Parametric modeling of concentric fringing electric field sensors

Fringing electric field (FEF) sensors are widely used for non-invasive measurement of material properties, such as porosity, viscosity, temperature, hardness, and degree of cure. FEF sensors have also been used to detect the presence of a material or estimate the concentration of a material within the test environment. There are no generic analytical models for FEF sensors. Their design optimization process often involves complex and time-consuming finite element simulations. This paper presents a tool for improvement of the design process through formulating a universal equation for three-electrode concentric FEF sensors. The equation models the effect of sensor geometry and substrate material on sensor output. The model parameters are determined from a 3-D surface fit of finite element simulation results for the most common type of sensor geometry. The variables in the model are non-dimensionalized, which makes the model applicable to a wider range of sensor designs. Based on the model, the terminal capacitance can be estimated for three-electrode concentric sensors of wide range of sizes.