# Measurement of the Dielectric Properties of Tropical Wood Species for Application to Millimetre-Band Antennas

Ndanga Adamou Eric, Eke Samuel, Matanga Jacques, Doka Yamigno Serge, Tan-Phu Vuong

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## To cite this version:

Ndanga Adamou Eric, Eke Samuel, Matanga Jacques, Doka Yamigno Serge, Tan-Phu Vuong. Measurement of the Dielectric Properties of Tropical Wood Species for Application to Millimetre-Band Antennas. Material Design & Processing Communications, 2024, 2024, pp.7777701. 10.1155/2024/7777701. hal-04984428

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WILEY

Research Article

# Measurement of the Dielectric Properties of Tropical Wood Species for Application to Millimetre-Band Antennas

Ndanga Adamou Eric<sup>1</sup>, Eke Samuel,<sup>1,2</sup> Matanga Jacques,<sup>1,2</sup> Doka Yamigno Serge,<sup>3</sup> and Tan Phu Vuong<sup>4</sup>

Correspondence should be addressed to Ndanga Adamou Eric; eric.adamou@gmail.com

Received 25 October 2023; Revised 14 May 2024; Accepted 24 May 2024

Academic Editor: Andrea Tridello

Copyright © 2024 Ndanga Adamou Eric et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

The purpose of this article is to determine the dielectric characteristics of wood species from Central African forests at microwave frequency for use as patch antenna substrate. The measurements were carried out on dried wood at frequencies of 930 MHz and 2.48 GHz. The suitability of the wood as a printed microwave antenna substrate will be determined by the values taken by the complex parameters “permittivity” $\epsilon'$, loss tangent “tan$\delta$,” and “permeability” $\mu = 1$. The measurement method chosen in this work is the method of small disturbances in a cylindrical cavity operating in the TM$_{010}$ mode. The values obtained for each species confirm the anisotropic nature of the wood. These measurements will also confirm that losses, which are the main criterion for selecting wood as substrate, increase with the wood species category and its density. The design and simulation results at 28 GHz of a travelling wave antenna on a wood substrate show that antennas can radiate with these materials in the millimetre band.

## 1. Introduction

The main purpose of this article is to determine the dielectric properties of certain wood species to determine whether they can be used as patch antenna substrate. The design of millimetre-band printed antennas requires a good knowledge of the dielectric materials used to optimize their efficiency. Several measurement methods have been developed over the years to characterize the dielectric properties of materials [1–6]. We have the experimental method and the numerical procedure used by the authors of [1]; in [2], on the other hand, a numerical method describing the 3D structure of wood containing fibers, rays, vessels, and cracks whose dimensions and material composition can be modified has been used. This model is fed into an efficient solver that calculates the effective dielectric constant of any 3D

structure of dielectric materials. The waveguide method and the open resonator technique were used by [3]. The former provided reference values, while the latter enabled them to confirm previous measurements. The weak perturbation method was used with a rectangular cavity in dural material by the authors of [4]. Finally, Perrin and Reynaud and Guelmami et al. [5, 6] use the free-space method to measure the dielectric properties of materials. Each method has its own field of application depending on several factors such as the specific frequency of application, the precision required for the measurement, the isotropic and homogeneous properties, the shape of the material (powder, liquid, or solid), its size, nondestructive or noncontact test requirements, and the temperature range. We want to determine the complex relative permittivity values and the total losses. As the wood is nonmagnetic, it therefore has a relative

<footnote n="1"><sup>1</sup>Laboratory E3M, National Higher Polytechnic School of Douala, University of Douala, P.O. Box 2107, Douala, Cameroon</footnote>

<footnote n="2"><sup>2</sup>Polytechnic Higher National School, University of Douala, P.O. Box 2701, Douala, Cameroon</footnote>

<footnote n="3"><sup>3</sup>Faculty of Science, University of Ngaoundéré, P.O. Box 454, Ngaoundéré, Cameroon</footnote>

<footnote n="4"><sup>4</sup>Institute of Microelectronics Electromagnetism and Photonics-Microwave Laboratory and Characterization, Grenoble Alps University, P.O. Box 38000, Grenoble, France</footnote>
permeability (equal to the unit; we also expect to get “low” permeability values for $ε_r'(1 < μ_r' = 1, μ_r'' = 0) < 3$) which will increase the bandwidth of the printed coils. Otherwise, when the permittivity becomes too high, parasitic surface waves can spread over the substrate. We want to achieve as low a tangent loss as possible. The method of measuring the permeability and dielectric losses of the wood available in the laboratory is the method of small disturbances in a cylindrical cavity operating in the TM₀₁₀ mode. This method has been widely used since 1946 and can make it possible to obtain errors in the order of 1% and 5% for excluding measurement errors on the sample size [7]. This method uses samples as close as possible to 40 × 3.8 × 1.62 mm, 40 × 4.18 × 1.79 mm, 40 × 4.34 × 1.5 mm, and 40 × 4.5 × 1.8 mm which does not allow for machining the samples with sufficient precision in any direction with the wood that comes mainly from the forest of Central Africa. The wood samples that we will use for these measures are dried wood, which can be easily bought on the Cameroonian market. Several investigations and measurements were carried out on the wood material [8, 9]. Wood dielectric properties were measured at microwave frequencies [10–12], even for wood species from Central African forests [13]. As wood is anisotropic, losses are expected to increase with the class and density of the wood. This is why we are going to select wood species, starting with wood that has the lowest air-dry density among all the wood species listed in the Cameroonian forest with high air-dry density $ε_r'$ and $ε_r''$.

