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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Mater.</journal-id>
<journal-title>Frontiers in Materials</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Mater.</abbrev-journal-title>
<issn pub-type="epub">2296-8016</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">1364159</article-id>
<article-id pub-id-type="doi">10.3389/fmats.2024.1364159</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Materials</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>Design of novel microstrip patch antenna for millimeter-wave B5G communications</article-title>
<alt-title alt-title-type="left-running-head">Tiang et al.</alt-title>
<alt-title alt-title-type="right-running-head">
<ext-link ext-link-type="uri" xlink:href="https://doi.org/10.3389/fmats.2024.1364159">10.3389/fmats.2024.1364159</ext-link>
</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname>Tiang</surname>
<given-names>Jun Jiat</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<role content-type="https://credit.niso.org/contributor-roles/conceptualization/"/>
<role content-type="https://credit.niso.org/contributor-roles/formal-analysis/"/>
<role content-type="https://credit.niso.org/contributor-roles/resources/"/>
<role content-type="https://credit.niso.org/contributor-roles/writing-original-draft/"/>
</contrib>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Alsekait</surname>
<given-names>Deema Mohammed</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
<role content-type="https://credit.niso.org/contributor-roles/software/"/>
<role content-type="https://credit.niso.org/contributor-roles/validation/"/>
<role content-type="https://credit.niso.org/contributor-roles/methodology/"/>
<role content-type="https://credit.niso.org/contributor-roles/resources/"/>
<role content-type="https://credit.niso.org/contributor-roles/Writing - review &#x26; editing/"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Khan</surname>
<given-names>Imran</given-names>
</name>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
<xref ref-type="aff" rid="aff4">
<sup>4</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/974079/overview"/>
<role content-type="https://credit.niso.org/contributor-roles/funding-acquisition/"/>
<role content-type="https://credit.niso.org/contributor-roles/investigation/"/>
<role content-type="https://credit.niso.org/contributor-roles/methodology/"/>
<role content-type="https://credit.niso.org/contributor-roles/project-administration/"/>
<role content-type="https://credit.niso.org/contributor-roles/resources/"/>
<role content-type="https://credit.niso.org/contributor-roles/supervision/"/>
<role content-type="https://credit.niso.org/contributor-roles/Writing - review &#x26; editing/"/>
</contrib>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Wang</surname>
<given-names>Pi-Chung</given-names>
</name>
<xref ref-type="aff" rid="aff5">
<sup>5</sup>
</xref>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
<role content-type="https://credit.niso.org/contributor-roles/investigation/"/>
<role content-type="https://credit.niso.org/contributor-roles/methodology/"/>
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</contrib>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Madsen</surname>
<given-names>Dag &#xd8;ivind</given-names>
</name>
<xref ref-type="aff" rid="aff6">
<sup>6</sup>
</xref>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1879225/overview"/>
</contrib>
</contrib-group>
<aff id="aff1">
<sup>1</sup>
<institution>Faculty of Engineering</institution>, <institution>Centre for Wireless Technology</institution>, <institution>Multimedia University</institution>, <addr-line>Cyberjaya</addr-line>, <country>Malaysia</country>
</aff>
<aff id="aff2">
<sup>2</sup>
<institution>Department of Computer Science and Information Technology, Applied College of Computer and Information Science, Princess Nourah Bint Abdulrahman University</institution>, <addr-line>Riyadh</addr-line>, <country>Saudi Arabia</country>
</aff>
<aff id="aff3">
<sup>3</sup>
<institution>Department of Electrical Engineering</institution>, <institution>University of Engineering and Technology</institution>, <addr-line>Peshawar</addr-line>, <country>Pakistan</country>
</aff>
<aff id="aff4">
<sup>4</sup>
<institution>Islamic University Centre for Scientific Research</institution>, <institution>The Islamic University</institution>, <addr-line>Najaf</addr-line>, <country>Iraq</country>
</aff>
<aff id="aff5">
<sup>5</sup>
<institution>Department of Computer Science and Engineering, National Chung Hsing University</institution>, <addr-line>Taichung</addr-line>, <country>Taiwan</country>
</aff>
<aff id="aff6">
<sup>6</sup>
<institution>University of South-Eastern Norway</institution>, <addr-line>H&#xf8;nefoss</addr-line>, <country>Norway</country>
</aff>
<author-notes>
<fn fn-type="edited-by">
<p>
<bold>Edited by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/253781/overview">Muhammad Danang Birowosuto</ext-link>, &#x141;ukasiewicz Research Network&#x2013;PORT Polish Center for Technology Development, Poland</p>
</fn>
<fn fn-type="edited-by">
<p>
<bold>Reviewed by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/2633068/overview">Kemal Gokhan Nalbant</ext-link>, Beykent University, T&#xfc;rkiye</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/2637108/overview">Jos&#xe9; Escorcia-Gutierrez</ext-link>, Costa University Corporation, Colombia</p>
</fn>
<corresp id="c001">&#x2a;Correspondence: Deema Mohammed Alsekait, <email>dmalskait@pnu.edu.sa</email>; Pi-Chung Wang, <email>pcwang@nchu.edu.tw</email>; Dag &#xd8;ivind Madsen, <email>dag.oivind.madsen@usn.no</email>
</corresp>
</author-notes>
<pub-date pub-type="epub">
<day>04</day>
<month>04</month>
<year>2024</year>
</pub-date>
<pub-date pub-type="collection">
<year>2024</year>
</pub-date>
<volume>11</volume>
