锁相放大器的研究进展

郭忠凯; 李永刚; 于博丞; 周世超; 孟庆宇; 陆鑫鑫; 黄一帆; 刘贵鹏; 陆俊

doi:10.7498/aps.72.20230579

摘要

锁相放大器可同时在时间与幅度两个维度实现高精度信号测量, 是精密系统测控的关键部件. 本文以锁相放大器的概念、技术与应用的概貌作为导引, 先以模拟、数字以及虚拟锁相放大器的主要关系与区分方法说明锁相放大器的发展演变, 继而按照锁相环的阶与型从数学角度对锁相放大器进行分类. 随后介绍锁相放大器的幅度、频率与相位噪声等主要性能的测试流程与计量标定进展, 讨论相位噪声、时域抖动、阿伦方差等关键指标之间的换算关系以及和幅度噪声之间的耦合关联. 最后, 列举锁相放大器在光谱增强、阻抗分析、磁性测量、显微成像、空间探测领域的应用形式与效果, 通过一些新型应用展望它通过智能计算、精准物联等途径从科学仪器走向工业甚至民品的前景.

关键词:

Abstract

The lock-in amplifier can perform high-precision measurement in both time and amplitude dimensions, so that it becomes a key component of instrumental system for precision measurement and control. This article overviews the concept, technology, and application of phase-locked amplifiers as a guide. It first explains the development and evolution of phase-locked amplifiers of analog, digital, and virtual phase-locked amplifiers, demonstrating their relationship and differences. Then, it classifies phase-locked amplifiers from a mathematical perspective based on the order and type of phase-locked loops. Subsequently, the testing process and metrological calibration progress of the main performance of phase-locked amplifiers, such as amplitude, frequency, and phase noise, are introduced. The conversion relationship between key indicators such as phase noise, time-domain jitter, Allan variance, and the coupling relationship with amplitude noise are discussed. Finally, the application forms and effects of phase-locked amplifiers in the fields of spectral enhancement, impedance analysis, magnetic measurement, microscopic imaging, and space exploration are listed. Through some new applications, the prospects of their transition from scientific instruments to industrial and even civilian products through intelligent computing, precise IoT, and other means are briefly given.

Keywords:

更正

更正: 锁相放大器的研究进展 [物理学报 2023, 72(22): 224206]

郭忠凯, 李永刚, 于博丞, 周世超, 孟庆宇, 陆鑫鑫, 黄一帆, 刘贵鹏, 陆俊. 锁相放大器的研究进展. 物理学报, 2023, 72(22): 224206. doi: 10.7498/aps.72.249901

作者及机构信息

1.
中国科学院物理研究所, 工程师之家, 北京　100190

2.
北京空间机电研究所, 北京　100094

3.
兰州大学物理科学与技术学院, 兰州　730000

4.
大恒新纪元科技股份有限公司, 北京　100085

5.
东南大学电子科学与工程学院, 南京　210096

通信作者: 陆俊, lujun@iphy.ac.cn

基金项目: 国家重点研发计划(批准号: 2021YFF0701000)资助的课题.

Authors and contacts

1.
Commune of Scientific Engineers, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China

2.
Beijing Institute of Space Mechanics and Electricity, Beijing 100094, China

3.
School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China

4.
Daheng New Epoch Technology, Inc., Beijing 100085, China

5.
School of Electronic Science and Engineering, Southeast University, Nanjing 210096, China

Corresponding author: Lu Jun, lujun@iphy.ac.cn

Funds: Project supported by the National Key R&D Program of China (Grant No. 2021YFF0701000).

