Caracterização de Material Magneto Dielétrico

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<p>1</p><p>2</p><p>3</p><p>4</p><p>5</p><p>6</p><p>7</p><p>8</p><p>9</p><p>10</p><p>11</p><p>12</p><p>13</p><p>14</p><p>15</p><p>16</p><p>17</p><p>18</p><p>19</p><p>20</p><p>21</p><p>22</p><p>23</p><p>24</p><p>25</p><p>26</p><p>27</p><p>28</p><p>29</p><p>30</p><p>31</p><p>32</p><p>33</p><p>34</p><p>35</p><p>36</p><p>37</p><p>38</p><p>39</p><p>40</p><p>41</p><p>42</p><p>43</p><p>44</p><p>45</p><p>46</p><p>47</p><p>48</p><p>49</p><p>50</p><p>51</p><p>52</p><p>53</p><p>54</p><p>55</p><p>56</p><p>57</p><p>60</p><p>61</p><p>62</p><p>63</p><p>64</p><p>65</p><p>Characterization of Magneto Dielectric Material based on</p><p>Microwave Resonator</p><p>First Author #1, Second Author *2, Third Author #3</p><p>#Tpc Department, RFM University</p><p>Address Including Country Name</p><p>1first.author@apace.org</p><p>3third.author@RFM.org</p><p>*Ieice Company</p><p>Address Including Country Name</p><p>2second.author@ieice.or</p><p>Abstract — Precise determination of dielectric properties of</p><p>material is highly demanded especially after the rise of</p><p>magneto dielectric material which can fulfil the device</p><p>miniaturization of printed circuit board in various applications.</p><p>It is important to characterize dielectric properties of material</p><p>so that the performance of the devices can be predicted</p><p>accurately. There are numerous dielectric characterization</p><p>methods and each of the methods have its own benefits and</p><p>limitations. In this work, a simple complementary double split</p><p>ring resonator operating at 3.5 GHz is proposed for dielectric</p><p>measurement. The advantage of this design is the convenience</p><p>in preparation of samples. Empirical models are proposed to</p><p>predict the relative permittivity and relative permeability of</p><p>material under test. The reliability of the mathematical</p><p>equations is proven from its R2 and RMSE values.</p><p>Index Terms — complementary double split ring resonator,</p><p>dielectric measurement, dielectric constant, relative</p><p>permeability, electric loss tangent, magnetic loss tangent.</p><p>I. INTRODUCTION</p><p>The determination of dielectric properties of materials are</p><p>inevitable in many areas, such as agriculture, microwave</p><p>circuits design, food industry and biomedical</p><p>characterization [1], [2]. There are many methods that could</p><p>be used to characterize material in different form such as</p><p>liquid, powder, and solid such as free-space method,</p><p>transmission/reflection method, open-ended coaxial probe</p><p>and resonance method. These methods are selected based on</p><p>the measurement requirement such as operating frequency,</p><p>required sensitivity, amount/type of sample and so on.</p><p>Resonance methods which is based on split-ring resonator</p><p>and complementary split ring resonators are famous due to</p><p>its high sensitivity. This method does not require tedious</p><p>sample preparation process and it is cheap. The</p><p>measurements is working based on the principle of resonant</p><p>frequency and quality factor variation as the material under</p><p>test (MUT) is introduced at the sensing area [3] – [7].</p><p>Nowadays, the issue of miniaturization is significant</p><p>during the technology revolution and this phenomenon can</p><p>be observed from the size and weight reduction of the</p><p>cellular phone. The sustainable demand for the issue</p><p>miniaturization encourages the engineers to discover and</p><p>develop more suitable materials to surpass the existing</p><p>function with a smaller size and lighter weight [8]. The</p><p>demand for different dielectric properties for various</p><p>applications emphasizes that it is essential to understand the</p><p>dielectric materials by creating a simple manner in detecting</p><p>its properties [3].</p><p>Magneto dielectric materials which have higher relative</p><p>permeability are used as substrates to achieve extra</p><p>compactness due to one more degree of freedom [5].</p><p>However, it is important to find out the electromagnetic</p><p>properties of these materials by using the suitable detection</p><p>technique.