Our measurements will determine the relative permittivity and the solid losses of the wood material. The measurement method used here makes it possible to determine the complex permittivity of any dielectric, even when dielectric losses are not negligible, but we obtain reliable values. Measurements using an HP 8720D network analyzer and a computer program allow us to simultaneously determine $ε_r$, tanδ, and quality factor Q.

This paper summarizes the results of dielectric measurements carried out at frequencies of 930 MHz and 2.48 GHz on two hardwoods (bubinga and makore), which are the species most commonly used for industrial applications in Cameroon; a softwood (ayous) used for interior joinery, for making moldings, as well as for creating and making plywood; and a medium-hardwood (bibolo), renowned for interior joinery and fittings. This document is organized into five parts, the first of which explains the interest of our work, and the second part outlines the methodology and tools used to characterize the various samples. The results of the characterizations are presented in the third part of this document; in the fourth part, a travelling wave antenna has been designed and simulated in a millimetre band using the CST Microwave software; and the fifth part allows us to conclude this work.

## 2. Materials and Methods

### 2.1. Measurement of Permittivity with a Cylindrical Cavity.
A cylindrical cavity of radius (r) and height (h), as illustrated in Figure 1, can be seen as a waveguide with two closed ends.

<figure><img src="image_3.png" /><figcaption>FIGURE 1: Geometry of a cylindrical cavity.</figcaption></figure>

In this cavity, TEmn0 modes may also be present. Their resonance frequencies ($f_r$)$_{TEmn0}$ (1) are given by the following equation [14]:

$$ (f_r)_{TEmn0} = \frac{1}{2\pi\sqrt{\mu_0\varepsilon_0}} \left(\frac{p'_{nm}}{r}\right), \quad (1) $$

where the values of $p'_{nm}$ correspond to the same root of the first derivative of the first-order $J'(x)$ Bessel function and are given in Table 1.

For a sample of a permeability dielectric material (2) placed in the center of the cavity, the method of small disturbances allows to determine the following:

$$ \begin{align} \varepsilon &= \varepsilon_0 (\varepsilon_r' - j\varepsilon_r''), \nonumber \\ \varepsilon_r' &= \alpha_1 \frac{V_{\text{cavit\'e}}}{V_{\text{\'echantillon}}} \cdot \frac{f_{r0} - f_{r1}}{f_{r0}} + 1, \nonumber \\ \varepsilon_r'' &= \frac{\alpha_1}{2} \left( \frac{V_{\text{cavit\'e}}}{V_{\text{\'echantillon}}} \right) \cdot \left( \frac{1}{Q_{u1}} - \frac{1}{Q_{u0}} \right), \nonumber \\ \alpha_1 &= \frac{1}{2J_1^2(x_{01})}, \end{align} \quad (2) $$

where $f_{r0}$ is the resonant frequency of the empty TM₀₁₀ mode; $f_{r0}$ is the resonance frequency of the TM₀₁₀ mode in the presence of the sample; $V_{\text{cavit\'e}}$ is the volume of the cylindrical cavity; $Q_{u0}$ is the quality coefficient of the vacuum cavity; $V_{\text{\'echantillon}}$ is the volume of the sample, taken as $V_{\text{\'echantillon}} \ll V_{\text{cavity}}$; $x_{01}$ is the first root of the Bessel function of the first order $J_0(x_{01}) = 0$; $\alpha_1 = 0, 53903$; and $Q_{u1}$ is the quality coefficient of the cavity loaded with a sample.

The tangent of losses is then given by

$$ \tan \delta = \frac{\varepsilon_r''}{\varepsilon_r'} = \frac{\alpha_1}{2\varepsilon_r'} \left( \frac{V_{\text{cavit\'e}}}{V_{\text{\'echantillon}}} \right) \cdot \left( \frac{1}{Q_{u1}} - \frac{1}{Q_{u0}} \right). \quad (3) $$

The measurement uncertainty depends mainly on the measurement error on the dimensions of the sample and the cavity. It also depends, to a lesser extent, on the openings allowing the insertion of the sample [15]. The measurement uncertainty due to the measurement uncertainty of the measured sample volume is given by (4)–(6). The samples were
<table><caption>TABLE 1: Values of $P'_m$ for TEMode$_{nm0}$ in a cylindrical cavity.</caption><thead><tr><th>n</th><th>p'<sub>n1</sub></th><th>p'<sub>n2</sub></th><th>p'<sub>n3</sub></th></tr></thead><tbody><tr><td>0</td><td>3,832</td><td>7,016</td><td>10,174</td></tr><tr><td>1</td><td>1,841</td><td>5,331</td><td>8,536</td></tr><tr><td>2</td><td>3,054</td><td>6,706</td><td>9,970</td></tr><tr><td>3</td><td>4,2012</td><td>—</td><td>—</td></tr><tr><td>4</td><td>5,3175</td><td>—</td><td>—</td></tr></tbody></table>

measured using a Palmer with an uncertainty of 10 µm. In the case of a material without losses, these quantities are real.

