Electrical Measurement Techniques: For the Physics Laboratory

Preface
Contents
Acronyms
1 Introduction
	1.1 Electrical Measurement Systems
	1.2 Common and Normal Mode
	1.3 Signal-To-Noise Ratio
	1.4 Decibel Units
	1.5 Differential-Ended Versus Single-Ended
	1.6 Signals
		1.6.1 Risetime and Falltime
		1.6.2 Bandwidth
	1.7 Systems
	1.8 Solved Problems
2 Noise: Sources and Remedies
	2.1 Introduction
	2.2 Internal Noise
		2.2.1 Johnson Noise
		2.2.2 Shot Noise
		2.2.3 1/f-Noise
		2.2.4 Quantization Noise
	2.3 Coupling By Radiation
		2.3.1 Electric Dipole Antennas
		2.3.2 Magnetic Dipole Antennas
	2.4 Capacitive Crosstalk
	2.5 Inductive Crosstalk
	2.6 Common Impedances
	2.7 Summary and Recommendations
	2.8 Solved Problems
	Reference
3 Sensors
	3.1 Introduction
	3.2 Temperature Sensors
		3.2.1 Thermocouples
		3.2.2 Metal Temperature Sensors
		3.2.3 Measuring Resistance
		3.2.4 Bandgap Sensors
		3.2.5 Cryogenic Temperatures
		3.2.6 Extremely High Temperatures
	3.3 The Strain Gauge Principle
		3.3.1 Strain Gauges
		3.3.2 The Wheatstone Bridge
		3.3.3 Accelerometers
		3.3.4 Pressure Sensors
		3.3.5 Flow Sensors
		3.3.6 Fluid Level Sensors
		3.3.7 Torque Sensors
		3.3.8 Viscosity Sensors
		3.3.9 Load Cell
	3.4 Piezoelectric Crystals
	3.5 Hall Sensors
	3.6 Position Sensors
	3.7 Photo Sensors
		3.7.1 Light Units
		3.7.2 Photodiodes
		3.7.3 Avalanche Photodiodes
		3.7.4 Position-Sensitive Detectors
		3.7.5 Photomultipliers
	3.8 Particle Detectors
		3.8.1 Channel Electron Multipliers
		3.8.2 Microchannel Plates
	3.9 Vacuum Gauges
		3.9.1 Introduction
		3.9.2 The Pirani Gauge
		3.9.3 Gas Ionization Gauges
	3.10 Solved Problems
	References
4 The Instrumentation Amplifier
	4.1 Introduction
	4.2 Implementations
		4.2.1 Classic IA Circuit
	4.3 CMRR Versus SNR
	4.4 Solved Problems
5 Transmission Lines
	5.1 Introduction
	5.2 The Characteristic Impedance
	5.3 Termination
	5.4 Splitting and Splicing
	5.5 Attenuation
	5.6 Time Domain Reflectometry
	5.7 Solved Problems
	References
6 Probes
	6.1 Introduction
	6.2 Passive Probes
	6.3 Active Probes
	6.4 Current Probes
	6.5 Solved Problems
7 Transform Theory
	7.1 Introduction
	7.2 The Fourier Transform
		7.2.1 Case 1: Signal is Periodic
		7.2.2 Case 2: Signal is Non-Periodic, But ‘Time-Limited’
		7.2.3 Case 3: Signal is Non-Periodic and Infinite
		7.2.4 FFT Outputs
		7.2.5 Aliasing
	7.3 Describing Systems
		7.3.1 Distortion-Free Systems
	7.4 Complex Frequencies
		7.4.1 Laplace Representation of Systems
		7.4.2 The z Transform
	7.5 Solved Problems
	Reference
8 Spectrum Analyzers
	8.1 Introduction
	8.2 Windows
	8.3 Resolution Bandwidth
		8.3.1 Quantifying the Leakage
		8.3.2 Resolution Bandwidth
	8.4 Heterodyne Analyzers
	8.5 Solved Problems
9 Analog Filters
	9.1 Introduction
	9.2 First-Order Filters
		9.2.1 Passive Filters
	9.3 Second-Order Filters
		9.3.1 ‘Biquad’
		9.3.2 Lowpass: b2 = b1 = 0
		9.3.3 Bandpass: b2 = b0 = 0
		9.3.4 Highpass: b1 = b0 = 0
	9.4 Implementations
		9.4.1 The Double Integral Method
		9.4.2 The Sallen–Key Link
		9.4.3 Switched Capacitors
		9.4.4 More About Passive Filters
		9.4.5 Special Cases
	9.5 Filter Models
		9.5.1 Butterworth
		9.5.2 Chebyshev
