Microwave and Wireless Synthesizers Theory and Design

The new edition of the leading resource on designing digital frequency synthesizers from microwave and wireless applications, fully updated to reflect the most modern integrated circuits and semiconductors

Microwave and Wireless Synthesizers: Theory and Design, Second Edition, remains the standard text on the subject by providing complete and up-to-date coverage of both practical and theoretical aspects of modern frequency synthesizers and their components. Featuring contributions from leading experts in the field, this classic volume describes loop fundamentals, noise and spurious responses, special loops, loop components, multiloop synthesizers, and more. Practical synthesizer examples illustrate the design of a high-performance hybrid synthesizer and performance measurement techniques—offering readers clear instruction on the various design steps and design rules.

The second edition includes extensively revised content throughout, including a modern approach to dealing with the noise and spurious response of loops and updated material on digital signal processing and architectures. Reflecting today's technology, new practical and validated examples cover a combination of analog and digital synthesizers and hybrid systems. Enhanced and expanded chapters discuss implementations of direct digital synthesis (DDS) architectures, the voltage-controlled oscillator (VCO), crystal and other high-Q based oscillators, arbitrary waveform generation, vector signal generation, and other current tools and techniques. Now requiring no additional literature to be useful, this comprehensive, one-stop resource:

• Provides a fully reviewed, updated, and enhanced presentation of microwave and wireless synthesizers
• Presents a clear mathematical method for designing oscillators for best noise performance at both RF and microwave frequencies
• Contains new illustrations, figures, diagrams, and examples
• Includes extensive appendices to aid in calculating phase noise in free-running oscillators, designing VHF and UHF oscillators with CAD software, using state-of-the-art synthesizer chips, and generating millimeter wave frequencies using the delay line principle

Containing numerous designs of proven circuits and more than 500 relevant citations from scientific journal and papers, Microwave and Wireless Synthesizers: Theory and Design, Second Edition, is a must-have reference for engineers working in the field of radio communication, and the perfect textbook for advanced electrical engineering students.

ULRICH L. ROHDE, PhD, is President of Compact Software, Inc., in Paterson, New Jersey, a partner of Rohde & Schwarz in Munich, Germany, and Chairman of the Board of Synergy Microwave Corporation in Paterson. Formerly a professor of electrical engineering at George Washington University and the University of Florida, Dr. Rohde, as president of Communication Consulting Corporation, has also consulted on a number of communication projects in industry and government. He is the author of the Wiley title Microwave and Wireless Synthesizers: Theory and Design (1998).

ENRICO RUBIOLA, PhD, is a professor at the Université de Franche Comté and a researcher with the Department of Time and Frequency of the CNRS FEMTO-ST Institute, Besançon, France, and an associated researcher at INRiM, the Italian institute of primary metrology in Torino. In 2012, Enrico founded 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 the Vice President for Standards Development of the Advanced Television Systems Committee. He also serves as Secretary Technology Group on Next Generation Broadcast Television, and is closely involved in work relating to educational programs. Mr. Whitaker is a Fellow the Society of Broadcast Engineers and a Life Fellow of the Society of Motion Picture and Television Engineers. He has served as a Board member and Vice President of the Society of Broadcast Engineers.

