**Reversible electric control of exchange bias in a multiferroic...**

Reversible electric control of exchange bias in a multiferroic field-effect device

(Parte **1** de 11)

Magnetoelectric Devices

Gordon R. Slemon

Professor and Head, Department of ElectricaI Engineering University of Toronto

John Wiley and Sons, Ine.

New York . London . Sydney

Copyright © 1966 by John Wiley & Sons, Inc,

Ali rights reserved. This book or any part thereof must not be reproduced in any form without the written permission of the publisher.

Library of Congress Catalog Card Number: 6-21039 Printed in the United States of America

This book is concerned with understanding, modeling, analyzing, and designing those devices that are used to convert, transfonn, and control electrical energy. Included are transducers, actuators, transforrners, magnetic arnplifiers, anel rotating machines. In introducing the generic term "magnetoelectric" to denote this group of devices, 1 have sought to emphasize their predorninantly magnetic nature, while distinguishing them from other well-established groupings such as electronic and microwave devices.

Chapter 1 is devoted to a study of some of the basic energy conversion processes anel to an examination 01' the properties 01' lhe importam materiais used in exploiting thcsc processes. Particular emphasis is placcd ou a study ofIerromagnctism, inclueling thc mechanism offorce production betwcen sections 01' ferrornagneric material.

Chapter 2 introduces some 01' the concepts that are useful in elcvising approximate analytical models for nonlinear magnetic elements. Thc derivation of equivalent electric circuirs to represent rnultilirnbed magnetic systems is discussed.

ln Chapter 3, the modcling concepts of Chapter 2 are applicd in analyzing the performance of transforrners, saturable reactors, and other static magnetic devices.

Chapters 4 anel 5 are devoted to rotaling electric machines. General equivalent circuit rnodels are developed for two broad classes ofmachines, narnely cornrnutator and polyphase rnachines. Specific machine lypessuch as shunt, series, cornpound, induction, synchronous, reluctancc, polyphase commutator, single-phase, anel synchro machines-are analyzcd by adaptation of the two basic equivalem circuit models. A featurc 01' lhe analytical approach is that the effects 01' magnetic n on linearitv can be includcd approxirnately in any 01' the modcIs.

It is my conviction that lhe essence 01' cngineering is designo Thc ultimare objective of each phase 01' preparatory study should therefore be to incrcase lhe studenls' capabil ity to design uscful components ând syslems. The routc to this ultimate objcctive has four distinct but vi PREFACE interrelated àspects: an understanding of the physical processes, the derivation of approximate models, techniques of analysis, and, finally, designo The first objective of this book is the development of a physical under- standing of the forces and energies arising from electric and magnetic phenomena. To appreciate the implications of this objective, consider, for example, the force tending to elose an air gap in a ferromagnetic core. This force can be detcrrnincd by use of thc principies of energy conservation and virtual displacement. While this method is analytically simple, it gives little physical appreciation of the origin and arca of action of the force. In Chapter I, this force is developed frorn direct interaction of magnetic moments in the material and is also deduced indirectly from energy considerations. The first approach is intended to give a qualitative physical understanding; the second approach is intended for quantitative analysis. A large part of the book is devoted to developing models for devices.

All models are by nature approximate in that they retain only that inforrnation which is considered necessary for prediction of perforrnance. Thus, engineering judgment is required in choosing an adequate model for each situation. Various kinds of model (e.g., simultaneous equations, linear graphs, block diagrams) can be used to represent magnetoelectric devices. 1 have chosen to emphasize the use of equivalent circuit models bccausc these are also encountered in parallel studies of other electric and clectronic systems. A familiarity with methods of analysis for linear anel nonlinear electric circuits can be reasonably assumed. A further advantage of equivalent circuits is that individual parameters generally can be related

directly to the dirncnsions and material properties of the device. Much has been written in recent years about generalized models for

clectric machines. In many of the proposed modcls, linearity has been assumcd. But most electrical devices have important operating regions for which magnetic nonlinearity is signiflcant. Thus the purely linear models have been highly restricted in the gencrality of their engineering usefulness. In the 'models that appear in this book, provision has been made for the inclusion of magnetic nonlinearity while retaining general models that can be adapted to represent various classes of machines. Since most of the models are in the Iorm of equivalent circuits, very

little space has been given to methods of analysis of these models. It has been assumed that parallel courses in electric circuits, differential equations, computer programming, and system analysis wiI1have provided an adequate range of analytical techniques. Some analysis is included to derive typical operating characteristics. Most of the models derived in this book are appropriate for the solution of either dynamic or stcadystate performance. They can therefore be integrated directly into

