Contents
Chapter 1 Introduction—Oscillators and Synchronization
1.1 Early Work in Mathematical Biology and Electronic Circuits
1.3 Injection Locking (Adler’s Formalism) and Its Spectra (Locked and Unlocked)
1.4 Mutual Injection Locking of Two Oscillators
Chapter 2 Coupled-Oscillator Arrays—Basic Analytical Description and Operating Principles
2.2 Discrete Model Solution (Linearization and Laplace Transformation)
2.4 Stability of the Phase Solution in the Full Nonlinear Formulation
2.5 External Injection Locking
2.6 Generalization to Planar Arrays
Chapter 3 The Continuum Model for Linear Arrays
3.1 The Linear Array without External Injection
3.2 The Linear Array with External Injection
3.3 Beam-Steering via End Detuning
3.4 Beam-Steering via End Injection
Chapter 4 The Continuum Model for Planar Arrays
4.1 Cartesian Coupling in the Continuum Model without External Injection
4.2 Cartesian Coupling in the Continuum Model with External Injection
4.3 Non-Cartesian Coupling Topologies
Chapter 5 Causality and Coupling Delay
5.2 The Discrete Model with Coupling Delay
5.3 The Continuum Model with Coupling Delay
5.4 Beam Steering in the Continuum Model with Coupling Delay
PART II: EXPERIMENTAL WORK AND APPLICATIONS
Chapter 6 Experimental Validation of the Theory
Chapter 7 Perturbation Models for Stability, Phase Noise, and Modulation
7.1 Preliminaries of Dynamical Systems
7.1.1 Introduction to Stability Analysis of Nonlinear Dynamical Systems
7.2 Bifurcations of Nonlinear Dynamical Systems
7.2.1 Bifurcations of Equilibrium Points
7.2.2 Bifurcations of Periodic Orbits
7.3 The Averaging Method and Multiple Time Scales
7.4 Averaging Theory in Coupled Oscillator Systems
7.5 Obtaining the Parameters of the van der Pol Oscillator Model
7.6 An Alternative Perturbation Model for Coupled-Oscillator Systems
7.7 Matrix Equations for the Steady State and Stability Analysis
7.8 A Comparison between the Two Perturbation Models for Coupled Oscillator Systems
7.9 Externally Injection-Locked COAs
7.12 Coupled Phase-Locked Loops
Chapter 8 Numerical Methods for Simulating Coupled-Oscillator Arrays
8.1 Introduction to Numerical Methods
8.1.2 Harmonic Balance Simulation
8.1.4 Envelope Transient Simulation
8.2 Obtaining Periodic Steady-State Solutions of Autonomous Circuits in Harmonic-Balance Simulators
8.3 Numerical Analysis of a Voltage-Controlled Oscillator
8.4 Numerical Analysis of a Five-Element Linear Coupled-Oscillator Array
8.6 Harmonic Radiation for Extended Scanning Range
8.7 Numerical Analysis of a Self-Oscillating Mixer
Chapter 9 Beamforming in Coupled-Oscillator Arrays
9.1 Preliminary Concepts of Convex Optimization
9.3 Stability Optimization of the Coupled-Oscillator Steady-State Solution
9.4 Multi-Beam Pattern Generation Using Coupled-Oscillator Arrays
9.5 Control of the Amplitude Dynamics
9.6 Adaptive Coupled-Oscillator Array Beamformer
Chapter 10 Overall Conclusions and Possible Future Directions