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Coupled-Oscillator Based Active-Array Antennas

Book Description

Describing an innovative approach to phased-array control in antenna design

This book explores in detail phased-array antennas that use coupled-oscillator arrays, an arrangement featuring a remarkably simple beam steering control system and a major reduction in complexity compared with traditional methods of phased-array control. It brings together in one convenient, self-contained volume the many salient research results obtained over the past ten to fifteen years in laboratories around the world, including the California Institute of Technology's Jet Propulsion Laboratory.

The authors examine the underlying theoretical framework of coupled-oscillator systems, clearly explaining the linear and nonlinear formalisms used in the development of coupled-oscillator arrays, while introducing a variety of state-of-the-art methodologies, design solutions, and tools for applying this control scheme. Readers will find:

  • Numerous implementation examples of coupled-oscillator array prototypes

  • A continuum model that permits application of diffusion theory to the analysis of phase dynamics

  • A demonstration of the array behavior through experimental results that validate the linearized theory

  • Examples of how incorporating coupling delay restores causality, including the latest published results

  • Guidance on how to accurately analyze and optimize coupled-oscillator arrays using modern simulation tools

  • A review of current developments, including the design of compact couple-oscillator array antennas

Complete with 150 diagrams and photographs, Coupled-Oscillator Based Active-Array Antennas is a highly useful tutorial for antenna designers and a valuable reference for researchers and engineers wishing to learn about this cutting-edge technology.

Table of Contents

  1. Coverpage
  2. Titlepage
  3. Copyright
  4. Dedication
  5. Contents
  6. Foreword
  7. Preface
  8. Acknowledgments
  9. Authors
  10. PART I: THEORY AND ANALYSIS
    1. Chapter 1 Introduction—Oscillators and Synchronization
      1. 1.1 Early Work in Mathematical Biology and Electronic Circuits
      2. 1.2 van der Pol’s Model
      3. 1.3 Injection Locking (Adler’s Formalism) and Its Spectra (Locked and Unlocked)
      4. 1.4 Mutual Injection Locking of Two Oscillators
      5. 1.5 Conclusion
    2. Chapter 2 Coupled-Oscillator Arrays—Basic Analytical Description and Operating Principles
      1. 2.1 Fundamental Equations
      2. 2.2 Discrete Model Solution (Linearization and Laplace Transformation)
      3. 2.3 Steady-State Solution
      4. 2.4 Stability of the Phase Solution in the Full Nonlinear Formulation
      5. 2.5 External Injection Locking
      6. 2.6 Generalization to Planar Arrays
      7. 2.7 Coupling Networks
      8. 2.8 Conclusion
    3. Chapter 3 The Continuum Model for Linear Arrays
      1. 3.1 The Linear Array without External Injection
      2. 3.2 The Linear Array with External Injection
      3. 3.3 Beam-Steering via End Detuning
      4. 3.4 Beam-Steering via End Injection
      5. 3.5 Conclusion
    4. Chapter 4 The Continuum Model for Planar Arrays
      1. 4.1 Cartesian Coupling in the Continuum Model without External Injection
      2. 4.2 Cartesian Coupling in the Continuum Model with External Injection
      3. 4.3 Non-Cartesian Coupling Topologies
      4. 4.4 Conclusion
    5. Chapter 5 Causality and Coupling Delay
      1. 5.1 Coupling Delay
      2. 5.2 The Discrete Model with Coupling Delay
      3. 5.3 The Continuum Model with Coupling Delay
      4. 5.4 Beam Steering in the Continuum Model with Coupling Delay
      5. 5.5 Conclusion
  11. PART II: EXPERIMENTAL WORK AND APPLICATIONS
    1. Chapter 6 Experimental Validation of the Theory
      1. 6.1 Linear-Array Experiments
      2. 6.2 Planar-Array Experiments
      3. 6.3 Receive-Array Experiments
      4. 6.4 Phase Noise
      5. 6.5 The Unlocked State
      6. 6.6 Conclusion
  12. PART III: NONLINEAR BEHAVIOR
    1. Chapter 7 Perturbation Models for Stability, Phase Noise, and Modulation
      1. 7.1 Preliminaries of Dynamical Systems
        1. 7.1.1 Introduction to Stability Analysis of Nonlinear Dynamical Systems
        2. 7.1.2 Equilibrium Point
        3. 7.1.3 Periodic Steady State
        4. 7.1.4 Lyapunov Exponents
      2. 7.2 Bifurcations of Nonlinear Dynamical Systems
        1. 7.2.1 Bifurcations of Equilibrium Points
        2. 7.2.2 Bifurcations of Periodic Orbits
      3. 7.3 The Averaging Method and Multiple Time Scales
      4. 7.4 Averaging Theory in Coupled Oscillator Systems
      5. 7.5 Obtaining the Parameters of the van der Pol Oscillator Model
      6. 7.6 An Alternative Perturbation Model for Coupled-Oscillator Systems
      7. 7.7 Matrix Equations for the Steady State and Stability Analysis
      8. 7.8 A Comparison between the Two Perturbation Models for Coupled Oscillator Systems
      9. 7.9 Externally Injection-Locked COAs
      10. 7.10 Phase Noise
      11. 7.11 Modulation
      12. 7.12 Coupled Phase-Locked Loops
      13. 7.13 Conclusion
    2. Chapter 8 Numerical Methods for Simulating Coupled-Oscillator Arrays
      1. 8.1 Introduction to Numerical Methods
        1. 8.1.1 Transient Simulation
        2. 8.1.2 Harmonic Balance Simulation
        3. 8.1.3 Conversion Matrix
        4. 8.1.4 Envelope Transient Simulation
        5. 8.1.5 Continuation Methods
      2. 8.2 Obtaining Periodic Steady-State Solutions of Autonomous Circuits in Harmonic-Balance Simulators
      3. 8.3 Numerical Analysis of a Voltage-Controlled Oscillator
      4. 8.4 Numerical Analysis of a Five-Element Linear Coupled-Oscillator Array
      5. 8.5 Numerical Analysis of an Externally Injection-Locked Five-Element Linear Coupled-Oscillator Array
      6. 8.6 Harmonic Radiation for Extended Scanning Range
      7. 8.7 Numerical Analysis of a Self-Oscillating Mixer
      8. 8.8 Conclusion
    3. Chapter 9 Beamforming in Coupled-Oscillator Arrays
      1. 9.1 Preliminary Concepts of Convex Optimization
      2. 9.2 Beamforming in COAs
      3. 9.3 Stability Optimization of the Coupled-Oscillator Steady-State Solution
      4. 9.4 Multi-Beam Pattern Generation Using Coupled-Oscillator Arrays
      5. 9.5 Control of the Amplitude Dynamics
      6. 9.6 Adaptive Coupled-Oscillator Array Beamformer
      7. 9.7 Conclusion
    4. Chapter 10 Overall Conclusions and Possible Future Directions
  13. REFERENCES
  14. ACRONYMS AND ABBREVIATIONS
  15. INDEX