Coupled-Oscillator Based Active-Array Antennas

by Pogorzelski, Ronald J.; Georgiadis, Apostolos

• ISBN13: 9781118235294
• ISBN10: 1118235290
• Edition: 1st
• Format: Hardcover
• Copyright: 2012-07-10
• Publisher: Wiley

Summary

This book presents the theory of phased array antennas that use arrays of electronic oscillators coupled to each other so as to mutually injection lock and thus oscillate as an ensemble. This arrangement provides a remarkably simple beam steering control system replacing the complicated array of computer controlled phase shifters traditionally used for this purpose. The book also describes a large number of laboratory demonstrations that have been reported over the past three decades that experimentally verify the various aspects of the theory. The theory is initially presented using a linear approximation permitting derivation of much of the array behavior analytically. Then, at a deeper level, a nonlinear formulation is used to obtain, computationally, more detailed aspects of the array behavior. The primary purpose of the book is to gather the salient results of the past ten to fifteen years of research in this area into one convenient volume providing both a tutorial explanation of this approach to phased array control and a guide to the literature on the subject.

Author Biography

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 Tecnolgic 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.

Table of Contents

Foreword	p. xi
Preface	p. xiii
Acknowledgments	p. xvii
Authors	p. xix
Theory and Analysis	p. 1
Introduction-Oscillators and Synchronization	p. 3
Early Work in Mathematical Biology and Electronic Circuits	p. 3
van der Pol's Model	p. 5
Injection Locking (Adler's Formalism) and Its Spectra (Locked and Unlocked)	p. 7
Mutual Injection Locking of Two Oscillators	p. 21
Conclusion	p. 26
Coupled-Oscillator Arrays-Basic Analytical Description and Operating Principles	p. 27
Fundamental Equations	p. 28
Discrete Model Solution (Linearization and Laplace Transformation)	p. 31
Steady-State Solution	p. 37
Stability of the Phase Solution in the Full Nonlinear Formulation	p. 41
External Injection Locking	p. 46
Generalization to Planar Arrays	p. 50
Coupling Networks	p. 54
Conclusion	p. 66
The Continuum Model for Linear Arrays	p. 67
The Linear Array without External Injection	p. 68
The Linear Array with External Injection	p. 81
Beam-Steering via End Detuning	p. 93
Beam-Steering via End Injection	p. 95
Conclusion	p. 102
The Continuum Model for Planar Arrays	p. 103
Cartesian Coupling in the Continuum Model without External Injection	p. 103
Cartesian Coupling in the Continuum Model with External Injection	p. 109
Non-Cartesian Coupling Topologies	p. 118
Conclusion	p. 137
Causality and Coupling Delay	p. 139
Coupling Delay	p. 139
The Discrete Model with Coupling Delay	p. 141
The Continuum Model with Coupling Delay	p. 146
Beam Steering in the Continuum Model with Coupling Delay	p. 159
Conclusion	p. 173
Experimental Work and Applications	p. 175
Experimental Validation of the Theory	p. 177
Linear-Array Experiments	p. 177
Planar-Array Experiments	p. 188
Receive-Array Experiments	p. 201
Phase Noise	p. 210
The Unlocked State	p. 213
Conclusion	p. 215
Nonlinear Behavior	p. 217
Perturbation Models for Stability, Phase Noise, and Modulation	p. 219
Preliminaries of Dynamical Systems	p. 220
Introduction to Stability Analysis of Nonlinear Dynamical Systems	p. 223
Equilibrium Point	p. 223
Periodic Steady State	p. 224
Lyapuhov Exponents	p. 225
Bifurcations of Nonlinear Dynamical Systems	p. 226
Bifurcations of Equilibrium Points	p. 226
Bifurcations of Periodic Orbits	p. 228
The Averaging Method and Multiple Time Scales	p. 230
Averaging Theory in Coupled Oscillator Systems	p. 231
Obtaining the Parameters of the van der Pol Oscillator Model	p. 235
An Alternative Perturbation Model for Coupled-Oscillator Systems	p. 238
Matrix Equations for the Steady State and Stability Analysis	p. 242
A Comparison between the Two Perturbation Models for Coupled Oscillator Systems	p. 246
Externally Injection-Locked COAs	p. 247
Phase Noise	p. 250
Modulation	p. 256
Coupled Phase-Locked Loops	p. 258
Conclusion	p. 261
Numerical Methods for Simulating Coupled-Oscillator Arrays	p. 263
Introduction to Numerical Methods	p. 264
Transient Simulation	p. 264
Harmonic Balance Simulation	p. 266
Conversion Matrix	p. 267
Envelope Transient Simulation	p. 268
Continuation Methods	p. 269
Obtaining Periodic Steady-State Solutions of Autonomous Circuits in Harmonic-Balance Simulators	p. 270
Numerical Analysis of a Voltage-Controlled Oscillator	p. 272
Numerical Analysis of a Five-Element Linear Coupled-Oscillator Array	p. 278
Numerical Analysis of an Externally Injection-Locked Five-Element Linear Coupled-Oscillator Array	p. 286
Harmonic Radiation for Extended Scanning Range	p. 288
Numerical Analysis of a Self-Oscillating Mixer	p. 291
Conclusion	p. 296
Beamforming in Coupled-Oscillator Arrays	p. 297
Preliminary Concepts of Convex Optimization	p. 297
Beamforming in COAs	p. 301
Stability Optimization of the Coupled-Oscillator Steady-State Solution	p. 308
Multi-Beam Pattern Generation Using Coupled-Oscillator Arrays	p. 311
Control of the Amplitude Dynamics	p. 315
Adaptive Coupled-Oscillator Array Beamformer	p. 317
Conclusion.	p. 320
Overall Conclusions and Possible Future Directions	p. 321
References	p. 325
Acronyms and Abbreviations	p. 341
Index	p. 345
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