Transmission-line equivalent and microstrip structure for planar Möbius loop resonator

A transmission line model for planar Möbius loop resonator is presented. Theoretical background for the Möbius loop is developed by treating it as a ring resonator. Even-Odd mode analysis is used to account for the dual mode nature of the resonator. Also, the presence of two transmission zeroes is explained using the proposed model. The transmission line model is then used to implement a simple microstrip version of the Möbius loop resonator. A single resonator is then used to implement a dual-mode bandpass filter. Simulation and test results of the structure are presented.