低损耗材料微波介电性能测试中识别TE<sub>01δ</sub>模式的新方法

李雷; 颜涵; 陈湘明

doi:10.7498/aps.69.20200275

摘要

工作于TE_01δ模式的金属谐振腔法是评价低损耗材料微波介电性能的通用方法. 微波介质谐振器均为多模式谐振器, 故正确识别TE_01δ模式是微波介电测试的基础. TE_01δ模式的识别可通过预测谐振频率及其随谐振器尺寸的变化、根据激励条件排除寄生模式等手段实现, 但已有方法存在复杂、易识别错误等缺点. 为此, 本文发展了一种准确识别TE_01δ模式的简单方法. 这种方法引入了介电性能已知的低损耗参考试样, 通过测试金属谐振腔中只放置参考试样及同时放置参考试样和待测试样时TE_01δ模式的谐振频率, 利用有限单元分析计算出待测试样的粗略介电常数, 并进一步预测只放置待测试样时TE_01δ模式的谐振频率. 此谐振频率的预测值与测试结果相差1%以内, 因此很容易将TE_01δ模式与其他寄生模式区分开, 进而实现TE_01δ模式的准确识别.

关键词:

Abstract

The metal resonant cavity method working with TE_01δ mode is a universal method for evaluating the microwave dielectric properties of low-loss materials. All the microwave dielectric resonators are multi-mode resonators, so the correct identification of TE_01δ mode is the basis for the microwave dielectric measurements. The TE_01δ mode can be identified by predicting the resonant frequency and its variation with resonator size, expelling the spurious modes according to the exciting conditions, etc., while these methods are relatively complex and sometimes unreliable. In the present work, a simple method for accurately identifying the TE_01δ mode is developed. A low-loss reference sample with known dielectric properties is introduced and placed in the cavity for the first step, and the to-be-measured sample is placed on the reference sample for the second step. The rough permittivity of the to-be-measured sample can be calculated from the TE_01δ-mode resonant frequencies in the two steps through the finite element analysis, and is used to predict the resonant frequency for TE_01δ mode when only the to-be-measured sample is placed in the cavity. The difference between the predicted and measured TE_01δ-mode resonant frequencies for the to-be-measured sample is less than 1%, so that the TE_01δ mode can be easily distinguished from the spurious modes and accurately identified.

Keywords:

作者及机构信息

浙江大学材料科学与工程学院, 杭州　310027

通信作者: 李雷, zjulilei@zju.edu.cn

Authors and contacts

School of Materials Science and Engineering, Zhejiang University, Hangzhou 310027, China

