One-Port Coaxial Line Sample Holder Characterisation Method of Dielectric Spectra

Abstract

A technique for solving the one-port closed coaxial transmission line sample holder scattering equation for complex permittivity inversion for lossy materials is presented. A non-linear least-squares procedure is used for the determination of parameters for the specification of the spectral functional form of the complex permittivity. The method allows for accurate retrieval of many low- and high-permittivity dielectric materials in the frequency range of 1 GHz to 3 GHz inserted into the coaxial cell. Using this method, the complex permittivity of a number of liquids and a Maltese soil known as Bajjad soil have been extracted by measurements using a short terminated coaxial transmission line sample holder. The proposed novel inversion method is mainly based on the reflection coefficient of the test material. The measured results of the complex permittivity of liquid dielectrics such as ethanol, methanol, and TX100 are validated and compared with previously published data obtained from measurements made by the National Physical Laboratory (NPL) using a two-port measurement setup made with the same commercial coaxial transmission line sample holder used in the one-port setup. Since the technique allows broadband measurements, it has been used to characterise the soil dielectric spectrum in the frequency range of 1-3 GHz, which is also compared with results from a two-port setup of the same coaxial line. The experimental results are a validation of the proposed approach for different types of materials.

Keywords: coaxial line; dielectric measurements; dielectric properties; material under test; microwave measurement; sample holder; vector network analyser.

Figure 1

Schematic model of the coaxial transmission line cell.

Figure 2

Schematic diagram of the coaxial TEM transmission line terminated in short.

Figure 3

Experimental setup showing the closed coaxial transmission line attached to the VNA.

Figure 4

The closed coaxial transmission line and the point $z=-L$ at which the calibration was conducted.

Figure 5

The commercial two-port coaxial transmission line.

Figure 6

Real (left panel) and imaginary (right panel) parts of the retrieved permittivity as a function of the frequency of TX100, ethanol, and methanol, respectively.

Figure 7

Comparison of the complex permittivity retrieved using the proposed method and PTFE data extracted from two-port coaxial cell data measurement as reference.

Figure 8

Retrieved permittivity of dry (left panel) and hydrated (right panel) CST Microwave Studio material library soil and Bajjad sample, respectively, as a function of frequency.