As many circuits and applications now enter the Gigahertz frequency range, accurate digital timing measurements have become crucial in the design, verification, characterization, and application of electronic circuits. To be successful in this endeavour, an engineer needs a knowledge base covering instrumentation, measurement techniques, signal integrity, jitter and timing concepts, and statistics. Very often even the most experienced digital test engineers, while mastering some of those subjects, lack systematic knowledge or experience in the high speed signal area.
Digital Timing Measurements gives a compact, practice-oriented overview on all those subjects. The emphasis is on useable concepts and real-life guidelines that can be readily put into practice, with references to the underlying mathematical theory. It unites in one place a variety of information relevant to high speed testing, measurement, signal fidelity, and instrumentation.
Chapter 1: Electrical Basics.
1. Time domain and frequency domain. 1.1 What Is The Frequency Domain, Anyway? 1.2 Moving between domains. 1.2.1 The Discrete Fourier Transformation. 1.2.2 Linear Systems. 1.2.3 Non-periodic signals. 1.3 Digital data streams. 1.4 Signal Bandwidth
2. Transmission line theory. 2.1 Low-pass filters. 2.1.1 Rise Times. 2.1.2 Filter Bandwidth, Time Constant, and Rise Time. 2.1.3 Adding Rise Times. 2.1.4 Effects on Signal Propagation. 2.2 Transmission Lines. 2.2.1 Key Parameters of Ideal (Loss-less) Transmission Lines. 2.2.2 Reflections, Timing, and Signal Integrity. 2.2.3 Parasitics in the Transmission Path. 2.2.4 Lumped vs. Distributed Elements. 2.2.5 Lossy Transmission Lines. 2.2.5.1 Ohmic Resistance. 2.2.5.2 Skin Effect and Proximity Effect. 2.2.5.3 Dielectric Losses. 2.2.5.4 Radiation and Induction Losses. 2.2.6 Effects of Parasitics and Losses on Signal Shape and Timing. 2.2.7 Differential Transmission Lines. 2.3 Termination. 2.3.1 Diode clamps. 2.3.2 Current loads (I-loads). 2.3.3 Matched termination (resistive load). 2.3.4 Differential Termination
Chapter 2: Measurement Hardware.
1. Oscilloscopes & CO. 1.1 A Short Look on Analog Oscilloscopes. 1.2 Digital Real-Time Sampling Oscilloscopes. 1.3 Digital Equivalent Time Sampling Oscilloscopes. 1.4 Time Stampers. 1.5 Bit Error Rate Testers. 1.6 Digital Testers (Comparators). 1.7 Spectrum Analyzers.
2. Key instrument parameters. 2.1 Analog Bandwidth. 2.2 Digital Bandwidth; Nyquist Theorem. 2.3 Time Interval Errors, Time Base Stability.
3. Probes. 3.1 The Ideal Voltage Probe. 3.2 Passive Probes. 3.3 Active Probes. 3.4 Probe Effects on the Signal. 3.4.1 Basic Probe Model. 3.4.2 Probe DC Resistance. 3.4.3 Parasitic Probe Capacitance. 3.4.4 Parasitic Probe Inductance. 3.4.5 Noise Pickup. 3.4.6 Avoiding Pickup from Probe Shield Currents. 3.4.7 Rise Time / Bandwidth. 3.5 Differential Signals. 3.5.1 Probing Differential Signals. 3.5.2 Single-Ended Jitter Measurements on Differential Signals. 3.5.3 Passive Differential Probing.
4. Accessories. 4.1 Cables and Connectors. 4.1.1 Cable Rise Time / Bandwidth. 4.1.2 Skin Effect Compensation. 4.1.3 Dielectric Loss Minimization. 4.1.4 Cable Delay. 4.1.5 Connectors. 4.2 Signal Conditioning. 4.2.1 Splitting and Combining Signals. 4.2.2 Baluns – Conversion between Differential and Single-Ended. 4.2.3 Rise Time Filters. 4.2.4 AC coupling. 4.2.5 Providing Termination Bias. 4.2.6 Attenuators. 4.2.7 Delay Lines.