<elocation-id>1364159</elocation-id>
<history>
<date date-type="received">
<day>01</day>
<month>01</month>
<year>2024</year>
</date>
<date date-type="accepted">
<day>16</day>
<month>02</month>
<year>2024</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2024 Tiang, Alsekait, Khan, Wang and Madsen.</copyright-statement>
<copyright-year>2024</copyright-year>
<copyright-holder>Tiang, Alsekait, Khan, Wang and Madsen</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/">
<p>This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</p>
</license>
</permissions>
<abstract>
<p>
<bold>Introduction</bold>: The simplicity of integration and co-type features of microstrip antennas make them intriguing for a broad variety of applications, particularly with the growing usage of mmWave bands in wireless communications and the constant rise in data transfer in communication situations.</p>
<p>
<bold>Method:</bold> This paper proposes a novel design of micrstrip patch antenna for mmWave B5G communication. The main idea is to realize four-mode antenna the operates in four different frequencies. The geometry is rectangular patch whose resonance frequency is adjusted by varying the walls and pins of the structure.</p>
<p>
<bold>Results:</bold> Simulation results show that the proposed antenna design has improved fractional bandwidth and performance as compared with existing antennas.</p>
<p>
<bold>Discussion:</bold> The observed curve indicates that, in agreement with the modeling findings, there are four resonance spots in the operational frequency region of 2.5&#x2013;3.4 GHz: 2.68 GHz, 2.9 GHz, 3.05 GHz, and 3.3 GHz, which correspond to TM1/2,0, TM3/2,0, and TMRS, respectively, and TM1/2,2 four resonant modes, within the frequency range, the observed antenna gain peak is around 9 dBi, which is consistent with the measured results.</p>
</abstract>
<kwd-group>
<kwd>microstrip patch</kwd>
<kwd>antenna design</kwd>
<kwd>waveguide</kwd>
<kwd>resonator</kwd>
<kwd>beamform</kwd>
</kwd-group>
<custom-meta-wrap>
<custom-meta>
<meta-name>section-at-acceptance</meta-name>
<meta-value>Metamaterials</meta-value>
</custom-meta>
</custom-meta-wrap>
</article-meta>
</front>
<body>
<sec sec-type="intro" id="s1">
<title>1 Introduction</title>
<p>Millimeter-wave (mmWave) technologies, which need more capacity for high-speed data transmission, have been more in demand in the wake of beyond 5G (B5G) development. The low-profile planar structure of the microstrip antenna is easily conformable to carriers with shapes such as cylinders and curved surfaces, and has been widely used. However, the low-profile structure also causes the microstrip patch antenna to behave like a leaky wave cavity, with resonance characteristics similar to an RLC parallel resonant circuit and a high Q value, so the impedance bandwidth of the antenna is very narrow (<xref ref-type="bibr" rid="B58">Ullah et al., 2019</xref>; <xref ref-type="bibr" rid="B33">Kumar et al., 2022</xref>). Currently, there are three main methods to broaden the bandwidth of microstrip antennas: 1) Use high thickness or low dielectric constant dielectric substrates to reduce the equivalent circuit Q value, thereby increasing the impedance bandwidth (<xref ref-type="bibr" rid="B58">Ullah et al., 2019</xref>; <xref ref-type="bibr" rid="B33">Kumar et al., 2022</xref>), but the surface wave leakage in this planar antenna increases (<xref ref-type="bibr" rid="B41">Liu et al., 2018a</xref>; <xref ref-type="bibr" rid="B18">Ge et al., 2018</xref>; <xref ref-type="bibr" rid="B20">Hao et al., 2019</xref>), resulting in poor radiation efficiency. 2) Improve the feeding method, such as electromagnetic coupling feeding (<xref ref-type="bibr" rid="B13">Fan et al., 2018</xref>; <xref ref-type="bibr" rid="B54">Soliman et al., 2022</xref>), L-shaped probe (<xref ref-type="bibr" rid="B13">Fan et al., 2018</xref>; <xref ref-type="bibr" rid="B15">Farooq et al., 2021</xref>; <xref ref-type="bibr" rid="B54">Soliman et al., 2022</xref>) or M-shaped probe (<xref ref-type="bibr" rid="B67">Yang et al., 2020a</xref>; <xref ref-type="bibr" rid="B34">Kumar et al., 2021</xref>) feeding, <italic>etc.</italic>, but the antenna radiation pattern will change with frequency, and the cross-pole higher. 3) Use parasitic elements to combine multiple coupled resonance modes to increase the bandwidth, but its volume will increase a lot (<xref ref-type="bibr" rid="B1">Beguad et al., 2018</xref>; <xref ref-type="bibr" rid="B55">Srivastava et al., 2020</xref>; <xref ref-type="bibr" rid="B30">Karami et al., 2022</xref>). The authors in (<xref ref-type="bibr" rid="B19">Hannan et al., 2021</xref>; <xref ref-type="bibr" rid="B11">Dicarlofelice et al., 2022</xref>) etched U-shaped grooves on the radiation patch and introduced additional resonance modes near the main resonance point to broaden the bandwidth, but the thickness of the antenna was larger. Similar structures include single-layer E-shaped microstrip antenna, stacked E-shaped microstrip antenna (<xref ref-type="bibr" rid="B12">Dong et al., 2021</xref>), <italic>etc.