		9.5.3 Cauer
	9.6 Filter Transformations
		9.6.1 Lowpass to Lowpass
		9.6.2 Lowpass to Highpass
		9.6.3 Lowpass to Bandpass
		9.6.4 Lowpass to Bandstop
	9.7 Time Domain
		9.7.1 Convolution
	9.8 Solved Problems
10 Digital Filters
	10.1 Introduction
	10.2 FIR Filters
	10.3 IIR Filters
	10.4 Designing Digital Filters
		10.4.1 FIR Filters: The Inverse Fourier Transform Method
		10.4.2 IIR Filters: The Bilinear Transformation Method
	10.5 Solved Problems
11 ADCs and Sampling
	11.1 Introduction
	11.2 Sampling
	11.3 Quantization and Quantization Noise
	11.4 Digital-to-Analog Converters
	11.5 SAR ADCs
	11.6 Flash ADCs
	11.7 Pipeline ADCs
	11.8 Dual Slope ADCs
		11.8.1 The Integrator
		11.8.2 The Dual Slope Circuit
	11.9 Level-Crossing ADCs
	11.10 Equivalent Number of Bits
	11.11 Oversampling
		11.11.1 As a Means to Reduce Noise
		11.11.2 As a Means to Improve Resolution
	11.12 Dithering
	11.13 Sigma-Delta ADCs
		11.13.1 Background
		11.13.2 Theory
	11.14 Extreme Sampling Rates
		11.14.1 Interleaved SARs
		11.14.2 Equivalent-Time Sampling
	11.15 Solved Problems
	References
12 Time-to-Digital Converters
	12.1 Introduction
	12.2 The Vernier Principle
		12.2.1 Vernier TDC with no Reference Clock
		12.2.2 Vernier TDC with a Reference Clock
	12.3 Delaylines
	12.4 Time Stretching
	12.5 Solved Problems
	References
13 Statistics
	13.1 Introduction
	13.2 Expectation and Variance
	13.3 Unbiased Estimators
	13.4 Interval Estimations
	13.5 The Uniform Distribution
	13.6 Solved Problems
14 Uncertainty Budgets
	14.1 Introduction
	14.2 Signal Models
	14.3 Uncertainty Budgets
		14.3.1 Examples
	14.4 ‘Guesstimating’
	14.5 Summary
	14.6 Solved problems
	References
15 The Lock-In Amplifier
	15.1 Introduction
	15.2 Phase Sensitive Detector
		15.2.1 PSDs
		15.2.2 Analog PSDs
		15.2.3 Multiplying PSDs
	15.3 Phase-Locked Loops
	15.4 LIAs
	15.5 Solved Problems
	References
16 Correlation
	16.1 Introduction
	16.2 Cross-Correlation
		16.2.1 Implementation: Matched Filters
	16.3 Auto-Correlation
		16.3.1 Auto-Correlation Applications
	16.4 Discrete-Time Correlation
		16.4.1 Cross-Correlation
		16.4.2 Auto-Correlation
		16.4.3 Circular Correlation
	16.5 Solved Problems
	References
17 Curve Fitting
	17.1 Introduction
	17.2 The Orthogonality Principle
	17.3 Curve Fitting to Exponential Functions
	17.4 MATLAB Tips
	17.5 Matrix Uncertainties and Pitfalls
		17.5.1 Error Propagation in Matrices
		17.5.2 Ill-Conditioned Matrices
	17.6 The Sampling Theorem Revisited
	17.7 Solved Problems
18 Introduction to Control Theory
	18.1 Control Systems
	18.2 Feedback Systems
	18.3 Control Systems
	18.4 The PI Controller
	18.5 The PD Controller
	18.6 The PID Controller
	18.7 Identifying the System
		18.7.1 First-Order Systems
		18.7.2 Second-Order Systems
	18.8 Finding the Control Parameters
		18.8.1 Ziegler–Nichol’s Rule of Thumb
		18.8.2 Using Phase and Gain Margin Criteria
	18.9 Discretizing
		18.9.1 Euler Transformation
		18.9.2 Bilinear Transformation
Appendix Operational Amplifiers
1. Introduction
2. Amplifiers
3. Summing
4. Integrals and Derivatives
5. Constant Current Generator
6. Voltage Follower
7. Negative Resistance
8. Inductor Replacement
Index