A theoretical study of an improved capacitive pressure sensor: Closed-form solution of uniformly loaded annular membranes

•The upper structure of conventional capacitive pressure sensors was modified.•The non-parallel plate capacitor was changed into the parallel plate capacitor.•The closed-form solution of the simplified mechanical model was presented.•The input-output relationship of the improved sensors was derived. In this study, the conductive diaphragm in conventional capacitive pressure sensors with dual function (the deformable element and the upper electrode plate of a non-parallel plate capacitor) was modified into a non-conductive elastic annular thin-film (as the deformable element) centrally connected with a conductive rigid circular plate or alternatively with a non-conductive rigid circular plate adhered by a conductive thin-film (as the upper electrode plate of a parallel plate capacitor). This modification brings two advantages: the parallel plate capacitor is more convenient in the accurate calculation of capacitance than a non-parallel plate capacitor; it is easier to select a deformable element with good elastic behavior in non-conductive elastic thin-films than to select such a deformable element in conductive diaphragms. These advantages could provide convenience for further improving the performance of sensors. The presented closed-form solution can meet the needs of the research and development of this improved capacitive pressure sensor.