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<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Commun. Netw.</journal-id>
<journal-title>Frontiers in Communications and Networks</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Commun. Netw.</abbrev-journal-title>
<issn pub-type="epub">2673-530X</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">1613225</article-id>
<article-id pub-id-type="doi">10.3389/frcmn.2025.1613225</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Communications and Networks</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>Low-profile, wideband, wide-scanning tightly coupled dipole phased array antenna</article-title>
<alt-title alt-title-type="left-running-head">Dang 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/frcmn.2025.1613225">10.3389/frcmn.2025.1613225</ext-link>
</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname>Dang</surname>
<given-names>Wen</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/3123028/overview"/>
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<role content-type="https://credit.niso.org/contributor-roles/Writing - review &#x26; editing/"/>
<role content-type="https://credit.niso.org/contributor-roles/visualization/"/>
<role content-type="https://credit.niso.org/contributor-roles/validation/"/>
<role content-type="https://credit.niso.org/contributor-roles/formal-analysis/"/>
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<role content-type="https://credit.niso.org/contributor-roles/writing-original-draft/"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Yong</surname>
<given-names>Wai Yan</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/2778177/overview"/>
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<role content-type="https://credit.niso.org/contributor-roles/Writing - review &#x26; editing/"/>
</contrib>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Glazunov</surname>
<given-names>Andr&#xe9;s Alay&#xf3;n</given-names>
</name>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
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<aff id="aff1">
<sup>1</sup>
<institution>Radio System Group</institution>, <institution>Faculty of Electrical Engineering</institution>, <institution>Mathematics and Computer Science</institution>, <institution>University of Twente</institution>, <addr-line>Enschede</addr-line>, <country>Netherlands</country>
</aff>
<aff id="aff2">
<sup>2</sup>
<institution>Rohde &#x26; Schwarz GmbH &#x26; Company KG</institution>, <addr-line>Munich</addr-line>, <country>Germany</country>
</aff>
<aff id="aff3">
<sup>3</sup>
<institution>Department of Science and Technology</institution>, <institution>Link&#xf6;ping University</institution>, <addr-line>Norrk&#xf6;ping</addr-line>, <country>Sweden</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/567722/overview">Francisco Falcone</ext-link>, Public University of Navarre, Spain</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/597138/overview">Jawad K. Ali</ext-link>, University of Technology, Iraq</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1722781/overview">Jianfeng Zheng</ext-link>, University of Houston, United States</p>
</fn>
<corresp id="c001">&#x2a;Correspondence: Andr&#xe9;s Alay&#xf3;n Glazunov, <email>andres.alayon.glazunov@liu.se</email>
</corresp>
</author-notes>
<pub-date pub-type="epub">
<day>28</day>
<month>08</month>
<year>2025</year>
</pub-date>
<pub-date pub-type="collection">
<year>2025</year>
</pub-date>
<volume>6</volume>
<elocation-id>1613225</elocation-id>
<history>
<date date-type="received">
<day>16</day>
<month>04</month>
<year>2025</year>
</date>
<date date-type="accepted">
<day>25</day>
<month>07</month>
<year>2025</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2025 Dang, Yong and Glazunov.</copyright-statement>
<copyright-year>2025</copyright-year>
<copyright-holder>Dang, Yong and Glazunov</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>This paper presents a low-profile, tightly coupled dipole array (TCDA) antenna to achieve broad-angle scanning with excellent impedance matching over a wide bandwidth. The antenna element is innovatively designed using two planar shorted patches, forming a compact structure. A pair of parasitic strips is incorporated between adjacent antenna elements to ensure surface current uniformity across a wide frequency range. A high-index semi-arc metasurface (MS) is engineered as a wide-angle impedance matching (WAIM) layer to enhance the scanning performance in both E&#x2212; and H-planes without compromising the low-profile form factor. Full-wave simulations demonstrate that the proposed antenna array supports a wide scanning range of up to <inline-formula id="inf1">
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</inline-formula> array prototype was fabricated and experimentally tested to validate the design concept. The measurement results exhibit good agreement with simulations, confirming the efficacy and practicability of the proposed TCDA design. The proposed array achieves wideband impedance matching and wide-angle scanning capability within a compact, planar structure, making it highly suitable for mobile satellite communications and emerging 6G systems requiring agile beam steering.</p>
</abstract>
<kwd-group>
<kwd>array antenna</kwd>
<kwd>high refractive index metamaterial</kwd>
<kwd>phased array antenna</kwd>
<kwd>tightly coupled dipole array antenna (TCDA)</kwd>
<kwd>ultra-wideband (UWB)</kwd>
<kwd>wide scanning</kwd>
</kwd-group>
<counts>
<page-count count="12"/>
</counts>
<custom-meta-wrap>
<custom-meta>
<meta-name>section-at-acceptance</meta-name>
<meta-value>System and Test-Bed Design</meta-value>
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</front>
<body>
<sec id="s1">
<title>1 Introduction</title>
<p>Over the last few years, satellite communication (SATCOM) has been explored for commercial services, such as television broadcasting and broadband internet services. Many of these applications function in the Ku-band because of its global accessibility and the substantial data rate capacity of satellite services. Furthermore, future 6G communication is anticipated to include Non-terrestrial networks (NTN) in commercial mobile services (<xref ref-type="bibr" rid="B1">Ansari et al., 2021</xref>; <xref ref-type="bibr" rid="B34">Xylouris et al., 2024</xref>), particularly for automobiles, trains, and aircraft. However, in contrast to traditional SATCOM, which necessitates a large dish reflector antenna, the antenna system utilised in mobile and vehicular platforms for SATCOM must possess a low-profile design and the capability for rapid beam switching. Phased array antennas, distinguished by their flexible beamforming capabilities, high gain, and low profile, have garnered considerable interest in the last few decades for several applications, including radar (<xref ref-type="bibr" rid="B11">Kim et al., 2024</xref>; <xref ref-type="bibr" rid="B12">Latha et al., 2021</xref>) and 5G communication (<xref ref-type="bibr" rid="B35">Yong and Alay&#xf3;n Glazunov., 2023</xref>; <xref ref-type="bibr" rid="B8">Gu et al., 2021</xref>). The phased array antenna is also a viable candidate for establishing a communication connection between mobile vehicles and satellite communication, owing to its rapid beam scanning capabilities while maintaining a low profile.</p>
