As the author says in his introduction, "Phase-locked loops are a well-established and very widely used circuit technique in modern electronic systems." They appear in many signal processing applications, in frequency generators and synthesisers, and are used as modulators and demodulators to impress and recover information onto and from sinusoidal carriers. As with many other non-linear control applications, the great usefulness and indispensibility of the technique has forced development beyond the theoretical understanding of the non-linear dynamics, and so there is a great body of practical knowledge justified principally by the fact that "if you do this, it works". As the engineering maxim has it: "The engineer does what he can, not what he'd ideally like to do."

Much of this accepted body of knowledge is laid bare in this book, which is aimed at busy practising graduate engineers who may seek to apply these techniques in a time-limited situation, rather than at the reflective and scholarly researcher. For instance, there are just seven references, one of which is to the classic text Phaselock techniques by F. M. Gardner, and two of the others to published papers of the author.

The PLL is a nonlinear control problem because the phase detector usually has a limited range of phase error which it can detect, and because there is a feedback loop around this nonlinear detection characteristic. PLLs behave predictably in the presence of well conditioned signals, and in the presence of limited classes of noise and interference.

However, in many practical applications in the modern world there are multiple signals competing for the PLL's attention and somehow it has to make up its mind on to which of these signals it will lock. As in any arbitration problem, small amounts of added noise can then completely change the behaviour observed.

We have, therefore, an interesting situation where there is a large amount of knowledge of the well-behaved PLL, but a great silence on the problem areas. The behaviour of PLLs in the presence of competing signals is a problem in electromagnetic compatibility (EMC), about which the European Union has recently laid down many rules. Thus it is an important research area, and while this book will help students get started in the field, serious discussion of the problems is lacking.

That said, the presentation of the ideas in this book is orderly and logical; it is accessible to those already trained in linear systems theory and the elements of control engineering. It is a useful book for pedagogical purposes and contains some interesting real-life practical applications.

With the great progress made recently in the area of non-linear dynamics and the mathematics of chaotic systems, it is possible that the art of using PLLs in practical situations may now be due for further advances.

David J. Jefferies is senior lecturer in electronic engineering, information technology and mathematics, University of Surrey.

## Phase-Locked Loops: Principles and Practice

Author - Paul V. Brennan

ISBN - 0 333 65571

Publisher - Macmillan

Price - £22.00

Pages - 204