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参考文献

[1]	陆俊 2020 物理 49 472 Google Scholar Lu J 2020 Physics 49 472 Google Scholar
[2]	Best R E 2003 Phase-locked Loops Design, Simulation and Applications (New York: McGraw-Hill) pp151–277
[3]	Gardner F M 2005 Phaselock Techniques (Hoboken: Wiley Interscience) pp6–96
[4]	Banerjee D 2006 PLL Performance, Simulation, and Design ( Dallas: Texas Instruments) pp9–243
[5]	杜勇 2016 锁相环技术原理及FPGA实现 (北京: 电子工业出版社) 第89—262页 Du Y 2016 Principle and FPGA Implementation of Phase Locked Loop Technology (Beijing: Publishing House of Electronics Industry) pp89–262
[6]	远坂俊昭 2006 锁相环(PLL)电路设计与应用 (北京: 科学出版社) 第31—105页 YuanBan J Z 2006 Design and Application of Phase Locked Loop (PLL) Circuit (Beijing: Science Press) pp31–105
[7]	田昭武 1984 电化学研究方法 (北京: 科学出版社) 第395—396页 Tian Z W 1984 Electrochemical Methods (Beijing: Science Press) pp395–396
[8]	高晋占 2004 微弱信号检测 (北京: 清华大学出版社) 第1—36页 Gao J Z 2004 Weak Signal Detection (Beijing: Tsinghua University Press) pp1–36
[9]	Meade M L 1983 Lock-In Amplifiers: Principles and Applications (London: Peter Peregrinus) pp7–147
[10]	De Bellescize 1933 U.K. Patent GB19310031 [1933-05-18
[11]	王福昌 1996 锁相技术 (武汉: 华中理工大学出版社) 第3—137页 Wang F C 1996 Phase-locked Technology (Wuhan: Huazhong University of Technology Press) pp3–137
[12]	Gaspar J, Chen S F, Gordillo A, Hepp M, Ferreyra P, Marques C 2004 Microprocess. Microsyst. 28 157 Google Scholar
[13]	Zurich-Instrument https://docs.zhinst.com/overview [2023-8-9
[14]	Liquid-Instrument https://www.liquidinstruments.com/products/hardware-platforms/mokupro https://www.thinksrs.com/downloads/man.html [2023-8-9
[15]	Stanford-Research-Systems https://www.thinksrs.com/downloads/man.html [2023-8-9
[16]	Sine Scientific Instruments https://www.ssi-instrument.com/products/LIA.html [2023-8-9
[17]	Huang K, Geng Y Y, Zhang X B, Chen D H, Cai Z G, Wang M, Zhu Z, Wang Z X 2019 Sensors 19 3519 Google Scholar
[18]	NF株式会社 http://www.nfcorp.com.cn/pro/mi/loc/loc/li5600 [2023-8-9] NF Corporation http://www.nfcorp.com.cn/pro/mi/loc/loc/li5600 [2023-8-9
[19]	国仪量子 https://www.cigtek.com/products. html [2023-8-9] CIQTEK https://www.cigtek.com/products.html [2023-8-9
[20]	南京鸿宾电子 https://www.ndwshb.com/product/105.html [2023-8-9] Nanjing Hongbin https://www.ndwshb.com/product/105.html [2023-8-9
[21]	AMETEK https://www.ameteksi.com/products/lock-in-amplifers/7265-dual-phase-lock-in-amplifer [2023-8-9
[22]	Chen C 2004 Proc. Natl. Acad. Sci. 101 5303 Google Scholar
[23]	张勇, 李睿, 刘君华 1998 电测与仪表 35 30 Zhang Y, Li R, Liu J H 1998 Electr. Meas. Instrum. 35 30
[24]	Bobalo Y, Bondariev A, Altunin S, Kiselychnyk M, Maksymiv I 2018 International Conference on Advanced Trends in Radioelecrtronics, Telecommunications and Computer Engineering Lviv-Slavske, Ukraine, February 20–24, 2018
[25]	Lu J, Pan D A, Bai Y, Qiao L 2008 Meas. Sci. Technol. 19 045702 Google Scholar
[26]	陆俊 https://www.instrument.com.cn/download/shtml/062888.shtml [2008-8-9] Lu J https://www.instrument.com.cn/download/shtml/062888.shtml [2008-8-9
[27]	Stimpson G A, Skilbeck M S, Patel R L, Green B L, Morley G W 2019 Rev. Sci. Instrum. 90 094701 Google Scholar
[28]	Wang Z, Shi X, Wang W, Cai W 2023 IEEE Trans. Instrum. Meas. 72 1 Google Scholar
[29]	Lu J 2020 Rev. Sci. Instrum. 91 075106 Google Scholar
[30]	《手册》编写组 2017 数学手册 (北京: 高等教育出版社) Handbook Writing Group 2017 Mathematical Manual (Beijing: Higher Education Press
[31]	Ziemer R, Tranter W 2015 Principles of Communications Systems, Modulation, and Noise (Hoboken: Wiley) pp184– 195
[32]	Wullch D, Bar M 1990 Int. J. Circuit Theory Appl. 18 135 Google Scholar
[33]	Ugarte M, Carlosena A 2015 Circuits Syst. Signal Process. 34 3395 Google Scholar
[34]	Kudrewicz J, Wasowicz S 2007 Equations of Phase-Locked Loops Dynamics on the Circle, Torus and Cylinder (New Jersey: World Scientific) pp9–123
[35]	Kittel P 1977 Rev. Sci. Instrum. 48 1214 Google Scholar
[36]	原力超导 https://eastfs.com/glpmd [2003-8-9] Force superconductivity https://eastfs.com/glpmd [2003-8-9
