High-Resolution Group Delay Measurement and Calculation Method Based on Tikhonov Regularization
LUO Rui1,2, LIU Li1,2, 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
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.
骆睿, 刘莉, 佟瑞, 李凌云. 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, LI Ling-yun. High-Resolution Group Delay Measurement and Calculation Method Based on Tikhonov Regularization. Acta Electronica Sinica, 2019, 47(5): 1044-1048.
[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.
2019, Vol. 47 
