Equivalent Circuit Modeling of a Single-Ended Patch Sensing Element in Integrated Technology

Abstract

In this article, we present an analytical formulation based on an equivalent circuit model to support the challenging task of designing and analyzing single-ended patch sensing elements to be integrated in planar technologies. The proposed approach further allows for differentiating the permittivity values of the individual layers when sensing over dense and stratified mediums. The equivalent model of the sensing pixel is derived resorting to equivalence theorem and transmission-line theory. The relative impact of the material under test and the metal thickness of the sensing element is accurately included in the evaluation of the endpoint load of the radial transmission line, equivalent to the patch radius. This approach of representing the single-ended sensing element isolates the capacitance contributions associated with the patch radius, patch thickness, and the medium under test. The computationally fast tool is further utilized in absolute permittivity measurements using a 0.14- $\mu \text{m}$ CMOS 2-D permittivity imaging matrix prototype operating from 100 MHz to 2.9 GHz, reporting excellent agreement with theoretical values.