The design, especially the numerical calibration, of a circular touch mode capacitive pressure sensor is highly dependent on the accuracy of the analytical solution of the contact problem between the circular conductive membrane and the rigid plate of the sensor. In this paper, the plate/membrane contact problem is reformulated using a more accurate in-plane equilibrium equation, and a new and more accurate analytical solution is presented. On this basis, the design and numerical calibration theory for circular touch mode capacitive pressure sensors has been greatly improved and perfected. The analytical relationships of pressure and capacitance are numerically calculated using the new and previous analytical solutions, and the gradually increasing difference between the two numerical calculation results with the gradual increase in the applied pressure is graphically shown. How to use analytical solutions and analytical relationships to design and numerically calibrate a circular touch mode capacitive pressure sensor with a specified pressure detecting range is illustrated in detail. The effect of changing design parameters on capacitance-pressure analytical relationships is comprehensively investigated; thus, the direction of changing design parameters to meet the required or desired range of pressure or capacitance is clarified.
Keywords: analytical solution; capacitive sensor; circular conductive membrane; numerical calibration; pressure sensor; touch mode of operation.