[37]	Rubiola E 2008 Phase Noise and Frequency Stability in Oscillators (London: Cambridge University Press) pp1–135
[38]	Schwartz M 1970 Information Transmission Modulation and Noise—A Unified Approach to Communication System (New York: McGRAW-Hill) pp390–570
[39]	Bodson M 2005 Int. J. Adapt. Control Signal Process. 19 67 Google Scholar
[40]	陆俊, 沈保根, 邵晓萍 2018 中国专利 201510182065.7 [2018-01-26] Lu J, Shen B G, Shao X P 2018 CHN Patent 201510182065.7 [2018-01-26
[41]	张靖悉, 胡勇, 潘柳2020锁相放大器校准规范 Zhang J X, Hu Y, Pan L 2020 Calibration Specification for Lock-in Amplifiers
[42]	大恒新纪元科技股份有限公司 2022 精密大带宽锁相放大器企业标准 Daheng New Era Technology Co., Ltd 2022 Enterprise Standards for Broadband High Precision Lock-in Amplifiers
[43]	王彪, 张江涛, 李艳强, 谷扬, 潘仙林 2012 电测与仪表 49 170 Wang B, Zhang J T, Li Y Q, Gu Y, Pan X L 2012 Electr. Meas. Instrum. 49 170
[44]	Cultrera A, Corminboeuf D, D’Elia V, Tran N T M, Callegaro L, Ortolano M 2021 Metrologia 58 025001 Google Scholar
[45]	Jia Z S, Liu Z Y, Wang L, He Q, Huang H T, Liu L Y 2018 Measurement 125 606 Google Scholar
[46]	陆祖良, 杨雁, 黄璐, 王磊 2019 计量学报 40 319 Lu Z L, Yang Y, Huang L, Wang L 2019 Acta Metrologica Sinica 40 319
[47]	陆祖良 2021 计量学报 42 913 Lu Z L 2021 Acta Metrologica Sinica 42 913
[48]	Van B, Herold G 2014 Am. J. Phys. 82 785 Google Scholar
[49]	Arora H, Klemmer N, Morizio J C, Wolf P D 2005 IEEE Trans. Circuits Syst. Regul. Pap. 52 379 Google Scholar
[50]	Demir A 2006 IEEE Trans. Circuits Syst. Regul. Pap. 53 1869 Google Scholar
[51]	Goldman S J 2007 Phase-Locked Loops Engineering Handbook for Integrated Circuits (Norwood: Artech House) pp5–161
[52]	Bondariev A P, Altunin S I 2017 International Conference on Information and Telecommunication Technologies and Radio Electronics (UkrMiCo) Odessa, September 11–15, 2017
[53]	Eulalia B, Luca D, Francesco P, Sergio R, Ioan T 2020 Acta Imeko 9 52 Google Scholar
[54]	刘河山 2015 博士学位论文 (北京: 中国科学院大学) Liu H S 2015 Ph. D. Dissertation (Beijing: University of Chinese Academy of Sciences
[55]	Shaddock D, Ware B, Halverson P G, Spero R E, Klipstein B 2006 Laser Interferometer Space Antenna: 6th International LISA Symposium Greenbelt, Maryland, USA, June 19–23, 2006
[56]	Cervantes F G, Heinzel G, Marín A F G, Wand V, Steier F, Jennrich O, Danzmann K 2007 Appl. Opt. 46 4541 Google Scholar
[57]	Gerberding O, Sheard B, Bykov I, Kullmann J, Delgado J J E, Danzmann K, Heinzel G 2013 Classical Quantum Gravity 30 235029 Google Scholar
[58]	Libbrecht K G, Black E D, Hirata C M 2003 Am. J. Phys. 71 1208 Google Scholar
[59]	Sterczewski L A, Grzelczak M P, Plinski E F 2016 Rev. Sci. Instrum. 87 014702 Google Scholar
[60]	Deninger A J, Göbel T, Schönherr D, Kinder T, Roggenbuck A, Köberle M, Lison F, Müller-Wirts T, Meissner P 2008 Rev. Sci. Instrum.79 044702 Google Scholar
[61]	Zhang Z, Liu Y, Zhu X 2021 J. Phys. Conf. Ser. 1865 022010 Google Scholar
[62]	Balgos M H, Hayazawa N, Tani M, Tanaka T 2023 Rev. Sci. Instrum. 94 043002 Google Scholar
[63]	Ardekani H, Wilmington R L, Vutukuru M, Chen Z, Brandt R, Swan A, Gundogdu K 2021 Rev. Sci. Instrum. 92 104706 Google Scholar
[64]	Kierzek M, Deal P E, Miller E W, Mukherjee S, Wachten D, Baumann A, Kaupp U B, Strünker T, Brenker C 2021 eLife 10 63129 Google Scholar
[65]	陆俊, 杜昱光, 王倬, 张琛, 赵雪, 李国强, 谭广文, 竺晓山, 丁玮 2023 中国专利 202010361964.4 [2023-04-21] Lu J, Du Y G, Wang Z, Zhang C, Zhao X, Li G Q, Tan G W, Zhu X S, Ding W 2020 CHN Patent 202010361964.4 [2023-04-21
[66]	Sarra A, Stanchieri G D P, De M, Bordi F, Postorino P, Palange E 2021 IEEE Trans. Biomed. Circuits Syst. 15 177 Google Scholar
[67]	Song X, Jin Y, Zhang X, Yu Y, Zhang D L 2009 Rev. Sci. Instrum. 80 086104 Google Scholar
[68]	Song D, Yang W, Zhu J, Bai M, Liu Y 2022 J. Supercond. Novel Magn. 35 95 Google Scholar
[69]	Barnard A W, Mikheev E, Finney J, Hiller H S, Goldhaber-Gordon D 2023 Rev. Sci. Instrum. 94 013902 Google Scholar
[70]	邓荣, 江国栋 2013 电测与仪表 50 105 Deng R, Jiang G D 2013 Electr. Meas. Instrum. 50 105
[71]	宋改青, 董有尔 2006 中国测试技术 32 78 Song G Q, Dong Y E 2006 China Meas. Technol. 32 78
