Analysis of Multimode Circular Cross-Shaped Resonator With Asymmetric Via and Its Application to Microwave Angular Displacement Sensor

Abstract

In this letter, the multimode circular cross-shaped resonator (MMC-CSR) with asymmetric via is proposed and analyzed. The formulation of via placement on the resonator asymmetrical to the input and output ports is given and exploited compared with the conventional symmetric formulation. An equivalent implementation structure is thus developed for angular displacement sensing, which is attributed to a circular stub that is printed on the top layer and held by a circular rotatable plate, while the remainder is printed on the fixed bottom layer. Rotating the circular stub along the asymmetric via leads to the linear variation of the transmission zero with angular displacement leveraging rotational displacement sensing with higher sensitivity and dynamic range. A prototyped sensor centered at 2 GHz with a 310 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{\circ}$</tex-math> </inline-formula> dynamic range in a clockwise rotation and average sensitivity of 4.03 MHz/ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{\circ}$</tex-math> </inline-formula> and 0.083 dB/ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{\circ}$</tex-math> </inline-formula> has been experimentally characterized.