</italic> Etching a slit on the surface of the patch antenna changes the surface current distribution to achieve dual-frequency resonance. Adjusting the position and size of the slit can make the resonant frequencies closer to each other, and construct dual-mode resonance to obtain wide-band characteristics. The authors in (<xref ref-type="bibr" rid="B57">Tewary et al., 2021</xref>) proposed loading multiple slits on a rectangular patch to simultaneously excite two orthogonal modes, TM<sub>10</sub> and TM<sub>01</sub>, to achieve bandwidth enhancement and compact structure, achieving 3.8% on the basis of a low profile of 0.01&#x3bb;<sub>0</sub> impedance bandwidth, but due to the use of high-loss FR4 substrate and etching of multiple slits, the antenna gain is low and the cross-polarization is as high as &#x2212;5 dB. The authors in (<xref ref-type="bibr" rid="B31">Khan et al., 2022</xref>) loaded a short circuit on the circular patch needle, the resonant frequencies of the TM<sub>01</sub> and TM<sub>02</sub> modes are reconstructed, a wide impedance bandwidth of 18% is achieved in the monopole radiation mode, and the low profile characteristics of 0.024&#x3bb;<sub>0</sub> can be maintained. The disadvantage is that the radiation peak cannot be stable within the operating frequency band. The authors in (<xref ref-type="bibr" rid="B7">Chinnagurusamy et al., 2021</xref>) placed short-circuit pins under the equilateral triangle patch and etched V-shaped gaps to excite the TM<sub>10</sub> and TM<sub>20</sub> modes, making the antenna bandwidth reach 32%, but the antenna thickness also increased to 0.09&#x3bb;<sub>0</sub>. The authors in (<xref ref-type="bibr" rid="B66">Yang et al., 2020b</xref>) designed a patch antenna based on TM<sub>1/2,0</sub>, TM<sub>1/2,2</sub> and TM<sub>3/2,2</sub> three-mode resonance, and improved the radiation performance of the antenna by loading multiple short-circuit walls, which enhances the bandwidth to 26.2% at a profile height of 0.059&#x3bb;<sub>0</sub>. The authors in (<xref ref-type="bibr" rid="B45">Lu et al., 2018</xref>) designed a broadband circular sector patch antenna based on TM<sub>4/3,1</sub> and TM<sub>8/3,1</sub> modes. The design criteria were determined by multi-mode dipole and cavity models. At 0.05&#x3bb;<sub>0</sub>, a useable radiation bandwidth of 14.5% is achieved under low profile conditions. The authors in (<xref ref-type="bibr" rid="B53">Sharaf et al., 2020</xref>) designed a three-mode sector patch antenna based on TM<sub>12/17,1</sub>, TM<sub>36/17,1</sub> and TM<sub>60/17,1</sub> based on the zero-frequency scanning working principle of a direct electric dipole, the antenna operating bandwidth is enhanced to 24%, and the thickness is maintained at 0.05&#x3bb;<sub>0</sub>.</p>
<p>In order to address the above problem, this paper reduces the high cross-polarization of the H-plane pattern by loading a short-circuit wall on the non-radiating side of the rectangular patch, and loading a short-circuit pin under the patch to increase the resonant frequency of the TM<sub>1/2,0</sub> mode.</p>
<p>The main contributions of this work are as follows.<list list-type="simple">
<list-item>
<p>&#x2022; In the TM<sub>3/2,0</sub> mode, a rectangular slot is cut at the zero current position to excite the radiation slot mode, forming a three-mode resonant patch antenna with low profile, wide bandwidth and reduced H-plane cross-polarization performance.</p>
</list-item>
<list-item>
<p>&#x2022; The antenna is only 3 mm thick (0.029&#x3bb;<sub>0</sub>) In this case, an impedance bandwidth of 18% (2.64&#x2013;3.17 GHz) is achieved, and the H-plane cross-polarization is reduced to below &#x2212;20 dB.</p>
</list-item>
<list-item>
<p>&#x2022; By appropriately increasing the patch width and adjusting the antenna structure, the frequency of the TM<sub>1/2,2</sub> mode is reduced and brought closer to the TM<sub>1/2,0</sub>, TM<sub>3/2,0</sub> and TMRS modes, thereby further achieving four-mode resonance while maintaining the antenna with the thickness unchanged (3 mm), the bandwidth is further increased to 21.7% (2.67&#x2013;3.32 GHz).</p>
</list-item>
</list>
</p>
<p>The remaining of this paper is organized as follows. In <xref ref-type="sec" rid="s2">Section 2</xref>, the proposed model design and working principle is discussed. In <xref ref-type="sec" rid="s3">Section 3</xref>, the practical implementation of the proposed antenna is presented and the experimental analysis is performed with comparative evaluation. Finally, <xref ref-type="sec" rid="s4">Section 4</xref> concludes the paper.</p>
</sec>
<sec id="s2">
<title>2 Model design and working principle</title>
<sec id="s2-1">
<title>2.1 Developing three-mode broadband patch antennas</title>
<p>The illustration in <xref ref-type="fig" rid="F1">Figure 1A</xref> shows a rectangular microstrip patch antenna (<italic>P</italic>
<sub>
<italic>x</italic>
</sub> &#x3d; 56 mm, <italic>P</italic>
<sub>
<italic>y</italic>
</sub> &#x3d; 100 mm). By loading short-circuit walls on three sides. It is even-order mode can be suppressed and the E-plane (<italic>x</italic>-<italic>z</italic> plane) high side lobes of the pattern and high cross-polarization of the H-plane (<italic>y</italic>-<italic>z</italic> plane) pattern (<xref ref-type="bibr" rid="B55">Srivastava et al., 2020</xref>; <xref ref-type="bibr" rid="B56">Subha et al., 2020</xref>; <xref ref-type="bibr" rid="B32">Koutinos et al., 2022</xref>), the resonance of the antenna in the three modes are TM<sub>1/2,0</sub>, TM<sub>3/2,0</sub>, TM<sub>1/2,2</sub>, and frequencies <italic>f</italic>
<sub>1/2,0</sub>, <italic>f</italic>
<sub>3/2,0</sub>, <italic>f</italic>
<sub>1/2,2</sub> are 1.35 GHz, 2.84 GHz, and 3.21 GHz respectively. An array of four short-circuiting pins (shown in the inset of <xref ref-type="fig" rid="F1">Figure 1B</xref>) is then loaded under the radiation patch, boosting <italic>f</italic>
<sub>1/2,0</sub> to around 2.68 GHz while keeping <italic>f</italic>
<sub>3/2,0</sub> at 2.83 GHz, <italic>f</italic>
<sub>1/2,2</sub> is also boosted to 3.75 GHz. Finally, a rectangular gap is etched near the zero current line of the TM<sub>3/2,0</sub> mode (as shown in the inset of <xref ref-type="fig" rid="F1">Figure 1C</xref>) to excite the gap radiation mode TM<sub>RS</sub> (<xref ref-type="bibr" rid="B56">Subha et al., 2020</xref>; <xref ref-type="bibr" rid="B32">Koutinos et al., 2022</xref>). The TM<sub>RS</sub> mode operates at 3.07 GHz, close to <italic>f</italic>
<sub>1/2,0</sub> and <italic>f</italic>
