{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:11:06Z","timestamp":1760148666507,"version":"build-2065373602"},"reference-count":21,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2023,5,22]],"date-time":"2023-05-22T00:00:00Z","timestamp":1684713600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"FEDER\/Ministerio de Ciencia e Innovaci\u00f3n-Agencia Estatal de Investigaci\u00f3n","award":["PID2020-119788RB-I00"],"award-info":[{"award-number":["PID2020-119788RB-I00"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Despite playing a central role in antenna design, aperture efficiency is often disregarded. Consequently, the present study shows that maximizing the aperture efficiency reduces the required number of radiating elements, which leads to cheaper antennas with more directivity. For this, it is considered that the boundary of the antenna aperture has to be inversely proportional to the half-power beamwidth of the desired footprint for each \u03d5-cut. As an example of application, it has been considered the rectangular footprint, for which a mathematical expression was deduced to calculate the aperture efficiency in terms of the beamwidth, synthesizing a rectangular footprint of a 2:1 aspect ratio by starting from a pure real flat-topped beam pattern. In addition, a more realistic pattern was studied, the asymmetric coverage defined by the European Telecommunications Satellite Organization, including the numerical computation of the contour of the resulting antenna and its aperture efficiency.<\/jats:p>","DOI":"10.3390\/s23104982","type":"journal-article","created":{"date-parts":[[2023,5,23]],"date-time":"2023-05-23T02:02:27Z","timestamp":1684807347000},"page":"4982","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Maximizing Antenna Array Aperture Efficiency for Footprint Patterns"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3949-5058","authenticated-orcid":false,"given":"Cibr\u00e1n","family":"L\u00f3pez-\u00c1lvarez","sequence":"first","affiliation":[{"name":"Center for Research in NanoEngineering, Polytechnic University of Catalonia, Campus Diagonal-Bes\u00f2s, 08019 Barcelona, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9322-1229","authenticated-orcid":false,"given":"Mar\u00eda Elena","family":"L\u00f3pez-Mart\u00edn","sequence":"additional","affiliation":[{"name":"Department of Morphological Sciences, University of Santiago de Compostela, 15782 Santiago de Compostela, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8561-093X","authenticated-orcid":false,"given":"Juan Antonio","family":"Rodr\u00edguez-Gonz\u00e1lez","sequence":"additional","affiliation":[{"name":"Department of Applied Physics, University of Santiago de Compostela, 15782 Santiago de Compostela, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5651-8883","authenticated-orcid":false,"given":"Francisco Jos\u00e9","family":"Ares-Pena","sequence":"additional","affiliation":[{"name":"Department of Applied Physics, University of Santiago de Compostela, 15782 Santiago de Compostela, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,22]]},"reference":[{"key":"ref_1","unstructured":"(2014). IEEE Standard for Definitions of Terms for Antennas. Standard No. IEEE Std 145-2013."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1163\/156939388X00224","article-title":"Extensions of the Tseng-Cheng Pattern Synthesis Technique","volume":"2","author":"Kim","year":"1988","journal-title":"J. Electromagn. Waves Appl."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1222","DOI":"10.1109\/8.247748","article-title":"A Contoured Beam Synthesis Technique for Planar Antenna Arrays with Quadrantal and Centro-Symmetry","volume":"41","author":"Botha","year":"1993","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"358","DOI":"10.1109\/5.272140","article-title":"Antenna Pattern Synthesis: A New General Approach","volume":"82","author":"Bucci","year":"1994","journal-title":"Proc. IEEE"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1109\/LAWP.2004.837504","article-title":"A Fast DFT Planar Array Synthesis Tool for Generating Contoured Beams","volume":"3","author":"Chou","year":"2004","journal-title":"IEEE Antennas Wirel. Propag. Lett."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1745","DOI":"10.1109\/TAP.2007.898601","article-title":"Parallel Genetic-Algorithm Optimization of Shaped Beam Coverage Areas Using Planar 2-D Phased Arrays","volume":"55","author":"Villegas","year":"2007","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Federico, G., Caratelli, D., Theis, G., and Smolders, A.B. (2021). A Review of Antenna Array Technologies for Point-to-Point and Point-to-Multipoint Wireless Communications at Millimeter-Wave Frequencies. Int. J. Antennas Propag., 2021.","DOI":"10.1155\/2021\/5559765"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"5514972","DOI":"10.1155\/2021\/5514972","article-title":"A Review of Synthesis Techniques for Phased Antenna Arrays in Wireless Communications and Remote Sensing","volume":"2021","author":"Ogurtsov","year":"2021","journal-title":"Int. J. Antennas Propag."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1954","DOI":"10.1109\/TAP.2021.3119113","article-title":"Phase-Only Synthesis for Large Planar Arrays via Zernike Polynomials and Invasive Weed Optimization","volume":"70","author":"Angeletti","year":"2020","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2779","DOI":"10.1109\/TAP.2021.3137200","article-title":"Development of a New Method for Pattern Synthesizing of Linear and Planar Arrays Using Legendre Transform With Minimum Number of Elements","volume":"70","author":"Alijani","year":"2022","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"5973","DOI":"10.1109\/ACCESS.2017.2786862","article-title":"A Review of High Gain and High Efficiency Reflectarrays for 5G Communications","volume":"6","author":"Dahri","year":"2018","journal-title":"IEEE Access"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"5468","DOI":"10.1109\/TAP.2022.3161558","article-title":"An Innovative Inverse Source Approach for the Feasibility-Driven Design of Reflectarrays","volume":"70","author":"Salucci","year":"2022","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"744","DOI":"10.1109\/8.564102","article-title":"Synthesis of Amplitude-Phase Distribution and Shape of a Planar Antenna Aperture for a Given Power Pattern","volume":"45","author":"Savenko","year":"1997","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2539","DOI":"10.1109\/TAP.2010.2050420","article-title":"Flat-Top Footprint Pattern Synthesis Through the Design of Arbitrary Planar-Shaped Apertures","volume":"58","author":"Aghasi","year":"2010","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_15","first-page":"108","article-title":"Footprint Patterns Obtained by Planar Arrays","volume":"137","author":"Elliott","year":"1990","journal-title":"IEE Proc. H"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1509","DOI":"10.1109\/8.362787","article-title":"Design of Planar Arrays to Obtain Efficient Footprint Patterns With an Arbitrary Footprint Boundary","volume":"42","author":"Ares","year":"1944","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"635","DOI":"10.1109\/TAP.2004.823997","article-title":"Optimization of Array Boundaries for Arbitrary Footprint Patterns","volume":"52","author":"Trastoy","year":"2004","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2358","DOI":"10.3390\/s21072358","article-title":"An Improved Pattern Synthesis Iterative Method in Planar Arrays for Obtaining Efficient Footprints with Arbitrary Boundaries","volume":"21","year":"2021","journal-title":"Sensors"},{"key":"ref_19","first-page":"366","article-title":"Shaped Patterns from a Continuous Planar Aperture Distribution","volume":"135","author":"Elliott","year":"1988","journal-title":"IEE Proc. H"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Elliott, R.S. (2003). Antenna Theory and Design, Revised Edition, IEEE Press.","DOI":"10.1109\/9780470544174"},{"key":"ref_21","unstructured":"Silver, S. (1939). Microwave Antenna Theory and Design, MIT Radiation Laboratory."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/10\/4982\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T19:40:12Z","timestamp":1760125212000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/10\/4982"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,22]]},"references-count":21,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2023,5]]}},"alternative-id":["s23104982"],"URL":"https:\/\/doi.org\/10.3390\/s23104982","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2023,5,22]]}}}