Trap filter using bracelet resonator

The bracelet resonator is a low cost resonator made from printed circuit technology. The resonance frequency was first computed in [1], unfortunately the whole transfert function of the resonator was not yet computed, particularly coupling with external circuit. The coaxial shape of this kind of resonator may render it particularly suitable as a trap filter for coaxial line Unfortunately, for these resonators, the extremely small metalisation depth compared to radius renders the simulation by finite element (FEM) extremely hard (slow) and memory consuming. Moreover, the simulation should be carried in 3D due to asymmetric nature of the gaps, and the finite height, increasing the complexity. Time domain methods are not well suited due to high quality coefficient of this kind of resonator. Thus a physical approximation of this resonator will be carried. † This paper is dedicated to the memory of the late Professor Jean-Yves le Huerou 1959-2020.