Table of contents
Preface
Acknowledgments
Chapter 1 Introduction
1.1 References
Chapter 2 Basic concepts in lock-in recovery
2.1 Introduction
2.2 Evaluating the signal recovery problem
2.3 Demodulators for signal recovery
2.4 Operation of synchronous detectors
2.4.1 Introduction
2.4.2 Demodulation with a synchronous reference
2.4.3 Amplitude demodulation
2.4.4 Phase demodulation
2.4.5 Mixed modulations
2.4.6 Noise rejection
2.5 Basic lock-in amplifiers
2.5.1 Introduction
2.5.2 The signal channel
2.5.3 Signal conditioning
2.5.4 The multiplier
2.5.5 The reference channel
2.5.6 The low-pass filter
2.6 Signal recovery 'capability'
Chapter 3 Phase-sensitive detectors
3.1 Introduction
3.2 Principles of operation
3.3 Harmonic transmission windows
3.4 Noise bandwidth of phase-sensitive detectors
3.5 Non-sinusoidal signals
3.5.1 Introduction
3.5.2 General considerations
3.5.3 Symmetrical periodic signals
3.5.4 Asymmetrical periodic signals
3.5.5 Squarewave signals: a special case
3.6 Phase-sensitive detector specifications
3.6.1 Introduction
3.6.2 Full-scale sensitivity
3.6.3 Linearity and out-of-phase rejection
3.6.4 Dynamic reserve
3 6.5 Output stability and minimum detectable signal
3.6.6 Dynamic-reserve/output-stability trade-off
3.6.7 Dynamic range
3.6.8 Summary of specifications
3.7 References
Chapter 4 Lock-in amplifier specifications
4.1 Introduction
4.2 Calibration: full-scale sensitivity
4.3 Phase-sensitive detector related specifications
4.3.1 Introduction
4.3.2 System dynamic reserve
4.3.3 System overload capability
4.3.4 Dynamic reserve and output stability trade-off
4.3.5 Overload capability and output stability trade-off
4.3.6 Dynamic range and linearity trade-off
4.4 Using a tuned filter in the signal channel of a conventional lock-in amplifier
4.4.1 Influence on overload capability
4.4.2 Suppression of harmonic responses
4.5 Reference-channel specifications
4.5.1 Introduction
4.5.2 Phase accuracy: points of specification
4.5.3 Phase noise (phase jitter) and phase drift
4.5.4 Reference-channel slew rate
4.6 Measurement of phase accuracy
4.6.1 Introduction
4.6.2 Trigger phase errors
4.6.3 Defining in-phase signal and reference
4.6.4 Errors due to oscillator distortion
4.6.5 Phase noise, phase drift and phase-sensitive detector instability
4.7 References
Chapter 5 Two-phase lock-in amplifiers
5.1 Introduction
5.2 Examples of 'classic' two-phase applications
5.2.1 A.C. bridge balancing
5.2.2 A.C. impedance measurements
5.2.3 Phase measurements
5.3 Noise limitations of the vector computer
5.4 Vector tracking
5.5 Asynchronous operation
5.5.1 Introduction
5.5.2 Operation as a wave analyser
5.5.3 High-resolution spectrum analysis
5.6 References
Chapter 6 Limitations of conventional lock-in systems
6.1 Introduction
6.2 Limitations arising from harmonic responses
6.2.1 Susceptibility to interference
6.2.2 Ambiguity due to the harmonic responses
6.2.3 Detection of non-sinusoidal signals
6.3 Slew-rate limitations
Chapter 7 Phase-locking to noisy signals
7.1 Introduction
7.2 'Static' analysis of a phase-locked loop
7.2.1 Phase detector output
7.2.2 Static phase error
7.2.3 'Hold-in' range
7.3 Dynamic response
7.3.1 Introduction
7.3.2 The loop equation
7.4 The second-order loop
7.5 Noise and phase-locked loops
7.6 Optimization procedure
7.7 Notes on acquisition and tracking
7.8 Using a lock-in amplifier for phase-locking
7.8.1 Introduction
7.8.2 Identifying the loop constants
7.8.3 Optimization procedures for lock-in amplifiers
7.9 The final measurement
7.10 References
Chapter 8 Heterodyne lock-in amplifiers
8.1 Introduction
8.2 Principles of heterodyne operation
8.3 Practical considerations
8.3.1 Frequency translation
8.3.2 Formulation of spurious responses
8.3.3 Suppression of the spurious responses
8.3.4 Tuned filter requirements
8.3.5 Phase-shifting
8.4 Practical limitations
8.4.1 The frequency synthesizer
8.4.2 The image filter
8.4.3 The signal mixer
8.4.4 The phase-sensitive detector
8.5 Overload capability of heterodyne systems
8.6 Double heterodyne lock-in amplifiers
8.7 Brief comparison of single and double heterodyne systems
8.8 8ynchronous heterodyning
8.8.1 Introduction
8.8.2 Dynamic range improvement
8.8.3 Application to heterodyne lock-in amplifiers
8.9 Conclusions
8.10 References
Chapter 9 P.W.M. systems
9.1 Introduction
9.2 Principles of operation
9.3 Frequency composition of the p.w.m. waveform
9.4 Basic design considerations
9.4.1 Dynamic range
9.4.2 Spurious responses
9.4.3 Choice of switching frequency
9.5 Reference phase-shifting
9.6 Two-phase systems
9.7 Analogue correlation
9.7.1 Matched detection
9.7.2 Double frequency lock-in analysis
9.7.3 High slew rate applications
9.8 Interference rejection filters
9.9 Comparison of p.w.m. systems with heterodyne lock-in amplifiers
9.10 References
Chapter 10 Computer-controlled lock-in amplifiers
10.1 Introduction
10.2 Programmable lock-in amplifiers
10.3 Microprocessor-based systems
10.4 Automatic sensitivity selection
10.5 Automatic phase selection
Appendix 1 Principal Applications
Appendix 2 Selected topics on signals and noise
A2.1 Introduction
A2.2 Voltage noise and current noise spectra
A2.3 Signal spectra
A2.4 Thermal noise and shot noise
A2.5 Noise bandwidth
A2.6 Signal-to-noise-ratio improvement by filtering
A2.7 Low-frequency noise
A2.8 More about narrowband noise
Appendix 3 Synchronous detection and noise
A3.1 Signal-to-noise-ratio improvement
A3.2 Noise measurements
Appendix 4 Signal-conditioning filters
A4.1 Low-pass filters
A4.1.1 First order
A4.1.2 Second order
A4.2 High-pass filters
A4.2.1 First order
A4.2.2 Second order
A4.3 Active tuned filters
A4.3.1 Band-pass
A4.3.2 Low pass
A4.4 Active notch filter
Appendix 5 Amplifier selection and noise matching
A5.1 Introduction
A5.2 What type of amplifier?
A5.3 Noise in voltage amplifiers
A5.3.1 Introduction
A5.3.2 Noise-figure calculations
A5.3.3 Minimum noise figure and optimum source resistance
A5.3.4 Noise-figure contours
A5.3.5 Cryogenic sources
A5.3.6 Transformer noise matching
A5.4 Noise in current amplifiers
A5.5 References
Appendix 6 Interference and ground loop suppression
A6.1 Introduction
A6.2 Ground loops: single-ended amplifiers
A6.3 Ground loops: differential amplifiers
A6.4 Ground loops and lock-in recovery
A6.5 References