{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,7]],"date-time":"2026-09-07T09:08:16Z","timestamp":1788772096620,"version":"build-2803163510"},"reference-count":42,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2026,9,6]],"date-time":"2026-09-06T00:00:00Z","timestamp":1788652800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Micromachines"],"abstract":"<jats:p>Pixelated electromagnetic representations enable topology-free numerical exploration of microwave layouts without enforcing a predefined circuit template. This work presents a simulation-based electromagnetic modeling and analysis framework for pixelated microstrip low-pass filters within a physical footprint comparable to that of a classical stepped-impedance reference. A binary metallization encoding is embedded in a fixed microstrip domain and explored through full-wave electromagnetic optimization under consistent material, excitation, and specification conditions. The objective is not extreme miniaturization or hardware prototyping, but to assess whether topology-free pixelated layouts can produce useful low-pass responses within the same general physical scale and to analyze the structural properties of the resulting feasible layouts. Across 20 independent optimization runs, 12 specification-compliant and geometrically unique metallization layouts were identified. Aggregate analysis of 360 single-pixel perturbations reveals topology-dependent sensitivity, while finite-width regularization of ideal corner contacts preserves modeled specification compliance after refined-mesh verification, with the suitable bridge width depending on the topology. The scope is deliberately limited to full-wave EM modeling and numerical analysis; experimental fabrication and measurement are left as a subsequent validation stage. These findings support topology-free pixelated EM modeling and analysis as a route for investigating non-obvious low-pass filter layouts under comparable footprint constraints.<\/jats:p>","DOI":"10.3390\/mi17091060","type":"journal-article","created":{"date-parts":[[2026,9,7]],"date-time":"2026-09-07T08:07:06Z","timestamp":1788768426000},"page":"1060","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Topology-Free EM Modeling and Analysis of Pixelated Microstrip Low-Pass Filters Under Comparable Footprint"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8267-9261","authenticated-orcid":false,"given":"Jorge","family":"Davalos-Guzman","sequence":"first","affiliation":[{"name":"Divisi\u00f3n de Ingenier\u00edas, Subdirecci\u00f3n de Investigaci\u00f3n y Extensi\u00f3n, Centro de Ense\u00f1anza T\u00e9cnica Industrial, Plantel Tonal\u00e1, Tonal\u00e1 45402, Jalisco, Mexico"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"software","vocabulary":"credit"},{"role":"formal-analysis","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"},{"role":"data-curation","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"visualization","vocabulary":"credit"},{"role":"validation","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4115-0999","authenticated-orcid":false,"given":"Jose L.","family":"Chavez-Hurtado","sequence":"additional","affiliation":[{"name":"Department of Electronics, Systems, and Informatics, Instituto Tecnol\u00f3gico y de Estudios Superiores de Occidente (ITESO), The Jesuit University of Guadalajara, Tlaquepaque 45604, Jalisco, Mexico"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"software","vocabulary":"credit"},{"role":"validation","vocabulary":"credit"},{"role":"formal-analysis","vocabulary":"credit"},{"role":"resources","vocabulary":"credit"},{"role":"data-curation","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"supervision","vocabulary":"credit"},{"role":"project-administration","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"},{"role":"visualization","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0896-5320","authenticated-orcid":false,"given":"Lina M.","family":"Aguilar-Lobo","sequence":"additional","affiliation":[{"name":"Departamento de Computaci\u00f3n e Industrial, Universidad Aut\u00f3noma de Guadalajara, Av. Patria 1201, Zapopan 45129, Jalisco, Mexico"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"methodology","vocabulary":"credit"},{"role":"validation","vocabulary":"credit"},{"role":"formal-analysis","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"}]}],"member":"1968","published-online":{"date-parts":[[2026,9,6]]},"reference":[{"key":"ref_1","unstructured":"Pozar, D.M. (2011). Microwave Engineering, Wiley. [4th ed.]."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Hong, J.-S., and Lancaster, M.J. (2011). Microstrip Filters for RF\/Microwave Applications, Wiley. [2nd ed.].","DOI":"10.1002\/9780470937297"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1353","DOI":"10.1109\/22.299729","article-title":"Microstrip filter design using direct EM field simulation","volume":"42","author":"Bandler","year":"1994","journal-title":"IEEE Trans. Microw. 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