基于Tikhonov正则化的高分辨率群时延测量与计算方法

doi:10.3969/j.issn.0372-2112.2019.05.010

电子学报 ›› 2019, Vol. 47 ›› Issue (5): 1044-1048.DOI: 10.3969/j.issn.0372-2112.2019.05.010

基于Tikhonov正则化的高分辨率群时延测量与计算方法

骆睿^1,2, 刘莉^1,2, 佟瑞¹, 李凌云¹

1. 中国科学院上海微系统与信息技术研究所, 中科院太赫兹固态技术重点实验室, 上海 200050;
2. 中国科学院大学材料与光电研究中心, 北京 100049

收稿日期:2018-10-15 修回日期:2019-02-22 出版日期:2019-05-25
- 通讯作者:
- 李凌云
- 作者简介:
- 骆睿男,1994年出生于湖北黄冈.中国科学院上海微系统与信息技术研究所中科院太赫兹固态技术重点实验室硕士生,主要研究方向为微电子学与微波测量技术.E-mail:rui.luo@mail.sim.ac.cn;刘莉女,汉族,1994年出生于宁夏回族自治区.现为中国科学院上海微系统与信息技术研究所太赫兹固态技术重点实验室硕士研究生.主要研究方向为微电子学与微波技术,毫米波器件与电路.E-mail:maolili@mail.sim.ac.cn
- 基金资助:
- 国家自然科学基金 (No.61731021）

High-Resolution Group Delay Measurement and Calculation Method Based on Tikhonov Regularization

LUO Rui^1,2, LIU Li^1,2, TONG Rui¹, LI Ling-yun¹

1. Key Laboratory of Terahertz Solid-State Technology, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai 200050, China;
2. Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, China

Received:2018-10-15 Revised:2019-02-22 Online:2019-05-25 Published:2019-05-25
- Supported by:
- National Natural Science Foundation of China (No.61731021)

摘要/Abstract

摘要： 在衡量传输网络对信号传输时间延迟和信号失真影响时，群时延是非常重要的一项指标.基于差分法计算群时延是目前测量仪器普遍使用的方法，该方法存在着分辨率和精度之间的矛盾，在提高频率分辨率的同时势必引起测量精度的下降.本文在分析差分法误差来源的基础上，基于Tikhonov正则化给出了一种新的群时延计算方法.比较分析得出该方法能够在存在测量误差的情况下，精确得到具有较高频率分辨率的群时延.在实际给出的测量验证中，通过与矢量网络分析仪得到的群时延数据对比，验证了该方法的有效性.

关键词: 群时延, 差分法, Tikhonov正则化

Abstract: Group delay is a very important indicator when measuring the impact of a transmission network on signal transmission time delay and signal distortion.The calculation of group delay based on the difference method is a commonly used in current measuring instruments,and there is a contradiction between frequency resolution and precision.It will inevitably lead to the decrease of measurement accuracy while improving the frequency resolution.Based on the analysis of the error source of the difference method,this paper presents a novel method of group delay measurement based on the Tikhonov regularization.The comparative analysis shows that the method can obtain the group delay value more precisely with higher frequency resolution when the measurement error is included.In the actual data calculation and verification,the validity of the method verified by comparison to the group delay data obtained by the vector network analyzer.

Key words: group delay, difference method, Tikhonov regularization

中图分类号:

TN98

骆睿, 刘莉, 佟瑞, 等. 基于Tikhonov正则化的高分辨率群时延测量与计算方法[J]. 电子学报, 2019, 47(5): 1044-1048.

LUO Rui, LIU Li, TONG Rui, et al. High-Resolution Group Delay Measurement and Calculation Method Based on Tikhonov Regularization[J]. Acta Electronica Sinica, 2019, 47(5): 1044-1048.

参考文献

[1] Li Y,Hua Y,Yan B R,et al.A method of obtaining high precision propagation delay for BPL timing signal[A].2018 IEEE International Frequency Control Symposium[C].USA:IEEE Press,2018.1-5.
[2] Ascarrunz F G.Timing errors in two-way satellite time and frequency transfer using spread spectrum modulation[D].Boulder:University of Colorado,1999.40-56.
[3] Agilent Technologies.Agilent PNA series network analyzer printed version of PNA help user's and programming guide[DB/OL].http://nasupportkeysightcom/pna/help/PNAHelp9_42.pdf,2011-09-16/2019-02-22.
[4] 朱祥维,李垣陵,雍少为,等.群时延的新概念,测量方法及其应用[J].电子学报,2008,36(9):1819-1823. Zhu Xiang-wei,Li Yuan-ling,Yong Shao-wei,et al,A new definition,measurement method of group delay and its application[J].Acta Electronica Sinica,2008,36(9):1819-1823.(in Chinese)
[5] Lin H Y,Song Z F,Wang X T,et al.An improved antenna group delay measurement method using a three-antenna extrapolation technique[J].Radioengineering,2017,26(3):675-681.
[6] Wang J W,Feng Z H.Time-domain nature of group delay[J].Chinese Physics B,2015,24(10):100301-1-100301-5.
[7] Keysight Technologies.Understanding the Fundamental Principles of Vector Network Analysis[DB/OL].https://literaturecdnkeysightcom/litweb/pdf/5965-7707E.pdf,2019-02-22.
[8] Ostwald O.Group and phase delay measurements with vector network analyzer ZVR[DB/OL].https://scdn.rohde-schwarz.com/ur/pws/dl_downloads/dl_application/application_notes/1ez35/1ez35_1e.pdf,1997-07-28/2019-02-22.
[9] 王希云,黄建国,陈宇.基于正则化方法的一个新型数值微分算法[J].高等学校计算数学学报,2009,31(03):246-256. Wang Xi-yun,Huang Jian-guo,Chen Yu,et al.A new numerical differentiation algorithm with regularization[J].Numerical Mathematics A Journal of Chinese Universities,2009,31(03):246-256.(in Chinese)
[10] Whitney M L.Theoretical and numerical study of Tikhonov's regularization and morozov's discrepancy principle[D].Georgia State:Georgia State University,2009.15-19.
[11] 王彦博.数值微分及其应用[D].上海:复旦大学,2005.8-21. Wang Yan-bo.Numerical differentiation and its application[D].Shanghai:Fudan University,2005.8-21(in Chinese)
[12] Cheng J,Yamamoto M.One new strategy for a priori choice of regularizing parameters in Tikhonov's regularization[J].Inverse Problems,2000,16(4):L31-L38(8).
[13] 朱立勋.三次样条插值的收敛性及一类三次广义样条插值的误差估计[D].吉林:吉林大学,2006.11-17. Zhu Li-xun.The convergence of cubic spline interplation and the error estimations of certain generalized cubic spline interpolation[D].Jilin:Jilin University,2006.11-17.(in Chinese)
[14] Formfactor.Cascade Impedance Standard Substrate Map[DB/OL].https://www.formfactor.com/download/iss-map-101-190/?wpdmdl=3159&refresh=5c6fa8a5a88be1550821541,2019-02-22.

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基于Tikhonov正则化的高分辨率群时延测量与计算方法

High-Resolution Group Delay Measurement and Calculation Method Based on Tikhonov Regularization

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