[72]	Tang T, Liu X, Yuan Y, Kiya R, Zhang T, Yang Y, Suetsugu S, Yamazaki Y, Ota N, Yamamoto K, Kamikubo H, Tanaka Y, Li M, Hosokawa Y, Yalikun Y 2023 Sens. Actuators, B 374 132698 Google Scholar
[73]	Sandoval B, Janićijević Ž, Palestina R, et al. 2023 ACS Sens. 8 576 Google Scholar
[74]	Kitta K, Sakamoto M, Hayakawa K, Nukazuka A, Kano K, Yamamoto T 2023 ACS Omega 8 14684 Google Scholar
[75]	苏少奎 2019 低温物性及测量: 一个实验技术人员的理解合经验总结 (北京: 科学出版社) Su S K 2019 Low Temperature Physical Properties and Measurement: An Experimental Technician’s Understanding and Experience Summary (Beijing: Science Press
[76]	Carminati M, Ferrari G, Guagliardo F, Sampietro M 2011 Sens. Actuators, A 172 117 Google Scholar
[77]	陆俊, 沈保根, 邵晓萍 2015 中国专利 201210081375.6 [2015-02-02] Lu J, Shen B G, Shao X P 2015 CHN Patent 201210081375.6 [2015-02-02
[78]	Heng X, Wei K, Zhao T, Xu Z, Cao Q, Huang X, Zhai Y, Ye M, Quan W 2023 IEEE Trans. Instrum. Meas. 72 1 Google Scholar
[79]	Li J J, Du P C, Fu J Q, Wang X T, Zhou Q, Wang R Q 2019 Chin. Phys. B 28 040703 Google Scholar
[80]	詹文山 1982 物理 12 732 Zhan W S 1982 Physics 12 732
[81]	Pu Y, Zhao H, Murayama T, Tonthat L, Okita K, Watanabe Y, Yabukami S 2023 J. Magn. Soc. Jpn. 47 66 Google Scholar
[82]	Meng Z, He X, Li Y, Huang J, Chen D, Wang Z 2023 IEEE Sens. J. 23 16123 Google Scholar
[83]	Zhang Z, Xu Z, He J, Lu J 2022 IEEE Trans. Instrum. Meas. 71 1006009 Google Scholar
[84]	Roos W, Hempel K A, Voigt C, Dederichs H, Schippan R 1980 Rev. Sci. Instrum. 51 612 Google Scholar
[85]	Chen J, Xi X, Wang S, Lu J, Guo C, Wang W, Liu E, Wang W, Liu L, Wu G 2016 Rev. Sci. Instrum. 87 043902 Google Scholar
[86]	陆俊, 郗学奎, 王利晨, 蒋建旺 2022 中国专利 202210373018.0 [2022-04-11] Lu J, Chi X K, Wang L C, Jiang J W 2022 CHN Patent 202210373018.0 [2022-04-11
[87]	Hayek J N, Herreño-Fierro C A, Patiño E J 2016 Rev. Sci. Instrum. 87 103113 Google Scholar
[88]	Lu J, Pan D A, Bai Y, Su Y J, Qiao L J 2008 IEEE Trans. Magn. 44 2127 Google Scholar
[89]	Drobac D, Marohnic Z, Zivkovic I, Prester M 2013 Rev. Sci. Instrum.84 054708 Google Scholar
[90]	Krishnan R V, Banerjee A 1999 Rev. Sci. Instrum. 70 85 Google Scholar
[91]	Harcombe D M, Ruppert M G, Fleming A J 2020 Beilstein J. Nanotechnol. 11 76 Google Scholar
[92]	Shi Y, Lu Q 2012 Microsc. Microanal. 18 1016 Google Scholar
[93]	刘凡微, 陈思丹, 张嘉未, 陈欣中, 毛寒青, 黄思思, 陈曦 2022 电子显微学报 41 627 Liu F W, Chen S D, Zhang J W, Chen X Z, Mao H Q, Huang S S, Chen X 2022 J. Chin. Electron Microsc. Soc. 41 627
[94]	Li X, Sun J, Jin L, Shangguan Y, Chen K, Qin H 2023 Opt. Express 31 19754 Google Scholar
[95]	Leung M S, Stupian G W 1986 Appl. Surf. Sci. 25 435 Google Scholar
[96]	徐欣, 谈宜东, 穆衡霖, 李岩, 王加刚, 金景峰 2023 激光与光电子学进展 60 0312006 Google Scholar Xu X, Tan Y D, Mu H L, Li Y, Wang J G, Jin J F 2023 Laser OptoElectron. Prog. 60 0312006 Google Scholar
[97]	Finneran I A, Welsch R, Allodi M A, Miller I I I, Blake G A 2017 J. Phys. Chem. Lett. 8 4640 Google Scholar
[98]	Li H, Li Z, Wan W, Zhou K, Liao X, Yang S, Wang C, Cao J C, Zeng H 2020 ACS Photonics 7 49 Google Scholar
[99]	Jain P, Priya P, Ram T V S, Parikh K S, Bandi T N 2021 Rev. Sci. Instrum. 92 124705 Google Scholar
[100]	Slim J, Nikolaev N, Rathmann F, Wirzba A, Zurek M 2021 Phys. Rev. Accel. Beams 2 4 Google Scholar
[101]	Boss J, Cujia K, Zopes J, Degen C 2017 Science 356 837 Google Scholar
[102]	Lu J 2021 A Reconfigurable Electrical Circuit Auto-Processing Method for Direct Electromagnetic Inversion, As a Chapter in Intelligent Computing and Block Chain (Singapore: Springer Nature) pp190–203
[103]	Jung S M 2016 Ph. D. Dissertation (Tucson: The University of Arizona
[104]	Kaptein M, Van E, Iannuzzi D, Braunstein L A 2017 Plos One 12 e0174182 Google Scholar
[105]	Golestan S, Guerrero J M, Vasquez J C 2017 IEEE Trans. Power Electron. 32 9013 Google Scholar
[106]	Uzzaman T, Kim U, Choi W 2022 IEEE Access 10 32870 Google Scholar
[107]	Neunteufel D, Grebien S, Arthaber H 2022 Sensors 22 2663 Google Scholar
[108]	Aguirre J, Medrano N, Calvo B, Celma S 2011 IEEE Sensors Conference Limerick, Ireland, October 28–31, 2011 6127317

