Frequency-Variation Sensors for Permittivity Measurements Based on Dumbbell-Shaped Defect Ground Structures (DB-DGS): Analytical Method and Sensitivity Analysis

It is shown in this paper that a microstrip line loaded with a dumbbell-shaped defect ground structure (DB-DGS) is useful for complex permittivity measurements. The working principle of the sensor is the variation in the notch (resonance) frequency and depth caused by the material under test (MUT), when it is put in contact with the sensitive region of the device, i.e., the capacitive slot. It is demonstrated that the relative sensitivity of the sensor, defined as the variation of the resonance frequency of the DB-DGS with the dielectric constant of the MUT relative to the resonance frequency of the bare structure, does not depend on the geometry of the DB-DGS, provided the substrate is thick enough. The relative sensitivity, the key figure of merit, is dictated by the equivalent dielectric constant of the substrate, and it increases as the substrate permittivity decreases. Using the circuit model of the sensing structure, simple analytical expressions providing the dielectric constant and the loss tangent of the MUT are derived. Such analytical formulas depend on the notch frequency and depth of the sensor with and without MUT in contact with it, i.e., easily measurable quantities. The analysis carried out is corroborated through full-wave electromagnetic simulation and experiments.