</p><p>In this project, a complementary double split ring</p><p>microstrip resonator is designed by using CST</p><p>MICROWAVE STUDIO. The final design that has the</p><p>highest quality factor, Q-factor is proposed for the dielectric</p><p>properties predictions. MUT with different dielectric</p><p>properties are defined at the sensing areas and the simulated</p><p>resonance frequency and magnitude of S21 are recorded for</p><p>fitting purpose. The reliability of the fitting formulation is</p><p>discussed.</p><p>II. METHODOLOGY</p><p>A. Design of the Sensor</p><p>Fig. 1 and Fig. 2 show the top and bottom view of the</p><p>proposed sensor in this project, its size is a 35 mm x 21 mm.</p><p>The top of the design consists of a straight copper line with</p><p>width of 4 mm. While the bottom of the design is a</p><p>complementary double split ring with different ring design.</p><p>The inner ring has a common gap, but the outer ring has a</p><p>capacitor gap design. The substrate material used in this</p><p>project is Rogers RO3003. It has a dielectric constant of 3,</p><p>electric loss tangent of 0.001 and thickness of 1.52 mm.</p><p>Fig. 1: Top view of the resonator</p><p>APACE 2021 1570752384</p><p>1</p><p>20</p><p>21</p><p>IE</p><p>EE</p><p>A</p><p>si</p><p>a-</p><p>Pa</p><p>ci</p><p>fic</p><p>C</p><p>on</p><p>fe</p><p>re</p><p>nc</p><p>e</p><p>on</p><p>A</p><p>pp</p><p>lie</p><p>d</p><p>El</p><p>ec</p><p>tro</p><p>m</p><p>ag</p><p>ne</p><p>tic</p><p>s (</p><p>A</p><p>PA</p><p>C</p><p>E)</p><p>|</p><p>97</p><p>8-</p><p>1-</p><p>66</p><p>54</p><p>-2</p><p>82</p><p>7-</p><p>9/</p><p>21</p><p>/$</p><p>31</p><p>.0</p><p>0</p><p>©</p><p>20</p><p>21</p><p>IE</p><p>EE</p><p>|</p><p>D</p><p>O</p><p>I:</p><p>10</p><p>.1</p><p>10</p><p>9/</p><p>A</p><p>PA</p><p>C</p><p>E5</p><p>31</p><p>43</p><p>.2</p><p>02</p><p>1.</p><p>97</p><p>60</p><p>56</p><p>9</p><p>Authorized licensed use limited to: ITA - Instituto Tecnológico de Aeronáutica. Downloaded on October 15,2023 at 15:01:32 UTC from IEEE Xplore. Restrictions apply.</p><p>Fig. 2: Bottom view of the resonator</p><p>B. Characterization of Permittivity and Permeability</p><p>Sensing Area</p><p>The designed sensor in Section A is used to determine</p><p>the relative permittivity and permeability of the MUT.</p><p>Before it could be used, it is important to identify the</p><p>suitable sensing areas for both relative permittivity and</p><p>relative permeability. These areas must have highest electric</p><p>field and magnetic field respectively []. Hence the electric</p><p>field and magnetic field distribution are simulated at the</p><p>frequency of 3.502 GHz (resonance frequency). Based on</p><p>the simulation, it is found that area that has highest electric</p><p>field intensity is located at the inner ring while the capacitor</p><p>gap at the outer ring has the highest magnetic field intensity.</p><p>Following this, these areas are selected as the location for</p><p>MUT placement. The sample placement at these sensing</p><p>zones is shown in Fig. 3 and Fig. 4. The thickness of the</p><p>sample is fixed at 2 mm in the simulation.</p><p>Fig. 3: Highest electric field intensity is detected at the inner ring</p><p>at 3.502GHz.</p><p>Fig. 4: Highest magnetic field intensity is detected at the capacitor</p><p>gap of the outer ring at 3.502GHz.</p><p>Fig. 5: Sample placement for relative permeability measurement.</p><p>Fig. 6: Sample placement for relative permittivity measurement.</p><p>In order to determine the response of the resonator</p><p>towards various dielectric properties, four material</p><p>properties are investigated, namely dielectric constant,</p><p>electric loss tangent, real relative permeability, and</p><p>magnetic loss tangent. The range of these properties under</p><p>investigation is tabulated in Table 1. Only one of the</p><p>material properties is varied in each simulation. When the</p><p>properties are not investigated, their values are set to 1</p><p>(dielectric constant and real relative permeability) and 0</p><p>(electric and magnetic loss tangent).