plasticnewsПластические массыPlasticheskie massy0554-2901PLASTMASSY Publishing House (Moscow)10.35164/0554-2901-2024-06-33-35plasticnews-1064Research ArticleАНАЛИЗ И МЕТОДЫ РАСЧЁТАANALYSIS AND CALCULATION METHODSМетод расчета эффективной диэлектрической проницаемости материала с периодически распределенными неоднородностямиMethod for calculating the effective dielectric constant of a material with periodically distributed inhomogeneitiesПлатоновР. А.PlatonovR. A.r.a.platonov@gmail.comАлтынниковА. Г.AltynnikovA. G.КомлевА. Е.KomlevA. E.ЦымбалюкА. А.TsymbalyukA. A.КудрявцеваД. А.KudriavtsevaD. A.Санкт-Петербургский государственный электротехнический университет «ЛЭТИ» им. В.И. Ульянова (Ленина)РоссияSt. Petersburg State Electrotechnical University “LETI” named after V.I. Ulyanov (Lenin)Russian Federation202413012025063335Copyright © Платонов Р.А., Алтынников А.Г., Комлев А.Е., Цымбалюк А.А., Кудрявцева Д.А., 20252025Платонов Р.А., Алтынников А.Г., Комлев А.Е., Цымбалюк А.А., Кудрявцева Д.А.Platonov R.A., Altynnikov A.G., Komlev A.E., Tsymbalyuk A.A., Kudriavtseva D.A.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.plastics-news.ru/jour/article/view/1064

В статье предложен метод расчёта эффективной диэлектрической проницаемости материала с периодически распределёнными неоднородностями. Метод основан на расчете эквивалентной электрической цепи элементарной ячейки материала. Для проведения экспериментальных исследований методом трехмерной DLP печати были изготовлены образцы материала с цилиндрическими воздушными полостями различного диаметра. Сравнение результатов расчета и измерения эффективной диэлектрической проницаемости показало малую расходимость (не более 5%).

The article proposes a method for calculating the effective permittivity of a material with periodically distributed inhomogeneities. The method is based on the calculation of the equivalent electrical circuit of a unit cell of the material. To conduct experimental studies using three-dimensional DLP printing, samples of material with cylindrical air cavities of various diameters were manufactured. Comparison of the results of calculation and measurement of the effective dielectric constant showed a small divergence (up to 5%).

эффективная диэлектрическая проницаемостьмоделированиеэквивалентные цепи3D печатьполимерСВЧeffective dielectric constantmodelingequivalent circuits3D printingpolymermicrowavesИсследование выполнено в рамках государственного задания № 075-01438-22-07 от 28 октября 2022 года (FSEE-2022-0019).The study was carried out within the framework of the state assignment No. 075-01438-22-07 of 28.10.2022 (FSEE-2022-0019).ReferencesWang Y. et al. Microwave-frequency experiment validation of a novel magneto-photonic crystals circulator // IEEE Photonics Journal. 2017. V. 10(3). P. 1–6. DOI:10.1109/JPHOT.2017.2783341.Wang Y. et al. Microwave-frequency experiment validation of a novel magneto-photonic crystals circulator // IEEE Photonics Journal. 2017. V. 10(3). P. 1–6. DOI:10.1109/JPHOT.2017.2783341.Khatami S.A. et al. Photonic crystal 180 ring-shaped hybrid: From microwave to optics // IEEE Photonics Technology Letters. 2021. V. 33(21). P. 1165–1168. DOI:10.1109/LPT.2021.3109633.Khatami S.A. et al. Photonic crystal 180 ring-shaped hybrid: From microwave to optics // IEEE Photonics Technology Letters. 2021. V. 33(21). P. 1165–1168. DOI:10.1109/LPT.2021.3109633.Li Q.L. et al. Microwave lens using periodic dielectric sheets for antenna-gain enhancement // IEEE Transactions on Antennas and Propagation. 