{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:15:13Z","timestamp":1760148913032,"version":"build-2065373602"},"reference-count":44,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2023,6,8]],"date-time":"2023-06-08T00:00:00Z","timestamp":1686182400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012190","name":"Ministry of Science and Higher Education of the Russian Federation","doi-asserted-by":"publisher","award":["FEWM-2022-0001","19-79-10162"],"award-info":[{"award-number":["FEWM-2022-0001","19-79-10162"]}],"id":[{"id":"10.13039\/501100012190","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100006769","name":"Russian Science Foundation","doi-asserted-by":"publisher","award":["FEWM-2022-0001","19-79-10162"],"award-info":[{"award-number":["FEWM-2022-0001","19-79-10162"]}],"id":[{"id":"10.13039\/501100006769","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>The article proposes a generalized algorithm for evaluating the shielding effectiveness (SE) of electronic equipment enclosures. The algorithm is based on a number of analytical models that use equivalent circuits to obtain SE values. The article begins with a brief review and interpretation of the mathematical formulation used in the algorithm. Then, we describe the proposed algorithm using flowcharts, and we perform its validation. The validation results show that the proposed algorithm has acceptable accuracy and gives SE values comparable to numerical methods or measurements, with much less time costs. The last part of the article presents the software developed to evaluate SE based on analytical models.<\/jats:p>","DOI":"10.3390\/a16060294","type":"journal-article","created":{"date-parts":[[2023,6,9]],"date-time":"2023-06-09T01:32:34Z","timestamp":1686274354000},"page":"294","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Generalized Algorithm Based on Equivalent Circuits for Evaluating Shielding Effectiveness of Electronic Equipment Enclosures"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1867-0689","authenticated-orcid":false,"given":"Anton A.","family":"Ivanov","sequence":"first","affiliation":[{"name":"Department of Television and Control, Tomsk State University of Control Systems and Radioelectronics, 634050 Tomsk, Russia"}]},{"given":"Aleksey A.","family":"Kvasnikov","sequence":"additional","affiliation":[{"name":"Department of Television and Control, Tomsk State University of Control Systems and Radioelectronics, 634050 Tomsk, Russia"}]},{"given":"Alexander V.","family":"Demakov","sequence":"additional","affiliation":[{"name":"Department of Television and Control, Tomsk State University of Control Systems and Radioelectronics, 634050 Tomsk, Russia"}]},{"given":"Maxim E.","family":"Komnatnov","sequence":"additional","affiliation":[{"name":"Department of Television and Control, Tomsk State University of Control Systems and Radioelectronics, 634050 Tomsk, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9713-458X","authenticated-orcid":false,"given":"Sergei P.","family":"Kuksenko","sequence":"additional","affiliation":[{"name":"Department of Television and Control, Tomsk State University of Control Systems and Radioelectronics, 634050 Tomsk, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1192-4853","authenticated-orcid":false,"given":"Talgat R.","family":"Gazizov","sequence":"additional","affiliation":[{"name":"Department of Television and Control, Tomsk State University of Control Systems and Radioelectronics, 634050 Tomsk, Russia"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Ott, H.W. (2009). Electromagnetic Compatibility Engineering, John Wiley & Sons, Inc.. [1st ed.].","DOI":"10.1002\/9780470508510"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Kallambadi Sadashivappa, P., Venkatachalam, R., Pothu, R., Boddula, R., Banerjee, P., Naik, R., Radwan, A.B., and Al-Qahtani, N. (2023). Progressive review of functional nanomaterials-based polymer nanocomposites for efficient EMI shielding. J. Compos. Sci., 7.","DOI":"10.3390\/jcs7020077"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1109\/15.3297","article-title":"Shielding theory and practice","volume":"30","author":"Schulz","year":"1988","journal-title":"IEEE Trans. Electromagn. Compat."