, novel fractal-shaped branch-line couplers operated at 2.4 GHz using Koch fractal shapes of different iteration orders have been designed successfully, and the designed couplers all operated at the designed frequency and achieved a maximum 81.8 size reduction. And furthermore, the operating frequency and its bandwidth are virtually unaltered. The proposed method is verified by the measurement results.