Microwave and Wireless Synthesizers

Dr.Ing.habil Ulrich L. Rohde, is a Professor of Technical Informatics, University of the Joint Armed Forces, Munich Germany; member of the staff of other Universities world-wide; partner of Rohde & Schwarz, Munich; and Chairman of the Board of Synergy Microwave Corporation. Formerly Professor of Electrical Engineering at George Washington University and the University of Florida, Dr. Rohde has consulted on numerous communication projects in industry and government, has more than 300 publications, and written many textbooks including this one. He is the author of the first edition of Microwave and Wireless Synthesizers: Theory and Design. Enrico Rubiola, PhD, is Professor at the Université de Franche Comté (The University of Franche-Comté), Researcher at the Department of Time and Frequency of the CNRS FEMTO-ST Institute, France, and Associated Researcher at INRiM, Italy’s National Metrology Institute (NMI). He is Founder the Oscillator IMP project, a platform for the measurement of short-term frequency stability and AM/PM noise of oscillators and related components. Jerry Whitaker is Vice President for Standards Development of the Advanced Television Systems Committee. He also serves as Secretary of the Technology Group on Next Generation Broadcast Television, and is closely involved in work relating to educational programs. He is a Fellow and previous Vice President of the Society of Broadcast Engineers, and a Life Fellow of the Society of Motion Picture and Television Engineers.

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

F-2-2 Phase Noise Measurements 708

F-2-3 Thermal Sensitivity Analysis of Standard Fibers 709

F-2-4 Temperature Sensitivity Measurements 710

F-2-5 Temperature Sensitivity Improvement with HC-PCF 712

F-2-6 Improve Thermal Stability Versus Phase Noise Degradation 712

F-2-7 Passive Temperature Compensation 713

F-2-8 Improving Effective Q with Raman Amplification 714

F-3 Forced Oscillation Techniques of OEO 718

F-3-1 Analysis of Standard Injection-Locked (IL) Oscillators 718

F-3-2 Analysis of Self-Injection Locked (SIL) Oscillators 720

F-3-3 Experimental Verification of Self-Injection Locked (SIL) Oscillators 721

F-3-4 Analysis of Standard Phase Locked Loop (PLL) Oscillators 723

F-3-5 Analysis of Self Phase Locked Loop (SPLL) Oscillators 725

F-3-6 Experimental Verification of Self-Phase Locked Loop (SPLL) Oscillators 726

F-3-7 Analysis of Self-Injection Locked Phase Locked Loop (SILPLL) Oscillators 728

F-4 SILPLL Based X- and K-Band Frequency Synthesizers 731

F-4-1 X-Band Frequency Synthesizer 732

F-4-2 19′′Rack-Mountable K-Band Frequency Synthesizer 737

F-5 Integrated OEO Realization Using Si-Photonics 742

F-6 Compact OEO Using InP Multi-Mode Semiconductor Laser 744

F-6-1 Structure of Multi-mode InP Laser 744

F-6-2 Multi-mode Laser and Inter-Modal RF Oscillation 745

F-6-3 Self-Forced Frequency Stabilizations 747

F-7 Discussions 752

Acknowledgments 753

References 754

G Phase Noise Analysis, then and Today 761

G-1 Introduction 761

G-2 Large-Signal Noise Analysis 762

References 769

H A Novel Approach to Frequency and Phase Settling Time Measurements on PLL Circuits 771

H-1 Introduction 771

H-2 Settling Time Measurement Overview 771

H-2-1 Theoretical Background of Frequency Settling Time 771

H-2-2 Frequency Settling Measurement in the Past 772

H-3 R&S FSWP Phase Noise Analyzer 774

H-3-1 Phase Noise Analyzer Architecture 774

H-3-2 Typical Test Setup for Settling Time Measurements 776

H-4 Frequency Hopping and Settling Time Measurements in Practice 776

H-4-1 Trigger on Wideband Frequency Hopping Signals 776

H-4-2 Frequency and Phase Settling Time Measurement 777

H-5 Conclusion 780

Index 783