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Discrete Oscillator Design

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Discrete Oscillator Design Discrete Oscillator Design Linear, Nonlinear, Transient, and Noise Domains Randall W. Rhea ARTECH HOUSE BOSTON|LONDON artechhouse.com Contents Preface xv 1 Linear Techniques 1 1.1 Open-Loop Method 1 1.2 Starting Conditions 2 1.2.1 Match Requirements 3 1.2.2 Aligning the Maximum Phase Slope 10 1.2.3 Stable Amplifier 11 1.2.4 Gain Peak at Phase Zero Intersection 11 1.2.5 Moderate Gain 11 1.3 Random Resonator and Amplifier Combination 12 1.4 Naming Conventions 13 1.5 Amplifiers for Sustaining Stages 15 1.5.1 Bipolar Amplifier Configurations 15 1.5.2 Stabilizing Bipolar Amplifiers 19 1.5.3 Stabilized FET Amplifier Configurations 21 1.5.4 Basic Common Emitter Amplifier 23 1.5.5 Statistical Analysis of the Amplifier 25 1.5.6 Amplifier with Resistive Feedback 26 1.5.7 General-Purpose Resistive-Feedback Amplifier 29 1.5.8 Transformer-Feedback Amplifiers 33 1.5.9 Monolythic Microwave Integrated Circuit Amplifiers 34 1.5.10 Differential Amplifiers 35 1.5.11 Phase-Lead Compensation 37 1.5.12 Amplifier Summary 39 1.6 Resonators 40 1.6.1 R-C Phase Shift Network 40 1.6.2 Delay-Line Phase-Shift Network 41 1.6.3 L-C Parallel and Series Resonators 43 1.6.4 Loaded Q 45 1.6.5 Unloaded Q 46 1.6.6 Resonator Loss 47 1.6.7 Colpitts Resonator 49 1.6.8 Resonator Coupling 51 1.6.9 Matching with the Resonator 52 1.6.10 Measuring the Unloaded Q 55 1.6.11 Coupled Resonator Oscillator Example 56 vii viii Discrete Oscillator Design 1.6.12 Resonator Summary 56 1.7 One-Port Method 57 1.7.1 Negative-Resistance Oscillators 58 1.7.2 Negative-Conductance Oscillators 69 1.8 Analyzing Existing Oscillators 74 1.9 Optimizing the Design 76 1.10 Statistical Analysis 78 1.11 Summary 80 References 81 2 Nonlinear Techniques 83 2.1 Introduction 83 2.2 Harmonic Balance Overview 83 2.3 Nonlinear Amplifiers 84 2.3.1 Quiescent Current and Compression 86 2.3.2 Impedance Shift 87 2.3.3 Phase Shift 88 2.3.4 Output Spectrum 89 2.3.5 Time Domain Waveform 91 2.3.6 Conversion Efficiency 92 2.3.7 Operating Class 93 2.3.8 Power Amplifier Case Study 99 2.4 Nonlinear Open-Loop Cascade 109 2.4.1 Nonlinear Open-Loop Cascade Example 1 109 2.4.2 Nonlinear Open-Loop Cascade Example 2 111 2.5 Nonlinear HB Colpitts Example 112 2.5.1 Closing the Loop and Excitation 112 2.5.2 Harmonic Balance Colpitts Output Spectrum 114 2.5.3 Excitation Current Versus Oscillator Parameters 115 2.6 Nonlinear Negative-Resistance Oscillator 116 2.7 Output Coupling 120 2.7.1 Coupling Node 120 2.7.2 Load Pulling 121 2.7.3 Loaded Q and Load Pulling 122 2.7.4 Degree of Coupling 123 2.7.5 Loaded Q and Coupling 124 2.7.6 Coupling Reactance and Load Pulling 125 2.7.7 Coupling Reactance and Harmonics 125 2.7.8 Output Coupling Example 2 126 2.7.9 Coupling Summary 128 2.8 Passive Level Control 128 2.9 Supply Pushing 132 2.10 Spurious Modes 134 2.10.1 Unstable Amplifiers 134 2.10.2 Multiple