Parametric analysis of the edge capacitance of uniform slots and application to frequency-variation permittivity sensors

This paper presents a parametric analysis relative to the effects of the dielectric constant of the substrate, substrate thickness and slot width on the edge capacitance of a slot-based resonator. The interest is to find the conditions (ranges of the previously cited parameters) compatible with the presence of a quasi-magnetic wall in the plane of the slot (or plane of the metallization). If such magnetic wall is present (or roughly present), the electric field in the plane of the slot is tangential (or quasi-tangential) to it and the edge capacitance can be considered to be the parallel combination of the capacitances at both sides of the slot. Moreover, variations in one of such capacitances, e.g., caused by a change in the material on top of the slot, or by a modification of the dielectric constant of the substrate do not affect the opposite capacitance. Under the magnetic wall approximation, the capacitance of certain electrically small slot-based resonators can be easily linked to the dielectric constant of the material present on top of it. The consequence is that such resonators can be used as sensing elements in a permittivity sensor and the dielectric constant of the so-called material under test (MUT) can be determined from the measured resonance frequency and a simple analytical expression. In this paper, the results of this parametric analysis are validated by considering several sensing structures based on dumbbell defect ground structure (DB-DGS) resonators of different dimensions.