$$ \delta\varepsilon'_{r} = \alpha_{1} \frac{V_{\text{cavité}}}{(V_{\text{échantillon}})^{2}} \cdot \frac{f_{r0} - f_{r1}}{f_{r0}} \cdot \delta V_{\text{échantillon}}, \quad (4) $$

$$ \delta\varepsilon''_{r} = \frac{\alpha_{1}}{2} \frac{V_{\text{cavité}}}{(V_{\text{échantillon}})^{2}} \cdot \frac{1}{Q_{u1}} - \frac{1}{Q_{u0}} \cdot \delta V_{\text{échantillon}}, \quad (5) $$

$$ \delta \tan \delta = \frac{1}{\varepsilon'_{r}} \delta\varepsilon''_{r} - \frac{\varepsilon''_{r}}{\varepsilon'_{r}^2} \delta\varepsilon_{r}. \quad (6) $$

However, in the case of a material with losses, they are complex. They are then expressed by

$$ \varepsilon_r(f) = \varepsilon'_r(f) - j\varepsilon''_r(f). \quad (7) $$

The actual part measures the amount of energy stored in the material, and the imaginary part represents the dielectric (polarization) losses in the material [14, 15].

## 2.2. Preparation of Wood Samples.
The samples were cut according to the three main axes (Figure 2): (Ex), (Ey), and (Ez). The samples were then machined to 40 × 3.8 × 1.62 mm, 40 × 4.18 × 1.79 mm, 40 × 4.34 × 1.5 mm, and 40 × 4.5 × 1.8 mmwaveguide dimensions at 930 MHz and 2.48 GHz within which they will be placed. They have been dried in an oven at 200°C to ensure that the moisture content is less than or equal to 12% and to keep them at that level.

Table 2 summarizes the characteristics of the wood species selected for the study.

## 2.3. Experimental Device.
The cavity was simulated using CST Microwave Studio software. Figure 3 shows the various elements that make up our system.

Figure 4 shows the measurement of a sample using an HP 8720D vector network analyzer.

# 3. Experimental Results

The measurements in Figure 4 were made using a waveguide in which the device tested is located. For characterization, we performed measurements on two samples for each type of wood, and for each sample, we have

(i) used two frequencies: 930 MHz and 2.48 GHz

<figure><img src="image_4.png" /><figcaption>FIGURE 2: Fiber direction (A1A2 direction).</figcaption></figure>

<table><caption>TABLE 2: Choice of wood species.</caption><thead><tr><th>No.</th><th>Designation</th><th>Availability</th><th>Hardness</th><th>Air dry density</th></tr></thead><tbody><tr><td>01</td><td>Ayous</td><td>Regular</td><td>Tender</td><td>0.38</td></tr><tr><td>02</td><td>Bubinga</td><td>Regular</td><td>Hard</td><td>0.92</td></tr><tr><td>03</td><td>Bibolo</td><td>Limited</td><td>Medium Hard</td><td>0.53</td></tr><tr><td>04</td><td>Makore</td><td>Regular</td><td>Hard</td><td>0.69</td></tr></tbody></table>

<figure><img src="image_5.png" /><figcaption>FIGURE 3: Exploded view of the cavity.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>FIGURE 4: Measuring a sample.</figcaption></figure>
(ii) performed two measurements (one measurement for width and max thickness and one measurement for width and min thickness) because the sample thicknesses are not stable

**3.1. Ayous Wood.** We implemented this measurement technique at 930 MHz and 2.48 GHz (Equation (1)), which defines the radius of the cavity as $r = 123.67$ mm and $r = 46$ mm for 930 MHz and 2.48 GHz, respectively. The respective heights ($h$) of the cavity should be small in front of the wavelengths, and we took $h = 40$ mm. The respective cavity volumes are $V_{cavité930MHz} = 1907674 \text{ mm}^3$ and $V_{cavité248GHz} = 265904 \text{ m}^3$. The measured values are summarized in Tables 3 and 4. The quality factor measured at 2.48 GHz ranges from 543 to 648, and at 930 MHz, it varied from 1236 to 1297, allowing the ayous to oscillate as a microwave cavity. The ayous have acceptable losses in the tens and a high-quality factor, which presages a directional antenna but with low bandwidth. Measurement errors, although very small, are slightly different.

**3.2. Bibolo Wood.** The measured values are summarized in Tables 5 and 6. The quality factor measured at 2.48 GHz varies from 396 to 523, and at 930 MHz, it varies from 1100 to 1199, allowing the ayous to oscillate as a microwave cavity. Bibolo has slightly higher losses and measurement errors than those obtained with ayous.