Author Bio

Preface

Important Notations

Chapter 1: Loop Fundamentals

1              Introduction to Linear Loops

2              Characteristics of a Loop

3              Digital Loops

4              Type 1 First-Order Loop

5              Type 1 Second-Order Loop

6              Type 2 Second-Order Loop

6.1          Transient Behavior of Digital Loops Using Tri-state Phase Detectors

6.1.1      Pull-in Characteristic

6.1.2      Active Filter of First Order

6.1.3      Passive Filter of First Order

6.1.4      Lock-In Characteristic

6.1.5      Active Filter

6.1.6      Passive Filter

7              Type 2 Third-Order Loop

7.1          Transfer Function of Type 2 Third-Order Loop

7.2          FM Noise Suppression

8              Higher-Order Loops

8.1          Fifth-Order Loop Transient Response

9              Digital Loops with Mixers

10           Acquisition

10.1        Example 1

10.2        Pull-in Performance of the Digital Loop

10.3        Coarse Steering of the VCO as an Acquisition Aid

10.4        Loop Stability

10.4.1    Example 2

10.4.2    Example 3

10.4.3    Example 4

10.4.4    Example 5

11           References

12           Bibliography and Suggested Reading

Chapter 2: Almost All About Phase Noise

1              Introduction to Phase Noise

1.1          The Clock Signal

1.2          The Power Spectral Density (PSD)

1.3          Basics of Noise

1.3.1      Thermal (Johnson) noise

1.3.2      Shot (Schottky) noise

1.3.3      Noise Factor, Noise Figure, and Noise Temperature

1.3.4      The Measurement of the Noise Temperature

1.3.5      Flicker Noise

1.3.6      Spurs and Other Unwanted Signals

1.4          Phase and Frequency Noise

1.4.1      The Quantities Sθ(f), S"x"(f), L(f) and Sα(f)

1.4.2      Heuristic Derivation of Lf and Sθf in the Simple Case of Additive Noise

1.4.3      Additive and Parametric Noise

1.4.4      The Polynomial Law

1.4.5      Frequency Stability PSD

1.4.6      The Low-Fourier-Frequency Part of the Phase Noise PSD

1.4.7      The RF Spectrum of the Oscillator Signal

2              The Allan Variance and Other Two-Sample Variances

2.1          Frequency Counters

2.1.1      The Π Frequency Counter

2.1.2      The Λ Frequency Counter

2.1.3      The Ω Frequency Counter

2.1.4      Comparison of the Frequency Counters

2.2          The Two-Sample Variances AVAR, MVAR and PVAR

2.2.1      The Allan Variance (AVAR)

2.2.2      The Modified Allan Variance (MVAR)

2.2.3      The Parabolic Variance (PVAR)

2.3          Conversion from Spectra to Two-Sample Variances

2.3.1      Comparison Between AVAR, MVAR, and PVAR

3              Phase Noise in Components

3.1          Amplifiers

3.1.1      White and Flicker Phase Noise

3.1.2      How to Choose a Low PM Noise Amplifier

3.1.3      Isolation Amplifiers

3.2          Frequency Dividers

3.2.1      Digital Frequency Dividers

3.2.2      Phase Noise Scaling

3.2.3      Time-Type and Phase-Type PM noise

3.2.4      The Λ Divider

3.2.5      Analog Frequency Dividers

3.3          Frequency Multipliers

3.4          Direct Digital Synthesizer (DDS)

3.4.1      Theory of Operation

3.4.2      Signal to Quantization Ratio (SQR)

3.4.3      Truncation Spurs

3.4.4      Phase Noise

3.4.5      Examples

3.5          Phase Detectors

3.5.1      Noise in the Phase-Frequency Detector

3.6          Noise Contribution from Power Supplies

4              Phase Noise in Oscillators

4.1          Modern View of the Leeson Model

4.1.1      The Resonator and Its Impulse Response

4.1.2      The Oscillator’s Phase-Noise Transfer Function

4.1.3      The Phase Noise of the Complete Oscillator

4.1.4      Some Lessons from the Examples

4.2          Circumventing the Resonator’s Thermal Noise

4.3          Oscillator Hacking

4.3.1      Moderate/Low-Q (Type A/C) Oscillators

4.3.2      High-Q (Type B/D) Oscillators

5              The Measurement of Phase Noise

5.1          Double Balanced Mixer Instruments

5.1.1      The Measurement of Oscillators

5.1.2      Background Noise, Spurs, and Other Experimental Issues

5.1.3      Asymmetric Driving for Low-Power Signals

5.1.4      Heterodyne Measurement of Oscillators

5.1.5      The Measurement of Amplifiers and Other Two-Port Components

5.1.6      The Discriminator Method

5.2          The Cross-Spectrum Method

5.2.1      The Rejection of the Background Noise

5.3          Digital Instruments

5.3.1      The Microsemi Family of Phase Noise and Allan Deviation Tester

5.3.2      The Jackson Labs PhaseStation 53100A

5.3.3      The Rohde & Schwarz FSWP Family of Phase Noise Analyzers

5.4          Pitfalls and Limitations of the Cross-Spectrum Measurements

5.4.1      The Effect of a Disturbing Signal

5.4.2      Some Concepts Related to the Measurement Uncertainty

