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This article presents an easy way to measure frequency dependence of the complex permittivity and complex permeability for any kind of material from 10 MHz to 6 GHz, with temperature variation between the ambient temperature and 85°C. This work is based on a well-known transmission/reflection technique using a coaxial line equipped with a thermoregulation system to manage temperature variations in the sample confinement area. The paper underlines some effects which have to be taken into account with temperature variation. APU10 and cyclohexanol are presented as examples of solid and liquid reference materials.

Measuring the electromagnetic properties of materials is widely studied nowadays. In the last twenty years, many useful measurement methods in microwave range [

In this section, the different processes to determine the frequency and temperature dependence of the electromagnetic characteristics of materials are detailed. We start with a brief definition of the classical mathematical equations and of an uncertainty estimation for the frequency dependence of the complex permittivity and the complex permeability. Afterwards, we propose a process to accurately manage the temperature in the sample to obtain the permittivity and permeability behaviours.

The permittivity and permeability are defined as complex values:

The setup is composed by a vector network analyser (Anritsu MS2038 C) and a tapered coaxial line. The coaxial line is divided into three parts.

The two tapered parts were designed to convert the 7 mm diameter line of the coaxial connector, into a 13 mm line, to significantly increase the sample volume. Furthermore, assuming the conical part as

The relation between the

With

Finally, with equation (

This method is useful to directly obtain the permittivity and permeability without any assumption on the material properties. Hence, the study of any kind of material (liquid, solid, powder, etc.) is possible.

In transmission/reflection method, we expect different sources of errors:

Errors in measuring

Gaps between sample and sample holder

Uncertainties in the length of the sample

Uncertainties in the plane reference position

In our case,

Measurement coaxial line. CST design.

Relative uncertainty in

We easily understand how it became important to have a good precision of the sample length. We did not plot the impact of the error of l1 and l2, but the higher the precision, the lower the error. Furthermore, Using a transmission reflection method, we can expect an error around 1% [

A heating ring is used to manage the temperature variation of the coaxial line, which is placed around the sample holder. This ring is connected to a PID thermoregulation system.

With the present setup (Figure

Picture and synoptic of the permittivity measurement setup with temperature variation.

Heating of the sample holder increases the temperature of the entire coaxial cell. Thus, the cell can expand and directly modify the measured

Picture of the real part of permittivity of air for an empty cell as a function of temperature at 1 GHz.

The literature shows that the permittivity of air is closed to 1 [

To accurately measure the correct temperature dependence of the permittivity and permeability, homogeneity of the temperature inside the material becomes important. To evaluate the temperature of the sample holder, a PT100 sensor is placed between the heating ring and the external part of the sample holder. We extrapolate the stabilization of the internal temperature of the sample holder, and thus of the sample itself, by applying a sufficient stabilization delay. This extrapolation generates a certain difference that disappears with sufficient waiting time (Figure

(a) Graphic representing the real part of permittivity of a sample of octanol with a positive and negative slope of temperature variation. (b) Graphic representing the real part of permittivity of ethanol at 100 MHz as a function of time. It shows a heating-up process where at the beginning, the temperature was 30°C and after 600s, 35°C.

Considering only the temperature of the sample holder, it is impossible to precisely know the sample’s temperature. The difference showed (Figure

The way to determine the SD depends on the material to test; the SD has to be defined correctly. In the Figure

The thermoregulation system is designed to reach hundreds of degrees. However, in the actual configuration, the temperature is limited to 85°C. This maximum is set by the maximum working temperature of the connectors placed between the VNA’s N-type cables and the cell. To avoid irreversible problems on connectors and coaxial cables, the maximum temperature of the setup is 85°C. The setup’s performance has been checked from ambient to 85°C.

Thanks to the frequency measurement part and temperature measurement part, it becomes easy to characterize any kind of material on a wide range of frequency and between ambient temperature and 85°C with the coaxial line (Figure

Figure

Real part and imaginary part of permittivity (a) and permeability (b) of a sample of 4 mm length of APU10 with frequency and temperature variations with the corresponding error. The frequency range is from 50 MHz to 6 GHz at two different temperatures, 25°C and 85°C.

In Figure

In the same way, Figure

Real part and imaginary part of permittivity (a) and permeability (b) of a sample of cyclohexanol with frequency and temperature variations with the corresponding error. The frequency range is from 50 MHz to 6 GHz at two different temperatures, 25°C and 45°C.

In Figure

This article presents a study on electromagnetic characteristic measurement with temperature variation. The goal of this study was to validate a wide-band measurement technique with temperature variation. The frequency measurement is obtained with a classical coaxial transmission line method, and the temperature measurement is managed with a thermoregulation system. The maximum temperature was set to the maximum temperature accepted by the connectors even if the actual setup could go further.

Two main effects of temperature measurement have been presented. Firstly, it is the cell dilation effect which may appear at high temperatures. In the actual configuration of the setup, the dilation effect was negligible throughout the temperature range. Secondly, it is the effect of sample temperature homogeneity, which is decisive when measuring the permittivity of samples of a certain considerable volume.

Finally, permittivity and permeability measurements have been conducted on different materials; as a solid material, APU10, which is magnetodielectric, has been chosen. The temperature variation behaviour of the material has been presented, as well as the frequency variation. Likewise, as a liquid material, a sample of cyclohexanol has been studied. This one was a dielectric material with a well-known frequency dependence.

As shown in this paper, the setup is a helpful technique to obtain an approximation of the permittivity and the permeability of any kind of material. Furthermore, on a temperature range of 25°C to 85°C, it is also possible to measure permittivity and permeability variations. The next challenge will be the proposition of an upgrade of this setup to reach higher temperatures with coaxial line to maintain the wide band frequency measurement.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This work was co-financed by DGA and “Club des partenaires (Aix-Marseille University)”. This project has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No 736937.