Integrated piezoelectric direct current sensor with actuating and sensing elements applicable to two-wire dc appliances: Theoretical considerations

An oscillating-type MEMS dc current sensor integrated with piezoelectric actuating and sensing elements was proposed to be utilized for monitoring electricity consumption by a one-wire or two-wire appliance cord. It enabled non-contact and constant measurement and could be applicable to two-wire appliances without using a cord separator. It was found experimentally that the relative change in the maximum value of the output voltage was approximately proportional to the applied dc current. Theoretical models are developed in this work to analyze the relationship between the relative change in the maximum value of the output voltage and the applied dc current. We find that as the applied dc current increases, the oscillating-type sensing system exhibits three response areas: a linear increase area, an abrupt increase area and a decrease area. A linear increase area is defined as the sensing area where the equations on the linear relationship and the sensitivity are derived. In addition, theoretical considerations are outlined on the effect of the displacement of the cantilever during the vibration on the nonlinear response, the restoring forces of the cantilever as the applied current increases, and the factors affecting sensitivity. Theoretical models can be utilized to predict the applicable magnetic forces and piezoelectric output voltage as well as guide the optimization of the sensor design.