**3.3. Bubinga Wood.** The measured values are summarized in Tables 7 and 8.

**3.4. Makore Wood.** The measured values are summarized in Tables 9 and 10.

The volume of the measured cavity decreases as the frequency increases; we went from a volume of $V_{cavité930MHz} = 1907674 \text{ mm}^3$ to $V_{cavité248GHz} = 265904 \text{ mm}^3$. However, as far as the results of the permittivity measurements are concerned, it can be seen that for the same dimensions, it increases when the frequency increases. The losses observed in the materials decrease as the frequency increases, and Equations (4) and (5) allowed us to calculate the measurement uncertainties due to uncertainty in the measurement of the volume of each sample measured. The measured uncertainties are less than or equal to a power, and this extremely low value shows that the measurements were made with very good accuracy. Ayous wood has a better quality factor at 2.48 GHz and 930 MHz, low dielectric losses, and the best relative permittivity values among all materials studied. This material can be considered a resonator capable of replacing a microwave cavity. This can be used as a substrate for antenna testing, as is the case with the FR4 material.

# 4. Analysis of Dielectric Constant and Loss Factor

Also known as relative permittivity ($\varepsilon_r$), the dielectric constant is a measure of the level of electrical insulation provided by the material and is a fundamental factor in ensuring signal integrity and impedance adjustment. This value depends strictly on the frequency of the signal and decreases as it increases. The loss factor, also called a loss

tangent (tanδ), indicates how easily a material has power losses. The lower the loss factor, the less power the dielectric material loses.

**4.1. Modelling the Ayous.** Ayous is a softwood, and Figure 5 shows the evolution of permittivity and dielectric losses according to the frequency obtained during the various measurements.

The permeability values obtained during the measurements vary from 1.98 to 2.45, respectively, for the 2.477 GHz and 2.478 GHz frequencies (see Figure 5(a)). The lowest measured dielectric loss is 0.11 and the largest is 0.13 at 2.478 GHz and 2.477 GHz, respectively (see Figure 5(b)). We also observed a decrease on both sides of each characteristic of the wood between the frequencies of 2.477 GHz and 2.478 GHz, and in this frequency range, the material loses less and less power.

**4.2. Bibolo Modelling.** Bibolo is a hard wood with a high air-dry density, and Figure 6 shows the changes in permittivity and dielectric losses as a function of frequency obtained during the various measurements. The permittivity values obtained during the measurements ranged from 2.8 to 3.4 at frequencies of 2.476 GHz and 2.474 GHz, respectively (Figure 6(a)).

The lowest dielectric loss measured is 0.153 and the highest is 0.176 at frequencies of 2.476 GHz and 2.474 GHz, respectively (Figure 6(b)). We observe a large decrease in the dielectric losses of bibolo wood between frequencies of 2.474 GHz and 2.476 GHz, and in this frequency range, the material will lose less and less power.

**4.3. Modelling Bubinga.** Bubinga is a moderately hard wood, and Figure 7 shows the change in permittivity and dielectric losses as a function of frequency obtained during the various measurements. Figure 7(a) shows the evolution of permittivity values as a function of the frequency obtained during the measurements; from 2.47267 GHz, these values continue to increase. The same applies to dielectric losses, where the values measured continue to increase from 2.47267 GHz (see Figure 7(b)).

The increase in these characteristics shows that the higher the frequency, the greater the power loss of the dielectric material.

**4.4. Makore Modelling.** Makore is a hardwood, and Figure 8 shows the evolution of permittivity and dielectric losses as a function of the frequency obtained during the various measurements. Figure 8(a) shows the evolution of permittivity values as a function of the frequency obtained during the measurements. From 2.47267 GHz onwards, these values continue to increase. The same applies to dielectric losses, where the values measured continue to increase from 2.47267 GHz (Figure 8(b)). The increase in these characteristics shows that the higher the frequency, the greater the power loss of the dielectric material.

Bubinga and makore are two types of hardwood, and the measurement results obtained for both show similar trends. In these materials, the higher the frequency, the higher the power losses, which have the direct consequence of obtaining
<table><caption>TABLE 3: Real and imaginary parts of the relative permittivity of 2.48 GHz dielectric losses of ayous dielectric materials.</caption><thead><tr><th>Sample</th><th>Frequency (GHz)</th><th>ε' measured</th><th>ε'' measured</th><th>ε<sub>r</sub>(f) measured</th><th>Tanδ measured</th></tr></thead><tbody><tr><td>Ayous LyEzminlx</td><td></td><td>2.1765 ± 9.55 * 10<sup>-8</sup></td><td>0.2713 ± 1.10 * 10<sup>-8</sup></td><td>2.19</td><td>0.1267</td></tr><tr><td>Ayous LyEzmaxlx</td><td>2.48</td><td>1.9734 ± 6.46 * 10<sup>-8</sup></td><td>0.223 ± 7.48 * 10<sup>-9</sup></td><td>1.98</td><td>0.113</td></tr><tr><td>Ayous LyEzminlx</td><td></td><td>2.4319 ± 8.54 * 10<sup>-8</sup></td><td>0.3335 ± 1.28 * 10<sup>-8</sup></td><td>2.45</td><td>0.1371</td></tr><tr><td>Ayous LyEzmaxlx</td><td></td><td>2.1705 ± 5.5 * 10<sup>-8</sup></td><td>0.2737 ± 8.44 * 10<sup>-9</sup></td><td>2.18</td><td>0.1261</td></tr></tbody></table>

