A Variable Capacitor for Measurements of Pressure and Mechanical Displacements; A Theoretical Analysis and Its Experimental Evaluation

Abstract

A variable capacitor is described for measuring (1) small displacements, (2) small volume changes, and (3) pressure differences. The capacitor consists of a deflectable diaphragm and a fixed electrode. The diaphragm is metallic, plane‐parallel, clamped at the edges, and at ground potential; the electrode, at an a.c. potential, has a plane surface parallel to the undeflected plate across an air gap. For use in displacement measurements, the diaphragm's center is deflected by a point contact from a mechanical link to the observed system, or by a uniform pressure load from a fluid link to the system. The fluid link is used also when measuring volume changes and pressure differences. The plate deflection results in a change in the air gap, and thus generates a capacitance signal. This signal is measured by electrical methods. A theoretical analysis of this variable capacitor is presented; sensitivity and alinearity factors for the three uses of the device are derived. The experimental performance shows reasonably satisfactory agreement with the derived theory. The displacement of the plate's center was measured with an interferometric method, using a yellow He line as a standard of reference; the applied pressure, with a liquid manometer; and the capacitance signal, with a standard capacitor substitution procedure. The gauge can be used so as to give quantitative electrical indications of displacement, volume change, or pressure difference; or can be used as a null indicator device in which an unknown pressure is balanced against a known one on opposite sides of the diaphragm. In order to achieve large volume an displacement sensitivities, small air gaps (5.10^–4 cm) are employed. Details of a construction method to assure small values are presented.