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Ren, J., Pan, Y., Zhou, Z., and Zhang, T. (2023). Research on testing method for shielding effectiveness of irregular cavity based on field distribution characteristics. Electronics, 12.","DOI":"10.3390\/electronics12041035"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1080\/08327823.2019.1607496","article-title":"The effect of aperture shape, angle of incidence and polarization on shielding effectiveness of metallic enclosures","volume":"53","author":"Basyigit","year":"2019","journal-title":"J. Microw. Power Electromagn. Energy"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"494","DOI":"10.1080\/09205071.2013.875862","article-title":"Electromagnetic interference from shielding effectiveness of a rectangular enclosure with apertures\u2014Circuital approach, FDTD and FIT modelling","volume":"28","author":"Azizi","year":"2014","journal-title":"J. Electromagn. Waves Appl."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1109\/TEMC.2017.2702595","article-title":"Representative Contents Design for Shielding Enclosure Qualification From 2 to 20 GHz","volume":"60","author":"Flintoft","year":"2018","journal-title":"IEEE Trans. Electromagn. Compat."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Kwon, J.H., Hyoung, C.H., Hwang, J.-H., and Park, H.H. (2021). Impact of absorbers on the shielding effectiveness of metallic rooms with apertures. Electronics, 10.","DOI":"10.3390\/electronics10030237"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"659","DOI":"10.1049\/iet-smt.2016.0060","article-title":"Internal stirring: An approach to approximate evaluation of shielding effectiveness of small slotted enclosures","volume":"10","author":"Rusiecki","year":"2016","journal-title":"IET Sci. Meas. Technol."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Kub\u00edk, Z., and Sk\u00e1la, J. (2015, January 10\u201313). Shielding effectiveness measurement and simulation of small perforated shielding enclosure using FEM. Proceedings of the 2015 IEEE 15th International Conference on Environment and Electrical Engineering, Rome, Italy.","DOI":"10.1109\/EEEIC.2015.7165478"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1075","DOI":"10.1109\/TMAG.2006.871638","article-title":"Subcell FDTD analysis of shielding effectiveness of a thin-walled enclosure with an aperture","volume":"42","author":"Jiao","year":"2006","journal-title":"IEEE Trans. Magn."},{"key":"ref_12","unstructured":"Attari, A.R., Barkeshli, K., Ndagijimana, F., and Dansou, J. (2002, January 16\u201321). Application of the transmission line matrix method to the calculation of the shielding effectiveness for metallic enclosures. Proceedings of the IEEE Antennas and Propagation Society International Symposium, San Antonio, TX, USA."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Celozzi, S., Araneo, R., and Lovat, G. (2008). Electromagnetic Shielding, John Wiley & Sons, Inc.","DOI":"10.1002\/9780470268483"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1109\/15.305461","article-title":"Aperture excitation of electrically large, lossy cavities","volume":"36","author":"Hill","year":"1994","journal-title":"IEEE Trans. Electromagn. Compat."},{"key":"ref_15","unstructured":"Jeong, I.H., Lee, J.W., Lee, Y.S., and Kwon, J.-H. (2014, January 1\u20134). Shielding effectiveness estimation in an electrically large cavity using power balance method and BLT equation. Proceedings of the 2014 International Symposium on Electromagnetic Compatibility, Gothenburg, Sweden."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"760","DOI":"10.1109\/TEMC.2016.2623356","article-title":"Evaluation of the diffusion equation for modeling reverberant electromagnetic fields","volume":"59","author":"Flintoft","year":"2017","journal-title":"IEEE Trans. Electromagn. Compat."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Yan, J., Dawson, J., and Marvin, A. (August, January 30). Estimating reverberant electromagnetic fields in populated enclosures by using the diffusion model. Proceedings of the 2018 IEEE Symposium on Electromagnetic Compatibility, Signal Integrity and Power Integrity, Long Beach, CA, USA.","DOI":"10.1109\/EMCSI.2018.8495445"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1109\/TEMC.2010.2053711","article-title":"Formula for the field excited in a rectangular cavity with a small aperture","volume":"53","author":"Solin","year":"2011","journal-title":"IEEE Trans. Electromagn. Compat."