施引文献

图 1 典型锁相放大器原理图

Fig. 1. Schematic diagram of a typical lock-in amplifier.

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图 2 锁相环、信号幅度与锁相放大器作为关键词的文献关键词聚类分析图

Fig. 2. Literature keyword clustering plot with phase-locked loop, signal amplitude and lock-in amplifier as keywords.

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图 3 锁相环与锁相放大器结构关联与差异示意图

Fig. 3. Schematic diagram of structural correlation and difference between phase-locked loop and lock-in amplifier.

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图 4 数字锁相环中的核心器件用数字电路实现

Fig. 4. Primary components in a digital lock-in amplifier are realized using digital circuits.

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图 5 虚拟锁相放大器中由CPU等指令工作流完成所有运算

Fig. 5. In the virtual lock-in amplifier, all computations are accomplished by the CPU instruction workflow.

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图 6 模拟、数字与虚拟锁相放大器的分类标准图示及说明

Fig. 6. Schematic description of classification criteria for analog, digital and virtual lock-in amplifiers.

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图 7 锁相环的型与阶分类以及典型结构功能与表达式列举示意图

Fig. 7. Schematic diagram of the type and order classification of phase-locked loops and the enumeration of typical structural functions and expressions.

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图 8 锁相放大器的典型测试系统各部分连接关系图

Fig. 8. Illustration of a typical test system for lock-in amplifiers.

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图 9 锁相放大器的幅度、频率与相位测量不确定度性能测试流程图

Fig. 9. Flow chart of evaluation process for lock-in amplifiers, to obtain performance on measuring amplitude, frequency and phase.