Chapter 3: Timing and Jitter
1. Statistical basics. 1.1 Statistical Parameters. 1.2 Distributions and Histograms. 1.3 Probability Density and Cumulative Density Function. 1.4 The Gaussian Distribution. 1.4.1 Some Fundamental Properties. 1.4.2 How Many Samples Are Enough?
2. Rise time measurements. 2.1 Uncertainty in Thresholds. 2.2 Bandwidth Limitations. 2.3 Insufficient Sample Rate. 2.4 Interpolation Artifacts. 2.5 Smoothing. 2.6 Averaging
3. Understanding jitter. 3.1 What Is Jitter? 3.2 Effects of Jitter – Why Measuring Jitter Is Important. 3.2.1 Definition of the Ideal Position. 3.2.1.1 Data Stream with Separate Clock. 3.2.1.2 Clock-Less Data Stream. 3.2.1.3 Data Stream with Embedded Clock – Clock Recovery. 3.2.1.4 Edge-to-Edge Jitter vs. Edge-to-Reference Jitter. 3.2.1.5 Jitter Trend. 3.3 Jitter Types and Jitter Sources. 3.3.1 CDF and PDF. 3.3.2 Random Jitter. 3.3.3 Noise Creates Jitter. 3.3.4 Noise Types and Noise Sources. 3.3.4.1 Thermal Noise. 3.3.4.2 Shot Noise. 3.3.4.3 1/f Noise. 3.3.4.4 Burst Noise (Popcorn Noise). 3.3.5 Periodic Jitter. 3.3.6 Duty Cycle Distortion. 3.3.7 Data Dependent Jitter. 3.3.8 Duty Cycle and Thermal Effects. 3.3.9 Uncorrelated Deterministic Jitter.
4. Jitter Analysis. 4.1 More Ways to Visualize Jitter. 4.1.1 Bit Error Rates. 4.1.2 Bathtub Curves. 4.1.3 Eye Diagrams and How to Read Them. 4.2 Jitter Extraction and Separation. 4.2.1 Why Analyze Jitter? 4.2.2 Composite Jitter Distributions. 4.2.3 Combining Random and Deterministic Jitter. 4.2.4 Spotting Deterministic Components. 4.2.5 A Word on Test Pattern Generation. 4.2.6 Random Jitter Extraction. 4.2.7 Periodic Jitter Extraction. 4.2.8 Duty Cycle Distortion Extraction. 4.2.9 Data Dependent Jitter Extraction. 4.2.10 Extraction of Duty Cycle Effects. 4.2.11 Uncorrelated Deterministic Jitter. 4.2.12 Commercial Jitter Analysis Software. 4.3 Jitter Performance Prediction (Extrapolation). 4.3.1 Extrapolation of Random Jitter. 4.3.2 Extrapolation of Deterministic Jitter. 4.3.3 Analytical Prediction of Worst-Case Pattern Dependent Errors.
Chapter 4: Measurement Accuracy.
1. Specialized Measurement Techniques. 1.1 Equivalent Time Sampling Scopes. 1.1.1 Phase References. 1.1.2 Eliminating Scope Time Base Jitter. 1.1.3 Time Interval Measurements. 1.1.3.1 Time Interval Errors. 1.1.3.2 How to Spot Time Interval Errors. 1.1.3.3 A Method for Sub-Picosecond Time Interval Accuracy. 1.2 Digital Testers and Bit Error Rate Testers. 1.2.1 Edge Searches and Waveform Scans. 1.2.2 Signal Rise Times. 1.2.3 Random and Data Dependent Jitter. 1.2.4 Probability Digitizing. 1.2.5 Spectral Error Density Analysis. 1.3 Spectrum Analyzers. 1.3.1 Periodic Jitter Measurements. 1.3.2 Random Jitter Measurements. 1.3.3 Maximum-Accuracy Phase Jitter Measurements.
2. Digital Signal Processing. 2.1 Averaging. 2.1.1 Noise Reduction. 2.1.2 Improving Timing and Amplitude Resolution. 2.2 Interpolation. 2.3 System De-Embedding
References
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