Research progress of lock-in amplifiers

Guo Zhong-Kai; Li Yong-Gang; Yu Bo-Cheng; Zhou Shi-Chao; Meng Qing-Yu; Lu Xin-Xin; Huang Yi-Fan; Liu Gui-Peng; Lu Jun

doi:10.7498/aps.72.20230579

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:

Erratum

Erratum: Research progress of lock-in amplifiers [Acta Phys. Sin. 2023, 72(22): 224206]

Guo Zhong-Kai, Li Yong-Gang, Yu Bo-Cheng, Zhou Shi-Chao, Meng Qing-Yu, Lu Xin-Xin, Huang Yi-Fan, Liu Gui-Peng, Lu Jun. Erratum: Research progress of lock-in amplifiers [Acta Phys. Sin. 2023, 72(22): 224206]. Acta Phys. Sin., 2023, 72(24): 249901. doi: 10.7498/aps.72.249901

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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Cited By

图 1 典型锁相放大器原理图

Figure 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

Figure 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

Figure 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

Figure 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

Figure 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

Figure 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

Figure 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

Figure 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

Figure 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

Figure 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

Figure 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]

Figure 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]

Figure 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]

Figure 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

Figure 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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