A Theorem on Asymmetric Structure Based Rat-Race Coupler

An asymmetric structure is in general never equivalent to a quarter-wavelength (symmetric) transmission line. However in this letter a theory has been derived, wherein each of the six quarter-wavelength transmission lines of a conventional rat-race coupler can be replaced by any arbitrary asymmetric structure connected in identical orientation. The theorem exploits the mirror-symmetry of a rat-race coupler, even when the asymmetric structure is used as its building block. It is also observed that every asymmetric structure has an equivalent frequency independent symmetric representation when used in a rat-race coupler. Asymmetric-T has been used as an example of the asymmetric-structure to demonstrate the accuracy of the theory and has been compared with that of the conventional and existing asymmetric-T based couplers.