Foreword |
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xi | |
Preface |
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xiii | |
Acknowledgments |
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xvii | |
Authors |
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xix | |
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PART I THEORY AND ANALYSIS |
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1 | (174) |
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Chapter 1 Introduction---Oscillators and Synchronization |
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3 | (24) |
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1.1 Early Work in Mathematical Biology and Electronic Circuits |
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3 | (2) |
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5 | (2) |
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1.3 Injection Locking (Adler's Formalism) and Its Spectra (Locked and Unlocked) |
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7 | (14) |
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1.4 Mutual Injection Locking of Two Oscillators |
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21 | (5) |
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26 | (1) |
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Chapter 2 Coupled-Oscillator Arrays---Basic Analytical Description and Operating Principles |
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27 | (40) |
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2.1 Fundamental Equations |
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28 | (3) |
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2.2 Discrete Model Solution (Linearization and Laplace Transformation) |
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31 | (6) |
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2.3 Steady-State Solution |
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37 | (4) |
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2.4 Stability of the Phase Solution in the Full Nonlinear Formulation |
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41 | (5) |
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2.5 External Injection Locking |
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46 | (4) |
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2.6 Generalization to Planar Arrays |
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50 | (4) |
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54 | (12) |
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66 | (1) |
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Chapter 3 The Continuum Model for Linear Arrays |
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67 | (36) |
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3.1 The Linear Array without External Injection |
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68 | (13) |
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3.2 The Linear Array with External Injection |
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81 | (12) |
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3.3 Beam-Steering via End Detuning |
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93 | (2) |
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3.4 Beam-Steering via End Injection |
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95 | (7) |
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102 | (1) |
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Chapter 4 The Continuum Model for Planar Arrays |
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103 | (36) |
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4.1 Cartesian Coupling in the Continuum Model without External Injection |
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103 | (6) |
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4.2 Cartesian Coupling in the Continuum Model with External Injection |
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109 | (9) |
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4.3 Non-Cartesian Coupling Topologies |
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118 | (19) |
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137 | (2) |
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Chapter 5 Causality and Coupling Delay |
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139 | (36) |
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139 | (2) |
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5.2 The Discrete Model with Coupling Delay |
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141 | (5) |
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5.3 The Continuum Model with Coupling Delay |
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146 | (13) |
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5.4 Beam Steering in the Continuum Model with Coupling Delay |
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159 | (14) |
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173 | (2) |
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PART II EXPERIMENTAL WORK AND APPLICATIONS |
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175 | (42) |
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Chapter 6 Experimental Validation of the Theory |
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177 | (40) |
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6.1 Linear-Array Experiments |
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177 | (11) |
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6.2 Planar-Array Experiments |
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188 | (13) |
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6.3 Receive-Array Experiments |
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201 | (9) |
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210 | (3) |
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213 | (2) |
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215 | (2) |
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PART III NONLINEAR BEHAVIOR |
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217 | (108) |
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Chapter 7 Perturbation Models for Stability, Phase Noise, and Modulation |
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219 | (44) |
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7.1 Preliminaries of Dynamical Systems |
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220 | (6) |
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7.1.1 Introduction to Stability Analysis of Nonlinear Dynamical Systems |
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223 | (1) |
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223 | (1) |
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7.1.3 Periodic Steady State |
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224 | (1) |
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225 | (1) |
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7.2 Bifurcations of Nonlinear Dynamical Systems |
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226 | (4) |
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7.2.1 Bifurcations of Equilibrium Points |
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226 | (2) |
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7.2.2 Bifurcations of Periodic Orbits |
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228 | (2) |
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7.3 The Averaging Method and Multiple Time Scales |
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230 | (1) |
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7.4 Averaging Theory in Coupled Oscillator Systems |
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231 | (4) |
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7.5 Obtaining the Parameters of the van der Pol Oscillator Model |
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235 | (3) |
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7.6 An Alternative Perturbation Model for Coupled-Oscillator Systems |
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238 | (4) |
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7.7 Matrix Equations for the Steady State and Stability Analysis |
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242 | (4) |
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7.8 A Comparison between the Two Perturbation Models for Coupled Oscillator Systems |
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246 | (1) |
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7.9 Externally Injection-Locked COAs |
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247 | (3) |
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250 | (6) |
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256 | (2) |
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7.12 Coupled Phase-Locked Loops |
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258 | (3) |
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261 | (2) |
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Chapter 8 Numerical Methods for Simulating Coupled-Oscillator Arrays |
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263 | (34) |
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8.1 Introduction to Numerical Methods |
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264 | (6) |
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8.1.1 Transient Simulation |
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264 | (2) |
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8.1.2 Harmonic Balance Simulation |
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266 | (1) |
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267 | (1) |
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8.1.4 Envelope Transient Simulation |
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268 | (1) |
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8.1.5 Continuation Methods |
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269 | (1) |
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8.2 Obtaining Periodic Steady-State Solutions of Autonomous Circuits in Harmonic-Balance Simulators |
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270 | (2) |
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8.3 Numerical Analysis of a Voltage-Controlled Oscillator |
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272 | (6) |
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8.4 Numerical Analysis of a Five-Element Linear Coupled-Oscillator Array |
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278 | (8) |
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8.5 Numerical Analysis of an Externally Injection-Locked Five-Element Linear Coupled-Oscillator Array |
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286 | (2) |
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8.6 Harmonic Radiation for Extended Scanning Range |
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288 | (3) |
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8.7 Numerical Analysis of a Self-Oscillating Mixer |
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291 | (5) |
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296 | (1) |
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Chapter 9 Beamforming in Coupled-Oscillator Arrays |
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297 | (24) |
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9.1 Preliminary Concepts of Convex Optimization |
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297 | (4) |
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301 | (7) |
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9.3 Stability Optimization of the Coupled-Oscillator Steady-State Solution |
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308 | (3) |
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9.4 Multi-Beam Pattern Generation Using Coupled-Oscillator Arrays |
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311 | (4) |
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9.5 Control of the Amplitude Dynamics |
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315 | (2) |
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9.6 Adaptive Coupled-Oscillator Array Beamformer |
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317 | (3) |
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320 | (1) |
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Chapter 10 Overall Conclusions and Possible Future Directions |
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321 | (4) |
References |
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325 | (16) |
Acronyms and Abbreviations |
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341 | (4) |
Index |
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345 | |