The Noisy Oscillator

The properties of the harmonic oscillator with random frequency or/and random damping formed the content of the first edition. The second edition includes hundreds of publications on this subject since 2005. The noisy oscillator continues to be the subject of intensive studies in physics, chemistry, biology, and social sciences. The new and the latest type of a stochastic oscillator has also been considered, namely, an oscillator with random mass. Such model describes, among other phenomena, Brownian motion with adhesion, where the molecules of the surrounding medium not only randomly collide, but also stick to the Brownian particle for some (random) time, thereby changing its mass. This edition contains two new chapters, eight new sections and an expanded bibliography. A wide group of researchers, students and teachers will benefit from this book.

Stochastic Processes; Fluctuation Phenomena; Classical Statistical Mechanics; Oscillator; Brownian Motion; Stochastic Resonance; Multiplicative Noise.

Presenting a comprehensive account of oscillator phase noise and frequency stability, this practical text is both mathematically rigorous and accessible. An in-depth treatment of the noise mechanism is given, describing the oscillator as a physical system, and showing that simple general laws govern the stability of a large variety of oscillators differing in technology and frequency range. Inevitably, special attention is given to amplifiers, resonators, delay lines, feedback, and flicker (1/f) noise. The reverse engineering of oscillators based on phase-noise spectra is also covered, and end-of-chapter exercises are given. Uniquely, numerous practical examples are presented, including case studies taken from laboratory prototypes and commercial oscillators, which allow the oscillator internal design to be understood by analyzing its phase-noise spectrum. Based on tutorials given by the author at the Jet Propulsion Laboratory, international IEEE meetings, and in industry, this is a useful reference for academic researchers, industry practitioners, and graduate students in RF engineering and communications engineering.

A classroom-tested book addressing key issues of electrical noise This book examines noise phenomena in linear and nonlinear high-frequency circuits from both qualitative and quantitative perspectives. The authors explore important noise mechanisms using equivalent sources and analytical and numerical methods. Readers learn how to manage electrical noise to improve the sensitivity and resolution of communication, navigation, measurement, and other electronic systems. Noise in High-Frequency Circuits and Oscillators has its origins in a university course taught by the authors. As a result, it is thoroughly classroom-tested and carefully structured to facilitate learning. Readers are given a solid foundation in the basics that allows them to proceed to more advanced and sophisticated themes such as computer-aided noise simulation of high-frequency circuits. Following a discussion of mathematical and system-oriented fundamentals, the book covers: * Noise of linear one- and two-ports * Measurement of noise parameters * Noise of diodes and transistors * Parametric circuits * Noise in nonlinear circuits * Noise in oscillators * Quantization noise Each chapter contains a set of numerical and analytical problems that enable readers to apply their newfound knowledge to real-world problems. Solutions are provided in the appendices. With their many years of classroom experience, the authors have designed a book that is ideal for graduate students in engineering and physics. It also addresses key issues and points to solutions for engineers working in the burgeoning satellite and wireless communications industries.

It is hardly a revelation to note that wireless and mobile communications have grown tremendously during the last few years. This growth has placed stringent requi- ments on channel spacing and, by implication, on the phase noise of oscillators. C- pounding the challenge has been a recent drive toward implementations of transceivers in CMOS, whose inferior 1/f noise performance has usually been thought to disqualify it from use in all but the lowest-performance oscillators. Low noise oscillators are also highly desired in the digital world, of course. The c- tinued drive toward higher clock frequencies translates into a demand for ev- decreasing jitter. Clearly, there is a need for a deep understanding of the fundamental mechanisms g- erning the process by which device, substrate, and supply noise turn into jitter and phase noise. Existing models generally offer only qualitative insights, however, and it has not always been clear why they are not quantitatively correct.

This book contains the general description of the mathematical pendulum subject to constant torque, periodic and random forces. The latter appear in additive and multiplicative form with their possible correlation. For the underdamped pendulum driven by periodic forces, a new phenomenon OCo deterministic chaos OCo comes into play, and the common action of this chaos and the influence of noise are taken into account. The inverted position of the pendulum can be stabilized either by periodic or random oscillations of the suspension axis or by inserting a spring into a rigid rod, or by their combination. The pendulum is one of the simplest nonlinear models, which has many applications in physics, chemistry, biology, medicine, communications, economics and sociology. A wide group of researchers working in these fields, along with students and teachers, will benefit from this book.

try to predict it using mathematical expressions. His heuristic model without mathematical proof is almost universally accepted. However, it entails a c- cuit specific noise factor that is not known a priori and so is not predictive. In this work, we attempt to address the topic of oscillator design from a diff- ent perspective. By introducing a new paradigm that accurately captures the subtleties of phase noise we try to answer the question: 'why do oscillators behave in a particular way?' and 'what can be done to build an optimum design?' It is also hoped that the paradigm is useful in other areas of circuit design such as frequency synthesis and clock recovery. In Chapter 1, a general introduction and motivation to the subject is presented. Chapter 2 summarizes the fundamentals of phase noise and timing jitter and discusses earlier works on oscillator's phase noise analysis. Chapter 3 and Chapter 4 analyze the physical mechanisms behind phase noise generation in current-biased and Colpitts oscillators. Chapter 5 discusses design trade-offs and new techniques in LC oscillator design that allows optimal design. Chapter 6 and Chapter 7 discuss a topic that is typically ignored in oscillator design. That is flicker noise in LC oscillators. Finally, Chapter 8 is dedicated to the complete analysis of the role of varactors both in tuning and AM-FM noise conversion.