Equations Of Phase Locked Loops

Applications of phase-locked loops play an increasingly important role in modern electronic systems, and the last 25 years have seen new developments in the underlying theories as well. Phase-Locked Loops presents the latest information on the basic theory and applications of PLLs. Organized in a logical format, it first introduces the subject in a qualitative manner and discusses key applications. Next, it develops basic models for components of a PLL, and these are used to develop a basic PLL model. The text then discusses both linear and nonlinear methods that are used to analyze the basic PLL model. This book includes extensive coverage of the nonlinear behavior of phase-locked loops, an important area of this field and one where exciting new research is being performed. No other book available covers this critical area in such careful detail. Improvements brought about by the advent of the personal computer, especially in the use of numerical results, are integrated into the text. This book also focuses on PLL component technologies used in system implementation.

Phase-Locked Loops (PLLs) are electronic systems that can be used as a synchronized oscillator, a driver or multiplier of frequency, a modulator or demodulator and as an amplifier of phase modulated signals. This book updates the methods used in the analysis of PLLs by drawing on the results obtained in the last 40 years. Many are published for the first time in book form. Nonlinear and deterministic mathematical models of continuous-time and discrete-time PLLs are considered and their basic properties are given in the form of theorems with rigorous proofs. The book exhibits very beautiful dynamics, and shows various physical phenomena observed in synchronized oscillators described by complete (not averaged) equations of PLLs. Specially selected mathematical tools are used ? the theory of differential equations on a torus, the phase-plane portraits on a cyclinder, a perturbation theory (Melnikov's theorem on heteroclinic trajectories), integral manifolds, iterations of one-dimensional maps of a circle and two-dimensional maps of a cylinder. Using these tools, the properties of PLLs, in particular the regions of synchronization are described. Emphasis is on bifurcations of various types of periodic and chaotic oscillations. Strange attractors in the dynamics of PLLs are considered, such as those discovered by R”ssler, Henon, Lorenz, May, Chua and others.

Phase-Locked Loops (PLLs) are electronic systems that can be used as a synchronized oscillator, a driver or multiplier of frequency, a modulator or demodulator and as an amplifier of phase modulated signals. This book updates the methods used in the analysis of PLLs by drawing on the results obtained in the last 40 years. Many are published for the first time in book form. Nonlinear and deterministic mathematical models of continuous-time and discrete-time PLLs are considered and their basic properties are given in the form of theorems with rigorous proofs. The book exhibits very beautiful dynamics, and shows various physical phenomena observed in synchronized oscillators described by complete (not averaged) equations of PLLs. Specially selected mathematical tools are used OCo the theory of differential equations on a torus, the phase-plane portraits on a cyclinder, a perturbation theory (Melnikov''s theorem on heteroclinic trajectories), integral manifolds, iterations of one-dimensional maps of a circle and two-dimensional maps of a cylinder. Using these tools, the properties of PLLs, in particular the regions of synchronization are described. Emphasis is on bifurcations of various types of periodic and chaotic oscillations. Strange attractors in the dynamics of PLLs are considered, such as those discovered by RAssler, Henon, Lorenz, May, Chua and others."

Good,No Highlights,No Markup,all pages are intact, Slight Shelfwear,may have the corners slightly dented, may have slight color changes/slightly damaged spine.

Unique book/disk set that makes PLL circuit design easier than ever. Table of Contents: PLL Fundamentals; Classification of PLL Types; The Linear PLL (LPLL); The Classical Digital PLL (DPLL); The All-Digital PLL (ADPLL); The Software PLL (SPLL); State Of The Art of Commercial PLL Integrated Circuits; Appendices; Index. Includes a 5 1/4" disk. 100 illustrations.

