Modeling of spatially periodic dielectric sensors in the presence of a top ground plane bounding the test dielectric

Semi-analytical models are used to simulate the response of periodic-field electroquasistatic dielectrometry sensors. Due to the periodic structure of the sensors it is possible to use Fourier series methods in combination with collocation point numerical techniques to generate accurate sensor simulations much more efficiently than with the more general finite-element methods. Previously, collocation-point models used to compute the response of periodic field dielectric sensors, also known as interdigitated electrode dielectrometers (IDED), have ignored the contribution of the constant (zero-order) term in the Fourier series expansion of the physical quantities. This is justifiable if the top dielectric material layer under test is infinitely thick, with any top ground plane bounding the dielectric removed too far from the sensor to influence its response. This is the assumption generally made until now in the application of these models. In practice, however, it is impossible to eliminate the cumulative effect of objects at ground potential in the vicinity of the sensor, which in general manifests itself as a ground plane electrode positioned at some effective distance within the top dielectric layer (usually air). In order to eliminate this source of uncertainty in the measurements, we suggest that a grounded electrode be explicitly placed at the top of the dielectric layer in the experimental setup, and its presence be accounted for in the models. Furthermore, in many cases, such as measurements on ceramic thermal barrier coatings, a metal layer is already present behind the material under test. In this paper we present how the models must be modified to account for this ground plane, and what effect it has on the dependence of the sensor response on the material properties. For example, the sensor transcapacitance may no longer be a monotonically increasing function of the material's permittivity, leading to non-uniqueness in permittivity measurements, as some held lines will terminate at the top ground plane rather than on the sensing electrode. We present experimental data that confirm these models.