Coupled-Oscillator Based Active-Array Antennas

RONALD J. POGORZELSKI, PhD, is Senior Research Scientist Emeritus and the former supervisor of the Spacecraft Antenna Research Group at the Jet Propulsion Laboratory. He has authored or coauthored over 100 technical publications and presentations and was editor of the IEEE Transactions on Antennas and Propagation.APOSTOLOS GEORGIADIS, PhD, is a Senior Research Associate at Centre Tecnològic de Telecomunicacions de Catalunya (CTTC) in Barcelona, Spain, where he is involved in active antennas and antenna arrays as well as RFID technology and energy harvesting.

• Foreword xiPreface xiiiAcknowledgments xviiAuthors xixPART I: THEORY AND ANALYSIS 1Chapter 1 Introduction—Oscillators and Synchronization 31.1 Early Work in Mathematical Biology and Electronic Circuits 31.2 van der Pol's Model 51.3 Injection Locking (Adier's Formalism) and Its Spectra (Locked and Unlocked) 71.4 Mutual Injection Locking of Two Oscillators 211.5 Conclusion 26Chapter 2 Coupled-Oscillator Arrays-Basic Analytical Description and Operating Principles 272.1 Fundamental Equations 282.2 Discrete Model Solution (Linearization and Laplace Transformation) 312.3 Steady-State Solution 372.4 Stability of the Phase Solution in the Full Nonlinear Formulation 412.5 External Injection Locking 462.6 Generalization to Planar Arrays 502.7 Coupling Networks 542.8 Conclusion 66Chapter 3 The Continuum Model for Linear Arrays 673.1 The Linear Array without External Injection 683.2 The Linear Array with External Injection 813.3 Beam-Steering via End Detuning 933.4 Beam-Steering via End Injection 953.5 Conclusion 102Chapter 4 The Continuum Model for Planar Arrays 1034.1 Cartesian Coupling in the Continuum Model without External Injection 1034.2 Cartesian Coupling in the Continuum Model with External Injection 1094.3 Non-Cartesian Coupling Topologies 1184.4 Conclusion 137Chapter 5 Causality and Coupling Delay 1395.1 Coupling Delay 1395.2 The Discrete Model with Coupling Delay 1415.3 The Continuum Model with Coupling Delay 1465.4 Beam Steering in the Continuum Model with Coupling Delay 1595.5 Conclusion 173PART II: EXPERIMENTAL WORK AND APPLICATIONS 175Chapter 6 Experimental Validation of the Theory 1776.1 Linear-Array Experiments 1776.2 Planar-Array Experiments 1886.3 Receive-Array Experiments 2016.4 Phase Noise 2106.5 The Unlocked State 2136.6 Conclusion 215PART III: NONLINEAR BEHAVIOR 217Chapter 7 Perturbation Models for Stability, Phase Noise, and Modulation 2197.1 Preliminaries of Dynamical Systems 2207.2 Bifurcations of Nonlinear Dynamical Systems 2267.3 The Averaging Method and Multiple Time Scales 2307.4 Averaging Theory in Coupled Oscillator Systems 2317.5 Obtaining the Parameters of the van der Pol Oscillator Model 2357.6 An Alternative Perturbation Model for Coupled-Oscillator Systems 2387.7 Matrix Equations for the Steady State and Stability Analysis 2427.8 A Comparison between the Two Perturbation Models for Coupled Oscillator Systems 2467.9 Externally Injection-Locked COAs 2477.10 Phase Noise 2507.11 Modulation 2567.12 Coupled Phase-Locked Loops 2587.13 Conclusion 261Chapter 8 Numerical Methods for Simulating Coupled-Oscillator Arrays 2638.1 Introduction to Numerical Methods 2648.2 Obtaining Periodic Steady-State Solutions of Autonomous Circuits in Harmonic-Balance Simulators 2708.3 Numerical Analysis of a Voltage-Controlled Oscillator 2728.4 Numerical Analysis of a Five-Element Linear Coupled-Oscillator Array 2788.5 Numerical Analysis of an Externally Injection-Locked Five-Element Linear Coupled-Oscillator Array 2868.6 Harmonic Radiation for Extended Scanning Range 2888.7 Numerical Analysis of a Self-Oscillating Mixer 2918.8 Conclusion 296Chapter 9 Beamforming in Coupled-Oscillator Arrays 2979.1 Preliminary Concepts of Convex Optimization 2979.2 Beamforming in COAs 3019.3 Stability Optimization of the Coupled-Oscillator Steady-State Solution 3089.4 Multi-Beam Pattern Generation Using Coupled-Oscillator Arrays 3119.5 Control of the Amplitude Dynamics 3159.6 Adaptive Coupled-Oscillator Array Beamformer 3179.7 Conclusion 320Chapter 10 Overall Conclusions and Possible Future Directions 321REFERENCES 325ACRONYMS AND ABBREVIATIONS 341INDEX 345