Analytical modeling of plus shape MEMS paddle bridge resonant sensor for weak magnetic fields

In this paper, we present an analytical model of novel plus shape MEMS paddle bridge resonant sensor to estimate electromechanical behavior, damping, electrostatic actuation and capacitive detection. The analytical model is derived using the Reynold´s method for squeeze film and Rayleigh method for resonant frequency. Working in a resonant condition, the sensor´s vibration amplitude is converted into the sensing current, which reflects the outside magnetic field. The first bending mode resonant frequency of optimized device is estimated at different values of damping ratios. The analytical results of the device are verified with the simulation. The results indicate its sensitivity 0.3163 pA/μT, when operating at optimized damping ratio 0.056 and 26.58% improvement in capacitive sensitivity with respect to ordinary paddle bridge. Our analytical model can be useful in the mechanical design of different shapes of paddle bridge resonators with complex structural configurations.