A Single-Line Single-Channel Method With Closed-Form Formulas for the Characterization of Dielectric Liquids

This paper presents a method for the measurement of liquid permittivity without using liquid reference materials or calibration standards. The method uses a single transmission line and a single microfluidic channel which intercept the line twice. As a result, two transmission line segments are formed with channel sections to measure liquid samples. In single-connection measurements, the scattering parameters of three transmission line states can be obtained. The three states are both segments filled with air, one segment filled with a liquid sample while the other with air, and both segments filled with liquid. By choosing a 2:1 ratio for the two line segment lengths, closed-form formulas are provided to calculate line propagation constants directly from measured S-parameters. Then, sample permittivity values are obtained. A coplanar waveguide is built and tested with deionized water, methanol, ethanol, and 2-propanol from 0.1 to 9 GHz. The obtained line performance agrees with the simulation results. The obtained sample permittivity values agree with commonly accepted values.