<p>Conventional phased array antennas based on patch antennas are often limited by their bandwidth or scanning capabilities (<xref ref-type="bibr" rid="B16">Li et al., 2023</xref>). To realise the phased array antenna with ultra-wideband and wide scanning capabilities, the Vivaldi antenna is a potential candidate (<xref ref-type="bibr" rid="B21">Logan et al., 2018a</xref>; <xref ref-type="bibr" rid="B22">Logan et al., 2018b</xref>. However, these Vivaldi antennas usually come with a high volumetric profile and nonplanar features, which pose challenges in integrating or installing them into the vehicle. On the other hand, the tightly coupled dipole array (TCDA) has gained significant interest owing to its characteristics of ultrawideband, compact, planar, and wide scanning features (<xref ref-type="bibr" rid="B15">Li et al., 2017</xref>; <xref ref-type="bibr" rid="B6">Doane et al., 2013</xref>). The design of the TCDA is initially inspired by Wheeler&#x2019;s theoretical current sheet model, proposed in 1949 (<xref ref-type="bibr" rid="B33">Wheeler, 1965</xref>). However, it did not gain significant attention in the earlier years. In the early 2000s, Munk extended Wheeler&#x2019;s current sheet into the current sheet array (CSA), which turns this theoretical concept into a practical array configuration (<xref ref-type="bibr" rid="B40">Munk, 2003</xref>; <xref ref-type="bibr" rid="B25">Munk, 2006</xref>). In 2003, the first TCDA phased array antenna with ultrawideband and wide scanning was proposed by <xref ref-type="bibr" rid="B26">Munk et al. (2003)</xref>. Since then, most TCDA antennas have emerged significantly to achieve ultra-wideband and wide-scanning performance (<xref ref-type="bibr" rid="B13">Lee and Nam, 2017</xref>; <xref ref-type="bibr" rid="B38">Zhou et al., 2018</xref>; <xref ref-type="bibr" rid="B14">Lee Hakjune and Yoon, 2019</xref>; <xref ref-type="bibr" rid="B17">Liang et al., 2020</xref>; <xref ref-type="bibr" rid="B39">Zhou et al., 2022</xref>; <xref ref-type="bibr" rid="B32">Wen et al., 2024</xref>). However, most existing TCDA antennas in publications share a common drawback: a high volumetric profile resulting from their structural configuration. In addition, TCDAs require the balun feeding networks to excite the antenna and ensure proper signal transmission (<xref ref-type="bibr" rid="B18">Lindberg et al., 2007</xref>; <xref ref-type="bibr" rid="B28">Shim et al., 2019</xref>). However, this approach further contributes to the high volumetric profile due to its nonplanar structure (<xref ref-type="bibr" rid="B5">Doane et al., 2012</xref>). As a result, traditional TCDAs consistently struggle to maintain a low volumetric profile while achieving optimal performance.</p>
<p>TCDA antennas often incorporate a well-designed radiating structure and an additional matching layer to achieve ultrawideband and wide-angle performance. This layer, known as the wide-angle impedance matching (WAIM) layer, is placed on top of the phased array to enhance impedance matching and minimise reflection across a wide range of incident angles. The WAIM layer can be realised utilising a simple dielectric substrate on top of the TCDA to enhance impedance matching and scanning capability (the dielectric substrate-based WAIM is also sometimes known as dielectric superstrate) (<xref ref-type="bibr" rid="B7">Gou et al., 2024</xref>; <xref ref-type="bibr" rid="B24">Moulder et al., 2013</xref>; <xref ref-type="bibr" rid="B27">Papantonis and Volakis, 2015</xref>; <xref ref-type="bibr" rid="B23">Moghaddam et al., 2020</xref>; <xref ref-type="bibr" rid="B20">Logan et al., 2017</xref>). In (<xref ref-type="bibr" rid="B24">Moulder et al., 2013</xref>), a dielectric superstrate is employed to realise an extremely wideband across <inline-formula id="inf5">
<mml:math id="m5">
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</inline-formula>. Similarly, in (<xref ref-type="bibr" rid="B27">Papantonis and Volakis, 2015</xref>), a dielectric superstrate with a thickness of approximately <inline-formula id="inf8">
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</inline-formula> is the wavelength of the highest operating frequency) is used to enhance the impedance bandwidth. In <xref ref-type="bibr" rid="B23">Moghaddam et al. (2020)</xref>, a planar TCDA with a wide scanning range up to <inline-formula id="inf10">
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</inline-formula> is proposed by using a dielectric superstrate. However, a higher profile and an increasing weight limit their applications. To reduce the overall profile of the WAIM, it is proposed to realise the WAIM using either the frequency selective surface (FSS) (<xref ref-type="bibr" rid="B9">Jiang et al., 2020</xref>) or metasurface (<xref ref-type="bibr" rid="B29">Sun et al., 2021</xref>; <xref ref-type="bibr" rid="B2">Bah et al., 2019</xref>). In (<xref ref-type="bibr" rid="B29">Sun et al., 2021</xref>), a capacitive metasurface layer is loaded to suppress the in-band coupled-loop modes. A square patch-based metasurface (MS) layer is introduced in <xref ref-type="bibr" rid="B31">Wang et al. (2023)</xref> to mitigate the surface waves when scanning in H-plane. In <xref ref-type="bibr" rid="B37">Zhang et al. (2022)</xref>, an MS layer composed of full-split rings is used to achieve a wide scanning range. Despite these advancements, the mentioned designs commonly operate at low frequencies.</p>
<p>Based on the above discussion, existing TCDA antennas offer unique advantages, including wide-angle scanning capability and ultrawideband performance, making them highly suitable for various advanced communication and data transmission applications. However, despite these benefits, TCDA antennas still face several critical limitations. One major drawback is their inherently high volumetric profile, which arises from their structural configuration, an additional component of balun feeding networks, and the presence of a WAIM layer (superstrate, FSS, and MS). In addition, the complex structure of the TCDA often makes fabrication and implementation more challenging and costly. Moreover, most current designs only apply to frequency bands below the Ku band, limiting their use in higher-frequency communication systems.</p>
<p>This paper uses a low-profile TCDA phased array antenna to support a wide-angle scanning capability of <inline-formula id="inf11">
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</inline-formula> while operating in the 12&#x2013;30&#xa0;GHz frequency range. The radiating element consists of a pair of dipole arms with six shorting posts connected to the ground. A <inline-formula id="inf12">
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</inline-formula>-shaped feeding probe is utilised beneath the radiator to maintain a planar structure. In addition, a semi-arc MS layer with a high refractive index is introduced to enhance impedance matching during wide-angle scanning. Moreover, the main advantage of the proposed TCDA phased array is that it is realised using a cost-effective dielectric substrate (Rogers 4350B), and it features a simple and fully planar design, making it attractive for mass production for commercialised industry applications.</p>
<p>The presented low-profile, wideband, wide-scanning phased array antenna addresses critical challenges in next-generation wireless and satellite communication systems, especially for mobile and vehicular platforms. By leveraging a tightly coupled dipole array (TCDA) enhanced with capacitive strips for common-mode suppression and a semi-arc metasurface for wide-angle impedance matching, the design achieves ultra-wideband operation (12&#x2013;30&#xa0;GHz), wide-angle scanning capability <inline-formula id="inf13">