<table><caption>TABLE 4: Real and imaginary parts of the relative permittivity of 930 MHz dielectric losses from ayous dielectric materials.</caption><thead><tr><th>Sample</th><th>Frequency (GHz)</th><th>ε' measured</th><th>ε'' measured</th><th>ε<sub>r</sub>(f) measured</th><th>Tanδ measured</th></tr></thead><tbody><tr><td>Ayous LyEzminlx</td><td></td><td>2.3059 ± 1.86 * 10<sup>-7</sup></td><td>0.2885 ± 1.10 * 10<sup>-8</sup></td><td>2.32</td><td>0.1251</td></tr><tr><td>Ayous LyEzmaxlx</td><td>0.93</td><td>2.0758 ± 1.25 * 10<sup>-7</sup></td><td>0.2396 ± 8.06 * 10<sup>-9</sup></td><td>2.08</td><td>0.1154</td></tr><tr><td>Ayous LyEzminlx</td><td></td><td>2.5837 ± 1.66 * 10<sup>-7</sup></td><td>0.3487 ± 1.35 * 10<sup>-8</sup></td><td>2.6</td><td>0.1349</td></tr><tr><td>Ayous LyEzmaxlx</td><td></td><td>2.2522 ± 1.07 * 10<sup>-7</sup></td><td>0.2716 ± 8.48 * 10<sup>-9</sup></td><td>2.26</td><td>0.1206</td></tr></tbody></table>

<table><caption>TABLE 5: Real and imaginary parts of the relative permittivity ε<sub>r</sub> and 2.48 GHz dielectric loss factors of bibolo dielectric materials.</caption><thead><tr><th>Sample</th><th>Frequency (GHz)</th><th>ε' measured</th><th>ε'' measured</th><th>ε<sub>r</sub>(f) measured</th><th>Tanδ measured</th></tr></thead><tbody><tr><td>Bibolo LyEzminlx</td><td></td><td>2.9316 ± 1.43 * 10<sup>-7</sup></td><td>0.466 ± 0.466 * 10<sup>-8</sup></td><td>2.9684</td><td>0.1589</td></tr><tr><td>Bibolo LyEzmaxlx</td><td>2.48</td><td>2.7752 ± 1.21 * 10<sup>-7</sup></td><td>0.426 ± 1.96 * 10<sup>-8</sup></td><td>2.8077</td><td>0.1536</td></tr><tr><td>Bibolo LyEzminlx</td><td></td><td>3.3508 ± 1.07 * 10<sup>-7</sup></td><td>0.593 ± 2.55 * 10<sup>-8</sup></td><td>3.4027</td><td>0.1768</td></tr><tr><td>Bibolo LyEzmaxlx</td><td></td><td>3.1702 ± 9.55 * 10<sup>-7</sup></td><td>0.539 ± 2.20 * 10<sup>-8</sup></td><td>3.2157</td><td>0.1701</td></tr></tbody></table>

<table><caption>TABLE 6: Real and imaginary parts of the relative permittivity ε<sub>r</sub> and dielectric loss factors tanδ to 930 MHz of bibolo dielectric materials.</caption><thead><tr><th>Sample</th><th>Frequency (GHz)</th><th>ε' measured</th><th>ε'' measured</th><th>ε<sub>r</sub>(f) measured</th><th>Tanδ measured</th></tr></thead><tbody><tr><td>Bibolo LyEzminlx</td><td></td><td>3.1797 ± 2.77 * 10<sup>-7</sup></td><td>0.529 ± 2.64 * 10<sup>-8</sup></td><td>3.2234</td><td>0.1664</td></tr><tr><td>Bibolo LyEzmaxlx</td><td>0.93</td><td>2.9835 ± 2.37 * 10<sup>-7</sup></td><td>0.475 ± 2.21 * 10<sup>-8</sup></td><td>3.0211</td><td>0.1593</td></tr><tr><td>Bibolo LyEzminlx</td><td></td><td>3.5235 ± 2.09 * 10<sup>-7</sup></td><td>0.4615 ± 2.68 * 10<sup>-8</sup></td><td>3.5768</td><td>0.1763</td></tr><tr><td>Bibolo LyEzmaxlx</td><td></td><td>3.4106 ± 1.86 * 10<sup>-7</sup></td><td>0.576 ± 2.37 * 10<sup>-8</sup></td><td>3.4589</td><td>0.1689</td></tr></tbody></table>