5.4.3      Thermal Energy in the Input Power Divider

5.4.4      The Effect of AM Noise

5.5          The Bridge (Interferometric) Method

5.5.1      Phase-to-Voltage Gain and Background Noise

5.5.2      Building Your Own System

5.5.3      A Practical Example

5.6          Artifacts and Oddities Often Found in the Real World

6              References

7              Suggested readings

7.1          Power spectra and Fourier transform

7.2          Electromagnetic Compatibility

7.3          General Aspects of Noise

7.4          Phase Noise, Frequency Stability, and Measurements

7.5          Amplifiers

7.6          Frequency Dividers

7.7          Frequency Multipliers

7.8          DDS

7.9          Phase-Frequency Detectors

7.10        Oscillators

7.11        Resonators

7.12        Double Balanced Mixer

Chapter 3: Special Loops

1              Introduction

2              Direct Digital Synthesis Techniques

2.1          A First Look at Fractional N

2.2          Digital Waveform Synthesizers

2.2.1      Fundamentals of the DDS Architecture

2.2.2      Systems Concerns

2.2.3      Digital Recursion Oscillator

2.2.4      Phase Accumulator Method

2.2.5      Other Considerations

2.2.6      Modulation with the Phase Accumulator Synthesizer

2.2.7      RAM-Based Synthesis

2.2.8      Components in a RAM-Based Synthesizer

2.2.9      Understanding the Design Variables in RAM Synthesis

2.2.10    Applications

2.2.11    Summary of Methods

2.3          Signal Quality

2.3.1      Spurious Sideband Mechanisms

2.4          3.1 Future Prospects

3              Loops with Delay Line as Phase Comparators

4              Fractional Division N Synthesizers

4.1          Example Implementation

4.2          Some Special Past Patents for Fractional Division N Synthesizers

5              References

6              Bibliography

6.1          Fractional Division N Readings

Chapter 4: Loop Components

1              Introduction to Oscillators and Their Mathematical Treatment

2              The Colpitts Oscillator

2.1          Linear Approach

2.1.2      Linear S-Parameters Approach

2.1.3      Selecting the Right Transistor

2.2          Design Example for a 350 MHz Fixed-frequency Colpitts Oscillator

2.2.1      Step 1: Basic Parameters

2.2.2      Step 2: Biasing

2.2.3      Step 3: Determination of the Large Signal Transconductance

2.2.4      Step 4: Calculation of the Coupling Capacitor Cc [5, eq. (C-23)]

2.2.5      Step 5: Calculation of the Phase Noise of the Colpitts Oscillator

2.2.6      Measured Results for a 350 MHz Oscillator

2.3          Validation Circuits [5]

2.3.1      Design Example for a 100 MHz Crystal Oscillator [5]

2.3.2      Design Example of a 1000 MHz CRO

2.3.3      4100 MHz Oscillator with Transmission Line Resonators

2.3.4      2000 MHz GaAs FET-Based Oscillator

2.3.5      77 GHZ SiGe Oscillator

2.3.6      900–1800 MHz Half-Butterfly Resonator-Based Oscillator

2.4          Series Feedback Oscillator

2.4.1      Example Implementation

2.5          2400 MHz MOSFET-Based Push-Pull Oscillator

2.5.1      Design Equations

2.5.2      Design Calculations

2.5.3      Phase Noise

2.5.4      1/f Noise

2.5.5      AM-to-PM Conversion from Tuning Diodes

2.6          Oscillators for IC Applications

2.7          Noise in Semiconductors and Circuits

2.8          Summary

3              Use of Tuning Diodes

3.1          Diode Tuned Resonant Circuits

3.1.1      Tuner Diode in Parallel Resonant Circuit

3.1.2      Capacitances Connected in Parallel or in Series with the Tuner Diode

3.1.3      Tuning Range

3.2          Practical Circuits

4              Use of Diode Switches

4.1          Diode Switches for Electronic Band Selection

4.2          Use of Diodes for Frequency Multiplication

5              Reference Frequency Standards

5.1          Specifying Oscillators

5.2          Typical Examples of Crystal Oscillator Specifications

6              Mixer Applications

7              Phase/Frequency Comparators

7.1          Diode Rings

7.2          Exclusive ORs

7.2.1      Example Implementation

7.3          Sample/Hold Detectors

7.3.1      Example Implementation

7.4          Edge-Triggered JK Master/Slave Flip-Flops

7.5          Digital Tri-State Comparators

8              Wideband High-Gain Amplifiers

8.1          Summation Amplifiers

8.2          Differential Limiters

8.3          Isolation Amplifiers

8.4          Example Implementations

9              Programmable Dividers

9.1          Asynchronous Counters

9.2          Programmable Synchronous Up/Down-Counters

9.3          Advanced Implementation Example

9.4          Swallow Counters/Dual-Modulus Counters

9.5          Look-Ahead and Delay Compensation

9.5.1      Division by 584

9.5.2      10/11 Counter (ECL)

