A METHOD FOR CALCULATING THE THICKNESS OF A RECTANGULAR MEMBRANE FOR A SEMICONDUCTOR PRESSURE PIEZORESISTIVE TRANSDUCER TAKING INTO ACCOUNT NONLINEAR BENDING 

Vadim S. Volkov, Candidate of technical sciences, associate professor, associate professor of the sub-department of instrument engineering, Penza State University (40 Krasnaya street, Penza, Russia), E-mail: vadimv_1978@mail.ru
Sergey N. Bazykin, Doctor of technical sciences, associate professor, head of the sub-department of instrument engineering, Penza State University (40 Krasnaya street, Penza, Russia), E-mail: cbazykin@yandex.ru
Aleksei A. Trofimov, Doctor of technical sciences, associate professor, professor of the sub-department of information and measuring equipment and metrology, Penza State University (40 Krasnaya street, Penza, Russia), E-mail: alex.t1978@mail.ru 

Background. The sensing elements of semiconductor pressure transducers are traditionally made in the form of round and square membranes, while the use of other geometric shapes, for example, rectangular, allows you to reduce the dimensions while maintaining high sensitivity. The aim of the work is to study the effect of nonlinear bending of a rectangular membrane for piezoresistive transducer under the influence of measured pressure on the output signal and to determine the error of nonlinearity. Materials and methods. Existing methods for determining the membrane thickness of pressure transducers take into account only linear bending, and the well-known equation of nonlinear membrane bending has no analytical solution and was previously solved by an approximate graphical method, therefore, a method for determining the thickness of a rectangular silicon membrane of a strain gauge was developed taking into account nonlinear bending according to the criterion of mechanical strength by solving the membrane deflection equation numerically in the MathCad program. Results. A technique has been developed to calculate the thickness of a rectangular flat membrane of a silicon pressure strain converter, and the dependence of the output voltage of the bridge circuit on the applied pressure has been constructed, taking into account the linear and nonlinear bending of the rectangular membrane. Conclusions. Using the developed technique, the error of the nonlinearity of the output signal was determined when taking into account only the linear bending of the membrane, it was shown that this error is 3 %, which does not meet modern requirements for pressure measuring instruments and requires the development of constructive solutions to reduce this error. 

semiconductor pressure transducer, rectangular silicon membrane, membrane thickness, non-linear bending, non-linearity error 

Volkov V.S., Bazykin S.N., Trofimov A.A. A method for calculating the thickness of a rectangular membrane for a semiconductor pressure piezoresistive transducer taking into account nonlinear bending. Izmerenie. Monitoring. Upravlenie. Kontrol' = Measuring. Monitoring. Management. Control. 2024;(3):64–70. (In Russ.). doi: 10.21685/2307-5538-2024-3-8