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</inline-formula>, and a compact, fully planar form factor. Unlike traditional phased arrays limited by bandwidth, scanning capability, or bulky Vivaldi-based antennas, the proposed TCDA array facilitates easier integration and cost-effective mass production. Such wideband capability is essential to accommodate diverse frequency bands and evolving spectral allocations in SATCOM and emerging 6G NTNs. Moreover, the wide-angle scanning capability ensures reliable connectivity in dynamic mobile scenarios, making this design particularly suitable for SATCOM-on-the-move terminals, radar systems requiring agile beamforming, and millimetre-wave applications where rapid and precise beam steering is critical.</p>
</sec>
<sec id="s2">
<title>2 Design of the proposed TCDA array</title>
<p>In this section, the fundamental operating mechanism of the proposed TCDA antenna is thoroughly discussed and analyzed from four key aspects. First, the fundamental property of the proposed unit cell TCDA is introduced. Next, the mechanisms of common-mode suppression and the role of the metasurface layer are examined in detail. Finally, the design and performance of the designed finite array antenna are presented.</p>
<sec id="s2-1">
<title>2.1 Configuration of TCDA element</title>
<p>
<xref ref-type="fig" rid="F1">Figure 1</xref> shows the proposed TCDA element with optimised dimensions, which comprises the proposed TCDA radiating element and a semi-arc MS layer. To ease overall fabrication of the proposed TCDA, as can be observed in <xref ref-type="fig" rid="F1">Figure 1B</xref>, the radiating element of the proposed TCDA antenna is realised using two identical 0.762&#xa0;mm dielectric substrates (Rogers RO4350B, <inline-formula id="inf14">
<mml:math id="m14">
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</inline-formula> &#x3d; 0.0037) and an additional laminated with a 0.1&#xa0;mm prepreg layer (Rogers RO4450B, <inline-formula id="inf16">
<mml:math id="m16">
<mml:mrow>
<mml:msub>
<mml:mrow>
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</inline-formula> &#x3d; 3.54, <inline-formula id="inf17">
<mml:math id="m17">
<mml:mrow>
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</inline-formula> &#x3d; 0.004). A pair of shorted planar patches with capacitive strips is placed on the top layer of the substrate. Notably, a through <inline-formula id="inf18">
<mml:math id="m18">
<mml:mrow>
<mml:mi mathvariant="normal">&#x393;</mml:mi>
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</inline-formula>-shaped probe is directly coupled from the ground plane to the radiating element, which achieves unbalanced impedance matching by transforming the input impedance of the dipole antenna from <inline-formula id="inf19">
<mml:math id="m19">
<mml:mrow>
<mml:mn>260</mml:mn>
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</inline-formula> to <inline-formula id="inf20">
<mml:math id="m20">
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</inline-formula>. The corresponding excitation power is supplied to the proposed TCDA antenna via a coaxial connector. In addition to that, an MS layer consisting of periodic semi-arcs is designed on a 0.254&#xa0;mm RO 4350B substrate, which is positioned 1.2&#xa0;mm above the radiating element to improve overall impedance matching both for the broadside and during scanning.</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>The geometry of the proposed unit cell TCDA antenna, <bold>(A)</bold> 3D view, <bold>(B)</bold> cross-section view, <bold>(C)</bold> top view of the radiating element, and <bold>(D)</bold> MS layer. <inline-formula id="inf21">
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</inline-formula> &#x3d; 0.1&#xa0;mm, <inline-formula id="inf22">
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</inline-formula> &#x3d; 1&#xa0;mm, W &#x3d; 6&#xa0;mm, L &#x3d; 3.9&#xa0;mm, Sd &#x3d; 1.45&#xa0;mm, Ds &#x3d; 0.44&#xa0;mm, Dr &#x3d; 0.4&#xa0;mm, Df &#x3d; 0.8&#xa0;mm, lf &#x3d; 1.55&#xa0;mm, ls &#x3d; 0.7&#xa0;mm, ws &#x3d; 0.38&#xa0;mm, ls1 &#x3d; 0.6&#xa0;mm, ws1 &#x3d; 0.55&#xa0;mm, ws2 &#x3d; 0.75&#xa0;mm.</p>
</caption>
<graphic xlink:href="frcmn-06-1613225-g001.tif">
<alt-text content-type="machine-generated">Diagram illustrating the structure and components of a metasurface antenna. (A) A layered perspective view showing the metasurface, radiating, laminated layers, and ground. (B) A side view detailing the coaxial connector, &#x393;-shaped probe, and height notations. (C) Top view of capacitive strips with labeled dimensions such as ws, ls, and Df. (D) Grid pattern of metasurface elements with dimensions labeled as w, l, t, and Mgap. Each section is labeled from A to D.</alt-text>
</graphic>
</fig>
</sec>
<sec id="s2-2">
<title>2.2 Common mode suppression</title>
<p>To illustrate the working mechanism of our proposed capacitive strips for the unwanted common-mode suppression, various antenna elements without or with additional capacitive structures are configured in <xref ref-type="fig" rid="F2">Figure 2</xref>. <xref ref-type="fig" rid="F3">Figure 3</xref> illustrates the simulated results among various radiating elements. As observed in <xref ref-type="fig" rid="F3">Figure 3</xref>, an unwanted common-mode resonance appeared at 23&#xa0;GHz for the case without any capacitive structures. To eliminate the unwanted common-mode resonance, a pair of E-wall structures as proposed in <xref ref-type="bibr" rid="B3">Dang et al. (2022)</xref> is first utilised to suppress common-mode resonance. By integrating an E-wall into our proposed TCDA, the common-mode resonance can be effectively shifted to a higher frequency around 28.5&#xa0;GHz. However, this shifting comes with the cost of worsening the impedance matching at the lower frequency band. Moreover, the additional E-wall requires the proposed antenna to be realised utilising a three-layer dielectric stack-up to ensure the designed via holes can be adequately fabricated, which will thus increase the fabrication complexity and cost. To address the issue above, the capacitive strips are integrated to suppress the common-mode resonance in this proposed design. As seen in <xref ref-type="fig" rid="F3">Figure 3</xref>, the common-mode resonance can be shifted up to 32&#xa0;GHz, moving it away from the desired frequency band while improving the impedance matching across the entire band.</p>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>The design evolution of the proposed TCDA element. <bold>(A)</bold> Without capacitive structures, <bold>(B)</bold> with E-wall, and <bold>(C)</bold> with capacitive strips.</p>
</caption>
<graphic xlink:href="frcmn-06-1613225-g002.tif">
<alt-text content-type="machine-generated">Diagram illustrating different configurations of a rectangular structure with gold sections labeled (A), (B), and (C). (A) shows a basic structure. (B) adds E-walls on the sides. (C) includes capacitive strips on both sides. A 3D coordinate system is depicted between (B) and (C), marked X, Y, and Z axes.</alt-text>
</graphic>
</fig>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>Simulated VSWR results of the different antenna elements.</p>
