Design of fractal rat-race coupler

This paper presents the implementation of fractal and space-filling curves in the design of a reduced size rat-race coupler. The large circuit area occupied by conventional rat-race coupler has been dramatically reduced through the use of space-filling curves having the same electrical length (1.5λ). Several space-filling curves have been investigated and compared. The design equations and area relations for some of the proposed space-filling curves have been developed. Two fractal rat-race couplers, operating at 2.4GHz, based on Moore´s 1st and 2nd iterations have been investigated. The 2nd iteration Moore rat-race coupler has an area of only 9.8% relative to conventional rat-race coupler. The performance of the proposed coupler is in good agreement with that of a conventional rat-race coupler, and has a better phase response. Moreover, smaller relative area observed in other space-filling curves may be considered as future candidates for system-on-package (SOP) integration. The design and simulation have been performed using full-wave analysis.