<sub>3/2,0</sub>, the impact of this gap on the TM<sub>1/2,0</sub> and TM<sub>3/2,0</sub> modes is controllable, achieving three-mode resonance based on TM<sub>1/2,0</sub>, TM<sub>3/2,0</sub> and TM<sub>RS</sub>. Through these measures, the bandwidth and radiation performance of the antenna are improved.</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>Development of patch antenna with three-mode capability. <bold>(A)</bold> Evaluation of S11 by shorting three walls. <bold>(B)</bold> Shorting four pins. <bold>(C)</bold> Rectangle etching.</p>
</caption>
<graphic xlink:href="fmats-11-1364159-g001.tif"/>
</fig>
</sec>
<sec id="s2-2">
<title>2.2 Design parameters and analysis</title>
<p>The number and position of short-circuit pins, the length, width and position of the gap are several key parameters that affect the performance of the patch antenna, and they will be analyzed in depth.</p>
<sec id="s2-2-1">
<title>2.2.1 Load short circuit pin reassign TM<sub>1/2,0</sub> mode</title>
<p>By appropriately adding short-circuit pins, the resonant frequency of the TM<sub>1/2,0</sub> mode can be effectively controlled, while it has little effect on the TM<sub>3/2,0</sub> mode, and the frequency ratio can be significantly reduced: <italic>f</italic>
<sub>3/2,0</sub>/<italic>f</italic>
<sub>1/2,0</sub>. <xref ref-type="fig" rid="F2">Figure 2</xref> shows how the resonant frequency and frequency ratio of the antenna change with the position and number of short-circuit pins. <xref ref-type="fig" rid="F2">Figure 2A</xref> shows the case where a single pin is located <italic>B</italic>
<sub>
<italic>x</italic>
</sub> from the short-circuit wall along the <italic>x</italic>-direction at the center plane of the patch (<xref ref-type="bibr" rid="B47">Lu et al., 2017</xref>; <xref ref-type="bibr" rid="B42">Liu et al., 2018b</xref>; <xref ref-type="bibr" rid="B36">Lee et al., 2019</xref>). When <italic>B</italic>
<sub>x</sub>/<italic>Px</italic> &#x3d; 0.1, <italic>f</italic>
<sub>1/2,0</sub> and <italic>f</italic>
<sub>3/2,0</sub> are approximately 1.4 GHz and 2.9 GHz respectively, resulting in a large frequency ratio of <italic>f</italic>
<sub>3/2,0</sub>/<italic>f</italic>
<sub>1/2,0</sub> &#x3d; 2.1. When <italic>B</italic>
<sub>
<italic>x</italic>
</sub>/<italic>P</italic>
<sub>
<italic>x</italic>
</sub> reaches about 0.75, because the short-circuit pin is properly placed around the node line of the electric field of the TM<sub>3/2,0</sub> mode, a minimum <italic>f</italic>
<sub>3/2,0</sub>/<italic>f</italic>
<sub>1/2,0</sub> of about 1.55 is obtained. After <italic>B</italic>
<sub>
<italic>x</italic>
</sub>/<italic>P</italic>
<sub>
<italic>x</italic>
</sub> is greater than 0.75, the frequency ratio of the dual modes gradually increases (<xref ref-type="bibr" rid="B44">Liu et al., 2017a</xref>; <xref ref-type="bibr" rid="B26">Jian et al., 2020</xref>; <xref ref-type="bibr" rid="B61">Wu et al., 2020</xref>), moving away from each other. The results show that the minimum frequency ratio can be obtained when <italic>B</italic>
<sub>
<italic>x</italic>
</sub> is 0.75<italic>P</italic>
<sub>
<italic>x</italic>
</sub>.</p>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>Variation of resonant frequency with different values of shorting pins. <bold>(A)</bold> With single short pin. <bold>(B)</bold> With two pins short. <bold>(C)</bold> With three pins short. <bold>(D)</bold> With four pins short.</p>
</caption>
<graphic xlink:href="fmats-11-1364159-g002.tif"/>
</fig>
<p>
<xref ref-type="fig" rid="F2">Figure 2B</xref> shows the analysis of loading two short-circuit pins when <italic>B</italic>
<sub>
<italic>x</italic>
</sub>/<italic>P</italic>
<sub>
<italic>x</italic>
</sub> &#x3d; 0.75. As <italic>B</italic>
<sub>
<italic>y</italic>
</sub>/<italic>P</italic>
<sub>
<italic>y</italic>
</sub> increases from 0.1 to 0.9, <italic>f</italic>
<sub>1/2,0</sub> has a maximum value of 2.2 GHz at <italic>B</italic>
<sub>y</sub>/<italic>P</italic>
<sub>
<italic>y</italic>
</sub> &#x3d; 0.3, whereas <italic>f</italic>
<sub>3/2,0</sub> almost remains around 2.85 GHz. Therefore, by choosing <italic>B</italic>
<sub>
<italic>x</italic>
</sub>/<italic>P</italic>
<sub>
<italic>x</italic>
</sub> &#x3d; 0.75 and <italic>B</italic>
<sub>
<italic>y</italic>
</sub>/<italic>P</italic>
<sub>
<italic>y</italic>
</sub> &#x3d; 0.3, the minimum value of <italic>f</italic>
<sub>3/2,0</sub>/<italic>f</italic>
<sub>1/2,0</sub> &#x2248; 1.30 can be achieved. <xref ref-type="fig" rid="F2">Figures 2C, D</xref> further study <italic>f</italic>
<sub>1/2,0</sub>, <italic>f</italic>
<sub>3/2,0</sub> and <italic>f</italic>
<sub>3/2,0</sub>/<italic>f</italic>
<sub>1/2,0-</sub> when loaded with three and four short-circuit pins respectively at <italic>B</italic>
<sub>
<italic>x</italic>
</sub>/<italic>P</italic>
<sub>
<italic>x</italic>
</sub> &#x3d; 0.75 (<xref ref-type="bibr" rid="B43">Liu et al., 2017b</xref>; <xref ref-type="bibr" rid="B16">Gao et al., 2019</xref>; <xref ref-type="bibr" rid="B48">Ma et al., 2021</xref>). Compared with <xref ref-type="fig" rid="F2">Figures 2A, B</xref>, similar trends for <italic>f</italic>
<sub>1/2,0</sub> and <italic>f</italic>
<sub>3/2,0</sub> are obtained. Therefore, when four short-circuit pins are loaded, and <italic>B</italic>
<sub>
<italic>x</italic>
</sub>/<italic>P</italic>
<sub>
<italic>x</italic>
</sub> &#x3d; 0.75 and <italic>B</italic>
<sub>
<italic>y</italic>
</sub>/<italic>P</italic>
<sub>
<italic>y</italic>
</sub> &#x3d; 0.5, the minimum value of <italic>f</italic>
<sub>3/2,0</sub>/<italic>f</italic>
<sub>1/2,0</sub> &#x2248; 1.06 can be reached.</p>
</sec>
<sec id="s2-2-2">
<title>2.2.2 Etching gap to excite TM<sub>RS</sub> mode</title>
<p>To further broaden the impedance bandwidth of the antenna, a linear groove is etched on the radiation patch near the TM<sub>3/2,0</sub> mode zero current line to excite the TM<sub>RS</sub> mode of the patch antenna and move it closer to TM<sub>1/2,0</sub> and TM<sub>3/2,0</sub> mode (<xref ref-type="bibr" rid="B3">Cao et al., 2021</xref>; <xref ref-type="bibr" rid="B40">Liu, 2021</xref>; <xref ref-type="bibr" rid="B2">Cao et al., 2022</xref>). By appropriately modifying the trunking length (<italic>S</italic>