9.5.3      Delays

10           Loop Filters

10.1        Passive RC Filters

10.2        Active RC Filters

10.3        Active Second-Order Low-Pass Filters

10.4        Passive LC Filters

10.5        Spur-Suppression Techniques

11           Microwave Oscillator Design

11.1        The Compressed Smith Chart

11.2        Series or Parallel Resonance

11.3        Two-Port Oscillator Design

12           Microwave Resonators

12.1        SAW Oscillators

12.2        Dielectric Resonators

12.3        YIG Oscillators

12.4        Varactor Resonators

12.5        Ceramic Resonators

12.5.1    Calculation of Equivalent Circuit

13           References

14           Bibliography

14.1        Section 4-3 Documents

14.2        Section 4-5 Documents

14.3        Section 4-6 Documents

14.4        Section 4-7 Documents

14.5        Section 4-8 Documents

14.6        Section 4-9 Documents

14.7        Section 4-10 Documents

14.8        Section 4-11 Documents

14.9        Section 4-12 Documents

14.10     Additional Suggested Reading

Chapter 5: Digital PLL Synthesizers

1              Multiloop Synthesizers Using Different Techniques

1.1          Direct Frequency Synthesis

1.2          Multiple Loops

2              System Analysis

3              Low-Noise Microwave Synthesizers

3.1          Building Blocks

3.2          Output Loop Response

3.3          Low Phase Noise References: Frequency Standards

3.4          Critical Stage

3.4.1      Oscillators

3.4.2      Other Key Components

3.4.3      Isolation Stage

3.4.4      Harmonic Generators

3.4.5      Millimeter-Wave Oscillators

3.5          Time Domain Analysis

3.6          Summary

3.7          Two Commercial Synthesizer Examples

4              Microprocessor Applications in Synthesizers

5              Transceiver Applications

6              About Bits, Symbols, and Waveforms [1]

6.1          Representation of a Modulated RF Carrier

6.2          Generation of the Modulated Carrier

6.2.1      Mapping the Data into the Baseband Waveforms

6.3          Putting it All Together

6.4          Combination of Techniques

7              References

8              Bibliography and Suggested Reading

9              Acknowledgements

Chapter 6: A High-Performance Hybrid Synthesizer

1              Introduction

2              Basic Synthesizer Approach

3              Loop Filter Design

4              Summary

5              Bibliography

Appendix A: Mathematical Review

1              Functions of a Complex Variable

2              Complex Planes

2.1          Functions in the Complex Frequency Plane

3              Bode Diagram

4              Laplace Transform

4.1          The Step Function

4.2          The Ramp

4.3          Linearity Theorem

4.4          Differentiation and Integration

4.5          Initial Value Theorem

4.6          Final Value Theorem

4.7          The Active Integrator

4.8          Locking Behavior of the PLL

5              Low-Noise Oscillator Design

5.1          Example Implementation

6              Oscillator Amplitude Stabilization

7              Very Low Phase Noise VCO for 800 MHz

8              References

Appendix B: A General-Purpose Nonlinear Approach to the Computation of Sideband Phase Noise in Free-Running Microwave and RF Oscillators

