Analysis and Design of Autonomous Microwave Circuits

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1 Analysis and Design of Autonomous Microwave Circuits ALMUDENA SUAREZ IEEE PRESS WILEY A JOHN WILEY & SONS, INC., PUBLICATION

2 Contents Preface xiii 1 Oscillator Dynamics Introduction Operational Principle of Free-Running Oscillators Impedance-Admittance Analysis of an Oscillator Steady-State Analysis Stability of Steady-State Oscillation Oscillation Startup Formulation of Perturbed Oscillator Equations as an Eigenvalue Problem Generalization of Oscillation Conditions to Multiport Networks Design of Transistor-Based Oscillators from a Single Observation Port Frequency-Domain Formulation of an Oscillator Circuit Steady-State Formulation Stability Analysis Oscillator Dynamics Equations and Steady-State Solutions Stability Analysis Phase Noise 62 References 64 2 Phase Noise Introduction Random Variables and Random Processes Random Variables and Probability Random Processes Correlation Functions and Power Spectral Density Stochastic Differential Equations 77 v

3 vi CONTENTS 2.3 Noise Sources in Electronic Circuits Thermal Noise Shot Noise Generation-Recombination Noise Flicker Noise Burst Noise Derivation of the Oscillator Noise Spectrum Using Time-Domain Analysis Oscillator with White Noise Sources White and Colored Noise Sources Frequency-Domain Analysis of a Noisy Oscillator Frequency-Domain Representation of Noise Sources Carrier Modulation Analysis Frequency-Domain Calculation of Variance of the Phase Deviation Comparison of Two Techniques for Frequency-Domain Analysis of Phase Noise Amplitude Noise 120 References Bifurcation Analysis Introduction Representation of Solutions Phase Space Poincare Map Bifurcations Local Bifurcations Transformations Between Solution Poles Global Bifurcations 173 References Injected Oscillators and Frequency Dividers Introduction Injection-Locked Oscillators Analysis Based on Linearization About a Free-Running Solution Nonlinear Analysis of Synchronized Solution Curves Stability Analysis Bifurcation Loci Phase Variation Along Periodic Curves 206

4 CONTENTS vii Analysis of a FET-Based Oscillator Phase Noise Analysis Frequency Dividers General Characteristics of a Frequency-Divided Solution Harmonic Injection Frequency Dividers Regenerative Frequency Dividers Parametric Frequency Dividers Phase Noise in Frequency Dividers Subharmonically and Ultrasubharmonically Injection-Locked Oscillators Self-Oscillating Mixers 254 References Nonlinear Circuit Simulation Introduction Time-Domain Integration Time-Domain Modeling of Distributed Elements Integration Algorithms Convergence Considerations Fast Time-Domain Techniques Shooting Methods Finite Differences in the Time Domain Harmonic Balance Formulation of a Harmonic Balance System Nodal Harmonic Balance Piecewise Harmonic Balance Continuation Techniques Algorithms for Calculation of Discrete Fourier Transforms Harmonic Balance Analysis of Autonomous and Synchronized Circuits Mixed Harmonic Balance Formulation Auxiliary Generator Technique Envelope Transient Expression of Circuit Variables Envelope Transient Formulation Extension of the Envelope Transient Method to the Simulation of Autonomous Circuits 318

5 viii CONTENTS 5.7 Conversion Matrix Approach 334 References Stability Analysis Using Harmonic Balance Introduction Local Stability Analysis Small-Signal Regime Large-Signal Regime Stability Analysis of Free-Running Oscillators Solution Curves Versus a Circuit Parameter Parameter Switching Applied to Harmonic Balance Equations Parameter Switching Applied to an Auxiliary Generator Equation Arc-Length Continuation Global Stability Analysis Bifurcation Detection from the Characteristic Determinant of a Harmonic Balance System Bifurcation Detection Using Auxiliary Generators Bifurcation Synthesis and Control Bifurcation Synthesis Bifurcation Control 394 References Noise Analysis Using Harmonic Balance Introduction Noise in Semiconductor Devices Noise in Field-Effect Transistors Noise in Bipolar Transistors Noise in Varactor Diodes Decoupled Analysis of Phase and Amplitude Perturbations in a Harmonic Balance System Perturbed Oscillator Equations Phase Noise Amplitude Noise Coupled Phase and Amplitude Noise Calculation Carrier Modulation Approach 423