<sub>
<italic>y</italic>
</sub>), TM<sub>3/2,0</sub> and TM<sub>RS</sub> modes can be combined to extend the bandwidth. It can be seen from <xref ref-type="fig" rid="F3">Figure 3A</xref> that as <italic>S</italic>
<sub>
<italic>y</italic>
</sub> increases from 40 mm to 50 mm, <italic>f</italic>
<sub>RS</sub> drops sharply from 3.5 GHz to 3.1 GHz, but <italic>f</italic>
<sub>1/2,0</sub> and <italic>f</italic>
<sub>3/2,0</sub> remain unchanged, so to obtain the widest bandwidth, <italic>S</italic>
<sub>
<italic>y</italic>
</sub> &#x3d; 50 mm (<xref ref-type="bibr" rid="B8">Chung et al., 2022</xref>; <xref ref-type="bibr" rid="B27">Jiang and Li, 2022</xref>). Further adjust the gap position (<italic>S</italic>
<sub>
<italic>x</italic>
</sub>) and width (<italic>S</italic>
<sub>
<italic>w</italic>
</sub>) to analyze the impedance matching problem. <xref ref-type="fig" rid="F3">Figures 3B, C</xref> show that <italic>S</italic>
<sub>
<italic>x</italic>
</sub> increases from 16.7 mm to 17.7 mm (<xref ref-type="bibr" rid="B61">Wu et al., 2020</xref>), <italic>S</italic>
<sub>
<italic>w</italic>
</sub> increases from 2 mm to 4 mm. The impedances are not always well matched, and only when <italic>S</italic>
<sub>
<italic>x</italic>
</sub> &#x3d; 17.2 mm and <italic>S</italic>
<sub>
<italic>w</italic>
</sub> &#x3d; 3 mm can a wider bandwidth and good impedance matching be achieved.</p>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>Impact of trunking length on the resonant frequency of the antenna. <bold>(A)</bold> Variation with <italic>S<sub>y</sub>
</italic>. <bold>(B)</bold> Variation with <italic>S<sub>x</sub>
</italic>. <bold>(C)</bold> Variation with <italic>S<sub>w</sub>
</italic>.</p>
</caption>
<graphic xlink:href="fmats-11-1364159-g003.tif"/>
</fig>
<p>What needs to be pointed out here is that the TM<sub>RS</sub> mode excited by the loading gap also radiates electromagnetic energy. Since the resonant frequencies of the TM<sub>RS</sub> mode and the TM<sub>3/2,0</sub> mode are close to each other, when the two slots operate at the same time (<xref ref-type="bibr" rid="B49">Mao et al., 2022a</xref>; <xref ref-type="bibr" rid="B50">Mao et al., 2022b</xref>; <xref ref-type="bibr" rid="B10">Dai et al., 2023</xref>), they will affect the pattern of the TM<sub>3/2,0</sub> mode, causing the main beam direction to be deflected. The resonant frequency of TM<sub>1/2,0</sub> mode is lower, and the frequency separation from TMRS is large. The electrical distance between them is very small for the TM<sub>1/2,0</sub> mode. Therefore, the loading gap has little impact on the pattern of the TM<sub>1/2,0</sub> mode.</p>
</sec>
<sec id="s2-2-3">
<title>2.2.3 The impact of loading short-circuit wall 2</title>
<p>To verify the effect of loading short-circuit wall 2 on H-plane cross-polarization, this paper uses a three-mode resonant broadband antenna without loading short-circuit wall 2 for comparison. To make both antennas resonate in the same mode and have close operating frequencies, the structure is optimized by adjusting the short-circuit pins, the position and size of the gaps, etc (<xref ref-type="bibr" rid="B38">Li et al., 2021a</xref>; <xref ref-type="bibr" rid="B9">Dai et al., 2022</xref>; <xref ref-type="bibr" rid="B71">Zhang et al., 2023a</xref>). <xref ref-type="fig" rid="F4">Figure 4A</xref> shows the port reflection coefficients of the two antennas. It can be seen that they have three identical resonance modes, but the bandwidth of the antenna without short-circuit wall 2 is slightly wider. <xref ref-type="fig" rid="F4">Figures 4B&#x2013;D</xref> is a comparison of the H-plane radiation patterns of the two antennas in three modes (<xref ref-type="bibr" rid="B72">Zhang et al., 2023b</xref>; <xref ref-type="bibr" rid="B59">Wang et al., 2023</xref>). It can be seen that the cross-polarization of the H-plane of the antenna loaded with short-circuit wall 2 is reduced by more than 15 dB, proving that short-circuit wall 2 can greatly improve the radiation performance of the antenna in the far area.</p>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>Impact of loading short-circuit wall 2 under different operating conditions. <bold>(A)</bold> S<sub>11</sub>. <bold>(B)</bold> TM<sub>1/2,0</sub>. (C) TM<sub>3/2,0</sub>. <bold>(D)</bold> TM<sub>RS</sub>.</p>
</caption>
<graphic xlink:href="fmats-11-1364159-g004.tif"/>
</fig>
</sec>
<sec id="s2-2-4">
<title>2.2.4 Implementation of three-mode antenna and experimental results</title>
<p>
<xref ref-type="fig" rid="F5">Figure 5A</xref> shows the top view and side view of the three-mode patch antenna, and its cross-sectional height is 0.029&#x3bb;<sub>0</sub> (3 mm). <xref ref-type="fig" rid="F5">Figure 5B</xref> shows the simulated and measured port return loss &#x7c;S<sub>11</sub>&#x7c;, and compares it with a conventional planar inverted-F antenna (PIFA) (<xref ref-type="bibr" rid="B73">Zhou et al., 2022a</xref>; <xref ref-type="bibr" rid="B74">Zhou et al., 2022b</xref>; <xref ref-type="bibr" rid="B60">Wen et al., 2023</xref>). It can be found from <xref ref-type="fig" rid="F5">Figure 5B</xref> that there are three minimum values in the operating frequency band of 2.6&#x2013;3.2 GHz, which are consistent with the three simulated resonance modes, namely, TM<sub>1/2,0</sub>, TM<sub>3/2,0</sub> and slot mode (TM<sub>RS</sub>). Due to the combination of three resonance modes, the measured center bandwidth extends to 18% (from 2.64 to 3.17 GHz), which is 3.4 times the traditional PIFA center bandwidth (5.2%, 2.81&#x2013;2.96 GHz).</p>
<fig id="F5" position="float">
<label>FIGURE 5</label>
<caption>
