Author Biography xii Preface xvi Important Notations xx 1 Loop Fundamentals 1 1-1 Introduction to Linear Loops 1 1-2 Characteristics of a Loop 3 1-3 Digital Loops 7 1-4 Type 1 First-Order Loop 10 1-5 Type 1 Second-Order Loop 12 1-6 Type 2 Second-Order Loop 20 1-6-1 Transient Behavior of Digital Loops Using Tri-state Phase Detectors 22 1-7 Type 2 Third-Order Loop 27 1-7-1 Transfer Function of Type 2 Third-Order Loop 28 1-7-2 FM Noise Suppression 35 1-8 Higher-Order Loops 36 1-8-1 Fifth-Order Loop Transient Response 36 1-9 Digital Loops with Mixers 40 1-10 Acquisition 44 Example 1 48 1-10-1 Pull-in Performance of the Digital Loop 49 1-10-2 Coarse Steering of the VCO as an Acquisition Aid 52 1-10-3 Loop Stability 54 References 62 Suggested Reading 62 2 Almost all About Phase Noise 65 2-1 Introduction to Phase Noise 65 2-1-1 The Clock Signal 65 2-1-2 The Power Spectral Density (PSD) 68 2-1-3 Basics of Noise 71 2-1-4 Phase and Frequency Noise 78 2-2 The Allan Variance and Other Two-Sample Variances 88 2-2-1 Frequency Counters 89 2-2-2 The Two-Sample Variances AVAR, MVAR, and PVAR 94 2-2-3 Conversion from Spectra to Two-Sample Variances 96 2-3 Phase Noise in Components 100 2-3-1 Amplifiers 100 2-3-2 Frequency Dividers 104 2-3-3 Frequency Multipliers 112 2-3-4 Direct Digital Synthesizer (DDS) 117 2-3-5 Phase Detectors 128 2-3-6 Noise Contribution from Power Supplies 132 2-4 Phase Noise in Oscillators 133 2-4-1 Modern View of the Leeson Model 134 2-4-2 Circumventing the Resonator''s Thermal Noise 144 2-4-3 Oscillator Hacking 146 2-5 The Measurement of Phase Noise 153 2-5-1 Double-Balanced Mixer Instruments 154 2-5-2 The Cross-Spectrum Method 166 2-5-3 Digital Instruments 171 2-5-4 Pitfalls and Limitations of the Cross-Spectrum Measurements 180 2-5-5 The Bridge (Interferometric) Method 187 2-5-6 Artifacts and Oddities Often Found in the Real World 190 References 193 Suggested Readings 197 3 Special Loops 201 3-1 Introduction 201 3-2 Direct Digital Synthesis Techniques 201 3-2-1 A First Look at Fractional N 202 3-2-2 Digital Waveform Synthesizers 203 3-2-3 Signal Quality 220 3-2-4 Future Prospects 235 3-3 Loops with Delay Line as Phase Comparators 236 3-4 Fractional Division N Synthesizers 237 3-4-1 Example Implementation 240 3-4-2 Some Special Past Patents for Fractional Division N Synthesizers 253 References 255 Bibliography 256 Fractional Division N Readings 256 4 Loop Components 259 4-1 Introduction to Oscillators and Their Mathematical Treatment 259 4-2 The Colpitts Oscillator 259 4-2-1 Linear Approach 260 4-2-2 Design Example for a 350MHz Fixed-Frequency Colpitts Oscillator 269 4-2-3 Validation Circuits 282 4-2-4 Series Feedback Oscillator 314 4-2-5 2400 MHz MOSFET-Based Push-Pull Oscillator 319 4-2-6 Oscillators for IC Applications 336 4-2-7 Noise in Semiconductors and Circuits 337 4-2-8 Summary 339 4-3 Use of Tuning Diodes 339 4-3-1 Diode Tuned Resonant Circuits 340 4-3-2 Practical Circuits 344 4-4 Use of Diode Switches 345 4-4-1 Diode Switches for Electronic Band Selection 346 4-4-2 Use of Diodes for Frequency Multiplication 347 4-5 Reference Frequency Standards 351 4-5-1 Specifying Oscillators 351 4-5-2 Typical Examples of Crystal Oscillator Specifications 352 4-6 Mixer Applications 354 4-7 Phase/Frequency Comparators 357 4-7-1 Diode Rings 357 4-7-2 Exclusive ORs 358 4-7-3 Sample/Hold Detectors 362 4-7-4 Edge-Triggered JK Master/Slave Flip-Flops 368 4-7-5 Digital Tri-State Comparators 369 4-8 Wideband High-Gain Amplifiers 378 4-8-1 Summation Amplifiers 378 4-8-2 Differential Limiters 382 4-8-3 Isolation Amplifiers 382 4-8-4 Example Implementations 387 4-9 Programmable Dividers 393 4-9-1 Asynchronous Counters 393 4-9-2 Programmable Synchronous Up-/Down-Counters 394 4-9-3 Advanced Implementation Example 405 4-9-4 Swallow Counters/Dual-Modulus Counters 407 4-9-5 Look-Ahead and Delay Compensation 411 4-10 Loop Filters 421 4-10-1 Passive RC Filters 421 4-10-2 Active RC Filters 422 4-10-3 Active Second-Order Low-Pass Filters 423 4-10-4 Passive LC Filters 426 4-10-5 Spur-Suppression Techniques 427 4-11 Microwave Oscillator Design 430 4-11-1 The Compressed Smith Chart 432 4-11-2 