Permittivity determination of liquid materials using waveguide measurements for industrial applications

Abstract

There is a need for a simple and relatively inexpensive microwave method for complex permittivity, ɛ, determination of liquid materials in industrial applications. Measurement cables that connect the measurement cell to the measuring instrument (usually a vector network analyser) may be either subject to severe phase instability particularly if they are long or metrology-grade cables are not available, or subject to thermal variation. In these instances, calibration techniques based on complex scattering parameter measurements may drastically suffer from extension of the reference plane to the boundaries of the measurement cell or sample end surfaces. In such situations, amplitude-only methods based on simplified calibration techniques such as response calibration are appropriate and very feasible. These methods have applications in industry such as thickness measurement and disbonding and delamination detection. The motivation of this study is to investigate a suitable method for ɛ determination of liquid materials using amplitude-only waveguide measurements. The analysis is restricted to lossy dielectric materials, which possess large enough attenuation such that the multiple reflections between their two end surfaces can be neglected. We derived an equation in terms of the loss tangent of these materials for selecting a suitable material thickness. We presented two approximations (frequency-independent and power-series representation) for ɛ determination of these materials. For validation of the method, we measured the ɛ of methanol and commercially available antifreeze solution by our method using a simple (frequency response) calibration and by another waveguide method using the thru–reflect–line calibration.