<table><caption>TABLE 7: Real and imaginary parts of the relative permittivity ε<sub>r</sub> and 2.48 GHz dielectric loss factors of bubinga dielectric materials.</caption><thead><tr><th>Sample</th><th>Frequency (GHz)</th><th>ε' measured</th><th>ε'' measured</th><th>ε<sub>r</sub>(f) measured</th><th>Tanδ measured</th></tr></thead><tbody><tr><td>Bubinga LyEzminlx</td><td></td><td>3.798 ± 1.27 * 10<sup>-7</sup></td><td>0.642 ± 3.02 * 10<sup>-8</sup></td><td>3.8527</td><td>0.1691</td></tr><tr><td>Bubinga LyEzmaxlx</td><td>2.48</td><td>3.454 ± 9.47 * 10<sup>-8</sup></td><td>0.572 ± 2.32 * 10<sup>-8</sup></td><td>3.5013</td><td>0.1657</td></tr><tr><td>Bubinga LyEzminlx</td><td></td><td>2.777 ± 4.58 * 10<sup>-8</sup></td><td>0.424 ± 1.19 * 10<sup>-8</sup></td><td>2.8097</td><td>0.1528</td></tr><tr><td>Bubinga LyEzmaxlx</td><td></td><td>3.682 ± 1.03 * 10<sup>-7</sup></td><td>0.647 ± 2.75 * 10<sup>-8</sup></td><td>3.7392</td><td>0.1758</td></tr></tbody></table>

<table><caption>TABLE 8: Real and imaginary parts of the relative permittivity ε<sub>r</sub> and dielectric loss factors tanδ to 930 MHz of bubinga dielectric materials.</caption><thead><tr><th>Sample</th><th>Frequency (GHz)</th><th>ε' measured</th><th>ε'' measured</th><th>ε<sub>r</sub>(f) measured</th><th>Tanδ measured</th></tr></thead><tbody><tr><td>Bubinga LyEzminlx</td><td></td><td>4.0124 ± 2.48 * 10<sup>-7</sup></td><td>0.6561 ± 3.11 * 10<sup>-8</sup></td><td>4.0646</td><td>0.1635</td></tr><tr><td>Bubinga LyEzmaxlx</td><td>0.93</td><td>3.613 ± 1.84 * 10<sup>-7</sup></td><td>0.5737 ± 2.35 * 10<sup>-8</sup></td><td>3.6582</td><td>0.1588</td></tr><tr><td>Bubinga LyEzminlx</td><td></td><td>2.9197 ± 8.89 * 10<sup>-7</sup></td><td>0.4582 ± 0.4582 * 10<sup>-8</sup></td><td>2.9554</td><td>0.1569</td></tr><tr><td>Bubinga LyEzmaxlx</td><td></td><td>3.8832 ± 2.023 * 10<sup>-7</sup></td><td>0.4582 ± 0.4582 * 10<sup>-8</sup></td><td>2.9554</td><td>0.1769</td></tr></tbody></table>
<table><caption>TABLE 9: Real and imaginary parts of the relative permittivity $ε_r$ and dielectric loss factors tanδ to 2.48 GHz of makore dielectric materials.</caption><thead><tr><th>Sample</th><th>Frequency (GHz)</th><th>ε' measured</th><th>ε'' measured</th><th>ε<sub>r</sub>(f) measured</th><th>Tanδ measured</th></tr></thead><tbody><tr><td>Makore LyEzminlx</td><td rowspan="4">2.48</td><td>3.8809 ± 1.05 * 10<sup>-7</sup></td><td>0.6778 ± 2.90 * 10<sup>-8</sup></td><td>3.9396</td><td>0.1746</td></tr><tr><td>Makore LyEzmaxlx</td><td>3.7615 ± 9.78 * 10<sup>-8</sup></td><td>0.6304 ± 2.59 * 10<sup>-8</sup></td><td>3.8139</td><td>0.1676</td></tr><tr><td>Makore LyEzminlx</td><td>3.8039 ± 7.06 * 10<sup>-8</sup></td><td>0.6667 ± 2.33 * 10<sup>-8</sup></td><td>3.8618</td><td>0.1752</td></tr><tr><td>Makore LyEzmaxlx</td><td>4.2099 ± 9.32 * 10<sup>-8</sup></td><td>0.7621 ± 3.07 * 10<sup>-8</sup></td><td>4.2783</td><td>0.181</td></tr></tbody></table>

<table><caption>TABLE 10: Real and imaginary parts of the relative permittivity $ε_r$ and dielectric loss factors tanδ to 930 MHz of makore dielectric materials.</caption><thead><tr><th>Sample</th><th>Frequency (GHz)</th><th>ε' measured</th><th>ε'' measured</th><th>ε<sub>r</sub>(f) measured</th><th>Tanδ measured</th></tr></thead><tbody><tr><td>Makore LyEzminlx</td><td rowspan="4">0.93</td><td>4.128 ± 2.05 * 10<sup>-7</sup></td><td>0.6904 ± 2.97 * 10<sup>-8</sup></td><td>4.1853</td><td>0.1672</td></tr><tr><td>Makore LyEzmaxlx</td><td>3.9737 ± 1.90 * 10<sup>-7</sup></td><td>0.1648 ± 2.72 * 10<sup>-8</sup></td><td>3.9771</td><td>0.1648</td></tr><tr><td>Makore LyEzminlx</td><td>3.9979 ± 1.37 * 10<sup>-7</sup></td><td>0.6822 ± 2.4 * 10<sup>-8</sup></td><td>4.0556</td><td>0.1706</td></tr><tr><td>Makore LyEzmaxlx</td><td>4.418 ± 1.81 * 10<sup>-7</sup></td><td>0.7788 ± 3.15 * 10<sup>-8</sup></td><td>4.4861</td><td>0.1762</td></tr></tbody></table>