Corresponding author: Li Lei, zjulilei@zju.edu.cn

文章全文 : translate this paragraph

参考文献

[1]	Sebastian M T 2008 Dielectric Materials for Wireless Communication. (Oxford: Elsevier Science Publishers) pp1–48
[2]	Narang S B, Bahel S 2010 J. Ceram. Process. Res. 11 316
[3]	Sebastian M T, Ubic R, Jantunen H 2015 Int. Mater. Rev. 60 392 Google Scholar
[4]	Chen L F, Ong C K, Neo C P, Varadan V V, Varadan V K 2004 Microwave Electronics: Measurement and Material Characterization (Chichester: John Wiley & Sons) pp37–141
[5]	Kajfez D, Guillon P 1998 Dielectric Resonators (2nd Ed.) (Atlanta: Noble) pp327–430
[6]	Hakki B W, Coleman P D 1960 IEEE Trans. Microwave Theory Tech. 8 402 Google Scholar
[7]	Courtney W E 1970 IEEE Trans. Microwave Theory Tech. 18 476 Google Scholar
[8]	Kajfez D 1984 IEEE Trans. Microwave Theory Tech. 32 941 Google Scholar
[9]	Kobayashi Y 1985 IEEE Trans. Microwave Theory Tech. 33 1361 Google Scholar
[10]	Dube D C, Zurmuhlen R, Bell A, Setter N, Wersing W 1997 J. Am. Ceram. Soc. 80 1095 Google Scholar
[11]	Fan X C, Chen X M, Liu X Q 2005 IEEE Trans. Microwave Theory Tech. 53 3130 Google Scholar
[12]	Krupka J, Huang W T, Tung M J 2005 Meas. Sci. Technol. 16 1014 Google Scholar
[13]	Li L, Zhu J Y, Chen X M 2016 IEEE Trans. Microwave Theory Tech. 64 3781 Google Scholar
[14]	Kajfez D, Gundavajhala A 1993 Electron. Lett. 29 1936 Google Scholar
[15]	Alford N M, Breeze J, Penn S J, Poole M 2000 IEE Proc.: Sci. Meas. Technol. 147 269 Google Scholar
[16]	Sebastian M T, Jawahar I N, Mohanan P 2003 Mater. Sci. Eng. B 97 258 Google Scholar
[17]	Cho J Y, Yoon K H, Kim E S 2003 J. Am. Ceram. Soc. 86 1330 Google Scholar
[18]	Li L, Chen X M 2006 J. Am. Ceram. Soc. 89 544 Google Scholar
[19]	Li L, Chen X M 2006 J. Am. Ceram. Soc. 89 557 Google Scholar
[20]	Li L, Chen X M, Fan X C 2006 J. Eur. Ceram. Soc. 26 3265 Google Scholar
[21]	Li L, Chen X M 2009 Ferroelectrics 387 7 Google Scholar
[22]	Wang D W, Zhou D, Zhang S Y, Vardaxoglou Y, Whittow W G, Cadman D, Reaney I M 2018 ACS Sustainable Chem. Eng. 6 2438 Google Scholar
[23]	Zhang J, Luo Y, Yue Z X, Li L T 2019 J. Am. Ceram. Soc. 102 342 Google Scholar
[24]	Li L, Chen X M, Ni L, Fu M S 2007 Appl. Phys. Lett. 91 092906 Google Scholar
[25]	Li L, Fang Y, Chen X M 2012 J. Am. Ceram. Soc. 95 982 Google Scholar
[26]	Li L, Zhang W, Chen X M, Zhu H Y 2012 J. Appl. Phys. 111 064108 Google Scholar
[27]	Li L, Zhang B Q, Chen X M 2013 Appl. Phys. Lett. 103 192902 Google Scholar
[28]	Li L, Wang Z W, Chen X M 2015 Mater. Res. Bull. 67 251 Google Scholar
[29]	Krupka J, Derzakowski K, Tobar M, Hartnett J, Geyer R G 1999 Meas. Sci. Technol. 10 387 Google Scholar
[30]	Kooi P S, Leong M S, Prakash A L S 1985 IEE Proc. H Microwave Opt. Antennas 32 7 Google Scholar
[31]	Yuan H X, Chen X M, Mao M M 2009 J. Am. Ceram. Soc. 92 2286 Google Scholar
[32]	O’Bryan H M, Thomson J, Plourde J K 1974 J. Am. Ceram. Soc. 57 450 Google Scholar
[33]	Huang C L, Chen Y C 2003 Mater. Sci. Eng. A 345 106 Google Scholar
[34]	Li L, Spreitzer M, Suvorov D 2014 Appl. Phys. Lett. 104 182902 Google Scholar
[35]	Hong W B, Li L, Yan H, Wu S Y, Yang H S, Chen X M 2020 J. Materiomics 6 233 Google Scholar
[36]	Li L, Hong W B, Chen G Y, Chen X M 2019 J. Alloys Compd. 774 706 Google Scholar

施引文献

图 1 识别待测试样TE_01δ模式谐振峰的三个步骤

Fig. 1. Three steps for identifying TE_01δ-mode resonant mode of to-be-measured sample.

下载: 全尺寸图片幻灯片

图 2 待测试样(a) S1, (b) S2, (c) S3, (d) S4及(e) S5的|S₂₁|随频率的变化

Fig. 2. |S₂₁| as a function of frequency for to-be-measured samples: (a) S1; (b) S2; (c) S3; (d) S4; (e) S5.

下载: 全尺寸图片幻灯片

图 3 (a) 谐振腔中放置R3及R3 + S2时TE_01δ模式的谐振峰; (b) 谐振腔中仅放置S2时|S₂₁|随频率的变化

Fig. 3. (a) TE_01δ-mode resonant peaks for R3 and R3 + S2 in the cavity; (b) |S₂₁| as a function of frequency for only S2 in the cavity.

下载: 全尺寸图片幻灯片

表 1 参考试样及待测试样的尺寸与介电常数

Table 1. Dimension and permittivity of references and to-be-measured samples.

