Table of contents



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