</p><p>Table 1</p><p>Range of dielectric properties</p><p>Dielectric Properties Range Step Size</p><p>Dielectric constant 1 – 10 1</p><p>Electric loss tangent 0.02 – 0.1 0.02</p><p>Real relative permeability 1 – 10 1</p><p>Magnetic loss tangent 0.02 – 0.1 0.02</p><p>2</p><p>Authorized licensed use limited to: ITA - Instituto Tecnológico de Aeronáutica. Downloaded on October 15,2023 at 15:01:32 UTC from IEEE Xplore. Restrictions apply.</p><p>III. RESULT AND DISCUSSION</p><p>The S21 of the complementary double split ring resonator</p><p>is shown in Fig. 7. It is resonated at 3.502 GHz at -30.57 dB.</p><p>The calculated Q-factor is 236.62.</p><p>The resonance frequency of the resonator is shifted</p><p>when it is exposed to different materials which have various</p><p>dielectric constant, real permeability, electric and magnetic</p><p>loss tangent. At the electric permittivity sensing zone, strong</p><p>electric field occurs</p><p>while the effects of magnetic field is</p><p>low. For the magnetic permeability sensing zone, the</p><p>magnetic field is strong while the electric field is weak.</p><p>Hence, the effects of magnetic field will not affect the</p><p>shifting of resonance frequency of the sensor when the</p><p>electric permittivity sensing zone is placed with the sample</p><p>and the theory is same as the magnetic permeability sensing</p><p>zone. The shifting of the resonance frequency for different</p><p>dielectric constant and real permeability values are tabulated</p><p>in Fig. 8 and Fig. 9. It is found that the resonance</p><p>frequencies are inverse proportional to the dielectric</p><p>constant and real relative permeability. Linear trend is</p><p>observed in Fig. 8 while exponential trend can be found in</p><p>Fig. 9.</p><p>Fig. 7: The S21 of the proposed design</p><p>Fig. 8: The resonance frequency is shifted when different dielectric</p><p>constant is defined.</p><p>Fig. 9: The resonance frequency is shifted when different real</p><p>relative permeability is defined.</p><p>On the other hand, the response of the resonator</p><p>toward the variation in electric loss tangent and magnetic</p><p>loss tangent is illustrated in Fig. 10 and Fig. 11.</p><p>Fig. 10: S21 (dB) is varied when different electric loss tangent is</p><p>defined.</p><p>Fig. 11: S21 (dB) is varied when different magnetic loss tangent is</p><p>defined.</p><p>Ideally, no change will occur in the resonance</p><p>frequency when the electric loss tangent is varied where the</p><p>dielectric constant, real permeability and magnetic loss</p><p>tangent are fixed. However, the increase in electric loss</p><p>tangent will cause an increase in the magnitude of S21 and a</p><p>decrease in Q-factor. The same theory is also applied on</p><p>magnetic loss tangent where the resonance frequency will</p><p>not be affected. The curve fitting technique is used in this</p><p>section to determine the mathematical equations based on</p><p>the relationship between the resonance frequency with the</p><p>electric permittivity, magnetic permeability, electric and</p><p>magnetic loss tangent. There are two important elements in</p><p>determining an equation which are R-square (R2) and root</p><p>mean square error (RMSE). The coefficients of R2 and</p><p>RMSE should be close to 1 and 0 respectively which are in</p><p>an opposite way. The mathematical equations are formed by</p><p>using the Matlab. The data that is used for curve fitting of</p><p>the dielectric constant is the results of the parameter sweep</p><p>of real permittivity from 1 to 10 when real permeability is</p><p>equal to 1. For the curve fitting of real permeability, the</p><p>input data is taken from results of the parameter sweep of</p><p>real permeability when dielectric constant is equal to 1.</p><p>When the magnetic loss tangent is equal to 0, the results of</p><p>the parameter sweep of electric loss tangent from 0.02 to 0.1</p><p>is used as the input data for curve fitting. The results of the</p><p>parameter sweep of the magnetic loss tangent from 0.02 to</p><p>0.1 when electric loss tangent is equal to 0 are used as the</p><p>input data for curve fitting. The input data of the curve</p><p>fitting of the dielectric constant versus resonance frequency</p><p>and the real permeability versus resonance frequency</p><p>3</p><p>Authorized licensed use limited to: ITA - Instituto Tecnológico de Aeronáutica. Downloaded on October 15,2023 at 15:01:32 UTC from IEEE Xplore. Restrictions apply.