<figure><img src="image_7.png" /><figcaption>FIGURE 5: Characteristics of ayous wood: (a) relative permittivity and (b) dielectric losses.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>FIGURE 6: Characteristics of bibolo wood: (a) relative permittivity and (b) dielectric losses.</figcaption></figure>

high permittivity and dielectric loss values and can only be used at microwave frequencies. However, ayous and bibolo, softwood and medium-hardwood, respectively, have low dielectric losses and low relative permittivity for certain bandwidths and can be used at millimetre frequencies.

# 5. Comparison with Work on Tropical Woods

## 5.1. Characterization Techniques and Measured Characteristics.
The only studies carried out in this respect on tropical woods found in Central Africa are those by authors [8, 13]. We
<figure><img src="image_9.png" /><figcaption>FIGURE 7: Characteristics of bubinga wood: (a) relative permittivity and (b) dielectric losses.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>FIGURE 8: Characteristics of makore wood: (a) relative permittivity and (b) dielectric losses.</figcaption></figure>

<table><caption>TABLE 11: Comparison of characterization techniques and measured characteristics.</caption><thead><tr><th rowspan="2">Ref. Bi.</th><th rowspan="2">Technical<br>characterization</th><th rowspan="2">Cavity<br>volume</th><th colspan="3">Measures</th></tr><tr><th>Tanδ</th><th>Q</th><th>ε<sub>r</sub></th></tr></thead><tbody><tr><td rowspan="2">[13]</td><td>Waveguide</td><td>x</td><td>✓</td><td>x</td><td>✓</td></tr><tr><td>Open resonator</td><td>x</td><td>✓</td><td>x</td><td>✓</td></tr><tr><td>Our<br>work</td><td>Small disturbances</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr></tbody></table>

<figure><img src="image_11.png" /><figcaption>FIGURE 9: Dielectric losses as a function of dry density at 2.48 GHz.</figcaption></figure>

carried out the studies at different frequencies, but on three species of wood studied by the previous authors according to three classification categories: softwood, medium-softwood, and hardwood. Table 11 shows the different characterization techniques used for tropical woods and the measurements that can be carried out in each case.

In our work, we present new characteristics that are no less important than those presented by previous authors [13]. The first parameter missing from the work of our predecessors and which gives us information about the bulk of the material is the volume of the cavity. The second gives us information not only about the selectivity that a material can have if it is used as an antenna substrate but also about the amount of energy stored and dissipated by the Joule effect for each material.

## 5.2. Dielectric Losses.
As we can see, dielectric losses such as permittivity in wood increase with its density. The results of our predecessors have also demonstrated this, although they worked in a wider frequency band than ours. From Figure 9, woods with a high surface dry density or hardwood will exhibit high dielectric losses, so softwoods are more advisable if we consider them as substrates for directional patch antennas.

The dielectric loss tensors are shown in Figure 9.

## 5.3. Comparisons with the Properties of Some Materials Used as Patch Antenna Substrates.
There is a very wide variety of substrates, and the most desirable are those with low dielectric constants for good antenna performance, but they are
<table><caption>TABLE 12: Comparison of the dielectric properties of some materials.</caption><thead><tr><th>Type of material</th><th>ε<sub>r</sub> ref.</th><th>Tanδ ref.</th><th>Typical thickness</th><th>Ref.</th></tr></thead><tbody><tr><td>Duroid 5880 (Rogers Corporation)</td><td>2.2</td><td>0.0009 (10 GHz)</td><td>5.00-125 mil</td><td>[16]</td></tr><tr><td>FR4</td><td>4.34 (1 GHz)</td><td>0.01 (1 GHz)</td><td>1.25 à 2.54 mm</td><td>[15]</td></tr><tr><td>Ayous</td><td>1.98 (2.48 GHz)</td><td>0.11 (2.48 GHz)</td><td>1.5 à 1.8 mm</td><td>Our work</td></tr><tr><td>Bibolo</td><td>2.8 (2.48 GHz)</td><td>0.153 (2.48 GHz)</td><td>1.2 à 1.4 mm</td><td>—</td></tr><tr><td>Bubinga</td><td>2.95 (2.48 GHz)</td><td>0.158 (2.48 GHz)</td><td>1.3 à 1.88 mm</td><td>—</td></tr><tr><td>Makore</td><td>3.8 (2.48 GHz)</td><td>0.16 (2.48 GHz)</td><td>1.33 à 1.59 mm</td><td>—</td></tr></tbody></table>

<figure><img src="image_12.png" /><figcaption>FIGURE 10: Architecture of the travelling wave antenna.</figcaption></figure>

