Preface ........................................................ xi
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
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