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图 10 锁相放大器的诸多噪声抑制性能及其相互转换关系示意图

Fig. 10. Various indicators of noise suppression properties and their relationship for evaluating lock-in amplifiers.

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图 11 锁相放大器用于光谱信噪比增强的两种光路图　(a)斩波器调制; (b)高速电控开关

Fig. 11. Lock-in amplifier is used to enhance the spectral signal-to-noise ratio in optical measurement via two kind of modulations: (a) Chopper modulation; (b) high speed electronic control switch.

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图 12 运用锁相放大器进行阻抗测量的几种典型场景电路　(a)电池内阻测量^[70]; (b)生物电阻抗在微流控中监测运动^[72]; (c)超导电阻测量^[68]; (d)精密电容监控^[76]

Fig. 12. Several typical application scenes with circuits for impedance measurement using Lock-in amplifier: (a) Battery internal resistance measurement^[70]; (b) bioimpedance for movement monitoring in microfluidic channels^[72]; (c) superconducting resistance measurement^[68]; (d) precision capacitor monitoring^[76].

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图 13 几种典型应用锁相放大器开展的磁测量场景示意图　(a)基于原子磁共振的磁强计^[79]; (b)振动样品磁强计测量直流磁矩^[83]; (c)交流磁化率仪; (d)动态磁致伸缩测量^[85]

Fig. 13. Schematic diagrams of typical magnetic measurements carried out by lock-in amplifier: (a) Magnetometer based on atomic magnetic resonance^[79]; (b) the vibrating sample magnetometer measures the DC magnetic moment^[83]; (c) AC magnetic susceptibility measurement; (d) dynamic magnetostriction measurement^[85].

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图 14 几种用到锁相放大器的显微成像系统　(a)原子力显微镜^[92]; (b)近场光谱显微镜^[94]; (c)扫描俄歇电子显微镜^[95]

Fig. 14. Several microscopic imaging systems using lock-in amplifier: (a) Atomic force microscopy^[92]; (b) near field spectroscopic microscope^[94]; (c) scanning Auger electron microscope^[95].

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图 15 激光外差干涉采取的两种运用锁相反馈的光路　(a)单激光源输出相位可控的一对激光束; (b)主从双激光源输出一对激光束

Fig. 15. Laser heterodyne interference two optical paths using phase-locked feedback: (a) A pair of laser beams with controllable phase coherence from a single Laser; (b) the master-slave dual light source outputs a pair of laser beams.

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表 1 国内外目前锁相放大器产品性能指标的对比

Table 1. Comparison of performance for current available lock-in amplifier products around the world.

地区	品牌	型号	工作频率范围	最大输出数据率	相位噪声	电压噪声/ (nV·Hz^–1/2)	动态储备 /dB	推出年份
国外	Standford	SR830	$1\ {\rm{mHz}} — 102\ {\rm{kHz}}$	256 kSa/s	87 μrad	6	100	1980
	Research (美国)	SR865A	$1\ {\rm{mHz}} — 4\ {\rm{MHz}}$	1.25 MSa/s	1.7 μrad	2.5	120	2015
	Zurich	HF2LI	$\rm{DC} — 50\ {\rm{MHz}}$	0.5 MSa/s	>17 nrad	5	120	2008
	Instrument	UHFLI	$\rm{DC} — 600\ {\rm{MHz}}$	1.6 MSa/s (LAN)	>17 nrad	4	100	2013
	(瑞士)	SHFLI	$\rm{DC} — 8.5\ {\rm{GHz}}$	1.6 MSa/s (LAN)	>17 nrad	4	100	2022
	Liquid	Moku:Lab	$1\ {\rm{kHz}} — 200\ {\rm{MHz}}$	1 MSa/s	1 nrad·Hz^–1/2	30	120	2017
	Instrument (澳洲)	Moku:Pro	$1\ {\rm{kHz}} — 300\ {\rm{MHz}}$	10 MSa/s	1 nrad·Hz^–1/2	20	120	2021
	AMETEK (美国)	Signal	$1\ {\rm{mHz}} —250\ {\rm{kHz}}$	1 MSa/s (典型)	1.7 μrad	5	100—120	1999
	AMETEK (美国)	Recovery 7265	$1\ {\rm{mHz}} —250\ {\rm{kHz}}$	1 MSa/s (典型)	1.7 μrad	5	100—120	1999
	NF(日本)	LI5660	$0.5\ \rm{\; Hz} — 11\ {\rm{MHz}}$	1.5 MSa/s	17 μrad	4.5	100	2018
国内	赛恩科仪	OE1022	$10\ \text{μ} {\rm{Hz}} — 250\ {\rm{kHz}}$	1 MSa/s	> 17 nrad	2.5	120	2012
	赛恩科仪	OE2041	$10\ \text{μ} {\rm{Hz}} — 60\ {\rm{MHz}}$	1 MSa/s	> 17 nrad	2.5	120	2020
	国仪量子	LIA001M	${\mathrm{DC}} — 1\ {\rm{MHz}}$	N.A.	> 170 nrad	2.5	120	2021
	南京鸿宾	HB293(JD-1)	$1\ \rm{\; Hz} — 100\ {\rm{kHz}}$	N.A.	N.A.	3	140	~1980