类型	编号	直径/mm	厚度/mm	ε_r
参考试样	R1	10.17	1.64	19.3
	R2	10.86	1.48	39.4
	R3	10.75	1.49	77.2
	R4	9.36	1.04	434

待测试样	S1	12.03	6.51	2.79
	S2	9.90	5.10	4.78
	S3	10.00	5.00	9.50
	S4	10.12	4.67	19.4
	S5	10.83	5.44	39.2

下载: 导出CSV

表 2 不同参考试样/待测试样组合时各谐振频率的测试及计算结果

Table 2. Measured and calculated resonant frequencies for different reference/to-be-measured sample combinations.

参考试样	待测试样	f_0,1/GHz	f_0,2/GHz	f_0,3/GHz	f_0,4/GHz	f_0,5/GHz
R3	S1	5.224	5.184	15.107	14.988	14.642
R3	S2	5.224	5.160	13.862	13.736	14.958
R3	S3	5.224	5.067	10.216	10.158	10.360
R3	S4	5.224	4.849	7.358	7.298	9.035
R3	S5	5.224	4.217	4.830	4.800	8.376

R1	S2	10.046	9.498	13.807	13.736	14.958
R2	S2	7.215	7.028	13.789	13.736	14.958
R4	S2	2.760	2.752	13.830	13.736	14.958

下载: 导出CSV

表 3 TE_01δ模式谐振频率、粗略介电常数的相对误差及介电性能测试结果

Table 3. Relative errors of TE_01δ-mode resonant frequency and rough permittivity, and measured results of dielectric properties

Reference	Sample	(f_0,3 – f_0,4)/ f_{0, 4}	ε_r,rou	ε_r,sam	(ε_r,rou – ε_r,sam)/ε_{r, sam}	tanδ
R3	S1	0.80%	2.73	2.79	–2.2%	1.08 × 10^–4
R3	S2	0.92%	4.68	4.78	–2.1%	2.75 × 10^–4
R3	S3	0.58%	9.38	9.50	–1.3%	2.56 × 10^–5
R3	S4	0.83%	19.1	19.4	–1.5%	7.63 × 10^–5
R3	S5	0.62%	38.7	39.2	–1.3%	1.21 × 10^–4

R1	S2	0.51%	4.72	4.78	–1.2%	2.75 × 10^–4
R2	S2	0.38%	4.74	4.78	–0.8%	2.75 × 10^–4
R4	S2	0.68%	4.70	4.78	–1.8%	2.75 × 10^–4