Phase Zero Crossings 135 Contents IX 2.10.3 Bias Relaxation Modes 135 2.10.4 Parametric Modes 136 2.10.5 Multiple Resonance Modes 137 2.10.6 Spurious Mode Summary 138 2.11 Ultimate Test 139 References 140 3 Transient Techniques 143 3.1 Introduction 143 3.2 Starting Modes 144 3.2.1 Noise Mode of Starting 146 3.2.2 Transient Mode of Starting 147 3.2.3 Time Constant of the Supply Step 148 3.3 Starting Basic Example 149 3.4 Simulation Techniques 151 3.4.1 SPICE 152 3.4.2 Cayenne 152 3.5 Second Starting Example 155 3.6 Starting Case Study 157 3.7 Triggering 160 3.8 Simulation Techniques for High Loaded Q 162 3.9 Steady-State Oscillator Waveforms 164 3.9.1 Clapp Oscillator Waveforms 164 3.9.2 The Resonator Voltage 166 3.9.3 Varactor Coupling 168 3.10 Waveform Derived Output Spectrum 169 References 171 4 Noise 173 4.1 Definitions 173 4.1.1 Vector Representation of the Oscillator Output 174 4.1.2 Jitter 174 4.1.3 The Output in the Frequency Domain 174 4.1.4 SSB Phase Noise 176 4.1.5 Residual FM and Residual PM 177 4.1.6 Two-Port Noise 178 4.1.7 Acoustic Disturbances 179 4.2 Predicting Phase Noise 179 4.2.1 Linear Time Invariant Theory 180 4.2.2 Extensions to LTI-Based Theory 181 4.2.3 Linear Time Variant Theory 184 4.3 Measuring Phase Noise 186 4.3.1 Direct Method with a Spectrum Analyzer 186 4.3.2 Selective Receiver Method 188 4.3.3 Heterodyne/Counter Method 189 4.3.4 Reference Oscillator Method 190 x Discrete Oscillator Design 4.3.5 Frequency Discriminator Method 192 4.3.6 Example Phase-Noise Measurement System 194 4.4 Designing for Low Phase Noise 196 4.4.1 Estimating the Predominant Noise Source 197 4.4.2 Reducing Leeson Noise 197 4.4.3 Reducing Pushing Induced Noise 201 4.4.4 Reducing Buffer Noise 202 4.4.5 Reducing Varactor Modulation Noise 203 4.4.6 Reducing Oscillator Noise Summary 204 4.5 Nonlinear Noise Simulation 205 4.5.1 Negative Resistance Oscillator Noise Example 206 4.5.2 Linear Oscillator Phase Noise Example 210 4.6 PLL Noise 213 References 216 5 General-Purpose Oscillators 219 5.1 Comments on the Examples 219 5.2 Oscillators Without Resonators 220 5.2.1 R-C Oscillators 220 5.2.2 Wien Bridge 226 5.2.3 Multivibrators 227 5.2.4 Ring Oscillators 230 5.2.5 Twin-T Oscillators 232 5.3 L-C Oscillators 235 5.3.1 Colpitts 236 5.3.2 Clapp 242 5.3.3 Seiler 243 5.3.4 Hartley 243 5.3.5 Pierce 249 5.3.6 Coupled Series Resonator 251 5.3.7 Rhea 253 5.3.8 Coupled Parallel Resonator 254 5.3.9 Gumm 256 5.3.10 Simplified Gumm 257 5.4 Oscillator Topology Selection 258 References 261 6 Distributed Oscillators 263 6.1 Resonator Technologies 263 6.2 Lumped and Distributed Equivalents 264 6.3 Quarter-Wavelength Resonators 268 6.3.1 The Quarter-Wavelength Resonator 268 6.3.2 Ceramic-Loaded Coaxial Resonators 268 6.3.3 Capacitor-Loaded Quarter-Wavelength Resonator 271 6.4 Distributed Oscillator Examples 273 6.4.1 Negative-Resistance Hybrid Oscillator 273 Contents 6.4.2 Negative-Resistance High-Power 1 GHz Oscillator 274 6.4.3 Quarter-Wavelength Hybrid Oscillator 276 6.4.4 