A Closed-Form Full-Wave Model for the Reflection Coefficient of an Open-Ended Coaxial Probe for Real-Time Dielectric Spectroscopy

Dielectric spectroscopy using open-ended coaxial probes characterizes the permittivity of a material based on its interference with a transmitted electromagnetic wave, offering many applications spanning from human health to non-destructive testing. The permittivity is uniquely tied to the material's reflection coefficient, that is, the ratio between the magnitude of the reflect wave to that of the incident wave. Various models have been proposed to relate the permittivity of the material to the measured reflection coefficient, but they all suffer from a common trade off: When they favour simplicity, they neglect higher order modes and become inaccurate. When using full-wave analysis, they are indeterminate, computationally intensive with no closed-form solution, and cannot be used in real-time. In this paper we introduce for the first time a novel full-wave, closed-form model for the reflection coefficient of an open-ended coaxial probe. Our novel model combines full-wave analysis with a Taylor series expansion to reduced the forward problem to a simple matrix inversion, significantly reducing the computational costs of full-wave analysis, while maintaining unparalleled accuracy. The proposed model is validated experimentally through 200 measurements in methanol and with extended permittivity ranges over 1800 simulations in Ansys. The average modelling errors compared to experimental and simulation results are 0.92 % and 1.5 %, respectively, making this model a significant step towards full-wave real-time spectroscopy.