下载: 导出CSV

map

[1]	Sebastian M T 2008 Dielectric Materials for Wireless Communication. (Oxford: Elsevier Science Publishers) pp1–48
[2]	Narang S B, Bahel S 2010 J. Ceram. Process. Res. 11 316
[3]	Sebastian M T, Ubic R, Jantunen H 2015 Int. Mater. Rev. 60 392 Google Scholar
[4]	Chen L F, Ong C K, Neo C P, Varadan V V, Varadan V K 2004 Microwave Electronics: Measurement and Material Characterization (Chichester: John Wiley & Sons) pp37–141
[5]	Kajfez D, Guillon P 1998 Dielectric Resonators (2nd Ed.) (Atlanta: Noble) pp327–430
[6]	Hakki B W, Coleman P D 1960 IEEE Trans. Microwave Theory Tech. 8 402 Google Scholar
[7]	Courtney W E 1970 IEEE Trans. Microwave Theory Tech. 18 476 Google Scholar
[8]	Kajfez D 1984 IEEE Trans. Microwave Theory Tech. 32 941 Google Scholar
[9]	Kobayashi Y 1985 IEEE Trans. Microwave Theory Tech. 33 1361 Google Scholar
[10]	Dube D C, Zurmuhlen R, Bell A, Setter N, Wersing W 1997 J. Am. Ceram. Soc. 80 1095 Google Scholar
[11]	Fan X C, Chen X M, Liu X Q 2005 IEEE Trans. Microwave Theory Tech. 53 3130 Google Scholar
[12]	Krupka J, Huang W T, Tung M J 2005 Meas. Sci. Technol. 16 1014 Google Scholar
[13]	Li L, Zhu J Y, Chen X M 2016 IEEE Trans. Microwave Theory Tech. 64 3781 Google Scholar
[14]	Kajfez D, Gundavajhala A 1993 Electron. Lett. 29 1936 Google Scholar
[15]	Alford N M, Breeze J, Penn S J, Poole M 2000 IEE Proc.: Sci. Meas. Technol. 147 269 Google Scholar
[16]	Sebastian M T, Jawahar I N, Mohanan P 2003 Mater. Sci. Eng. B 97 258 Google Scholar
[17]	Cho J Y, Yoon K H, Kim E S 2003 J. Am. Ceram. Soc. 86 1330 Google Scholar
[18]	Li L, Chen X M 2006 J. Am. Ceram. Soc. 89 544 Google Scholar
[19]	Li L, Chen X M 2006 J. Am. Ceram. Soc. 89 557 Google Scholar
[20]	Li L, Chen X M, Fan X C 2006 J. Eur. Ceram. Soc. 26 3265 Google Scholar
[21]	Li L, Chen X M 2009 Ferroelectrics 387 7 Google Scholar
[22]	Wang D W, Zhou D, Zhang S Y, Vardaxoglou Y, Whittow W G, Cadman D, Reaney I M 2018 ACS Sustainable Chem. Eng. 6 2438 Google Scholar
[23]	Zhang J, Luo Y, Yue Z X, Li L T 2019 J. Am. Ceram. Soc. 102 342 Google Scholar
[24]	Li L, Chen X M, Ni L, Fu M S 2007 Appl. Phys. Lett. 91 092906 Google Scholar
[25]	Li L, Fang Y, Chen X M 2012 J. Am. Ceram. Soc. 95 982 Google Scholar
[26]	Li L, Zhang W, Chen X M, Zhu H Y 2012 J. Appl. Phys. 111 064108 Google Scholar
[27]	Li L, Zhang B Q, Chen X M 2013 Appl. Phys. Lett. 103 192902 Google Scholar
[28]	Li L, Wang Z W, Chen X M 2015 Mater. Res. Bull. 67 251 Google Scholar
[29]	Krupka J, Derzakowski K, Tobar M, Hartnett J, Geyer R G 1999 Meas. Sci. Technol. 10 387 Google Scholar
[30]	Kooi P S, Leong M S, Prakash A L S 1985 IEE Proc. H Microwave Opt. Antennas 32 7 Google Scholar
[31]	Yuan H X, Chen X M, Mao M M 2009 J. Am. Ceram. Soc. 92 2286 Google Scholar
[32]	O’Bryan H M, Thomson J, Plourde J K 1974 J. Am. Ceram. Soc. 57 450 Google Scholar
[33]	Huang C L, Chen Y C 2003 Mater. Sci. Eng. A 345 106 Google Scholar
[34]	Li L, Spreitzer M, Suvorov D 2014 Appl. Phys. Lett. 104 182902 Google Scholar
[35]	Hong W B, Li L, Yan H, Wu S Y, Yang H S, Chen X M 2020 J. Materiomics 6 233 Google Scholar
[36]	Li L, Hong W B, Chen G Y, Chen X M 2019 J. Alloys Compd. 774 706 Google Scholar

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低损耗材料微波介电性能测试中识别TE_01δ模式的新方法

A new method for identifying TE_01δ mode during microwave dielectric measurements of low-loss materials

摘要

Abstract

作者及机构信息

浙江大学材料科学与工程学院, 杭州　310027

通信作者: 李雷, zjulilei@zju.edu.cn

Authors and contacts

School of Materials Science and Engineering, Zhejiang University, Hangzhou 310027, China

Corresponding author: Li Lei, zjulilei@zju.edu.cn

文章全文 : translate this paragraph

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低损耗材料微波介电性能测试中识别TE01δ模式的新方法

A new method for identifying TE01δ mode during microwave dielectric measurements of low-loss materials

摘要

Abstract

作者及机构信息

浙江大学材料科学与工程学院, 杭州 310027

通信作者: 李雷, zjulilei@zju.edu.cn

Authors and contacts

School of Materials Science and Engineering, Zhejiang University, Hangzhou 310027, China

Corresponding author: Li Lei, zjulilei@zju.edu.cn

文章全文 : translate this paragraph

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低损耗材料微波介电性能测试中识别TE_01δ模式的新方法

A new method for identifying TE_01δ mode during microwave dielectric measurements of low-loss materials

浙江大学材料科学与工程学院, 杭州　310027