0n the Use of Resonant Diaphragms as FM Pressure Transducers

Abstract
A theoretical pressure-frequency characteristic for thin diaphragms, used as resonant pressure sensors in FM pressure transducers, s derived. The characteristic is valid for both low and high pressures (where the diaphragm deflection is a nonlinear function of pressure) and agrees well with experimental data in the range of 0-3 atmospheres. The use of a deflection diaphragm in the resonant sensor mode reduces the pressure hysteresis by a factor of 2 at high pressures. By combining two diaphragms in a pressure capsule configuration, the advantages of a dual-sensor transducer can be realized with a single set of oscillator electronics. When the diaphragms are identical, the fundamental capsule natural frequency is equal to the natural frequency of either diaphragm. The sensitivity of the capsule configuration to external accelerations is much less than the sensitivity of an individual diaphragm. A calibration technique based on least squares fitting of data to a theoretical pressure-frequency characteristic is described. The technique accounts for the quadratic diaphragm deflection term, which is produced by numerical solution of the nonlinear differential elasticity equations, but which does not appear in the approximate analytic solution. This quadratic term accounts for the nonzero sensitivity of the pressure sensor at vacuum. An extension of the least squares curve fitting, using multiple linear regression methods, is proposed to provide temperature correction and thereby increase the versatility of the pressure transducer. The temperature sensitivity of the capsule is essentially due entirely to the thermoelastic coefficient of the diaphragrm material.

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