Lumped parameter modeling of absolute and differential micro pressure sensors

Mechanical systems may be modeled as systems of lumped masses (rigid bodies) or as distributed mass (continuous) systems. The latter are modeled by partial differential equations, whereas the former are represented by ordinary differential equations [1] In this paper a lumped parameter model of absolute and differential pressure sensors are developed, whose diaphragm is designed to undergo very small deflections (typically less than 25% of the thickness). A simple approximate model with proper assumptions are considered and analyzed first. A more appropriate model with refined approximation is considered later. Estimation of various parameters like mass, spring constant and damping of the diaphragm & fluid are done and used to estimate the transfer function. The transfer function is then used to understand the frequency and stability analysis of the system. A square, rigidly fixed diaphragm pressure sensor is considered in this work. By limiting the maximum deflection to one-fourth of the thickness, the analysis has been done for a maximum applied pressure of 100 MPa. MATLAB® is used as a tool to carry out the analysis.