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[1]	陆俊 2020 物理 49 472 Google Scholar Lu J 2020 Physics 49 472 Google Scholar
[2]	Best R E 2003 Phase-locked Loops Design, Simulation and Applications (New York: McGraw-Hill) pp151–277
[3]	Gardner F M 2005 Phaselock Techniques (Hoboken: Wiley Interscience) pp6–96
[4]	Banerjee D 2006 PLL Performance, Simulation, and Design ( Dallas: Texas Instruments) pp9–243
[5]	杜勇 2016 锁相环技术原理及FPGA实现 (北京: 电子工业出版社) 第89—262页 Du Y 2016 Principle and FPGA Implementation of Phase Locked Loop Technology (Beijing: Publishing House of Electronics Industry) pp89–262
[6]	远坂俊昭 2006 锁相环(PLL)电路设计与应用 (北京: 科学出版社) 第31—105页 YuanBan J Z 2006 Design and Application of Phase Locked Loop (PLL) Circuit (Beijing: Science Press) pp31–105
[7]	田昭武 1984 电化学研究方法 (北京: 科学出版社) 第395—396页 Tian Z W 1984 Electrochemical Methods (Beijing: Science Press) pp395–396
[8]	高晋占 2004 微弱信号检测 (北京: 清华大学出版社) 第1—36页 Gao J Z 2004 Weak Signal Detection (Beijing: Tsinghua University Press) pp1–36
[9]	Meade M L 1983 Lock-In Amplifiers: Principles and Applications (London: Peter Peregrinus) pp7–147
[10]	De Bellescize 1933 U.K. Patent GB19310031 [1933-05-18
[11]	王福昌 1996 锁相技术 (武汉: 华中理工大学出版社) 第3—137页 Wang F C 1996 Phase-locked Technology (Wuhan: Huazhong University of Technology Press) pp3–137
[12]	Gaspar J, Chen S F, Gordillo A, Hepp M, Ferreyra P, Marques C 2004 Microprocess. Microsyst. 28 157 Google Scholar
[13]	Zurich-Instrument https://docs.zhinst.com/overview [2023-8-9
[14]	Liquid-Instrument https://www.liquidinstruments.com/products/hardware-platforms/mokupro https://www.thinksrs.com/downloads/man.html [2023-8-9
[15]	Stanford-Research-Systems https://www.thinksrs.com/downloads/man.html [2023-8-9
[16]	Sine Scientific Instruments https://www.ssi-instrument.com/products/LIA.html [2023-8-9
[17]	Huang K, Geng Y Y, Zhang X B, Chen D H, Cai Z G, Wang M, Zhu Z, Wang Z X 2019 Sensors 19 3519 Google Scholar
[18]	NF株式会社 http://www.nfcorp.com.cn/pro/mi/loc/loc/li5600 [2023-8-9] NF Corporation http://www.nfcorp.com.cn/pro/mi/loc/loc/li5600 [2023-8-9
[19]	国仪量子 https://www.cigtek.com/products. html [2023-8-9] CIQTEK https://www.cigtek.com/products.html [2023-8-9
[20]	南京鸿宾电子 https://www.ndwshb.com/product/105.html [2023-8-9] Nanjing Hongbin https://www.ndwshb.com/product/105.html [2023-8-9
[21]	AMETEK https://www.ameteksi.com/products/lock-in-amplifers/7265-dual-phase-lock-in-amplifer [2023-8-9
[22]	Chen C 2004 Proc. Natl. Acad. Sci. 101 5303 Google Scholar
[23]	张勇, 李睿, 刘君华 1998 电测与仪表 35 30 Zhang Y, Li R, Liu J H 1998 Electr. Meas. Instrum. 35 30
[24]	Bobalo Y, Bondariev A, Altunin S, Kiselychnyk M, Maksymiv I 2018 International Conference on Advanced Trends in Radioelecrtronics, Telecommunications and Computer Engineering Lviv-Slavske, Ukraine, February 20–24, 2018
[25]	Lu J, Pan D A, Bai Y, Qiao L 2008 Meas. Sci. Technol. 19 045702 Google Scholar
[26]	陆俊 https://www.instrument.com.cn/download/shtml/062888.shtml [2008-8-9] Lu J https://www.instrument.com.cn/download/shtml/062888.shtml [2008-8-9
[27]	Stimpson G A, Skilbeck M S, Patel R L, Green B L, Morley G W 2019 Rev. Sci. Instrum. 90 094701 Google Scholar
[28]	Wang Z, Shi X, Wang W, Cai W 2023 IEEE Trans. Instrum. Meas. 72 1 Google Scholar
[29]	Lu J 2020 Rev. Sci. Instrum. 91 075106 Google Scholar
[30]	《手册》编写组 2017 数学手册 (北京: 高等教育出版社) Handbook Writing Group 2017 Mathematical Manual (Beijing: Higher Education Press
[31]	Ziemer R, Tranter W 2015 Principles of Communications Systems, Modulation, and Noise (Hoboken: Wiley) pp184– 195
[32]	Wullch D, Bar M 1990 Int. J. Circuit Theory Appl. 18 135 Google Scholar
[33]	Ugarte M, Carlosena A 2015 Circuits Syst. Signal Process. 34 3395 Google Scholar
[34]	Kudrewicz J, Wasowicz S 2007 Equations of Phase-Locked Loops Dynamics on the Circle, Torus and Cylinder (New Jersey: World Scientific) pp9–123
[35]	Kittel P 1977 Rev. Sci. Instrum. 48 1214 Google Scholar
[36]	原力超导 https://eastfs.com/glpmd [2003-8-9] Force superconductivity https://eastfs.com/glpmd [2003-8-9
[37]	Rubiola E 2008 Phase Noise and Frequency Stability in Oscillators (London: Cambridge University Press) pp1–135
[38]	Schwartz M 1970 Information Transmission Modulation and Noise—A Unified Approach to Communication System (New York: McGRAW-Hill) pp390–570
[39]	Bodson M 2005 Int. J. Adapt. Control Signal Process. 19 67 Google Scholar
[40]	陆俊, 沈保根, 邵晓萍 2018 中国专利 201510182065.7 [2018-01-26] Lu J, Shen B G, Shao X P 2018 CHN Patent 201510182065.7 [2018-01-26
[41]	张靖悉, 胡勇, 潘柳2020锁相放大器校准规范 Zhang J X, Hu Y, Pan L 2020 Calibration Specification for Lock-in Amplifiers
[42]	大恒新纪元科技股份有限公司 2022 精密大带宽锁相放大器企业标准 Daheng New Era Technology Co., Ltd 2022 Enterprise Standards for Broadband High Precision Lock-in Amplifiers
[43]	王彪, 张江涛, 李艳强, 谷扬, 潘仙林 2012 电测与仪表 49 170 Wang B, Zhang J T, Li Y Q, Gu Y, Pan X L 2012 Electr. Meas. Instrum. 49 170
[44]	Cultrera A, Corminboeuf D, D’Elia V, Tran N T M, Callegaro L, Ortolano M 2021 Metrologia 58 025001 Google Scholar
[45]	Jia Z S, Liu Z Y, Wang L, He Q, Huang H T, Liu L Y 2018 Measurement 125 606 Google Scholar
[46]	陆祖良, 杨雁, 黄璐, 王磊 2019 计量学报 40 319 Lu Z L, Yang Y, Huang L, Wang L 2019 Acta Metrologica Sinica 40 319
[47]	陆祖良 2021 计量学报 42 913 Lu Z L 2021 Acta Metrologica Sinica 42 913
[48]	Van B, Herold G 2014 Am. J. Phys. 82 785 Google Scholar
[49]	Arora H, Klemmer N, Morizio J C, Wolf P D 2005 IEEE Trans. Circuits Syst. Regul. Pap. 52 379 Google Scholar
[50]	Demir A 2006 IEEE Trans. Circuits Syst. Regul. Pap. 53 1869 Google Scholar
[51]	Goldman S J 2007 Phase-Locked Loops Engineering Handbook for Integrated Circuits (Norwood: Artech House) pp5–161
[52]	Bondariev A P, Altunin S I 2017 International Conference on Information and Telecommunication Technologies and Radio Electronics (UkrMiCo) Odessa, September 11–15, 2017
[53]	Eulalia B, Luca D, Francesco P, Sergio R, Ioan T 2020 Acta Imeko 9 52 Google Scholar
[54]	刘河山 2015 博士学位论文 (北京: 中国科学院大学) Liu H S 2015 Ph. D. Dissertation (Beijing: University of Chinese Academy of Sciences