</caption>
<graphic xlink:href="frcmn-06-1613225-g003.tif">
<alt-text content-type="machine-generated">Graph showing VSWR versus frequency in GHz with three line types: black squares represent &#x22;without coupling structure,&#x22; red circles represent &#x22;with E-wall,&#x22; and blue triangles represent &#x22;with capacitive strips.&#x22; The graph illustrates varying VSWR performance across the frequency spectrum from 8 to 36 GHz for each condition.</alt-text>
</graphic>
</fig>
<p>To further verify the functions of the proposed capacitive structures for the common-mode resonance reduction, the current distributions among TCDA radiating elements without any capacitive structure, with E-wall, and with capacitive strips are presented in <xref ref-type="fig" rid="F4">Figure 4</xref>. As can be observed from the <xref ref-type="fig" rid="F4">Figure 4A</xref>, the case without any capacitive structure exhibits a strong common-mode current at 23&#xa0;GHz. On the other hand, the configurations with the E-wall and capacitive strips effectively suppress it at this frequency, as shown in <xref ref-type="fig" rid="F4">Figures 4B, C</xref>. Thus, it can be concluded that the proposed capacitive strip has a functionality similar to the conventional E-wall. However, compared with the E-wall, the main advantage of the proposed capacitive strips is that they can be seamlessly integrated in the same layer with the radiating elements of the TCDA, streamlining fabrication and reducing costs.</p>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>Current distributions at 23&#xa0;GHz for <bold>(A)</bold> without any capacitive structure, <bold>(B)</bold> with E-wall, <bold>(C)</bold> with capacitive strips.</p>
</caption>
<graphic xlink:href="frcmn-06-1613225-g004.tif">
<alt-text content-type="machine-generated">Three simulation panels displaying fluid flow in structures. (A) shows the flow without capacitive structures. (B) introduces E-wall structures altering the flow. (C) uses capacitive strips, further modifying the flow. Each includes red arrows indicating direction.</alt-text>
</graphic>
</fig>
</sec>
<sec id="s2-3">
<title>2.3 Metasurface</title>
<p>To further enhance the impedance matching, particularly for the beam scanning case, the WAIM layers are introduced respectively, including the superstrate and semi-arc MS layers, as shown in <xref ref-type="fig" rid="F5">Figure 5</xref>. Initially, a Rogers RT5880LZ dielectric superstrate with a thickness of <inline-formula id="inf25">
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<fig id="F5" position="float">
<label>FIGURE 5</label>
<caption>
<p>Various superstrate involved in the design process. <bold>(A)</bold> Dielectric superstrate, <bold>(B)</bold> semi-arc MS. <inline-formula id="inf28">
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</caption>
<graphic xlink:href="frcmn-06-1613225-g005.tif">
<alt-text content-type="machine-generated">Diagram split into two parts labeled A and B. Part A shows a rectangular block with dimensions labeled as Hsup1 and Wsup. Part B shows a similar block with two copper-like traces forming a split-ring resonator shape. Dimensions include Hsup, Wsup, Mgap for the space between traces, and other labels like l, w, and t. A 3D axis is marked with X, Y, and Z directions.</alt-text>
</graphic>
</fig>
<p>To design the MS to function as the WAIM layer, it is desired to realise the MS with a high permittivity, which effectively increases equivalent capacitance, as explained by <xref ref-type="disp-formula" rid="e1">Equation 1</xref>.<disp-formula id="e1">
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<fig id="F6" position="float">
<label>FIGURE 6</label>
<caption>
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</mml:mrow>
</mml:math>
</inline-formula> of semi-arc MS layer.</p>
</caption>
<graphic xlink:href="frcmn-06-1613225-g006.tif">
<alt-text content-type="machine-generated">Graph showing effective permittivity (black squares), permeability (red circles), and impedances (blue triangles) versus frequency from 5 to 50 GHz. Values for permittivity and permeability are constant near 8 and 2, respectively, while impedance fluctuates slightly around 0.1.</alt-text>
</graphic>
</fig>
<p>
<xref ref-type="fig" rid="F7">Figure 7</xref> shows the VSWR results of the proposed TCDA unit in an infinite array when loading or without various WAIM layers. As observed in <xref ref-type="fig" rid="F7">Figure 7</xref>, without any superstrate matching layer, the impedance matching is very limited, especially in the higher frequency band. After loading the dielectric superstrate, the impedance matching in the middle-frequency band is effectively enhanced, but still cannot cover the desired band. While the semi-arc MS layer can achieve good impedance matching, the latter offers the best impedance matching in the higher frequency band from 28 to 32&#xa0;GHz. Meanwhile, the semi-arc MS layer can provide more benefits for scanning applications.</p>
<fig id="F7" position="float">
<label>FIGURE 7</label>
<caption>
<p>VSWR results of the proposed TCDA unit cell with or without superstrate in an infinite array.</p>
</caption>
<graphic xlink:href="frcmn-06-1613225-g007.tif">
<alt-text content-type="machine-generated">Graph showing VSWR versus frequency from 8 to 36 GHz. Three curves represent conditions: without superstrate (gray squares), with dielectric superstrate (red circles), and with semiarc MS (blue triangles). The VSWR is lowest near 12 GHz for all cases, with varying performance at higher frequencies.</alt-text>
</graphic>
</fig>
</sec>
<sec id="s2-4">
<title>2.4 Finite array simulation results</title>
<p>The aforementioned discussions on the designed TCDA are evaluated using the unit cell periodic boundary condition in the CST Microwave Studio. To assess the beam scanning performance and the radiation performance of the proposed TCDA in the finite array environment, as in a real application, a <inline-formula id="inf57">
<mml:math id="m59">
<mml:mrow>
<mml:mn>5</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:mn>5</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> array is configured and simulated using the open boundary condition in the CST Microwave Studio. To mitigate the edge effect, the finite <inline-formula id="inf58">
<mml:math id="m60">
<mml:mrow>
<mml:mn>5</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:mn>5</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> array is surrounded with the additional outer elements (as shown in the blue colour area of <xref ref-type="fig" rid="F8">Figure 8</xref>), and they are set as passive elements that are terminated with <inline-formula id="inf59">
<mml:math id="m61">
<mml:mrow>
<mml:mn>50</mml:mn>
<mml:mi mathvariant="normal">&#x3a9;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> loads. It is worth noting that the internal <inline-formula id="inf60">
<mml:math id="m62">
<mml:mrow>
<mml:mn>5</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:mn>5</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> elements (as shown in the red colour area of <xref ref-type="fig" rid="F8">Figure 8</xref>) are excited as active elements. The simulated <inline-formula id="inf61">
<mml:math id="m63">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="normal">V</mml:mi>
<mml:mi mathvariant="normal">S</mml:mi>
<mml:mi mathvariant="normal">W</mml:mi>