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1109\/TEMC.2011.2179941","article-title":"Formula for the field excited in a rectangular cavity with an electrically large aperture","volume":"54","author":"Solin","year":"2012","journal-title":"IEEE Trans. Electromagn. Compat."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1559","DOI":"10.1049\/el:19961030","article-title":"Shielding effectiveness of a rectangular enclosure with a rectangular aperture","volume":"32","author":"Robinson","year":"1996","journal-title":"Electron. Lett."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Po\u2019ad, F.A., Jenu, M.Z.M., Christopoulos, C., and Thomas, D.W.P. (March, January 27). Analytical and experimental study of the shielding effectiveness of a metallic enclosure with off-centered apertures. Proceedings of the 2006 17th International Zurich Symposium on Electromagnetic Compatibility, Singapore.","DOI":"10.1109\/EMCZUR.2006.215010"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1109\/TEMC.2014.2383438","article-title":"An efficient and reliable circuit model for the shielding effectiveness prediction of an enclosure with an aperture","volume":"57","author":"Nie","year":"2015","journal-title":"IEEE Trans. Electromagn. Compat."},{"key":"ref_23","unstructured":"Shi, D., Shen, Y., and Gao, Y. (2007, January 23\u201326). 3 High-order Mode Transmission Line Model of Enclosure with Off-center Aperture. Proceedings of the 2007 International Symposium on Electromagnetic Compatibility, Qingdao, China."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"448","DOI":"10.1109\/TEMC.2016.2517163","article-title":"Improved circuit model for the prediction of the shielding effectiveness and resonances of an enclosure with apertures","volume":"58","author":"Yin","year":"2016","journal-title":"IEEE Trans. Electromagn. Compat."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1109\/15.709422","article-title":"Analytical formulation for the shielding effectiveness of enclosures with apertures","volume":"40","author":"Robinson","year":"1998","journal-title":"IEEE Trans. Electromagn. Compat."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Rabat, A., Bonnet, P., Ei Khamlichi Drissi, K., and Girard, S. (2018, January 27\u201330). Novel analytical formulation for shielding effectiveness calculation of lossy enclosures containing elliptical apertures. Proceedings of the 2018 International Symposium on Electromagnetic Compatibility, Amsterdam, The Netherlands.","DOI":"10.1109\/EMCEurope.2018.8485171"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Inbavalli, V.P., Venkatesh, C., and Suresh Kumar, T.R. (2018, January 13\u201316). Calculation of shielding effectiveness of an enclosure with arbitrary shaped apertures using hybrid approach. Proceedings of the 2018 15th International Conference on ElectroMagnetic Interference & Compatibility, Bengaluru, India.","DOI":"10.1109\/INCEMIC.2018.8704625"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"462","DOI":"10.1049\/iet-smt.2019.0278","article-title":"Hybrid model for estimating the shielding effectiveness of metallic enclosures with arbitrary apertures","volume":"14","author":"Hu","year":"2020","journal-title":"IET Sci. Meas. Technol."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1638","DOI":"10.1049\/el.2017.3178","article-title":"Analytically calculate shielding effectiveness of enclosure with horizontal curved edges aperture","volume":"53","author":"HongYi","year":"2017","journal-title":"Electron. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Dehkhoda, P., Tavakoli, A., and Moini, R. (2007, January 9\u201313). An efficient shielding effectiveness calculation (A rectangular enclosure with numerous square apertures). Proceedings of the 2007 IEEE International Symposium on Electromagnetic Compatibility, Honolulu, HI, USA.","DOI":"10.1109\/ISEMC.2007.156"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1376","DOI":"10.1109\/TEMC.2017.2761399","article-title":"An improved circuital method for the prediction of shielding effectiveness of an enclosure with apertures excited by a plane wave","volume":"60","author":"Nie","year":"2018","journal-title":"IEEE Trans. Electromagn. Compat."