Frequency Acquisition Techniques for Phase Locked Loops

How to acquire the input frequency from an unlocked state

A phase locked loop (PLL) by itself cannot become useful until it has acquired the applied signal's frequency. Often, a PLL will never reach frequency acquisition (capture) without explicit assistive circuits. Curiously, few books on PLLs treat the topic of frequency acquisition in any depth or detail. Frequency Acquisition Techniques for Phase Locked Loops offers a no-nonsense treatment that is equally useful for engineers, technicians, and managers.

Since mathematical rigor for its own sake can degenerate into intellectual "rigor mortis," the author introduces readers to the basics and delivers useful information with clear language and minimal mathematics. With most of the approaches having been developed through years of experience, this completely practical guide explores methods for achieving the locked state in a variety of conditions as it examines:

• Performance limitations of phase/frequency detector?based phase locked loops
• The quadricorrelator method for both continuous and sampled modes
• Sawtooth ramp-and-sample phase detector and how its waveform contains frequency error information that can be extracted
• The benefits of a self-sweeping, self-extinguishing topology
• Sweep methods using quadrature mixer-based lock detection
• The use of digital implementations versus analog

Frequency Acquisition Techniques for Phase Locked Loops is an important resource for RF/microwave engineers, in particular, circuit designers; practicing electronics engineers involved in frequency synthesis, phase locked loops, carrier or clock recovery loops, radio-frequency integrated circuit design, and aerospace electronics; and managers wanting to understand the technology of phase locked loops and frequency acquisition assistance techniques or jitter attenuating loops.
Errata can be found by visiting the Book Support Site at: http://booksupport.wiley.com