<mml:mi mathvariant="normal">R</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>scanned</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> results of the proposed TCDA array for E&#x2212; and H-plane scanning are presented in <xref ref-type="fig" rid="F9">Figure 9</xref>. As can be observed from the <xref ref-type="fig" rid="F7">Figure 7</xref>, the simulated VSWR of the proposed finite TCDA is always below 1.5 from 12 to 32&#xa0;GHz for broadside. In addition, the array can achieve scanning angles of up to <inline-formula id="inf62">
<mml:math id="m64">
<mml:mrow>
<mml:mn>60</mml:mn>
<mml:mo>&#xb0;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> in both E&#x2212; and H-planes while maintaining a <inline-formula id="inf63">
<mml:math id="m65">
<mml:mrow>
<mml:mi mathvariant="normal">V</mml:mi>
<mml:mi mathvariant="normal">S</mml:mi>
<mml:mi mathvariant="normal">W</mml:mi>
<mml:mi mathvariant="normal">R</mml:mi>
<mml:mo>&#x3c;</mml:mo>
<mml:mn>2.5</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> across the 12&#x2013;30&#xa0;GHz frequency range. To further evaluate the scanning capability of the designed array, <xref ref-type="fig" rid="F10">Figure 10</xref> indicates the simulated scanning patterns of the proposed array at 12&#xa0;GHz (the lowest operating frequency), 21&#xa0;GHz (the middle operating frequency), and 30&#xa0;GHz (the highest operating frequency) in E&#x2212; and H-planes, respectively. The radiation beam of the proposed TCDA array is scanned away from broadside <inline-formula id="inf64">
<mml:math id="m66">
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>&#x3b8;</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>0</mml:mn>
<mml:mo>&#xb0;</mml:mo>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> to <inline-formula id="inf65">
<mml:math id="m67">
<mml:mrow>
<mml:mi>&#x3b8;</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>60</mml:mn>
<mml:mo>&#xb0;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> at these three frequencies, with the gain dropping by less than 3&#xa0;dB in both planes. In addition, the array&#x2019;s relative cross-polarisation (X-pol) levels remain below <inline-formula id="inf66">
<mml:math id="m68">
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>40</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> dB for all scanning angles at both planes across the considered frequencies.</p>
<fig id="F8" position="float">
<label>FIGURE 8</label>
<caption>
<p>Feeding topology and <bold>(B)</bold> configuration of the 7<inline-formula id="inf67">
<mml:math id="m69">
<mml:mrow>
<mml:mo>&#xd7;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 7 array. <bold>(A)</bold> E-plane <bold>(B)</bold> H-plane.</p>
</caption>
<graphic xlink:href="frcmn-06-1613225-g008.tif">
<alt-text content-type="machine-generated">Diagram illustrating two views of elements. Panel A shows a grid with active elements in red and passive elements in blue. Panel B depicts the side view and main view of a structure consisting of recurring patterned elements, with a highlighted section in red.</alt-text>
</graphic>
</fig>
<fig id="F9" position="float">
<label>FIGURE 9</label>
<caption>
<p>Simulated <inline-formula id="inf68">
<mml:math id="m70">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi mathvariant="normal">V</mml:mi>
<mml:mi mathvariant="normal">S</mml:mi>
<mml:mi mathvariant="normal">W</mml:mi>
<mml:mi mathvariant="normal">R</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>scanned</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> in a finite array at <bold>(A)</bold> E-plane and <bold>(B)</bold> H-plane.</p>
</caption>
<graphic xlink:href="frcmn-06-1613225-g009.tif">
<alt-text content-type="machine-generated">Two graphs compare Voltage Standing Wave Ratio (VSWR) against frequency in gigahertz from 8 to 36. The left graph, labeled E-plane, and the right graph, labeled H-plane, both show patterns at angles of zero degrees, thirty degrees, and sixty degrees. Data lines are marked with different symbols and colors for each angle.</alt-text>
</graphic>
</fig>
<fig id="F10" position="float">
<label>FIGURE 10</label>
<caption>
<p>Simulated scanning radiation patterns of the <inline-formula id="inf69">
<mml:math id="m71">
<mml:mrow>
<mml:mn>7</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:mn>7</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> array at 12&#xa0;GHz, 21&#xa0;GHz, and 30&#xa0;GHz. <bold>(A)</bold>, <bold>(C)</bold>, and <bold>(E)</bold> for the E-plane, <bold>(B)</bold>, <bold>(D)</bold>, and <bold>(F)</bold> for the H-plane.</p>
</caption>
<graphic xlink:href="frcmn-06-1613225-g010.tif">
<alt-text content-type="machine-generated">Six line graphs labeled A to F showing \( G_0/G_{max} \) in decibels versus \( \theta \) in degrees at angles 0 degrees, 30 degrees, and 60 degrees. Panels A and B display 12 GHz, C and D show 21 GHz, E and F show 30 GHz. Each frequency is depicted at E-plane and H-plane, illustrating different patterns for each angle.</alt-text>
</graphic>
</fig>
<p>The gain, a crucial parameter, is frequently used to gauge the antenna performance. Detailed variations in gain at different scanning angles across both planes are meticulously detailed in <xref ref-type="table" rid="T1">Table 1</xref> for three distinct configurations: (Case 1: E-wall with superstrate, Case 2: E-wall with semi-arc MS, and Case 3: capacitive strips with semi-arc MS). In Case 1, where the E-wall is paired with a superstrate, this configuration supports scanning angles up to <inline-formula id="inf70">
<mml:math id="m72">
<mml:mrow>
<mml:mn>60</mml:mn>
<mml:mo>&#xb0;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> at frequencies covering from 12 to 20&#xa0;GHz in both planes. In addition, the integration of semi-arc MS in Case 2 notably extends the operational frequency up to 24&#xa0;GHz, showcasing semi-arc MS&#x2019;s capability to enhance wideband impedance matching during scanning procedures. Furthermore, replacing the E-wall with capacitive strips in Case 3 reduces common-mode interference and expands the bandwidth, signifying a substantial enhancement in antenna performance. On the other hand, the radiation efficiency remains consistently high, indicating that Case 3 does not compromise efficiency even at larger scanning angles.</p>
<table-wrap id="T1" position="float">
<label>TABLE 1</label>
<caption>
<p>Simulated realised gain and radiation efficiency of the proposed TCDA with scanning angle at different frequencies in both planes. (case 1: E-wall with superstrate, case 2: E-wall with semi-arc MS, case 3: capacitive strips with semi-arc MS.).</p>
</caption>
<table>
<thead valign="top">
<tr>
<th colspan="2" rowspan="2" align="center">Simulated realised gain at various <break/>Scanning angle</th>
<th colspan="1" rowspan="2" align="center">Radiation efficiency (%)</th>
<th colspan="5" align="center">Frequency</th>
</tr>
<tr>
<th align="center">12&#xa0;GHz</th>
<th align="center">16&#xa0;GHz</th>
<th align="center">20&#xa0;GHz</th>
<th align="center">24&#xa0;GHz</th>
<th align="center">30&#xa0;GHz</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td rowspan="3" align="center">
<inline-formula id="inf71">
<mml:math id="m73">
<mml:mrow>
<mml:mn>0</mml:mn>
<mml:mo>&#xb0;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> (dBi)</td>
<td align="center">Case 1</td>
<td align="center">92&#x2013;96</td>
<td align="center">12.1</td>
<td align="center">14.8</td>
