Transmission Lines Loaded With Bisymmetric Resonators and Their Application to Angular Displacement and Velocity Sensors

This paper is focused on the analysis of coplanar waveguides (CPWs) loaded with circularly shaped electric-LC (ELC) resonators, the latter consisting of two coplanar loops connected in parallel through a common gap. Specifically, the resonator axis is aligned with the CPW axis, and a dynamic loading with ELC rotation is considered. Since the ELC resonator is bisymmetric, i.e., it exhibits two orthogonal symmetry planes, the angular orientation range is limited to 90 degrees. It is shown that the transmission and reflection coefficients of the structure depend on the angular orientation of the ELC. In particular, the loaded CPW behaves as a transmission line-type (i.e., all-pass) structure for a certain ELC orientation (0 degrees) since the resonator is not excited. However, by rotating the ELC, magnetic coupling to the line arises, and a notch in the transmission coefficient (with orientation dependent depth and bandwidth) appears. This feature is exploited to implement angular displacement sensors by measuring the notch depth in the transmission coefficient. To gain more insight on sensor design, the lumped element equivalent-circuit model for ELC-loaded CPWs with arbitrary ELC orientation is proposed and validated. Based on this approach, a prototype displacement sensor is designed and characterized. It is shown that by introducing additional elements (a circulator and an envelope detector), novel and high precision angular velocity sensors can also be implemented. An angular velocity sensor is thus proposed, characterized, and satisfactorily validated. The proposed solution for angular sensing is robust against environmental variations since it is based on the geometrical alignment/misalignment between the symmetry planes of the coupled elements.