Phase-Lock Basics

Jan. 23, 2008
Phase-lock loops (PLLs) have become invaluable circuits in electronic circuits, in everything from frequency-modulated (FM) radio tuners to high-performance microwave frequency synthesizers. In the second edition of Phase-Lock Basics, author ...

Phase-lock loops (PLLs) have become invaluable circuits in electronic circuits, in everything from frequency-modulated (FM) radio tuners to high-performance microwave frequency synthesizers. In the second edition of Phase-Lock Basics, author William Egan builds upon the basic design principles contained in the first edition of his text, exploring the effects of noise on PLL performance.

Mr. Egan is uniquely qualified to present this textbook course on PLLs, having worked with the legendary Professor Tim Healy at Santa Clara University (Santa Clara, CA) in the 1980's and organized a twoquarter PLL course at the university which eventually became the basis for the first edition of his PLL book. He opens Part 1 of his text with an examination of ideal PLLs without noise and how to construct a basic loop, including how to perform a classical analysis of a basic loop and how to construct a mathematical block diagram of a PLL for analysis with mathematical software tools such as MATLAB. He offers a close look at the various components of a PLL, such as the different types of phase detectors (including the use of a balanced frequency mixer as a phase detector), voltage-controlled oscillators (VCOs), and different types of loop filters.

From the description of loop components, the book proceeds to a study of closed-loop and open-loop equations for analyzing a PLL's loop response and how to perform loop stability analysis for the sake of improving the overall stability of a PLL. Examples are presented for examining the stability of a variety of different PLL configurations, including first-order, second-order, and third-order loops, as well as examples for computing open-loop gain and phase. From there, the analysis continues with a study of loop transient response, and how the loop responses to different input conditions, such as ramp and parabolic inputs, and how to establish the initial conditions for a transient-response analysis.

The text includes methods for analyzing loop modulation responses, such as FM and phase modulation, and how to interpret various error responses, including the effects of phase and frequency modulation at the input of a PLL or its VCO. It offers acquisition formulas for a second-order loop with sinetype phase detectors as well as general equations for basic analysis approaches.

One of the more useful sections in the text is Chapter 10, which is devoted to extensions of earlier designs and specific applications. Some of these applications deal with the creation of a biphase Costas loop for carrier signal recovery, the design of a stabilized VCO, the design of a circuit for synchronizing to a pseudorandom bit sequence, and how to build simpler designs into higher-order loop circuits.

Just beyond the mid-point of the book begins Part 2, which is focused on the effects of noise on achieving phase-lock conditions. Mr. Egan shows how to represent noise modulation mathematically and how to interpret the results of typical measured oscillator spectra. He explores the limits of the noise spectrum and explains the power spectrum of a signal source along with spectral displays of noise sidebands and phase noise. One of the chapters in Part 2 covers different loop responses to phase noise, including how phase noise from the reference source is processed in the loop and how to achieve optimum loop performance under conditions of both input and VCO noise. One of the factors in achieving the best performance is finding the optimum loop bandwidth in terms of noise levels and the tradeoff suffered in tuning speed.

Additional chapters in Part 2 detail methods for representing additive noise, how a PLL responds to additive noise, how to treat a PLL as a demodulator, how the loop's various performance parameters are affected by the presence of noise, PLL cycle skipping due to noise, how to model nonlinear operation in a locked loop, how to incorporate acquisition aids in the presence of noise, and how to handle band limited noise in the design of a PLL source. For those needing more information, the final chapter provides additional sources for further studies in PLLs.

The text can serve as a standalone educational tool or as part of an instructional program with an educator. The book provides many classroom-type problems that help a reader understand the basic functions and operation of PLLs, with answers included for all of these example problems. As the author relates, the answers included in the book should be very accurate since most of them have been proven through actual design and use. The author has taught many electrical engineering graduate programs based on the material in the book, and has augmented a great deal of the information first presented in the first edition with models and examples using mathematical software tools, such as MATLAB. Price: $100; clothbound, 441 pages. Wiley-Interscience, John Wiley & Sons, 111 River St., MS-8-01, Hoboken, NJ 07030-5774; (201) 748- 6364, Internet:

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