An approximate analytical solution to the pull-in voltage of a micro bridge with an elastic boundary

This paper derives an approximate analytical solution to the pull-in voltage of a micro bridge with elastic boundaries. The analytical model considers the elastic boundary effect, fringing field capacitance, residual stresses and the distributed flexibility of the bridge. The accuracy of the present approximate analytical solution is verified by comparison with the simulation results of commercial FEM packages and other published closed-form solutions as well as experimental measured data. The deviation of the present approximate analytical solution is within 5% for a wide beam and a narrow beam in a small deflection regime. The present approximate analytical solution has explicit physical meaning and is highly accurate for device design.