Transmission-Mode Phase-Variation Microwave Sensor Applied to Highly Sensitive Micrometer-Scale Thickness Measurements

This paper proposes a highly sensitive two-port single-frequency permittivity sensor operating in transmission. The device consists of a shunt-connected short-circuited quarter-wavelength resonator (the sensing element) sandwiched between a symmetric configuration of cascaded impedance inverters with alternating high and low impedance. The output variable of the sensor is the phase of the transmission coefficient at the operating frequency, highly sensitive to variations in the permittivity of the medium surrounding the sensing resonator. In the proposed two-port sensor, the feeding (harmonic) signal and the output signal do not share the same port, which facilitates retrieving the output variable in scenarios where a vector network analyzer (VNA) cannot be used. The maximum sensitivity in the reported prototype is S<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> = −63.94° per unit of dielectric constant variation, whereas the figure of merit (FoM), or ratio between the maximum sensitivity and the area of the sensing region expressed in squared wavelengths, is FoM = 3384°/λ<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>, a high value achieved by virtue of the small sensing area. The sensor is applied to the micron-scale measurement of thickness in polytetrafluoroethylene (PTFE) samples, with a sensitivity and resolution of 7074°/mm and 5 μm, respectively.