[55]	Shaddock D, Ware B, Halverson P G, Spero R E, Klipstein B 2006 Laser Interferometer Space Antenna: 6th International LISA Symposium Greenbelt, Maryland, USA, June 19–23, 2006
[56]	Cervantes F G, Heinzel G, Marín A F G, Wand V, Steier F, Jennrich O, Danzmann K 2007 Appl. Opt. 46 4541 Google Scholar
[57]	Gerberding O, Sheard B, Bykov I, Kullmann J, Delgado J J E, Danzmann K, Heinzel G 2013 Classical Quantum Gravity 30 235029 Google Scholar
[58]	Libbrecht K G, Black E D, Hirata C M 2003 Am. J. Phys. 71 1208 Google Scholar
[59]	Sterczewski L A, Grzelczak M P, Plinski E F 2016 Rev. Sci. Instrum. 87 014702 Google Scholar
[60]	Deninger A J, Göbel T, Schönherr D, Kinder T, Roggenbuck A, Köberle M, Lison F, Müller-Wirts T, Meissner P 2008 Rev. Sci. Instrum.79 044702 Google Scholar
[61]	Zhang Z, Liu Y, Zhu X 2021 J. Phys. Conf. Ser. 1865 022010 Google Scholar
[62]	Balgos M H, Hayazawa N, Tani M, Tanaka T 2023 Rev. Sci. Instrum. 94 043002 Google Scholar
[63]	Ardekani H, Wilmington R L, Vutukuru M, Chen Z, Brandt R, Swan A, Gundogdu K 2021 Rev. Sci. Instrum. 92 104706 Google Scholar
[64]	Kierzek M, Deal P E, Miller E W, Mukherjee S, Wachten D, Baumann A, Kaupp U B, Strünker T, Brenker C 2021 eLife 10 63129 Google Scholar
[65]	陆俊, 杜昱光, 王倬, 张琛, 赵雪, 李国强, 谭广文, 竺晓山, 丁玮 2023 中国专利 202010361964.4 [2023-04-21] Lu J, Du Y G, Wang Z, Zhang C, Zhao X, Li G Q, Tan G W, Zhu X S, Ding W 2020 CHN Patent 202010361964.4 [2023-04-21
[66]	Sarra A, Stanchieri G D P, De M, Bordi F, Postorino P, Palange E 2021 IEEE Trans. Biomed. Circuits Syst. 15 177 Google Scholar
[67]	Song X, Jin Y, Zhang X, Yu Y, Zhang D L 2009 Rev. Sci. Instrum. 80 086104 Google Scholar
[68]	Song D, Yang W, Zhu J, Bai M, Liu Y 2022 J. Supercond. Novel Magn. 35 95 Google Scholar
[69]	Barnard A W, Mikheev E, Finney J, Hiller H S, Goldhaber-Gordon D 2023 Rev. Sci. Instrum. 94 013902 Google Scholar
[70]	邓荣, 江国栋 2013 电测与仪表 50 105 Deng R, Jiang G D 2013 Electr. Meas. Instrum. 50 105
[71]	宋改青, 董有尔 2006 中国测试技术 32 78 Song G Q, Dong Y E 2006 China Meas. Technol. 32 78
[72]	Tang T, Liu X, Yuan Y, Kiya R, Zhang T, Yang Y, Suetsugu S, Yamazaki Y, Ota N, Yamamoto K, Kamikubo H, Tanaka Y, Li M, Hosokawa Y, Yalikun Y 2023 Sens. Actuators, B 374 132698 Google Scholar
[73]	Sandoval B, Janićijević Ž, Palestina R, et al. 2023 ACS Sens. 8 576 Google Scholar
[74]	Kitta K, Sakamoto M, Hayakawa K, Nukazuka A, Kano K, Yamamoto T 2023 ACS Omega 8 14684 Google Scholar
[75]	苏少奎 2019 低温物性及测量: 一个实验技术人员的理解合经验总结 (北京: 科学出版社) Su S K 2019 Low Temperature Physical Properties and Measurement: An Experimental Technician’s Understanding and Experience Summary (Beijing: Science Press
[76]	Carminati M, Ferrari G, Guagliardo F, Sampietro M 2011 Sens. Actuators, A 172 117 Google Scholar
[77]	陆俊, 沈保根, 邵晓萍 2015 中国专利 201210081375.6 [2015-02-02] Lu J, Shen B G, Shao X P 2015 CHN Patent 201210081375.6 [2015-02-02
[78]	Heng X, Wei K, Zhao T, Xu Z, Cao Q, Huang X, Zhai Y, Ye M, Quan W 2023 IEEE Trans. Instrum. Meas. 72 1 Google Scholar
[79]	Li J J, Du P C, Fu J Q, Wang X T, Zhou Q, Wang R Q 2019 Chin. Phys. B 28 040703 Google Scholar
[80]	詹文山 1982 物理 12 732 Zhan W S 1982 Physics 12 732
[81]	Pu Y, Zhao H, Murayama T, Tonthat L, Okita K, Watanabe Y, Yabukami S 2023 J. Magn. Soc. Jpn. 47 66 Google Scholar
[82]	Meng Z, He X, Li Y, Huang J, Chen D, Wang Z 2023 IEEE Sens. J. 23 16123 Google Scholar
[83]	Zhang Z, Xu Z, He J, Lu J 2022 IEEE Trans. Instrum. Meas. 71 1006009 Google Scholar
[84]	Roos W, Hempel K A, Voigt C, Dederichs H, Schippan R 1980 Rev. Sci. Instrum. 51 612 Google Scholar
[85]	Chen J, Xi X, Wang S, Lu J, Guo C, Wang W, Liu E, Wang W, Liu L, Wu G 2016 Rev. Sci. Instrum. 87 043902 Google Scholar
[86]	陆俊, 郗学奎, 王利晨, 蒋建旺 2022 中国专利 202210373018.0 [2022-04-11] Lu J, Chi X K, Wang L C, Jiang J W 2022 CHN Patent 202210373018.0 [2022-04-11
[87]	Hayek J N, Herreño-Fierro C A, Patiño E J 2016 Rev. Sci. Instrum. 87 103113 Google Scholar
[88]	Lu J, Pan D A, Bai Y, Su Y J, Qiao L J 2008 IEEE Trans. Magn. 44 2127 Google Scholar
[89]	Drobac D, Marohnic Z, Zivkovic I, Prester M 2013 Rev. Sci. Instrum.84 054708 Google Scholar
[90]	Krishnan R V, Banerjee A 1999 Rev. Sci. Instrum. 70 85 Google Scholar
[91]	Harcombe D M, Ruppert M G, Fleming A J 2020 Beilstein J. Nanotechnol. 11 76 Google Scholar
[92]	Shi Y, Lu Q 2012 Microsc. Microanal. 18 1016 Google Scholar
[93]	刘凡微, 陈思丹, 张嘉未, 陈欣中, 毛寒青, 黄思思, 陈曦 2022 电子显微学报 41 627 Liu F W, Chen S D, Zhang J W, Chen X Z, Mao H Q, Huang S S, Chen X 2022 J. Chin. Electron Microsc. Soc. 41 627
[94]	Li X, Sun J, Jin L, Shangguan Y, Chen K, Qin H 2023 Opt. Express 31 19754 Google Scholar
[95]	Leung M S, Stupian G W 1986 Appl. Surf. Sci. 25 435 Google Scholar
[96]	徐欣, 谈宜东, 穆衡霖, 李岩, 王加刚, 金景峰 2023 激光与光电子学进展 60 0312006 Google Scholar Xu X, Tan Y D, Mu H L, Li Y, Wang J G, Jin J F 2023 Laser OptoElectron. Prog. 60 0312006 Google Scholar
[97]	Finneran I A, Welsch R, Allodi M A, Miller I I I, Blake G A 2017 J. Phys. Chem. Lett. 8 4640 Google Scholar
[98]	Li H, Li Z, Wan W, Zhou K, Liao X, Yang S, Wang C, Cao J C, Zeng H 2020 ACS Photonics 7 49 Google Scholar
[99]	Jain P, Priya P, Ram T V S, Parikh K S, Bandi T N 2021 Rev. Sci. Instrum. 92 124705 Google Scholar
[100]	Slim J, Nikolaev N, Rathmann F, Wirzba A, Zurek M 2021 Phys. Rev. Accel. Beams 2 4 Google Scholar
[101]	Boss J, Cujia K, Zopes J, Degen C 2017 Science 356 837 Google Scholar
[102]	Lu J 2021 A Reconfigurable Electrical Circuit Auto-Processing Method for Direct Electromagnetic Inversion, As a Chapter in Intelligent Computing and Block Chain (Singapore: Springer Nature) pp190–203
[103]	Jung S M 2016 Ph. D. Dissertation (Tucson: The University of Arizona
[104]	Kaptein M, Van E, Iannuzzi D, Braunstein L A 2017 Plos One 12 e0174182 Google Scholar
[105]	Golestan S, Guerrero J M, Vasquez J C 2017 IEEE Trans. Power Electron. 32 9013 Google Scholar
[106]	Uzzaman T, Kim U, Choi W 2022 IEEE Access 10 32870 Google Scholar
[107]	Neunteufel D, Grebien S, Arthaber H 2022 Sensors 22 2663 Google Scholar
[108]	Aguirre J, Medrano N, Calvo B, Celma S 2011 IEEE Sensors Conference Limerick, Ireland, October 28–31, 2011 6127317

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