<td align="center">16.8</td>
<td align="center">/</td>
<td align="center">/</td>
</tr>
<tr>
<td align="center">Case 2</td>
<td align="center">93&#x2013;94</td>
<td align="center">10.5</td>
<td align="center">14.5</td>
<td align="center">16.7</td>
<td align="center">18.2</td>
<td align="center">/</td>
</tr>
<tr>
<td align="center">
<bold>Case 3</bold>
</td>
<td align="center">
<bold>92&#x2013;94</bold>
</td>
<td align="center">
<bold>12.1</bold>
</td>
<td align="center">
<bold>14.8</bold>
</td>
<td align="center">
<bold>17.2</bold>
</td>
<td align="center">
<bold>18.4</bold>
</td>
<td align="center">
<bold>20.4</bold>
</td>
</tr>
<tr>
<td rowspan="3" align="center">
<inline-formula id="inf72">
<mml:math id="m74">
<mml:mrow>
<mml:mn>30</mml:mn>
<mml:mo>&#xb0;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> (dBi)</td>
<td align="center">Case 1</td>
<td align="center">93&#x2013;95</td>
<td align="center">11.6</td>
<td align="center">14.2</td>
<td align="center">16.3 (E) 16.2 (H)</td>
<td align="center">/</td>
<td align="center">/</td>
</tr>
<tr>
<td align="center">Case 2</td>
<td align="center">91&#x2013;94</td>
<td align="center">10.0 (E)9.4 (H)</td>
<td align="center">13.9</td>
<td align="center">16.1 (E)16.2 (H)</td>
<td align="center">17.5 (E) 17.9 (H)</td>
<td align="center">/</td>
</tr>
<tr>
<td align="center">
<bold>Case 3</bold>
</td>
<td align="center">
<bold>92&#x2013;94</bold>
</td>
<td align="center">
<bold>11.6 (E)11.5 (H)</bold>
</td>
<td align="center">
<bold>14.3 (E) 14.2 (H)</bold>
</td>
<td align="center">
<bold>16.5 (E) 17.9 (H)</bold>
</td>
<td align="center">
<bold>17.8 (E) 17.9 (H)</bold>
</td>
<td align="center">
<bold>18.6</bold>
</td>
</tr>
<tr>
<td rowspan="3" align="center">
<inline-formula id="inf73">
<mml:math id="m75">
<mml:mrow>
<mml:mn>60</mml:mn>
<mml:mo>&#xb0;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> (dBi)</td>
<td align="center">Case 1</td>
<td align="center">91.5&#x2013;93</td>
<td align="center">10.2 (E) 9.8 (H)</td>
<td align="center">12.3 (E) 12.4 (H)</td>
<td align="center">13.9 (E) 14.2 (H)</td>
<td align="center">/</td>
<td align="center">/</td>
</tr>
<tr>
<td align="center">Case 2</td>
<td align="center">92&#x2013;94</td>
<td align="center">10.0 (E) 7.6 (H)</td>
<td align="center">11.7 (E) 12.3 (H)</td>
<td align="center">13.9 (E) 14.4 (H)</td>
<td align="center">14.8 (E) 15.9 (H)</td>
<td align="center">/</td>
</tr>
<tr>
<td align="center">
<bold>Case 3</bold>
</td>
<td align="center">
<bold>92&#x2013;93</bold>
</td>
<td align="center">
<bold>9.9 (E)9.8 (H)</bold>
</td>
<td align="center">
<bold>12.3 (E)12.1 (H)</bold>
</td>
<td align="center">
<bold>14.2 (E)13.8 (H)</bold>
</td>
<td align="center">
<bold>15.7 (E)15.8 (H)</bold>
</td>
<td align="center">
<bold>17.4 (E)17.3 (H)</bold>
</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>The bold values are used to emphasize the performance of the proposed antenna.</p>
</fn>
</table-wrap-foot>
</table-wrap>
</sec>
</sec>
<sec id="s3">
<title>3 Measurement and discussion</title>
<p>To verify the working principle of the proposed TCDA, the finite 5 <inline-formula id="inf74">
<mml:math id="m76">
<mml:mrow>
<mml:mo>&#xd7;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> 5 array antenna with dummy elements was fabricated as shown in <xref ref-type="fig" rid="F11">Figure 11</xref>. Due to the limitations of measurement conditions, only the center port was measured for VSWR, while all other ports were terminated with <inline-formula id="inf75">
<mml:math id="m77">
<mml:mrow>
<mml:mn>50</mml:mn>
<mml:mi mathvariant="normal">&#x3a9;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> loads. The measured VSWR is in good agreement with the simulated one, within the frequency range of 12&#x2013;30&#xa0;GHz under VSWR <inline-formula id="inf76">
<mml:math id="m78">
<mml:mrow>
<mml:mo>&#x2264;</mml:mo>
<mml:mspace width="0.3333em"/>
<mml:mn>2.4</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>, as displayed in <xref ref-type="fig" rid="F12">Figure 12A</xref>. The realised gain of the array can also be obtained from the embedded element pattern. The simulated and measured realised gains show only a tiny deviation, less than 1&#xa0;dB is observed, shown in <xref ref-type="fig" rid="F12">Figure 12B</xref>, where the ideal aperture gain is also shown for reference. The disparities are mainly due to test errors and the connected cable.</p>
<fig id="F11" position="float">
<label>FIGURE 11</label>
<caption>
<p>Fabricated prototype of the proposed <inline-formula id="inf77">
<mml:math id="m79">
<mml:mrow>
<mml:mn>5</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:mn>5</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> finite array.</p>
</caption>
<graphic xlink:href="frcmn-06-1613225-g011.tif">
<alt-text content-type="machine-generated">Three rectangular panels labeled &#x22;Array,&#x22; &#x22;Radiating structure,&#x22; and &#x22;Semi-arc MS&#x22; are displayed in a row. Each panel has a distinct pattern of small holes. A ruler in centimeters is placed in front for scale.</alt-text>
</graphic>
</fig>
<fig id="F12" position="float">
<label>FIGURE 12</label>
<caption>
<p>
<bold>(A)</bold> Simulated and measured VSWR results of the center element, <bold>(B)</bold> Simulated and measured realised gain of the <inline-formula id="inf78">
<mml:math id="m80">
<mml:mrow>
<mml:mn>5</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:mn>5</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> array at broadside radiation.</p>
</caption>
<graphic xlink:href="frcmn-06-1613225-g012.tif">
<alt-text content-type="machine-generated">Two graphs are displayed side by side. Graph A on the left shows VSWR versus frequency from 10 to 35 GHz, comparing measured and simulated data with lines and symbols. Graph B on the right depicts gain in dBi against frequency from 12 to 30 GHz, showing measured, simulated, and calculated values with different colored lines and markers. The legends indicate the lines represent measurements, simulations, and calculations.</alt-text>
</graphic>
</fig>
<p>Similar to the VSWR measurement, the radiation patterns of the centre element were carefully measured, showing good consistency with the simulated results, as illustrated in <xref ref-type="fig" rid="F13">Figure 13</xref>. The simulated cross-polarisation patterns in the H-plane are below &#x2212;40&#xa0;dB, which are not shown here. It is noted that some fluctuations can be observed in the co-polarisation patterns, especially at the higher frequencies, as the array size is relatively small (<xref ref-type="bibr" rid="B9">Jiang et al., 2020</xref>).</p>
<fig id="F13" position="float">
<label>FIGURE 13</label>
<caption>
<p>Simulated scanning radiation patterns of the <inline-formula id="inf79">
<mml:math id="m81">
<mml:mrow>
<mml:mn>7</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:mn>7</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> array at 12&#xa0;GHz, 21&#xa0;GHz, and 30&#xa0;GHz. <bold>(A)</bold>, <bold>(C)</bold>, and <bold>(E)</bold> for the E-plane, <bold>(B)</bold>, <bold>(D)</bold>, and <bold>(F)</bold> for the H-plane.</p>
</caption>
<graphic xlink:href="frcmn-06-1613225-g013.tif">
<alt-text content-type="machine-generated">Six plots show radiation patterns at different frequencies: (A) and (B) display 12 GHz in E-plane and H-plane.(C) and (D) show 21 GHz in E-plane and H-plane.(E) and (F) present 30 GHz in E-plane and H-plane.Each plot has four lines representing measured and simulated results. The x-axis is Theta in degrees and the y-axis is Radiation Pattern in decibels.</alt-text>