</p><p>including the dielectric constant, real permeability and</p><p>resonance frequency. For the curve fitting of electric loss</p><p>tangent versus S21 magnitude and magnetic loss tangent</p><p>versus S21 magnitude, the values of both electric and</p><p>magnetic loss tangent and S21 magnitude are used as the</p><p>input data.</p><p>Four equations that is used to predict the values of</p><p>dielectric constant (ε), real relative permeability (µ), electric</p><p>loss tangent (tan 𝛿 ), magnetic loss tangent (tan 𝛿 ) are</p><p>listed in (1)-(4). Their R2 and RMSE are tabulated in Table</p><p>2. Based on the R2 values, it can be concluded that the</p><p>proposed empirical models can fit the experimental data</p><p>well with maximum RMSE of less than 1.</p><p>𝜀 = −54.26 𝑓 + 191.5 (1)</p><p>𝜇 = (7.807𝑒 + 24)𝑓 . (2)</p><p>tan 𝛿 = 0.04008𝑆 + 1.199 (3)</p><p>tan 𝛿 = 0.057 − 0.028 cos(0.413 𝑆 )</p><p>− 0.034 sin (0.413 𝑆 )</p><p>(4)</p><p>Table 2</p><p>R2 and RMSE of the proposed prediction model</p><p>Dielectric Properties R2 RMSE</p><p>Dielectric constant 0.9749 0.5084</p><p>Electric loss tangent 0.9955 0.002438</p><p>Real relative permeability 0.9206 0.9051</p><p>Magnetic loss tangent 0.9999 0.0006475</p><p>IV. CONCLUSION</p><p>In this research, a sensor based on the complementary</p><p>double split ring resonator with planar microstrip lines was</p><p>designed by using CST-MWS to be used for characterizing</p><p>the magneto dielectric materials. The resonance frequency</p><p>and Q-factor of the proposed sensor are 3.502 GHz and</p><p>236.62 respectively. The proposed sensor has two separate</p><p>electric and magnetic field sensing zones where the electric</p><p>field sensing zone has a strong electric field but weak</p><p>magnetic field while the magnetic field sensing zone is in</p><p>contrast. The advantages of the proposed sensor are</p><p>convenient and easy in sample preparation. Furthermore, the</p><p>relationships between the resonance frequency and S21</p><p>magnitude with the dielectric constant, real permeability,</p><p>electric and magnetic loss tangent were determined by</p><p>defining samples with dielectric constant and relative</p><p>permeability of 0 - 10 and electric and magnetic loss tangent</p><p>0 - 0.1 at different sensing zones. It is found that the shifting</p><p>of resonance frequency happens when the values of the</p><p>dielectric constant and real permeability are varied. Besides,</p><p>the variation of the electric and magnetic loss tangent have</p><p>caused an increase in the magnitude of S21 and a decrease</p><p>in Q-factor. Mathematical equations were proposed by using</p><p>the curve fitting tool in Matlab according to the R2 and</p><p>RMSE. The dielectric constant of the sample can be</p><p>predicted by a linear equation with R2 and RMSE of 0.9749</p><p>and 0.5084 respectively. On the other hand, a power</p><p>equation can predict the real permeability with R2 and</p><p>RMSE of 0.9206 and 0.9051 respectively. R2 and RMSE of</p><p>0.9955 and 0.002438 is achieved for a polynomial equation</p><p>used for electric loss tangent prediction. The coefficients of</p><p>R2 and RMSE for the prediction of the magnetic loss</p><p>tangent are 0.9999 and 0.0006475 respectively and it is</p><p>based on a fourier equation.</p><p>ACKNOWLEDGEMENT</p><p>The work described in this paper was partially supported</p><p>by a FRGS, K316 research grant by Ministry of Education</p><p>of Malaysia.</p><p>REFERENCES</p><p>[1] R. Mirzavand, M. M. Honari, and P. Mousavi, “High-</p><p>resolution balanced microwave material sensor with</p><p>extended dielectric range,” IEEE Trans. Ind. Electron., vol.</p><p>64, no. 2, pp. 1552–1560, Feb. 2017.</p><p>[2] S. Trabelsi and S. O. Nelson, “Microwave sensing of quality</p><p>attributes of agricultural and food products,” IEEE Instrum.</p><p>Meas. Mag., vol. 19, no. 1, pp. 36–41, Feb. 2016.</p><p>[3] R. A. Alahnomi, Z. Zakaria, E. Ruslan, A. A. M. Bahar, and</p><p>S. R. A. 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