2017. V. 65(4). P. 2068–2073. DOI:10.1109/TAP.2017.2670441.Li Q.L. et al. Microwave lens using periodic dielectric sheets for antenna-gain enhancement // IEEE Transactions on Antennas and Propagation. 2017. V. 65(4). P. 2068–2073. DOI:10.1109/TAP.2017.2670441.Paul S., Akhtar M. J. Novel metasurface lens-based RF sensor structure for SAR microwave imaging of layered media // IEEE Sensors Journal. 2021. 21(16). Р. 17827–17837. DOI 10.1109/JSEN.2021.3084614.Paul S., Akhtar M. J. Novel metasurface lens-based RF sensor structure for SAR microwave imaging of layered media // IEEE Sensors Journal. 2021. 21(16). Р. 17827–17837. DOI 10.1109/JSEN.2021.3084614.Gaufillet F., Akmansoy E. Graded photonic crystals for Luneburg lens // IEEE Photonics Journal. 2016. V. 8 (1). P. 1–11. DOI: 10.1109/JPHOT.2016.2521261.Gaufillet F., Akmansoy E. Graded photonic crystals for Luneburg lens // IEEE Photonics Journal. 2016. V. 8 (1). P. 1–11. DOI: 10.1109/JPHOT.2016.2521261.Colella R. et al. Customizing 3D-printing for electromagnetics to design enhanced RFID antennas // IEEE Journal of Radio Frequency Identification. 2020. V. 4(4). P. 452–460. DOI:10.1109/JRFID.2020.3001043.Colella R. et al. Customizing 3D-printing for electromagnetics to design enhanced RFID antennas // IEEE Journal of Radio Frequency Identification. 2020. V. 4(4). P. 452–460. DOI:10.1109/JRFID.2020.3001043.Rogers Corporation [Electronic resource]: Radix 2.8Dk Printable Dielectric Data Sheet / Rogers Corporation, 2024. URL: https://www.rogerscorp.com/-/media/project/rogerscorp/documents/advancedelectronics-solutions/english/data-sheets/radix-printable-dielectricdata-sheet.pdf (circulation date: 30.05.2024).Rogers Corporation [Electronic resource]: Radix 2.8Dk Printable Dielectric Data Sheet / Rogers Corporation, 2024. URL: https://www. rogerscorp.com/-/media/project/rogerscorp/documents/advancedelectronics-solutions/english/data-sheets/radix-printable-dielectricdata-sheet.pdf (circulation date: 30.05.2024).Paolella A.C. et al. Broadband millimeter wave characterization of 3-D printed materials // 2018. IEEE/MTT-S International Microwave Symposium-IMS. – IEEE. 2018. P. 1565–1568. DOI:10.1109/MWSYM.2018.8439634.Paolella A.C. et al. Broadband millimeter wave characterization of 3-D printed materials // 2018. IEEE/MTT-S International Microwave Symposium-IMS. – IEEE. 2018. P. 1565–1568. DOI:10.1109/MWSYM.2018.8439634.Rosker E.S. et al. Printable materials for the realization of high performance RF components: Challenges and opportunities // International Journal of Antennas and Propagation. 2018(3):1-19. DOI:10.1155/2018/9359528.Rosker E.S. et al. Printable materials for the realization of high performance RF components: Challenges and opportunities // International Journal of Antennas and Propagation. 2018(3):1-19. DOI:10.1155/2018/9359528.Muldavin J. B., Rebeiz G. M. Millimeter-wave tapered-slot antennas on synthesized low permittivity substrates // IEEE Transactions on Antennas and Propagation. 1999. V. 47. P. 1276–1280. DOI:10.1109/8.791943.Muldavin J. B., Rebeiz G. M. Millimeter-wave tapered-slot antennas on synthesized low permittivity substrates // IEEE Transactions on Antennas and Propagation. 