<p>Implemented prototype and return loss of three-mode microstrip patch antenna. <bold>(A)</bold> Implemented prototype of 3-mode antenna. <bold>(B)</bold> Simulation and measured S<sub>11</sub>.</p>
</caption>
<graphic xlink:href="fmats-11-1364159-g005.tif"/>
</fig>
<p>
<xref ref-type="fig" rid="F6">Figure 6</xref> further shows the simulation and test pattern of the antenna at three resonance points. Due to the asymmetric structure of the antenna along the <italic>x</italic>-direction, the radiation pattern is slightly tilted, and the simulation results are in good agreement with the measured results (<xref ref-type="bibr" rid="B16">Gao et al., 2019</xref>; <xref ref-type="bibr" rid="B69">Yang et al., 2023a</xref>; <xref ref-type="bibr" rid="B25">Jannat et al., 2023</xref>). In addition, due to the loading of short-circuit wall 1, the side lobes of the E-plane (x-z plane) radiation pattern are lower. After loading the short-circuit wall 2, the cross-polarization of the H-plane (<italic>y-z</italic> plane) radiation pattern is better. The overall gain within the frequency band is greater than 6.5 dB<sub>i</sub>, and the peak gain is about 8 dB<sub>i</sub>.</p>
<fig id="F6" position="float">
<label>FIGURE 6</label>
<caption>
<p>Comparison of radiation pattern and normalized gain of three-mode antenna. <bold>(A)</bold> 2.7 GHz. <bold>(B)</bold> 2.9 GHz. <bold>(C)</bold> 3.1 GHz.</p>
</caption>
<graphic xlink:href="fmats-11-1364159-g006.tif"/>
</fig>
</sec>
</sec>
</sec>
<sec id="s3">
<title>3 Implementation and analysis of four-mode microstrip antenna</title>
<p>It can be seen from <xref ref-type="fig" rid="F1">Figure 1B</xref> that as the short-circuit pin is loaded, the resonant frequency <italic>f</italic>
<sub>1/2,2</sub> of the TM<sub>1/2,2</sub> mode will be far away from <italic>f</italic>
<sub>3/2,0</sub> and cannot be directly used to increase the bandwidth (<xref ref-type="bibr" rid="B4">Chen et al., 2022a</xref>; <xref ref-type="bibr" rid="B70">Yin et al., 2022</xref>; <xref ref-type="bibr" rid="B29">Jiang and Xu, 2023</xref>). The resonant frequency (<italic>f</italic>
<sub>
<italic>mn</italic>
</sub>) of TM<sub>
<italic>mn</italic>
</sub> in traditional PIFA can be obtained from the cavity model theory:<disp-formula id="e1">
<mml:math id="m1">
<mml:mrow>
<mml:msub>
<mml:mi>f</mml:mi>
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mi>n</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mi>c</mml:mi>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:msqrt>
<mml:msub>
<mml:mi>&#x3b5;</mml:mi>
<mml:mi>r</mml:mi>
</mml:msub>
</mml:msqrt>
</mml:mrow>
</mml:mfrac>
<mml:msqrt>
<mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mi>m</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>P</mml:mi>
<mml:mi>x</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
<mml:mo>&#x2b;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mi>n</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>P</mml:mi>
<mml:mi>y</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
</mml:msqrt>
</mml:mrow>
</mml:math>
<label>(1)</label>
</disp-formula>
</p>
<p>In the formula: <inline-formula id="inf1">
<mml:math id="m2">
<mml:mrow>
<mml:mi>m</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>/</mml:mo>
<mml:mn>2</mml:mn>
<mml:mo>,</mml:mo>
<mml:mn>3</mml:mn>
<mml:mo>/</mml:mo>
<mml:mn>2</mml:mn>
<mml:mo>,</mml:mo>
<mml:mn>5</mml:mn>
<mml:mo>/</mml:mo>
<mml:mn>2</mml:mn>
<mml:mo>,</mml:mo>
<mml:mo>&#x2026;</mml:mo>
<mml:mo>;</mml:mo>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi>n</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>0</mml:mn>
<mml:mo>,</mml:mo>
<mml:mn>2</mml:mn>
<mml:mo>,</mml:mo>
<mml:mn>4</mml:mn>
<mml:mo>,</mml:mo>
<mml:mo>&#x2026;</mml:mo>
<mml:mo>.</mml:mo>
<mml:mo>;</mml:mo>
<mml:mtext>&#x2009;</mml:mtext>
<mml:mi>c</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is the speed of light. Eq. <xref ref-type="disp-formula" rid="e1">1</xref> shows that increasing the patch width (<italic>P</italic>
<sub>
<italic>y</italic>
</sub>) can effectively reduce <italic>f</italic>
<sub>1/2,2</sub>. The <italic>f</italic>
<sub>RS</sub> can be adjusted by adjusting the gap length <italic>S</italic>
<sub>
<italic>y</italic>
</sub>. To further increase the center bandwidth, the patch width can be increased to reduce <italic>f</italic>
<sub>1/2,2</sub> (<xref ref-type="bibr" rid="B28">Jiang et al., 2022</xref>; <xref ref-type="bibr" rid="B63">Xu et al., 2023a</xref>; <xref ref-type="bibr" rid="B14">Fang et al., 2023</xref>). Make it close to <italic>f</italic>
<sub>3/2,0</sub> and <italic>f</italic>
<sub>RS</sub>, and simultaneously correct other parameters of the antenna, such as the size of the short-circuit pin and the position of the gap, <italic>etc.</italic>, so that TM<sub>1/2,0</sub>, TM<sub>3/2,0</sub>, TM<sub>RS</sub> and TM<sub>1/2,2</sub> four modes are close to each other, further broadening the bandwidth.</p>
<p>The specific parameter analysis of the four-mode resonant antenna is similar to that in <xref ref-type="sec" rid="s2-2">Section 2.2</xref> and will not be repeated here. The specific structure of the four-mode resonant broadband antenna is shown in <xref ref-type="fig" rid="F7">Figure 7A</xref>, and the antenna structural parameters are shown in <xref ref-type="table" rid="T1">Table 1</xref>. <xref ref-type="fig" rid="F7">Figure 7B</xref> shows the simulated and measured return loss and gain (<xref ref-type="bibr" rid="B21">Hu et al., 2019</xref>; <xref ref-type="bibr" rid="B39">Liu et al., 2022</xref>). It can be found from the measured curve that there are four resonance points in the operating frequency band of 2.5&#x2013;3.4 GHz: 2.68 GHz, 2.9 GHz, 3.05 GHz, 3.3 GHz, corresponding to TM<sub>1/2,0</sub>, TM<sub>3/2,0</sub>, TM<sub>RS</sub> respectively, and TM<sub>1/2,2</sub> four resonant modes, consistent with the simulation results. The measured antenna gain peak within the frequency band is approximately 9 dB<sub>i</sub>. The small differences between simulation and actual measurements of return loss and gain are mainly caused by processing errors (<xref ref-type="bibr" rid="B5">Chen et al., 2022b</xref>). Due to the combination of four resonant modes, the measured center bandwidth of the antenna is further extended from 18% (2.64&#x2013;3.17 GHz) of the three-mode antenna to 21.7% (2.67&#x2013;3.32 GHz).</p>