1 Introduction 1

2 A Review of PLL Fundamentals 3

2.1 What is a PLL?, 3

2.2 Second-Order PLL, 7

2.3 Second-Order PLL Type One, 7

2.4 Second-Order PLL Type Two, 7

2.5 Higher-Order PLL’s, 8

2.6 Disturbances, 8

2.7 Frequency Steering and Capture, 9

2.8 Effect of DC Offsets or Noise Prior to the Loop Filter, 10

2.9 Injection-Locked Oscillations, 15

3 Simulating the PLL Linear Operation Mode 17

3.1 Linear Model, 17

3.2 A Word About Damping, 19

4 Sideband Suppression Filtering 21

4.1 Reference Sidebands and VCO Pushing, 21

4.2 Superiority of the Cauer (or Elliptical) Filter, 22

5 Pros and Cons of Sampled Data Phase Detection 25

5.1 What are the Forms of Sampled Data Phase Detectors?, 25

5.2 A. Ramp and Sample Analog Phase Detector, 25

5.3 B. The RF Sampling Phase Detector, 28

5.4 C. Edge-Triggered S-R Flip-Flop, 29

5.5 D. Edge-Triggered Flip-Flop Ensemble, 31

5.6 E. Sample and Hold as a Phase Detector, 31

6 Phase Compression 33

7 Hard Limiting of a Signal Plus Noise 35

8 Phase Noise and Other Spurious Interferers 39

8.1 The Mechanism for Phase Noise in an Oscillator, 42

8.2 Additive Noise in an FM Channel and the Bowtie, 42

8.3 Importance of FM Theory to Frequency Acquisition, 45

9 Impulse Modulation and Noise Aliasing 47

9.1 Impulse Train Spectrum, 47

9.2 Sampling Phase Detector Noise, 47

9.3 Spur Aliasing, 50

10 Time and Phase Jitter, Heterodyning, and Multiplication 53

10.1 Heterodyning and Resulting Time Jitter, 53

10.2 Frequency Multiplication and Angle Modulation Index, 54

10.3 Frequency Multiplication’s Role in Carrier Recovery, 54

11 Carrier Recovery Applications and Acquisition 57

11.1 Frequency Multiplier Carrier Recovery in General, 57

11.2 The Simplest Form of Costas PLL, 59

11.3 Higher Level Quadrature Demodulation Costas PLL, 61

11.4 False Lock in BPSK Costas PLL, 62

11.5 Additional Measures for Prevention of False Locking, 65

11.6 False Lock Prevention Using DC Offset, 72

12 Notes on Sweep Methods 73

12.1 Sweep Waveform Superimposed Directly on VCO Input, 73

12.2 Maximum Sweep Rate (Acceleration), 74

12.3 False Lock due to High-Order Filtering, 77

12.4 Sweep Waveform Applied Directly to PLL Loop Integrator, 79

12.5 Self-Sweeping PLL, 79

13 Nonsweep Acquisition Methods 85

13.1 Delay Line Frequency Discriminator, 85

13.2 The Fully Unbalanced Quadricorrelator, 87

13.3 The Fully Balanced Quadricorrelator, 88

13.4 The Multipulse Balanced Quadricorrelator, 89

13.5 Conclusion Regarding Pulsed Frequency Detection, 91

13.6 Quadricorrelator Linearity, 92

13.7 Limiter Asymmetry due to DC Offset, 97

13.8 Taylor Series Demonstrates Second-Order-Caused DC Offset, 100

13.9 Third-Order Intermodulation Distortion and Taylor Series, 101

14 AM Rejection in Frequency Detection Schemes 105

14.1 AM Rejection with Limiter and Interferer, 105

14.2 AM Rejection of the Balanced Limiter/Quadricorrelator Versus the Limiter/Discriminator in the Presence of a Single Spur, 106

14.3 Impairment due to Filter Response Tilt (Asymmetry), 110

14.4 Bandpass Filter Geometric and Arithmetic Symmetry, 114

14.5 Comments on Degree of Scrutiny, 117

15 Interfacing the Frequency Discriminator to the PLL 119

15.1 Continuous Connection: Pros and Cons, 119

15.2 Connection to PLL via a Dead Band, 120

15.3 Switched Connection, 121

16 Actual Frequency Discriminator Implementations 125

16.1 Quadricorrelator, Low-Frequency Implementation, 125

16.2 Frequency Ratio Calculating Circuit for Wide-Bandwidth Use, 128

16.3 Dividing the Frequency and Resultant Implementation, 131

16.4 Marriage of Both Frequency and Phaselock Loops, 135

16.5 Comments on Spurs’ Numerical Influence on the VCO, 141

16.6 Frequency Compression, 143

17 Clock Recovery Using a PLL 145

17.1 PLL Only, 145

17.2 PLL with Sideband Crystal Filter(s), 152

17.3 PLL with Sideband Cavity Filter, 153

17.4 The Hogge Phase Detector, 161

17.5 Bang–Bang Phase Detectors, 162

18 Frequency Synthesis Applications 165

18.1 Direct Frequency Synthesis with Wadley Loop, 166

18.2 Indirect Frequency Synthesis with PLLs, 173

18.3 Simple Frequency Acquisition Improvement for a PLL, 175

18.4 Hybrid Frequency Synthesis with DDS and PLL, 176

18.5 Phase Noise Considerations, 181

18.6 Pros and Cons of DDS-Augmented Synthesis, 185

18.7 Multiple Loops, 185

18.8 Reference Signal Considerations and Filtering, 186

18.9 SNR of Various Phase Detectors, 187

18.10 Phase Detector Dead Band (Dead Zone) and Remediation, 187

18.11 Sideband Energy due to DC Offset Following Phase Detector, 191

18.12 Brute Force PLL Frequency Acquisition via Speedup, 193

18.13 Short-Term and Long-Term Settling, 193

18.14 N-over-M Synthesis, 193

19 Injection Pulling of Multiple VCO’s as in a Serdes 195

19.1 Allowable Coupling Between any Two VCOs Versus Q and BW, 195

19.2 Topology Suggestion for Eliminating the Injection Pulling, 195

20 Digital PLL Example 199

21 Conclusion 203

References 205

Index 209

DANIEL B. TALBOT currently runs a product development business specializing in RF/analog engineering. He has years of industry experience as a chief technical engineer at DBX Corporation, LTX Corporation, and a principal or research engineer or equivalent at Raytheon, RCA David Sarnoff Labs, General Instrument, and several other aerospace and commercial electronics firms; has been granted eight U.S. patents in the field of RF/analog/fiber optic engineering; and is an elected Fellow of the Audio Engineering Society and a Life Member of the IEEE.