Series or Parallel Resonance 434 4-11-3 Two-Port Oscillator Design 435 4-12 Microwave Resonators 444 4-12-1 SAW Oscillators 445 4-12-2 Dielectric Resonators 445 4-12-3 YIG Oscillators 448 4-12-4 Varactor Resonators 452 4-12-5 Ceramic Resonators 455 References 461 Suggested Readings 464 5 Digital PLL Synthesizers 471 5-1 Multiloop Synthesizers Using Different Techniques 471 5-1-1 Direct Frequency Synthesis 471 5-1-2 Multiple Loops 473 5-2 System Analysis 477 5-3 Low-Noise Microwave Synthesizers 484 5-3-1 Building Blocks 485 5-3-2 Output Loop Response 489 5-3-3 Low Phase Noise References: Frequency Standards 490 5-3-4 Critical Stage 493 5-3-5 Time Domain Analysis 503 5-3-6 Summary 508 5-3-7 Two Commercial Synthesizer Examples 512 5-4 Microprocessor Applications in Synthesizers 518 5-5 Transceiver Applications 523 5-6 About Bits, Symbols, and Waveforms 526 5-6-1 Representation of a Modulated RF Carrier 527 5-6-2 Generation of the Modulated Carrier 529 5-6-3 Putting It all Together 533 5-6-4 Combination of Techniques 535 Acknowledgments 537 References 540 Bibliography and Suggested Reading 540 6 A High-Performance Hybrid Synthesizer 543 6-1 Introduction 543 6-2 Basic Synthesizer Approach 544 6-3 Loop Filter Design 548 6-4 Summary 556 Bibliography 557 A Mathematical Review 559 A-1 Functions of a Complex Variable 559 A-2 Complex Planes 561 A-2-1 Functions in the Complex Frequency Plane 565 A-3 Bode Diagram 568 A-4 Laplace Transform 582 A-4-1 The Step Function 583 A-4-2 The Ramp 584 A-4-3 Linearity Theorem 584 A-4-4 Differentiation and Integration 585 A-4-5 Initial Value Theorem 585 A-4-6 Final Value Theorem 585 A-4-7 The Active Integrator 585 A-4-8 Locking Behavior of the PLL 587 A-5 Low-Noise Oscillator Design 590 A-5-1 Example Implementation 590 A-6 Oscillator Amplitude Stabilization 594 A-7 Very Low Phase Noise VCO for 800 MHZ 602 References 605 B A General-Purpose Nonlinear Approach to the Computation of Sideband Phase Noise in Free-Running Microwave and RF Oscillators 607 B-1 Introduction 607 B-2 Noise Generation in Oscillators 608 B-3 Bias-Dependent Noise Model 609 B-3-1 Bias-Dependent Model 617 B-3-2 Derivation of the Model 617 B-4 General Concept of Noisy Circuits 619 B-4-1 Noise from Linear Elements 620 B-5 Noise Figure of Mixer Circuits 622 B-6 Oscillator Noise Analysis 624 B-7 Limitations of the Frequency-Conversion Approach 625 B-7-1 Assumptions 626 B-7-2 Conversion and Modulation Noise 626 B-7-3 Properties of Modulation Noise 626 B-7-4 Noise Analysis of Autonomous Circuits 627 B-7-5 Conversion Noise Analysis Results 627 B-7-6 Modulation Noise Analysis Results 627 B-8 Summary of the Phase Noise Spectrum of the Oscillator 628 B-9 Verification Examples for the Calculation of Phase Noise in Oscillators Using Nonlinear Techniques 628 B-9-1 Example 1: High- Q Case Microstrip DRO 628 B-9-2 Example 2: 10 MHz Crystal Oscillator 629 B-9-3 Example 3: The 1-GHz Ceramic Resonator VCO 630 B-9-4 Example 4: Low Phase Noise FET Oscillator 632 B-9-5 Example 5: Millimeter-Wave Applications 636 B-9-6 Example 6: Discriminator Stabilized DRO 639 B-10 Summary 641 References 643 C Example of Wireless Synthesizers Using Commercial ICs 645 D MMIC-Based Synthesizers 665 D-1 Introduction 665 Bibliography 668 E Articles on Design of Dielectric Resonator Oscillator 671 E-1 The Design of an Ultra-Low Phase Noise DRO 671 E-1-1 Basic Considerations and Component Selection 671 E-1-2 Component Selection 672 E-1-3 DRO Topologies 675 E-1-4 Small Signal Design Approach for the Parallel Feedback Type DRO 677 E-1-5 Simulated Versus Measured Results 683 E-1-6 Physical Embodiment 685 E-1-7 Acknowledgments 685 E-1-8 Final Remarks 688 References 692 Bibliography 692 E-2 A Novel Oscillator Design with Metamaterial-MöBius Coupling to a Dielectric Resonator 692 E-2-1 Abstract 692 E-2-2 Introduction 693 References 699 F Opto-Electronically Stabilized RF Oscillators 701 F-1 Introduction 701 F-1-1 Oscillator Basics 701 F-1-2 Resonator Technologies 701 F-1-3 Motivation for OEO 704 F-1-4 Operation Principle of the OEO 704 F-2 Experimental Evaluation and Thermal Stability of OEO 705 F-2-1 Experimental Setup 705 <.