Simple Hybrid Coaxial Resonator MMIC 277 6.4.5 Probe-Coupled Coaxial Resonator Bipolar 279 6.4.6 End-Coupled Hybrid Half-Wavelength Bipolar 281 6.4.7 Helical Transmission Line Resonator Bipolar 282 6.5 DRO Oscillators 284 6.5.1 Dielectric Resonator Basic Properties 284 6.5.2 Dielectric Resonator Resonant Frequency 286 6.5.3 Dielectric Resonator Unloaded Q 286 6.5.4 Dielectric Resonator Coupling 287 6.5.5 DRO Examples 289 6.5.6 Coupling Test by Modulation 293 References 294 7 Tuned Oscillators 295 7.1 Resonator Tuning Bandwidth 295 7.2 Resonator Voltage 297 7.3 Permeability Tuning 298 7.4 Tunable Oscillator Examples 299 7.4.1 Permeability Tuned Colpitts JFET 299 7.4.2 Vackar JFET VCO 300 7.4.3 Hybrid Negative Resistance VCO 301 7.4.4 Capacitor-Transformed Negative-Resistance VCO 304 7.4.5 Negative-Resistance VCO with Transformer 304 7.4.6 Negative-Conductance VCO 305 7.4.7 Hybrid Coaxial Resonator MMIC 308 7.4.8 Loaded Quarter-Wavelength MMIC 312 7.4.9 Seiler Coaxial-Resonator CC VCO 314 7.5 YIG Oscillators 316 References 319 8 Piezoelectric Oscillators 321 8.1 Bulk Quartz Resonators 321 8.1.1 Quartz Blank Cuts 322 8.1.2 Crystal Resonator Model 324 8.1.3 Calculating Crystal Resonator Parameters 325 8.1.4 Crystal Resonator Frequency Pulling 326 8.1.5 Inverted-Mesa Crystal Resonators 328 8.1.6 Crystal Oscillator Operating Mode 329 8.1.7 Crystal Oscillator Frequency Accuracy 332 8.1.8 Temperature Effects on Crystal Oscillators 334 8.1.9 Crystal Resonator Drive Level 334 8.1.10 Crystal Resonator Spurious Modes 337 8.1.11 Crystal Resonator Aging 338 8.1.12 Crystal Resonator 1/f Noise 338 XII Discrete Oscillator Design 8.1.13 Crystal Resonator Acceleration Effects 339 8.1.14 Crystal Resonator Standard Holders 341 8.2 Fundamental Mode Crystal Oscillators 341 8.2.1 Miller JFET Crystal 343 8.2.2 Colpitts Bipolar Crystal 344 8.2.3 Colpitts JFET Crystal 346 8.2.4 Pierce Bipolar Crystal 347 8.2.5 Pierce MMIC Crystal 350 8.2.6 Pierce Inverter TTL Crystal 350 8.2.7 Pierce Inverter CMOS Crystal 351 8.2.8 Butler Dual Bipolar Crystal 355 8.2.9 Driscoll Bipolar Crystal 357 8.2.10 Inverted-Mesa Pierce Bipolar Crystal 359 8.3 Overtone Mode Crystal Oscillators 361 8.3.1 Colpitts Overtone Bipolar Crystal 361 8.3.2 CB Butler Overtone Bipolar Crystal 364 8.3.3 CC Butler Overtone Bipolar Crystal 366 8.4 Crystal Oscillator Examples Summary 366 8.5 Oscillator with Frequency Multiplier 369 8.6 Crystal Oscillator Starting 371 8.7 Surface Acoustic Wave Resonators 371 8.7.1 SAW Resonator Models 372 8.7.2 SAW Resonator Frequency Stability 373 8.8 SAW Oscillators 374 8.8.1 SAW 1-Port Colpitts Bipolar 375 8.8.2 SAW 1-Port Butler Bipolar 377 8.8.3 SAW 2-Port Pierce MMIC 378 8.9 Piezoelectric Ceramic Resonators 380 8.9.1 Ceramic Resonator Models 380 8.9.2 Ceramic Resonator Accuracy and Stability 380 8.9.3 Ceramic Resonator Oscillators 381 8.10 MEMS and FBAR Resonators 386 References 387 Appendix A: Modeling 389 A.1 Capacitors 389 A.
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