<fig id="F7" position="float">
<label>FIGURE 7</label>
<caption>
<p>Implemented prototype of four-mode antenna and evaluation of return loss. <bold>(A)</bold> Decomposed and top view. <bold>(B)</bold> S<sub>11</sub> and gain comparison.</p>
</caption>
<graphic xlink:href="fmats-11-1364159-g007.tif"/>
</fig>
<table-wrap id="T1" position="float">
<label>TABLE 1</label>
<caption>
<p>Physical parameters of the proposed four-mode antenna.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Parameter</th>
<th align="center">Value (mm)</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">
<inline-formula id="inf2">
<mml:math id="m3">
<mml:mrow>
<mml:msub>
<mml:mi>P</mml:mi>
<mml:mi>x</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="center">56</td>
</tr>
<tr>
<td align="center">
<inline-formula id="inf3">
<mml:math id="m4">
<mml:mrow>
<mml:msub>
<mml:mi>P</mml:mi>
<mml:mi>y</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="center">122</td>
</tr>
<tr>
<td align="center">
<inline-formula id="inf4">
<mml:math id="m5">
<mml:mrow>
<mml:msub>
<mml:mi>G</mml:mi>
<mml:mi>x</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="center">86</td>
</tr>
<tr>
<td align="center">
<inline-formula id="inf5">
<mml:math id="m6">
<mml:mrow>
<mml:mi>R</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="center">3.15</td>
</tr>
<tr>
<td align="center">
<inline-formula id="inf6">
<mml:math id="m7">
<mml:mrow>
<mml:msub>
<mml:mi>B</mml:mi>
<mml:mi>x</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="center">40</td>
</tr>
<tr>
<td align="center">
<inline-formula id="inf7">
<mml:math id="m8">
<mml:mrow>
<mml:msub>
<mml:mi>B</mml:mi>
<mml:mi>y</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="center">30.9</td>
</tr>
<tr>
<td align="center">
<inline-formula id="inf8">
<mml:math id="m9">
<mml:mrow>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mi>x</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="center">16</td>
</tr>
<tr>
<td align="center">
<inline-formula id="inf9">
<mml:math id="m10">
<mml:mrow>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mi>y</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="center">57</td>
</tr>
<tr>
<td align="center">
<inline-formula id="inf10">
<mml:math id="m11">
<mml:mrow>
<mml:msub>
<mml:mi>S</mml:mi>
<mml:mi>w</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="center">4</td>
</tr>
<tr>
<td align="center">
<inline-formula id="inf11">
<mml:math id="m12">
<mml:mrow>
<mml:msub>
<mml:mi>F</mml:mi>
<mml:mi>x</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="center">25</td>
</tr>
<tr>
<td align="center">
<inline-formula id="inf12">
<mml:math id="m13">
<mml:mrow>
<mml:mi>H</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="center">3</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>
<xref ref-type="fig" rid="F8">Figure 8</xref> further shows the electric field distribution corresponding to these four modes. In <xref ref-type="fig" rid="F8">Figure 8A</xref>, there is only one zero value line in the <italic>y</italic> direction, corresponding to the TM<sub>1/2,0</sub> mode. In <xref ref-type="fig" rid="F8">Figure 8B</xref>, two zero value lines in the <italic>y</italic> direction appear, corresponding to the TM<sub>3/2,0</sub> mode (<xref ref-type="bibr" rid="B37">Li et al., 2021b</xref>; <xref ref-type="bibr" rid="B62">Xu et al., 2022</xref>; <xref ref-type="bibr" rid="B65">Xu et al., 2023b</xref>). In <xref ref-type="fig" rid="F8">Figure 8C</xref>, only the radiation around the gap is strong (<xref ref-type="bibr" rid="B24">Huang et al., 2018</xref>; <xref ref-type="bibr" rid="B52">Min et al., 2023</xref>; <xref ref-type="bibr" rid="B51">Min et al., 2024</xref>), and the rest are weak, corresponding to the TM<sub>RS</sub> mode. In <xref ref-type="fig" rid="F8">Figure 8D</xref>, there is a zero value line in the <italic>y</italic> direction, and two zero points appear in the <italic>x</italic>-direction, corresponding to the TM<sub>1/2,2</sub> mode (<xref ref-type="bibr" rid="B23">Huang et al., 2023</xref>; <xref ref-type="bibr" rid="B22">Huang and Liu, 2023</xref>; <xref ref-type="bibr" rid="B35">Lan et al., 2024</xref>). <xref ref-type="fig" rid="F9">Figures 9A&#x2013;D</xref> further shows the four resonance modes of the four-mode broadband antenna (<xref ref-type="bibr" rid="B46">Lu and Osorio, 2018</xref>; <xref ref-type="bibr" rid="B68">Yang et al., 2023b</xref>; <xref ref-type="bibr" rid="B17">Gao et al., 2023</xref>). The simulation and measured diagrams at the points are in good agreement with the actual measurement results (<xref ref-type="bibr" rid="B6">Chen et al., 2022c</xref>; <xref ref-type="bibr" rid="B64">Xu et al., 2023c</xref>).</p>
<fig id="F8" position="float">
<label>FIGURE 8</label>
<caption>
<p>Comparison of E-field distribution in different modes and frequencies. <bold>(A)</bold> TM<sub>1/2,0</sub> (2.68 GHz). <bold>(B)</bold> TM<sub>3/2,0</sub> (2.9 GHz). <bold>(C)</bold> TM<sub>RS</sub> (3.05 GHz). <bold>(D)</bold> TM<sub>1/2,2</sub> (3.3 GHz).</p>
</caption>
<graphic xlink:href="fmats-11-1364159-g008.tif"/>
</fig>
<fig id="F9" position="float">
<label>FIGURE 9</label>
<caption>
<p>Comparison of radiation patter and normalized gain of four-mode microstrip antenna. <bold>(A)</bold> 2.7 GHz. <bold>(B)</bold> 2.9 GHz. <bold>(C)</bold> 3.1 GHz. <bold>(D)</bold> 3.3 GHz.</p>
</caption>
<graphic xlink:href="fmats-11-1364159-g009.tif"/>
</fig>
<p>