</graphic>
</fig>
<p>To highlight the advancement of the proposed TCDA array, the figure of merit has been introduced to evaluate the overall performance of the proposed design (<xref ref-type="bibr" rid="B4">Doane, 2013</xref>). For a lossy array, the definition of the array figure of merit can be defined as <xref ref-type="disp-formula" rid="e3">Equations 3</xref>-<xref ref-type="disp-formula" rid="e5">5</xref>.<disp-formula id="e3">
<mml:math id="m82">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>P</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>A</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mi>B</mml:mi>
<mml:mfenced open="|" close="|">
<mml:mrow>
<mml:mi>log</mml:mi>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b7;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>min</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mo>&#x2061;</mml:mo>
<mml:mi>cos</mml:mi>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3b8;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>max</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(3)</label>
</disp-formula>
<disp-formula id="e4">
<mml:math id="m83">
<mml:mrow>
<mml:mi>B</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>f</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>max</mml:mi>
</mml:mrow>
</mml:msub>
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<mml:math id="m89">
<mml:mrow>
<mml:mn>60</mml:mn>
<mml:mo>&#xb0;</mml:mo>
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</inline-formula> in both planes across a wide bandwidth from 12 to 30&#xa0;GHz while maintaining the VSWR <inline-formula id="inf85">
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</inline-formula> 2.5. This performance is notable when compared to existing designs. For instance, while similar scanning capabilities are reported in the publication <xref ref-type="bibr" rid="B20">Logan et al. (2017)</xref> and <xref ref-type="bibr" rid="B19">Liu et al. (2024)</xref>, their bandwidth VSWR performances are inferior to our design, potentially resulting in higher reflection losses and degraded efficiency. From the perspective of VSWR, the designs in <xref ref-type="bibr" rid="B28">Shim et al. (2019)</xref> and <xref ref-type="bibr" rid="B23">Moghaddam et al. (2020)</xref> realise a lower VSWR but suffer from significant drawbacks: their scanning angles are reduced by half to <inline-formula id="inf86">
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</inline-formula>, and they are accompanied by a higher profile, restricting their practical applicability. The latest design <xref ref-type="bibr" rid="B10">Kim and Nam (2024)</xref> offers a competitive profile height and high-efficiency transmission, but the scanning performance is limited to <inline-formula id="inf87">
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<mml:mn>45</mml:mn>
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</inline-formula>, which is narrower than that of the proposed design. Overall, the proposed design achieves a figure of merit of 0.63, calculated using <xref ref-type="disp-formula" rid="e3">Equation 3</xref>, which exceeds that of all referenced publications. This highlights the key advantage of our design: it effectively balances a broader scanning range with a reasonable VSWR while maintaining a lower profile for enhanced practical implementation. These attributes underscore the excellent performance and applicability of the proposed design.</p>
<table-wrap id="T2" position="float">
<label>TABLE 2</label>
<caption>
<p>Comparisons between existing works and the proposed design (<inline-formula id="inf88">
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</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Reference</th>
<th align="center">Figure of merit</th>
<th align="center">Frequency (GHz)</th>
<th align="center">VSWR</th>
<th align="center">Scanning angle at both planes</th>
<th align="center">Element size</th>
<th align="center">Array size</th>
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<tbody valign="top">
<tr>
<td align="center">
<xref ref-type="bibr" rid="B28">Shim et al. (2019)</xref>
</td>
<td align="center">0.10</td>
<td align="center">22.6&#x2013;32.5</td>
<td align="center">
<inline-formula id="inf89">
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<mml:mrow>
<mml:mo>&#x3c;</mml:mo>
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</inline-formula>2</td>
<td align="center">up to 30&#xb0;</td>
<td align="center">
<inline-formula id="inf90">
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<mml:mo>&#xd7;</mml:mo>
<mml:mn>0.91</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:mn>0.04</mml:mn>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
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<td align="center">
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<mml:mrow>
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<mml:mo>&#xd7;</mml:mo>
<mml:mn>8</mml:mn>
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</inline-formula>
</td>
</tr>
<tr>
<td align="center">
<xref ref-type="bibr" rid="B23">Moghaddam et al. (2020)</xref>
</td>
<td align="center">0.32</td>
<td align="center">17&#x2013;42</td>
<td align="center">
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<td align="center">up to 45&#xb0;</td>
<td align="center">
<inline-formula id="inf93">
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<tr>
<td align="center">
<xref ref-type="bibr" rid="B20">Logan et al. (2017)</xref>
</td>
<td align="center">0.53</td>
<td align="center">3.53&#x2013;21.2</td>
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</td>
</tr>
<tr>
<td align="center">
<xref ref-type="bibr" rid="B29">Sun et al. (2021)</xref>
</td>
<td align="center">0.42</td>
<td align="center">4&#x2013;18</td>
<td align="center">
<inline-formula id="inf98">
<mml:math id="m103">
<mml:mrow>
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<td align="center">up to 45&#xb0;</td>
<td align="center">
<inline-formula id="inf99">
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</td>
</tr>
<tr>
<td align="center">
<xref ref-type="bibr" rid="B19">Liu et al. (2024)</xref>
</td>
<td align="center">0.29</td>
<td align="center">8&#x2013;18.5</td>
<td align="center">
<inline-formula id="inf101">
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<td align="center">up to 60&#xb0;</td>
<td align="center">
<inline-formula id="inf102">
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<td align="center">
<inline-formula id="inf103">
<mml:math id="m108">
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</mml:math>
</inline-formula>
</td>
</tr>
<tr>
<td align="center">
<xref ref-type="bibr" rid="B10">Kim and Nam. (2024)</xref>
</td>
<td align="center">0.53</td>
<td align="center">24.3&#x2013;42.1</td>
<td align="center">
<inline-formula id="inf104">
<mml:math id="m109">
<mml:mrow>
<mml:mo>&#x3c;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>2</td>
<td align="center">up to 45&#xb0;</td>
<td align="center">
<inline-formula id="inf105">
<mml:math id="m110">
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mn>0.42</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:mn>0.13</mml:mn>
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<mml:mn>0.07</mml:mn>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