1              Introduction

2              Noise Generation in Oscillators

3              Bias-Dependent Noise Model

3.1          Bias-Dependent Model

3.2          Derivation of the Model

4              General Concept of Noisy Circuits

4.1          Noise from Linear Elements

5              Noise Figure of Mixer Circuits

6              Oscillator Noise Analysis

7              Limitations of the Frequency-Conversion Approach

7.1          Assumptions

7.2          Conversion and Modulation Noise

7.3          Properties of Modulation Noise

7.4          Noise Analysis of Autonomous Circuits

7.5          Conversion Noise Analysis Result

7.6          Modulation Noise Analysis Results

8              Summary of the Phase Noise Spectrum of the Oscillator

9              Verification Examples for the Calculation of Phase Noise in Oscillators Using Nonlinear Techniques

9.1          Example 1: High-Q Case Microstrip DRO

9.2          Example 2

9.3          Example 3: The 1-GHz Ceramic Resonator VCO

9.4          Example 4: Low Phase Noise FET Oscillator

9.5          Example 5: Millimeter-Wave Applications

9.6          Example 6: Discriminator Stabilized DRO

10           Summary

11           References

Appendix C: Example of Wireless Synthesizers Using Commercial ICs \

Appendix D: MMIC-Based Synthesizers

1              Introduction

2              Bibliography and Further Reading

Appendix E: Articles on Design of Dielectric Resonator Oscillator

1              The Design of an Ultra-Low Phase Noise DRO

1.1          Basic Considerations and Component Selection

1.2          Component Selection

1.2.1      Lumped Passive Components

1.2.2      Substrate Considerations

1.2.3      Dielectrical Resonator Selection and Characterization

1.3          DRO Topologies

1.3.1      Series Feedback (Reflection) Type DRO

1.3.2      Parallel Feedback Type DRO

1.4          Small Signal Design Approach for the Parallel Feedback Type DRO

1.5          Simulated vs. Measured Results

1.6          Physical Embodiment

1.7          Acknowledgements

1.8          Final Remarks

1.9          References

1.10        Literature

2              A Novel Oscillator Design with Metamaterial-Möbius Coupling to a Dielectric Resonator

2.1          Abstract

2.2          Introduction

2.3          References

Appendix F: Optoelectronic Oscillators

1              Introduction

2              Opto-electronically Stabilized RF Oscillators

2.1          Introduction

2.1.1      Oscillator Basics

2.1.2      Resonator Technologies

2.1.3      Motivation for OEO

2.1.4      Operating Principles of the OEO

2.2          Experimental Evaluation and Thermal Stability of OEO

2.2.1      Experimental Set-up

2.2.2      Phase Noise Measurement

2.2.3      Thermal Sensitivity Analysis of Standard Fibers

2.2.4      Temperature Sensitivity Measurements

2.2.5      Temperature Sensitivity Improvement with HC-PCF

2.2.6      Improve Thermal Stability vs. Phase Noise Degradation

2.2.7      Passive Temperature Compensation

2.2.8      Improving Effective Q with Raman Amplification

2.3          Forced Oscillation Techniques of OEO

2.3.1      Analysis of Standard Injection Locked (IL) Oscillators

2.3.2      Analysis of Self-Injection Locked (SIL) Oscillators

2.3.3      Experimental Verification of Self-Injection Locked (SIL) Oscillators

2.3.4      Analysis of Standard Phase Locked Loop (PLL) Oscillator

2.3.5      Analysis of Self Phase Locked Loop (SPLL) Oscillators

2.3.6      Experimental Verification of Self-Phase Locked Loop (SPLL) Oscillators

2.3.7      Analysis of Self Injection Locked Phase Locked Loop (SILPLL) Oscillators

2.4          Conclusions

2.5          References

2.5.1      MJ Paper References

2.5.2      References Li’s Thesis

3              Optoelectronic Oscillators: Recent and Emerging Trends

3.1          Overview

3.2          Current OEO Technology

3.3          SILDPLL OEO Synthesizers

3.4          SILDPLL OEO Synthesizer Design

3.5          Monolithic OEOs

3.6          Conclusion

3.7          References

4              Computer-Controlled K-Band Frequency Synthesizers Using Self-Injection Locked Phase-Locked Opto-electronic Oscillator: Part I

4.1          Abstract

4.2          Index Terms

4.3          Introduction

4.4          19’’ Computer Control Realization of Synthesizer

4.5          Conclusions

4.6          References

5              Computer-Controlled K-Band Frequency Synthesizers Using Self-Injection Locked Phase-Locked Opto-electronic Oscillator: Part 2

5.1          Abstract

5.2          Index Terms

5.3          Introduction

5.4          Synthesizer Size Reduction and Operation Band Expansion

5.5          Si-Photonics Synthesizer Designs

5.6          In-P Synthesizer Designs

5.7          Conclusions

5.8          References

6              Self-forced stabilization of inter-modal oscillation in multi-section semiconductor lasers at X-band

6.1          Abstract

6.2          Introduction

6.3          Multi-Mode Laser and Inter-Modal RF Oscillation

6.4          Self-forced Oscillation Techniques

6.5          Discussions and Conclusions

6.6          References

Appendix G: Phase Noise Analysis, Then and Today

1              Introduction

2              Large signal noise analysis

3              References

Index

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