<xref ref-type="table" rid="T2">Table 2</xref> further shows the comparison between the antenna designed in this article and the reference broadband antennas. It can be seen that the proposed antenna has comprehensive advantages in terms of thickness and electrical performance.</p>
<table-wrap id="T2" position="float">
<label>TABLE 2</label>
<caption>
<p>Perforamance comparison of the proposed and existing antenna designs.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">References</th>
<th align="center">Dimension</th>
<th align="center">Peak gain (dB<sub>i</sub>)</th>
<th align="center">Maximum cross-polarization (dB)</th>
<th align="center">Impedance bandwidth (%)</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">
<xref ref-type="bibr" rid="B11">Dicarlofelice et al. (2022)</xref>
</td>
<td align="center">0.059 <inline-formula id="inf13">
<mml:math id="m14">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3bb;</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="center">8.0</td>
<td align="center">&#x2212;12.3</td>
<td align="center">26.2</td>
</tr>
<tr>
<td align="center">
<xref ref-type="bibr" rid="B19">Hannan et al. (2021)</xref>
</td>
<td align="center">0.054 <inline-formula id="inf14">
<mml:math id="m15">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3bb;</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="center">10.0</td>
<td align="center">&#x2212;8.0</td>
<td align="center">14.5</td>
</tr>
<tr>
<td align="center">
<xref ref-type="bibr" rid="B57">Tewary et al. (2021)</xref>
</td>
<td align="center">0.036 <inline-formula id="inf15">
<mml:math id="m16">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3bb;</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="center">10.8</td>
<td align="center">&#x2212;9.2</td>
<td align="center">33.3</td>
</tr>
<tr>
<td align="center">
<xref ref-type="bibr" rid="B31">Khan et al. (2022)</xref>
</td>
<td align="center">0.032 <inline-formula id="inf16">
<mml:math id="m17">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3bb;</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="center">6.8</td>
<td align="center">&#x2212;18.0</td>
<td align="center">15.2</td>
</tr>
<tr>
<td align="center">
<xref ref-type="bibr" rid="B7">Chinnagurusamy et al. (2021)</xref>
</td>
<td align="center">0.036 <inline-formula id="inf17">
<mml:math id="m18">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3bb;</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="center">5.0</td>
<td align="center">0</td>
<td align="center">15.3</td>
</tr>
<tr>
<td align="center">
<xref ref-type="bibr" rid="B66">Yang et al. (2020b)</xref>
</td>
<td align="center">0.037 <inline-formula id="inf18">
<mml:math id="m19">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3bb;</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
<td align="center">5.9</td>
<td align="center">&#x2212;16.0</td>
<td align="center">18.0</td>
</tr>
<tr>
<td rowspan="2" align="center">Proposed</td>
<td align="center">0.029 <inline-formula id="inf19">
<mml:math id="m20">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3bb;</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> (3-mode)</td>
<td align="center">8.0</td>
<td align="center">&#x3c;-20.0</td>
<td align="center">18.0</td>
</tr>
<tr>
<td align="center">0.03 <inline-formula id="inf20">
<mml:math id="m21">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3bb;</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> (4-mode)</td>
<td align="center">8.0</td>
<td align="center">&#x3c;-20.0</td>
<td align="center">21.7</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
<sec sec-type="conclusion" id="s4">
<title>4 Conclusion</title>
<p>This article designs a low-profile, multi-mode, broadband patch antenna that improves radiation performance. By loading a short-circuit wall on the non-radiating edge of the patch, the E-plane side lobes of the antenna radiation pattern are reduced, effectively reducing the H-plane cross-polarization. By adjusting the number and position of the pins, the size and position of the opening slit, and the width of the patch antenna, we further introduced the three-mode patch antenna based on TM<sub>1/2,0</sub>, TM<sub>3/2,0</sub> and TM<sub>RS</sub> made by predecessors. In TM<sub>1/2,2</sub> mode, a four-mode low-profile broadband patch antenna is designed, which achieves an operating bandwidth of 21.7% with a thickness of only 0.03&#x3bb;<sub>0</sub>.</p>
</sec>
</body>
<back>
<sec sec-type="data-availability" id="s5">
<title>Data availability statement</title>
<p>The original contributions presented in the study are included in the article/Supplementary material, further inquiries can be directed to the corresponding authors.</p>
</sec>
<sec id="s6">
<title>Author contributions</title>
<p>JT: Conceptualization, Formal Analysis, Resources, Writing&#x2013;original draft. DA: Software, Validation, Methodology, Resources, Writing&#x2013;review and editing. IK: Conceptualization, Project administration, Supervision, Visualization, Writing&#x2013;original draft. P-CW: Investigation, Methodology, Validation, Resources, Writing&#x2013;review and editing. DM: Funding acquisition, Investigation, Methodology, Project administration, Resources, Supervision, Writing&#x2013;review and editing.</p>
</sec>
<sec sec-type="funding-information" id="s7">
<title>Funding</title>
<p>The author(s) declare financial support was received for the research, authorship, and/or publication of this article. This work was supported by Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2024R435), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.</p>
</sec>
<sec sec-type="COI-statement" id="s8">
<title>Conflict of interest</title>
<p>The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
</sec>
<sec sec-type="disclaimer" id="s9">
<title>Publisher&#x2019;s note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p>
</sec>
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