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<mml:mrow>
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</inline-formula>
</td>
<td align="center">
<inline-formula id="inf106">
<mml:math id="m111">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:mn>4</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
</tr>
<tr>
<td align="center">
<bold>This Work</bold>
</td>
<td align="center">
<bold>0.63</bold>
</td>
<td align="center">
<bold>12&#x2013;30</bold>
</td>
<td align="center">
<inline-formula id="inf107">
<mml:math id="m112">
<mml:mrow>
<mml:mo>&#x3c;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>
<bold>2.5</bold>
</td>
<td align="center">
<bold>up to 60&#xb0;</bold>
</td>
<td align="center">
<inline-formula id="inf108">
<mml:math id="m113">
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mn>0.24</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:mn>0.24</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:mn>0.09</mml:mn>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3bb;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>L</mml:mi>
</mml:mrow>
</mml:msub>
</mml:math>
</inline-formula>
</td>
<td align="center">
<inline-formula id="inf109">
<mml:math id="m114">
<mml:mrow>
<mml:mn>5</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:mn>5</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>The bold values are used to emphasize the performance of the proposed antenna.</p>
</fn>
</table-wrap-foot>
</table-wrap>
</sec>
<sec sec-type="conclusion" id="s4">
<title>4 Conclusion</title>
<p>This work presents a low-profile, ultra-wideband, wide-scanning tightly coupled dipole array (TCDA) antenna, optimised for high-performance satellite and millimetre-wave communication systems. The proposed array operates across an extended frequency range of 12&#x2013;30&#xa0;GHz, supporting a wide-angle scanning capability up to <inline-formula id="inf110">
<mml:math id="m115">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
<mml:mn>60</mml:mn>
<mml:mo>&#xb0;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> in both E&#x2212; and H-planes while maintaining a voltage standing wave ratio (VSWR) below 2.5. Notably, the design maintains a compact profile of just <inline-formula id="inf111">
<mml:math id="m116">
<mml:mrow>
<mml:mn>0.09</mml:mn>
<mml:msub>
<mml:mrow>
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</mml:mrow>
<mml:mrow>
<mml:mi>L</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> (<inline-formula id="inf112">
<mml:math id="m117">
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</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the wavelength at the lowest operating frequency), addressing the volumetric constraints typical in mobile SATCOM platforms.</p>
<p>Key innovations include incorporating key implementations for enhanced array performance, e.g., using planar shorted dipole patches excited via a <inline-formula id="inf113">
<mml:math id="m118">
<mml:mrow>
<mml:mi mathvariant="normal">&#x393;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>-shaped probe and integrating capacitive strips to suppress common-mode resonances without added structural complexity. This proposed approach reduced the fabrication complexity compared to the conventional E-wall design for TCDA, offering a lower manufacturing cost. A novel semi-arc-shaped metasurface (MS) layer with high effective permittivity <inline-formula id="inf114">
<mml:math id="m119">
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
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</mml:mrow>
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</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> is introduced as a wide-angle impedance matching (WAIM) layer, enhancing impedance matching and enabling profile reduction. This MS exhibits stable wave impedance and low dispersion, contributing to consistent broadband performance.</p>
<p>Simulated and measured results from a fabricated <inline-formula id="inf115">
<mml:math id="m120">
<mml:mrow>
<mml:mn>5</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:mn>5</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> array prototype validate the design&#x2019;s performance. The array achieves broadside realised gains up to 20.4 dBi at 30&#xa0;GHz and maintains less than 3&#xa0;dB gain degradation even at <inline-formula id="inf116">
<mml:math id="m121">
<mml:mrow>
<mml:mn>60</mml:mn>
<mml:mo>&#xb0;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> scan angles. Cross-polarisation levels remain below <inline-formula id="inf117">
<mml:math id="m122">
<mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>40</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> dB across all scanned angles. Compared to existing solutions, the design achieves a superior figure of merit <inline-formula id="inf118">
<mml:math id="m123">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>P</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>A</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>0.63</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>, outperforming prior works in balancing bandwidth, scan angle, and physical profile.</p>
<p>Combining technical rigour with practical manufacturability&#x2014;using low-cost Rogers RO4350B substrates in a planar configuration&#x2014;establishes a new benchmark for future broadband, mobile, and low-profile phased array antennas. Its scalability and efficiency make it highly suitable for commercialised SATCOM, 6G non-terrestrial networks, and radar systems requiring agile beamforming under strict form factor constraints.</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 author.</p>
</sec>
<sec sec-type="author-contributions" id="s6">
<title>Author contributions</title>
<p>WD: Data curation, Investigation, Methodology, Writing &#x2013; review and editing, Visualization, Validation, Formal Analysis, Funding acquisition, Writing &#x2013; original draft. WY: Investigation, Conceptualization, Formal Analysis, Supervision, Methodology, Writing &#x2013; review and editing. AA: Investigation, Supervision, Writing &#x2013; review and editing, Funding acquisition, Formal Analysis, Project administration.</p>
</sec>
<sec sec-type="funding-information" id="s7">
<title>Funding</title>
<p>The author(s) declare that financial support was received for the research and/or publication of this article. Ms. Dang Wen&#x2019;s PhD project is supported by the China Scholarship Council (CSC). Additional support from the ELLIIT Strategic Research Environment (<ext-link ext-link-type="uri" xlink:href="https://elliit.se/">https://elliit.se/</ext-link>) for Andr&#xe9;s Alay&#xf3;n Glazunov is also appreciated.</p>
</sec>
<ack>
<p>WD would like to express her sincere gratitude to Dr. Qina Long, Dr. Xue Bing, and Dr. Chen Quangang for their assistance during the measurement.</p>
</ack>
<sec sec-type="COI-statement" id="s8">
<title>Conflict of interest</title>
<p>Author WY was employed by Rohde &#x26; Schwarz GmbH &#x26; Company KG.</p>
<p>The remaining 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="ai-statement" id="s9">
<title>Generative AI statement</title>
<p>The author(s) declare that no Generative AI was used in the creation of this manuscript.</p>
</sec>
<sec sec-type="disclaimer" id="s10">
<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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