A Modified SIW Re-Entrant Microfluidic Microwave Sensor for Characterizing Complex Permittivity of Liquids

In this paper, a modified substrate integrated waveguide (SIW) re-entrant microwave sensor is implemented by an annular slot loaded SIW re-entrant cavity resonator (RECR) to evaluate complex permittivity of liquid under test (LUT). The fringe electric field (E-Field) around metal post of the SIW RECR is suppressed by loading the plane disk. And then, by loading a narrow annular slot, the corresponding fringe non-linear capacitor is transferred as an annular capacitor which has linear response to real permittivity of LUT and is connected in parallel with the gap parallel plate capacitor of the RECR, and then the corresponding physical equivalent circuit model is accurately established. The dependence of the sensitivity of the proposed sensor on the dimension of the annular slot is discussed. The unique quantitative function relationship, instead of a mathematical fitted one, between the resonant frequency and the real permittivity of LUT is obtained to characterize the real permittivity predictive model by reasonably neglecting the ratio term of annular-slot capacitance to LUT effective capacitance. Additionally, an improved algorithm for more accurately extracting imaginary permittivity is proposed. A prototype of the proposed sensor is fabricated and measured. The predictive model of the complex permittivity is calibrated by using of methanol-water mixtures with known complex permittivity and is further verified by ethanol-water mixtures. The result of experiment verification, with the maximum measurement errors of real and imaginary permittivity of 4.07% and 7.79%, demonstrates that the complex permittivity of the liquid can be accurately characterized by using the proposed sensor.