This book introduces an intuitive, self-sustained oscillator model and applies it to describe some of the most critical performance metrics of LC oscillators, such as phase noise, entrainment, and pulling. It also covers the related topics of magnetic coupling and inductor design. The author emphasizes the basic principles and illuminates them with approximate calculations, adopting a design-oriented approach that imparts intuition and complements simulations. This book constitutes a novel and fresh perspective on the subject and can be helpful to electrical engineering students and practicing engineers. It also serves as a bridge between the mathematical treatises of the subject and the more practical circuit-oriented approaches.
Author(s): Konstantinos Manetakis
Publisher: Springer
Year: 2023
Language: English
Pages: 179
City: Cham
Preface
Contents
1 Basics of LC Oscillators
1.1 Introduction
1.2 The Simple Harmonic Oscillator
1.3 Phase Plane
1.4 The Damped Harmonic Oscillator
1.5 Energy in the Damped Harmonic Oscillator
1.6 The Driven Harmonic Oscillator
1.7 Energy in the Driven Harmonic Oscillator
1.8 Linear Models for LC Oscillators
2 Self-Sustained Oscillators
2.1 Introduction
2.2 Amplitude Regulation
2.3 Mathematical Model
2.4 The Van der Pol Oscillator
2.5 Solution by Perturbation
2.6 Alternative Method of Solution
2.7 NMOS-Only Oscillator
3 Noise in LC Oscillators
3.1 Introduction
3.2 Equipartition and Fluctuation-Dissipation Theorems
3.3 Damped Harmonic Oscillator Noise
3.4 Self-Sustained Oscillator Phase Noise—Dissipation
3.5 Self-Sustained Oscillator Phase Noise—Fluctuation
3.6 Stochastic Differential Equation for Phase
3.7 Comparison with Simulation
4 Thermal Noise in LC Oscillators
4.1 Introduction
4.2 The Phase Dynamics Equation
4.3 Noise to Phase Noise Conversion
4.4 Tank Noise and Leeson's Equation
4.5 Transconductor Modeling
4.6 Phase Noise Due to Transconductor Thermal Noise
4.7 Excess Noise Factor
4.8 Comparison with Simulations
5 Low-Frequency Noise in LC Oscillators
5.1 Introduction
5.2 The Modified Phase Dynamics Equation
5.3 Phase Noise Due to Transconductor Flicker Noise
5.4 Phase Noise Due to Supply Noise
5.5 Common-Mode Effects
5.6 Phase Noise Due to Varactors
6 LC Oscillator Entrainment and Pulling
6.1 Introduction
6.2 Magnetic Coupling on RLC Tank
6.3 Magnetic Coupling on Self-Sustained Oscillator
6.4 Entrainment of Self-Sustained Oscillator
6.5 Quasi-periodic Motion Region
6.6 Spur-Approximation Region
6.7 x2 LO Transmitter Architecture—Adler's Equation
6.8 Magnetic Coupling Between Loops
6.9 Magnetic Coupling Between Line and Loop
6.10 Reduction of the Mutual Inductance Between Loops
6.11 Reduction of the Mutual Inductance Between a Line and a Loop
7 Design of Integrated Inductors
7.1 Introduction
7.2 Mutual Inductance of Filamentary Loops
7.3 Mutual Inductance of Parallel Filaments
7.4 Mutual Inductance of Rectangular Parallel Bars
7.5 Self-inductance of Rectangular Bars
7.6 Inductance of Rectangular Planar Loops
7.7 Skin Effect
7.8 Segment Resistance at High Frequencies
7.9 Proximity Effect
7.10 Segment Capacitance
7.11 Inductor Equivalent Network
A Amplitude Noise
A.1 Stochastic Differential Equation for Amplitude
A.2 Amplitude Noise
B Derivation of Entrainment Equation
References
Index
