Dynamic Characteristics and Vibrational Response of a Capacitive Micro-Phase Shifter

The objective of this paper is to control the phase shifting by applying a bias DC voltage and changing the mechanical characteristics in electrostatically-actuated micro-beams. This problem can be more useful in the design of micro-phase shifters, which has not generally been investigated their mechanical behavior. By presenting a mathematical modeling, Galerkin-based step by step linearization method (SSLM) and Galerkin-based reduced order model have been used to solve the governing static and dynamic equations, respectively. The equilibrium positions or fixed pints of the system have been determined and the calculated static and dynamic pull-in parameters have been validated by previous experimental and theoretical results and a good agreement has been achieved. The frequency response of the system has been studied and illustrated that changing applied bias DC voltage affects the resonance frequency and maximum amplitude of the system vibrations. Then, phase diagram of the system for various damping ratio and excitation frequencies has been gained. It has been shown that by changing the bias DC voltage applied on the electrostatically-actuated micro-beam, which can be used as a varactor in phase shifter circuit, the stiffness of the micro-beam changes and consequently the phase shifting can be controlled. Finally, effect of the geometrical and mechanical properties of the micro-beam on the value of the phase shifting has been studied.