1999. V. 47. P. 1276–1280. DOI:10.1109/8.791943.Koledintseva M.Y. et al. Representation of permittivity for multiphase dielectric mixtures in FDTD modeling // 2004 International Symposium on Electromagnetic Compatibility (IEEE Cat. N 04CH37559). IEEE/ 2004. V. 1. P. 309–314. DOI:10.1109/ISEMC.2004.1350047.Koledintseva M.Y. et al. Representation of permittivity for multiphase dielectric mixtures in FDTD modeling // 2004 International Symposium on Electromagnetic Compatibility (IEEE Cat. N 04CH37559). IEEE/ 2004. V. 1. P. 309–314. DOI:10.1109/ISEMC.2004.1350047.K. Lichtenecker. Dielectric constant of natural and synthetic mixtures. Zeitschrift fur Physik. 1926. P. 115–158.K. Lichtenecker. Dielectric constant of natural and synthetic mixtures. Zeitschrift fur Physik. 1926. P. 115–158.Jayasundere N., Smith B. V. Dielectric constant for binary piezoelectric 0–3 composites // Journal of applied physics. 1993. V. 73(5). P. 2462–2466. DOI:10.1063/1.354057.Jayasundere N., Smith B. V. Dielectric constant for binary piezoelectric 0–3 composites // Journal of applied physics. 1993. V. 73(5). P. 2462–2466. DOI:10.1063/1.354057.Prasad A., Prasad K. Effective permittivity of random composite media: a comparative study // Physica B: Condensed Matter. 2007. V. 396(1–2). P. 132–137. DOI: 10.1016/j.physb.2007.03.025.Prasad A., Prasad K. Effective permittivity of random composite media: a comparative study // Physica B: Condensed Matter. 2007. V. 396(1–2). P. 132–137. DOI: 10.1016/j.physb.2007.03.025.Sareni B. et al. Complex effective permittivity of a lossy composite material // Journal of Applied Physics. 1996. V. 80(8). P. 4560–4565. DOI:10.1109/CEIDP.1996.564661.Sareni B. et al. Complex effective permittivity of a lossy composite material // Journal of Applied Physics. 1996. V. 80(8). P. 4560–4565. DOI:10.1109/CEIDP.1996.564661.Sareni B. et al. Effective dielectric constant of periodic composite materials // Journal of Applied Physics. 1996. V. 80(3). P. 1688–1696. https://doi.org/10.1063/1.362969.Sareni B. et al. Effective dielectric constant of periodic composite materials // Journal of Applied Physics. 1996. V. 80(3). P. 1688–1696. https://doi.org/10.1063/1.362969.Koledintseva M.Y. et al. Prediction of effective permittivity of diphasic dielectrics as a function of frequency // IEEE Transactions on Dielectrics and Electrical Insulation. 2009. V. 16(3). P. 793–808. DOI:10.1109/TDEI.2009.5128520.Koledintseva M.Y. et al. Prediction of effective permittivity of diphasic dielectrics as a function of frequency // IEEE Transactions on Dielectrics and Electrical Insulation. 2009. V. 16(3). P. 793–808. DOI:10.1109/TDEI.2009.5128520.Cheng Y. et al. Study on the dielectric property of composite materials based on electric network // International Journal of Applied Electromagnetics and Mechanics. 2010. V. 33(1–2). P. 439–445. DOI:10.3233/JAE-2010-1143.Cheng Y. et al. Study on the dielectric property of composite materials based on electric network // International Journal of Applied Electromagnetics and Mechanics. 2010. V. 33(1–2). P. 439–445. DOI:10.3233/JAE-2010-1143.Gagarin A. et al. An Adaptation of the Split-Cylinder Resonator Method for Measuring the Microwave Properties of Thin Ferroelectric Films in a «Thin Film-Substrate» Structure // Sensors. 2024. V. 24(3). P. 755. DOI:10.3390/s24030755.Gagarin A. et al. An Adaptation of the Split-Cylinder Resonator Method for Measuring the Microwave Properties of Thin Ferroelectric Films in a «Thin Film-Substrate» Structure // Sensors. 2024. V. 24(3). P. 755. DOI:10.3390/s24030755.

The authors declare that there are no conflicts of interest present.