An Analytical Method to Implement High-Sensitivity Transmission Line Differential Sensors for Dielectric Constant Measurements

A simple analytical method useful to optimize the sensitivity in differential sensors based on a pair of meandered microstrip lines is presented in this paper. Sensing is basedon the phase difference of the transmission coefficients of both lines, when such lines are asymmetrically loaded. The analysis provides the combination of operating frequency and line length (the main design parameters) that are necessary to obtain the maximum possible differential phase (+/- 180 degrees) for a given level of the differential dielectric constant (input dynamic range). The proposed sensor is useful to detect tiny defects of a sample under test (SUT) as compared to a reference (REF) sample. It can also be applied to the measurement of the complex dielectric constant of the SUT, where the real part is inferred from the differential phase, whereas the imaginary part, or the loss tangent, is derived from the modulus of the transmission coefficient of the line loaded with the SUT. It is experimentally demonstrated that the proposed device is able to detect the presence of few and small (purposely generated) defects in a commercial microwave substrate, as well as subtle variations in their density, pointing out the high achieved sensor sensitivity. Sensor validation is also carried out by determining the dielectric constant and loss tangent of commercial microwave substrates.