A Parallel Plate Variable Capacitor-Based Wind Pressure Sensor: Closed-Form Solution and Numerical Design and Calibration

TL;DR

This paper introduces a wind pressure sensor using a variable capacitor and a flexible membrane, with a detailed analytical solution and design method.

Contribution

A new analytical closed-form solution for a wind pressure sensor with a spring-reset capacitor and membrane is presented.

Findings

The elastic contact problem between the membrane and capacitor plate is solved without small rotation angle assumptions.

An analytical relationship between wind pressure and capacitance change is derived and validated.

Design parameters' effects on the sensor's performance are quantitatively analyzed.

Abstract

In this paper, a parallel plate variable capacitor-based wind pressure sensor is proposed, which uses a wind-driven peripherally fixed circular membrane as its pressure-sensitive element and a spring-reset parallel plate variable capacitor as its sensing element. The circular membrane is first driven by the wind, and then it pushes the spring-reset movable electrode plate of the parallel plate variable capacitor to move, resulting in a change in the capacitance of the capacitor. The wind pressure, i.e., the direct action force per unit area exerted by the wind on the circular membrane, is thus detected by measuring the capacitance change of the capacitor. The elastic contact problem between the circular membrane and the spring-reset movable electrode plate is analytically solved, and its closed-form solution is presented, where the usually adopted small rotation angle assumption of the membrane is given up. The analytical relationship between the input pressure and output capacitance of the capacitive wind pressure sensor proposed here is derived. The validity of the closed-form solution is proved, and how to use the closed-form solution and input/output analytical relationship for the numerical design and calibration of the capacitive wind pressure sensor proposed here is illustrated. Finally, the qualitative and quantitative effects of changing design parameters on the capacitance–pressure analytical relationship of the wind pressure measurement system are investigated comprehensively.

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