6 CONTENTS ix Direct Calculation of Phase and Amplitude Noise Spectra Calculation of Variance of the Phase Deviation a^r) Conversion Matrix Approach Calculation of Complex Sidebands AXy Determination of Phase and Amplitude Noise Spectra Noise in Synchronized Oscillators Conversion Matrix Approach Semianalytical Formulation 433 References Harmonic Balance Techniques for Oscillator Design Introduction Oscillator Synthesis Oscillation Startup Conditions Steady-State Design Using One-Harmonic Accuracy Multiharmonic Steady-State Design Design of Voltage-Controlled Oscillators Technique for Increasing Oscillation Bandwidth Technique to Preset the Oscillation Band Technique to Linearize the VCO Characteristic Maximization of Oscillator Efficiency Class E Design Class F Design General Load-Pull System Control of Oscillator Transients Reduction of Oscillator Startup Time Improvement in the Modulated Response of a Voltage-Controlled Oscillator Phase Noise Reduction 485 Appendix 490 References Stabilization Techniques for Phase Noise Reduction Introduction 496

7 x CONTENTS 9.2 Self-Injection Topology Steady-State Solution Stability Analysis Phase Noise Analysis Use of High- Q Resonators Stabilization Loop Transistor-Based Oscillators Harmonic Balance Analysis Semianalytical Formulation Application to a 5-GHz MESFET-Based Oscillator 518 References Coupled-Oscillator Systems Introduction Oscillator Systems with Global Coupling Simplified Analysis of Oscillation Modes Applications of Globally Coupled Oscillators Stability Analysis of a Steady-State Periodic Regime Phase Noise Analysis and Design Using Harmonic Balance Coupled-Oscillator Systems for Beam Steering Analytical Study of Oscillator-Array Operation Harmonic Balance Analysis Semianalytical Formulation Determination of Coexisting Solutions Stability Analysis Phase Noise Analysis Comparison Between Weak and Strong Oscillator Coupling Forced Operation of a Coupled-Oscillator Array 590 References Simulation Techniques for Frequency-Divider Design Introduction Types of frequency dividers Design of Transistor-Based Regenerative Frequency Dividers 597

8 CONTENTS xi Frequency-Divided Regime Control of Operation Bands in Frequency Dividers by Control of Divider Settling Time Design of Harmonic Injection Dividers Semianalytical Estimation of Synchronization Bands Full Harmonic Balance Design Introduction of a Low-Frequency Feedback Loop Control of Turning Points Extension of the Techniques to Subharmonic Injection Oscillators 624 References Circuit Stabilization Introduction Unstable Class AB Amplifier Using Power Combiners Oscillation Modes Analytical Study of the Mechanism for Frequency Division by Global Stability Analysis with Harmonic Balance Amplifier Stabilization Unstable Class E/F Amplifier Class E/F Operation Anomalous Experimental Behavior in a Class E/F 0 dd Power Amplifier Stability Analysis of a Class E/F 0 dd Power Amplifier Stability Analysis with Pole-Zero Identification Hopf Bifurcation Locus Analysis of an Undesired Oscillatory Solution Circuit Stabilization Unstable Class E Amplifier Amplifier Measurements Stability Analysis of the Power Amplifier Analysis of Noisy Precursors Elimination of the Hysteresis Phenomenon from the Power Transfer Curve P{ n P out Elimination of Noisy Precursors Stabilization of Oscillator Circuits Stability Analysis of an Oscillator Circuit Stabilization Technique for Fixed Bias Voltage 679

9 xii CONTENTS Stabilization Technique for the Entire Tuning Voltage Range Stabilization of Multifunction MMIC Chips Analyses at the Lumped-Element Schematic Level Analyses at the Layout Level 689 References 693 Index 697

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