<table><caption>TABLE 13: Antenna characteristics.</caption><thead><tr><th>Parameter</th><th>L</th><th>W</th><th>Lp0</th><th>Lp1</th><th>Lp2</th><th>Lp3</th><th>Lp4</th><th>Wp0</th><th>Wp1</th></tr></thead><tbody><tr><td>Value (mm)</td><td>21.10</td><td>15.00</td><td>3.95</td><td>1</td><td>2.20</td><td>4.00</td><td>0.05</td><td>0.17</td><td>5.00</td></tr></tbody></table>

<figure><img src="image_13.png" /><figcaption>FIGURE 11: Reflection coefficient.</figcaption></figure>

large. Table 12 shows some of the composite materials used as patch antenna substrates and the materials characterized in this work. The results of the measurements obtained during the characterization of four species of wood are shown in Table 12, and we can see that the dielectric losses obtained

for our materials are higher than for other composites commonly used in the manufacture of patch antennas. But when we look at the other characteristics in Table 12, we can conclude that our materials can be used in all the applications in which the FR4 composite can be used.

## 6. Design and Simulation of a Millimetre-Band Antenna on a Wooden Substrate

Millimetre waves operate in the frequency band between 24 GHz and 300 GHz. The 26 GHz and 28 GHz frequency bands have emerged as the most credible candidates for achieving the ultrahigh-speed vision of 5G. The main objective of the characterization of wood materials carried out above was to research the dielectric characteristics of different categories of wood to analyse their possible use as a substrate for millimetre-band antennas. Simulations of travelling wave antennas were carried out at 100 GHz, 60 GHz, 28 GHz, and 2.45 GHz to analyse the behaviour of antennae at these different frequencies using the CST Microwave simulator. The antenna was designed and optimized using the CST Microwave simulator on a wooden substrate,
<figure><img src="image_14.png" /><figcaption>FIGURE 12: Radiation diagram: (a) x-z plane; (b) y-z plane at 28 GHz.</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>FIGURE 13: Radiation efficiency as a function of frequency.</figcaption></figure>

<table><caption>TABLE 14: Radiation properties.</caption><thead><tr><td>Radio parameters</td><td>Value</td></tr></thead><tbody><tr><td>S11 (dB)</td><td>-16</td></tr><tr><td>BP (MHz)</td><td>230</td></tr><tr><td>G (dBi)</td><td>10</td></tr><tr><td>D (dBi)</td><td>10.7</td></tr><tr><td>Opening at half power (°)</td><td>55/43.8</td></tr></tbody></table>

and the general architecture of the antenna used for the simulations is shown in Figure 10.

6.1. *Travelling Wave Antenna on Wood Substrate at 28 GHz.* Table 13 shows the different values used to obtain the simulation results.

6.2. *The Reflection Coefficient.* Figure 11 shows the reflection coefficient of the proposed antenna. In contrast to the 100 GHz and 60 GHz frequencies, the bandwidth was measured and we can conclude that the wooden substrate enabled us to obtain a theoretical frequency band of 230 MHz at -10 dB. This is a narrow-band antenna with a bandwidth of between 27.88 GHz and 28.11 GHz, and the measured reflection coefficient is $S11 = -15.95$ dB.

6.3. *Diagram of Realized Gain and Radiation Efficiency.* The realized gain radiation pattern shown in Figure 12 shows

patch radiation in one mode. In effect, the antenna radiates the maximum energy it receives on the axis, and the radiation is attenuated for $\theta$ exceeding $\pm 90^{\circ}$.

6.4. *Radiation Diagrams with Realized Gain.* The antenna's radiation is assessed by examining the shape of the radiation patterns and the efficiency of each mode. We observe a resonance mode, and the existence of this resonance can be explained by the presence of the single-layer patch. Figure 13 shows the SWR obtained by the simulation.

6.5. *Radiation Efficiency.* From this study, the optimum operation of the antenna was obtained by adjusting the various elements involved in improving the antenna's performance. Over the antenna's matching band ($|S11| < -6$ dB), in an ideal field, the radiation efficiency is less than 2%. Table 14 summarizes the simulation results.

## 7. Conclusion

In this paper, the dielectric properties of wood samples mainly from the Central African forest were studied using the small perturbation method in a cylindrical cavity operating in the $TM_{010}$ mode at microwave frequencies of 930 MHz and 2.48 GHz. We wanted to measure the anisotropy of wood species, so it was necessary to have a sample cut along one of its main axes. The measurement results show that ayous wood has better dielectric properties than other woods. The results show that these materials can also be used in all the applications in which the FR4 composite can be used. By observing the errors in the measurements, it can be seen that the differences between the real and imaginary values of the permittivity $\epsilon_r$ of each type of wood are less than or equal to $1.10^{-1}$ in absolute value. Simulations of travelling wave antennas have been carried out at various frequencies, and the results show that the antenna radiates below 30 GHz with this type of antenna. Advanced simulations with other patch antenna architectures will undoubtedly enable us to carry out in-depth analyses for the production and applications of antennas with wooden substrates.

## Data Availability

The data from the characterization can be made available by the authors.