The Definitive Introduction to Phase-Locked Loops, Complete with Software for Designing Wireless Circuits! The Sixth Edition of Roland Best's classic Phase-Locked Loops has been updated to equip you with today's definitive introduction to PLL design, complete with powerful PLL design and simulation software written by the author. Filled with all the latest PLL advances, this celebrated sourcebook now includes new chapters on frequency synthesis...CAD for PLLs...mixed-signal PLLs...all-digital PLLs...and software PLLs_plus a new collection of sample communications applications. An essential tool for achieving cutting-edge PLL design, the Sixth Edition of Phase-Locked Loops features: A wealth of easy-to-use methods for designing phase-locked loops Over 200 detailed illustrations New to this edition: new chapters on frequency synthesis, including fractional-N PLL frequency synthesizers using sigma-delta modulators; CAD for PLLs, mixed-signal PLLs, all-digital PLLs, and software PLLs; new PLL communications applications, including an overview on digital modulation techniques Inside this Updated PLL Design Guide • Introduction to PLLs • Mixed-Signal PLL Components • Mixed-Signal PLL Analysis • PLL Performance in the Presence of Noise • Design Procedure for Mixed-Signal PLLs • Mixed-Signal PLL Applications • Higher Order Loops • CAD and Simulation of Mixed-Signal PLLs • All-Digital PLLs (ADPLLs) • CAD and Simulation of ADPLLs • The Software PLL (SPLL) • The PLL in Communications • State-of-the-Art Commercial PLL Integrated Circuits • Appendices: The Pull-In Process • The Laplace Transform • Digital Filter Basics • Measuring PLL Parameters

This book is intended for the reader who wishes to gain a solid understanding of Phase Locked Loop architectures and their applications. It provides a unique balance between both theoretical perspectives and practical design trade-offs. Engineers faced with real world design problems will find this book to be a valuable reference providing example implementations, the underlying equations that describe synthesizer behavior, and measured results that will improve confidence that the equations are a reliable predictor of system behavior. New material in the Fourth Edition includes partially integrated loop filter implementations, voltage controlled oscillators, and modulation using the PLL.

This second edition of Phaselock Techniques is -- as was the first -- the standard reference on the subject. Greatly expanded and largely rewritten to reflect a better understanding of the subject, the book presents much new material, some published here for the first time. Explanation of fundamentals is improved and expanded, and description of applications is greatly increased. The first portion of the book is a well-organized review of the fundamentals of phaselock, as well as a discussion of the underlying problems faced by designers. Most of this mateiral has been rewritten from the first edition. The material that follows deals with practical aspects of component circuits and with rational procedures for deciding upon phaselock loop parameters. The remaining chapters provide engineering descriptions and analyses of applications of phaselock. Most of this material is unique.Included are discussions of phaselocked modulators and demodulators, sythesizers, receivers, transponders, oscillator stabilizers, and data synchronizers.

A tutorial of phase-locked loops from analogue implementations to digital and optical designs. This text establishes a foundation of continuous-time analysis techniques and maintains a consistent notation as discrete-time and non-uniform sampling are presented. It examines charge pumps and the complementary sequential phase detector. Frequency synthesizers and digital divider analysis/techniques are also included in this edition.; Starting with a historical overview, presenting analogue, digital, and optical PLLs, discussing phase noise analysis, and including circuits/algorithms for data synchronization, this volume illustrates the techniques being used in this field.; The subjects covered include: development of phase-locked loops from analogue to digital and optical, with notation throughout; expanded coverage of the loop filters used to design second- and third-order PLLs; design examples on delay-locked loops used to synchronize circuits on CPUs and ASICS; new material on digital dividers that dominate a frequency synthesizer's noise floor; techniques to analytically estimate the phase noise of a divider; presentation of optical phase-locked loops with primers on the optical components and fundamentals of optical mixing; a section on automatic frequency control to provide frequency-locking of the lasers instead of phase-locking; and a presentation of charge pumps, counters, and delay-locked loops.; This volume includes the topics that should be of interest to wireless, optics, and the traditional phase-locked loop specialist to design circuits and software algorithms.