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"012078","DOI":"10.1088\/1757-899X\/734\/1\/012078","article-title":"Model for estimating the shielding effectiveness of an enclosure with a perforated wall","volume":"734","author":"Ivanov","year":"2020","journal-title":"IOP Conf. Ser. Mater. Sci. Eng."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"022035","DOI":"10.1088\/1757-899X\/569\/2\/022035","article-title":"Shielding effectiveness analysis of a rectangular enclosure with wire mesh covering","volume":"569","author":"Chen","year":"2019","journal-title":"IOP Conf. Ser. Mater. Sci. Eng."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"220","DOI":"10.54614\/electrica.2022.21152","article-title":"Semi-analytical approach for calculating shielding effectiveness of an enclosure with a filled aperture","volume":"22","author":"Ivanov","year":"2022","journal-title":"Electrica"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Kim, S., Park, D., and Lee, J. (2007, January 23\u201326). Shielding effectiveness of an enclosure with a dielectric-backed aperture using slotline method. Proceedings of the 2007 International Symposium on Electromagnetic Compatibility, Qingdao, China.","DOI":"10.1109\/ELMAGC.2007.4413524"},{"key":"ref_36","unstructured":"Wang, Y., Zhao, X., Chen, J., and Sun, X. (2010, January 24\u201326). The analysis of multi-mode cylindrical enclosure shielding effectiveness with apertures. Proceedings of the 2010 International Conference on Computer, Mechatronics, Control and Electronic Engineering, Changchun, China."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Collin, R.E. (1990). Field Theory of Guided Waves, IEEE Press. [2nd ed.].","DOI":"10.1109\/9780470544648"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Li, F., Han, J., and Zhang, C. (2019, January 15\u201317). Study on the influence of PCB parameters on the shielding effectiveness of metal cavity with holes. Proceedings of the 2019 IEEE 3rd Information Technology, Networking, Electronic and Automation Control Conference, Chengdu, China.","DOI":"10.1109\/ITNEC.2019.8729288"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"012020","DOI":"10.1088\/1757-899X\/560\/1\/012020","article-title":"Analytical model for estimating the shielding effectiveness of cylindrical connectors","volume":"560","author":"Ivanov","year":"2019","journal-title":"IOP Conf. Ser. Mater. Sci. Eng."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"022110","DOI":"10.1088\/1742-6596\/1889\/2\/022110","article-title":"Analytical model of a shielding enclosure populated with arbitrary shaped dielectric obstacles","volume":"1889","author":"Ivanov","year":"2021","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Thomas, D.W.P., Denton, A., Konefal, T., Benson, T.M., Christopoulos, C., Dawson, J.F., Marvin, A.C., and Porter, J. (1999, January 13\u201312). Characterisation of the shielding effectiveness of loaded equipment enclosures. Proceedings of the International Conference and Exhibition on Electromagnetic Compatibility, York, UK.","DOI":"10.1049\/cp:19990250"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"2307","DOI":"10.1109\/TEMC.2020.2968607","article-title":"Analytical model for evaluating shielding effectiveness of an enclosure populated with conducting plates","volume":"62","author":"Ivanov","year":"2020","journal-title":"IEEE Trans. Electromagn. Compat."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1109\/15.925536","article-title":"Model of the electromagnetic fields inside a cuboidal enclosure populated with conducting planes or printed circuit boards","volume":"43","author":"Thomas","year":"2001","journal-title":"IEEE Trans. Electromagn. Compat."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"537","DOI":"10.1109\/TEMC.2016.2615525","article-title":"Shielding effectiveness estimation of a metallic enclosure with an aperture using S-parameter analysis: Analytic validation and experiment","volume":"59","author":"Shourvarzi","year":"2017","journal-title":"IEEE Trans. Electromagn. 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