Theory of the Non-linear Analog Phase Locked Loop

01......Page 1
02......Page 14
1.1 PLL structure......Page 15
1.2 PLLs classification......Page 16
1.3 The weak points of the conventional PLL theory......Page 17
1.4 Scope and methodology......Page 18
2.2 Voltage controlled oscillator......Page 23
2.2-1 VCO representation......Page 24
2.2-2 Transformation of the VCO equation......Page 26
2.2-3 Averaged VCO equations......Page 29
2.3 Phase detector......Page 31
2.4-1 Phase lead-lag filter......Page 33
2.4-2 PI controller......Page 35
3.1 Representation of the first order PLL. General form......Page 40
3.2-1 Main synchronization......Page 43
3.3 Representation of the first order PLL. Specific form......Page 45
3.4 Preliminary investigation......Page 47
3.5 Conclusions......Page 50
4.1-1 Equilibrium points......Page 52
4.1-2 Effect of parameters on equilibrium points......Page 54
4.1-4 Local stability conditions......Page 58
4.2 Hold  in range......Page 60
4.3 Tracking range......Page 64
4.4-1 Transformation of the averaged equations......Page 70
4.4-2 Capture phenomenon......Page 71
4.4-3 Detuning......Page 79
4.5 Conclusions......Page 81
5.1 Local stability......Page 82
5.1-1 Equilibrium points......Page 83
5.1-2 Effect of parameters on equilibrium points......Page 84
5.1-3 Local stability conditions......Page 85
5.2 Hold in range......Page 87
5.3 Tracking range......Page 88
5.4-2 Capture phenomenon......Page 90
5.4-3 Detuning......Page 91
5.5 Conclusions......Page 92
07......Page 93
6.1 Representation of the second order type – I PLL......Page 94
6.1-1 Exact equations......Page 95
6.1-2 Averaged equations......Page 96
6.2 Preliminary investigation......Page 99
7.1 Local stability......Page 104
7.1-2 Local stability conditions......Page 105
7.1-3 Hold-in range......Page 107
7.2 Global stability......Page 108
7.3 Conclusions......Page 114
8.1-1 Equilibrium points......Page 115
8.1-2 Local stability conditions......Page 118
8.2-1 Effect of parameters on hold–in range......Page 120
8.3-1 Slow capture......Page 125
8.3-2 Mean capture range......Page 129
8.3-3 Effect of parameters on mean capture range......Page 135
8.3-5 Comment......Page 138
8.4 Dynamic behaviour......Page 139
8.4-1 Qualitative analysis......Page 140
8.4-2 Effect of parameters on loop dynamics......Page 144
8.4-3 Quantitative analysis. Fast capture......Page 147
8.5 Tracking range......Page 150
8.5-1 Local tracking limits......Page 151
8.5-2 Global tracking limits......Page 152
8.6 Hold-in and capture ranges......Page 154
8.7 Effect of noise and disturbances......Page 156
8.8 Design criteria......Page 158
8.9 Conclusion......Page 161
9.1-1 Exact equations......Page 163
9.1-2 Averaged equations......Page 166
9.2 Preliminary investigation......Page 168
9.3 Conclusions......Page 172
10.1 Local stability of the unsaturated loop......Page 173
10.1-1 Equilibrium points......Page 174
10.1-2 Local stability conditions......Page 175
10.1-3 Hold-in range......Page 177
10.1- 4 Effect of the loop parameters on hold-in range......Page 178
10.2-1 Qualitative analysis......Page 186
10.2-2 Quantative analysis......Page 189
10.3 Tracking range......Page 192
10.4 Conclusions......Page 198
11.1 Global stability......Page 199
11.2 Conclusions......Page 202
12.1 About the filters used in the third order loops......Page 203
12.2-1 Exact equations......Page 205
12.2-2 Averaged equations......Page 207
13.1 Local stability of the unsaturated loop......Page 210
13.1-1 Equilibrium points......Page 211
13.1-2 Local stability conditions......Page 213
13.2 Hold-in range......Page 215
13.2-1 Effect of loop parameters on hold-in range......Page 216
13.3 Tracking range......Page 221
13.4 Dynamic behaviour......Page 223
13.5 Conclusions......Page 226
14.1-1 Global stability......Page 227
I. First order PLL. Averaged equations......Page 232
II. First order PLL. Equilibrium points of the main synchronization range......Page 236
III. Second order type-I PLL. Averaged equations......Page 239
IV. Second order type-I PLL. State equation of the low-pass filter for the capture range calculation......Page 244
V. Second order typeI PLL. Effect of initial condition on capture range......Page 246
VI. Second order type-II PLL. Averaged equations......Page 248
VII. Third order type-II PLL. Averaged equations......Page 253
VIII. Resonant voltage controlled oscillator......Page 259
IX.. Vector phase detector......Page 262
X.  Experimental verification......Page 264
17......Page 271