Analysis of a concentric coplanar capacitive sensor using a spectral domain approach

Previously, concentric coplanar capacitive sensors have been developed to quantitatively characterize the permittivity or thickness of one layer in multi‐layered dielectrics. Electrostatic Green’s functions due to a point source at the surface of one‐ to three‐layered test‐pieces were first derived in the spectral domain, under the Hankel transform. Green’s functions in the spatial domain were then obtained by using the appropriate inverse transform. Utilizing the spatial domain Green’s functions, the sensor surface charge density was calculated using the method of moments and the sensor capacitance was calculated from its surface charge. In the current work, the spectral domain Green’s functions are used to derive directly the integral equation for the sensor surface charge density in the spectral domain, using Parseval’s theorem. Then the integral equation is discretized to form matrix equations using the method of moments. It is shown that the spatial domain approach is more computationally efficient, whereas the Green’s function derivation and numerical implementation are easier for the spectral domain approach.