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Complex permittivity is an important parameter to reflect the macroscopic electromagnetic properties of material. The selection, design, and application of related materials and devices in the electromagnetic field must be based on the electromagnetic parameters of materials in the working frequency band. The numerical iterative method is an important method to inverse and calculate the complex permittivity of material. But there always exists a difficult problem that the initial value of iteration is difficult to give accurately. Based on the relationship between the complex permittivity and the reflectivity of absorbing material, an initial value selecting method for iteration to invert permittivity of absorbing material is proposed in this work. For absorbing materials with arbitrary thickness at a certain frequency, the complex permittivity must be near the complex permittivity of perfect matching layer. Therefore, the permittivity of perfect matching layer can be used as the initial value of the iterative algorithm. On this basis, a method of calculating the complex permittivity of monolayer absorbing material by using the reflection parameter is constructed. The experimental results show that the complex permittivity of lossy material can be calculated more accurately at the frequency with absorbing performance. However a great error can be caused at the frequency where the reflectivity is close to zero. Based on the iterative solution of the complex permittivity of single-layer absorbing material, a new method of measuring the complex permittivity of material is constructed by combining multi-layer absorbing materials to enhance full-band reflectivity. Given the electromagnetic parameters of other layer materials , the permittivity of absorbing materials and low-loss materials can be obtained accurately.
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Keywords:
- absorbing materials /
- reflectivity /
- complex permittivity /
- S- parameters inversion
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图 1 3 mm吸波材料在16 GHz处的性能特征 (a)介电常数等反射率圆; (b)输入阻抗奈奎斯特图; (c)反射率幅度; (d)反射率相位
Figure 1. 3 mm thick absorbing material at 16 GHz: (a) Iso reflectivity curve of permittivity; (b) input impedance Nyquist diagram; (c) return loss; (d) phase of reflectivity.
图 2 3 mm不同反射率阈值对应介电常数范围 (a)介电常数实部; (b)介电常数虚部
Figure 2. The range of permittivity corresponding to different reflectivity thresholds of 3 mm thick absorbing materials: (a) Real part of εr; (b) imaginary part of εr.
图 3 不同反射率阈值对应中间层介电常数范围
Figure 3. Different reflectivity thresholds correspond to the permittivity range of the middle layer.
图 4 碳系吸波材料实测反射率幅度和相位
Figure 4. Measured reflectivity amplitude and phase of carbon absorbing materials.
图 5 迭代法反演值与实测值 (a)介电常数实部与虚部 (b)计算与实际值偏差
Figure 5. Inversion value and measured value: (a) Real and imaginary parts of permittivity; (b) calculated deviation from the actual value.
图 6 3 GHz和4 GHz实际值与初值位置关系
Figure 6. The relationship between the actual value and initial value of 3 GHz and 4 GHz.
图 7 多层吸波材料 (a)顶层和底层电磁参数 (b)反射率幅度和相位
Figure 7. Multilayer absorbing materials: (a) Electromagnetic parameters of top and bottom materials; (b) reflectivity amplitude and phase.
图 8 迭代法反演值与实测值 (a)介电常数实部与虚部; (b)计算与实际值偏差
Figure 8. Inversion value by iterative method and measured value: (a) Real part and imaginary part of permittivity; (b) deviation between calculation and actual value.
图 9 吸波材料加FR-4 (a)反射率幅度与相位值; (b)FR-4介电常数反演值
Figure 9. absorbing materials with FR-4: (a) Amplitude and phase of reflectivity; (b) inversion of FR-4 permittivity.
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[1] Zoughi R 2000 Microwave Non-destructive Testing and Evaluation Principles (Vol. 4) (Dordrecht: Springer Science & Business Media) pp12–13
[2] Chen L F, Ong C K, Neo C, Varadan V V, Varadan V K 2004 Microwave Electronics: Measurement and Materials Characterization (Vol. 1) (West Sussex: John Wiley & Sons) pp2–6
[3] Weir W B 1974 Proc. IEEE 62 33
Google Scholar
[4] Lau I, Frank M, Shi K, Lurz F, Talai A, Weigel R, Koelpin A 2018 2018 48 th European Microwave Conference (EuMC) Madrid, September 23–27, 2018 pp202–205
[5] Houtz D A, Gu D, Walker D K 2016 IEEE Trans. Microw. Theory Tech. 64 3820
Google Scholar
[6] Hasar U C 2017 IEEE Trans. Microw. Theory Tech. 66 1090
[7] Hasar U C 2009 Prog. Electromagn. Res. 95 365
Google Scholar
[8] Cuong H M, Duc N T, Van Yem V 2017 2017 International Conference on Advanced Technologies for Communications (ATC) Quy Nhon, October 18–20, 2017 pp156–160
[9] 田步宁, 杨德顺, 唐家明, 刘其中 2001 电波科学学报 16 57
Google Scholar
Tian B L, Yang D S, Tang J M, Liu Q Z 2001 Chin. J. Radio 16 57
Google Scholar
[10] Li Q, Chen Y, Caisse C, Horn A, Harris V G 2020 IEEE Trans. Microw. Theory Tech. 68 4940
Google Scholar
[11] 丁世敬, 黄刘宏, 李跃波, 薛凡喜 2012 物理学报 61 220601
Google Scholar
Ding S J, Huang L H, Li Y B, Xue F X 2012 Acta Phys. Sin. 61 220601
Google Scholar
[12] Qi Y, Bai Y, Mi B 2016 Progress in Electromagnetic Research Symposium (PIERS) Shanghai, China, August 8–11, 2016 pp4583–4586
[13] Baker-Jarvis J, Vanzura E J, Kissick W A 1990 IEEE Trans. Microw. Theory Tech. 38 1096
Google Scholar
[14] Baker-Jarvis J, Geyer R G, Domich P D 1992 IEEE Trans. Instrum. Meas. 41 646
Google Scholar
[15] Guo G, Li E, Li Z, Zhang Q, He F 2011 Meas. Sci. Technol. 22 045707
Google Scholar
[16] Pozar D M 2011 Microwave Engineering (Vol. 4) (Hoboken: John Wiley & Sons) pp57–58
[17] Rozanov K N, Koledintseva M Y 2017 Procedia Eng. 216 79
Google Scholar
[18] Li D, Li Y, Wang X, Yang J, Chen F, Luo H, Nie Y, Gong R 2021 J. Electromagnet. Wave 35 801
Google Scholar
[19] Zhou Q, Yin X, Ye F, Mo R, Liu X, Fan X, Cheng L, Zhang L 2018 J. Am. Ceram. Soc. 101 5552
Google Scholar
[20] 刘海韬, 黄文质, 周永江 2017 高温吸波结构材料 (第1版) (北京: 科学出版社) 第109页
Liu H T, Huang W Z, Zhou Y J 2017 High-Temperature Structural Materials for Microwave Absorption (Vol. 1) (Beijing: Science Press) p109 (in Chinese)
[21] Wang C, Li J, Guo S 2019 Compos. Part A: Appl. S. 125 105522
Google Scholar
[22] Zhou Q, Yin X, Xu H, Li M, Fan X, Yu Z, Ye F, Cheng L, Zhang L 2019 J. Phys. D: Appl. Phys. 52 435102
Google Scholar
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