An enhanced model for an open-ended coaxial probe used for making permittivity measurements is presented. A permittivity measurement system consisting of the coaxial probe and a network analyzer is described including details of the error correction and curve fitting techniques. Determination of the percent dissolved solids in fructose solutions from permittivity measurements is presented as example of the usefulness of the coaxial probe/network analyzer measurement system.

An improved technique for permittivity measurements using a coaxial probe

The requirements for dielectric measurements on polar liquids lie largely in two areas. First there is scientific interest in revealing the structure of and interactions between the molecules - this can be studied through dielectric spectroscopy. Secondly, polar liquids are widely used as dielectric reference and tissue equivalent materials for biomedical studies and for mobile telecommunications, health and safety related measurements. This review discusses these roles for polar liquids and surveys the techniques available for the measurement of their complex permittivity at RF and Microwave frequencies. One aim of the review is to guide researchers and metrologists in the choice of measurement methods and in their optimization. Particular emphasis is placed on the importance of traceability in these measurements to international standards

A review of RF and microwave techniques for dielectric measurements on polar liquids

The advantages and limitations of using partial differential analysis to assess the methodological uncertainty associated with the measurement of the dielectric properties of a material are discussed and an alternative pragmatic approach is proposed. It relies on repeat measurements of the dielectric properties of reference liquids and an analysis to estimate random and systematic uncertainties. Examples of measurement uncertainty are provided for well-defined monomolecular materials and for less homogeneous materials at microwave frequencies. All examples relate to measurement with an open-ended coaxial probe but the methodology is not specific to this technique. Examination of the components of uncertainty in the dielectric properties of biological tissue shows that, where the system is free of methodological bias, random fluctuations originating from sampling and natural inhomogeneity dominate the uncertainty budget. In such cases, the mean value of the measured parameter and the standard error of the mean can be taken as a good measure of the true value and its associated uncertainty.

https://iopscience.iop.org/article/10.1088/0031-9155/51/23/006/pdf

Dielectric measurement: error analysis and assessment of uncertainty

Starting from a rigorous formulation for the admittance of an open ended coaxial probe, the authors identify the simplifying assumptions that are introduced to obtain more practical solutions. The predictions of the models are compared to each other and to experimental data obtained on an independently calibrated experimental set-up. The advantages and limitations of a model are determined by the theoretical derivation and the numerical solution. The model identified as most suitable for the measurement of the dielectric properties of biological materials is used to determine the relative permittivity and conductivity of muscle and skull bone in the frequency range 1 MHz to 20 GHz.

https://iopscience.iop.org/article/10.1088/0031-9155/39/12/004/pdf

Admittance models for open ended coaxial probes and their place in dielectric spectroscopy.

A full-wave analysis is applied to the scheme of measuring electromagnetic (EM) properties of materials over the frequency range of 0.3-4 GHz using a flanged open-ended coaxial probe. The excitation of complex waves, which include surface waves, radiative waves and radial guided waves in layered material media, is considered. With an accurate theory, this scheme may be used to measure both complex permittivity and permeability of the material simultaneously. >

Determination of electromagnetic properties of materials using flanged open-ended coaxial probe-full-wave analysis

An integral equation is formulated for a coaxially fed annular aperture antenna. The integral equation in terms of the unknown tangential aperture electric field is solved numerically by the Method of Moments. The coaxial feed line is air filled while the exterior region consists of i) air, ii) fat or bone, and iii) muscle. Results are given for the aperture electric field, apparent input admittance, and contours of constant power absorption when the excitation frequency is 2.45 GHz.

W. Yablon

Papers

The Annular Slot Antenna in a Lossy Biological Medium (Short Papers)