PREFACE vii representations of systems either in the form of equívalent círcuits or as transfer functions. The methods of control system analysis have not been included, since it is assurned that most curricula provide for a general course in control systems.

The process of design is dependent on concepts obtained from the understanding, modeling, and analysis phases. It also requires an exerci se of cngineering judgment which initial1y may be sornewhat disconcertíng to the beginning student. The objective in most of the design problems is Iimited to choosing a reasonable set of principal dimensions for a device. The resulting device may be larger and costlier than the optimized design of an expert, but it is generally workable,

A number of problems have been included at the end of each chapter.

These problems draw on ali the concepts of understanding, modeling, analysis, and designo Many typical dcvice applications have been descríbed in the problem sections rather than in the text. Answers have been included for some sections of most problems to reassure the student in his progresso In design problems, approximate answers have been suggested to indicate to the student whether he is "within the ball park."

The student using this book should have previous farniliarity with electrical physics (particularly electric and magnetic fie1ds) and circuit analysis (preferably incJuding elementary Laplace transforms). At the University of Toronto, lhe study of magnetoelectric devices is given sornewhat greater emphasis than is usual in current American curricula. Ali the material in the book, with the exception of Section 5.5.5 to Section 5.7.4 and Section 5.8.5 to Section 5.9.3, is currently presented in about 60 lecture hours, partly in lhe third year and partly in the fourth year.

4.6.2 to 4.8, 5.2.3 to 5.2.5, 5.4.5 and 5.4.6, 5.5.5 to 5.9.3. Significant parts of Chapter 1 may be considered eJsewhere in some curricula. . I wish to thank my colleagues at the University of Toronto for their many helpful suggestions, criticism, and discussion. In particular, I wish to acknowledge the encouragement and assistance given to me by Professor J. M. Harn, Dean-elect of the Faculty of Applied Science and

Engineering. To the many undergraduate and postgraduate students who have studied with me during the development and final preparation ofthis book, I am particular1y grateful. It is to you that this book is dedicated.

Gordon R. Slemon

Toronto, Canada June, 1966

CONTENTS 1 Electrical Encrgy Conversion Processes 1

2 Analysis of Magnetic Systcms 106

2.1 Approximate Models for B-H Characteristics 106 2.2 Eddy Currents 121

2.3 Ideal Transformers 1262.4 Equivalent Circuits for Complex Magnetic Systems 129 2.5 Analysis 01' Permancnt-Magnet Systerns 137

3 Transformatíon of Electric Energy 167

4 Commutator Machínes 232

4.6 Performance of Motors 287 4.7 Control Systems Using Cornmutator Machines 306 4.8 Some Design Concepts and Constraints 312 Problems 317 l j

5 Polyphase Machines

5.1 General Magnetic and Winding Arrangements 5.2 Magnetic Field Analysis

5.3 Equivalent Circuits 5.4 Polyphase lnduction Machines

5.5 Polyphase Synchronous Machines 5.6 Polyphase Synchronous-Reluctance Machines 5.7 Polyphase Commutator Machines 5.8 Unbalanced Operation of Polyphase Machines

5.9 Synchronous ControI Devices Problems lndex

Magnetoelectric Devices TRANSDUCERS, TRANSFORMERS, AND MACHrnNES

Chapter 1

1.1 THE PURPOSE AND SCOPE OE THIS BOOK

This book is concerned with electrical devices that are used for the con- version of electric energy to or from mechanical energy, or to electric energy in a different formo Let us look first at sÇ>meof the needs for e1ectrical devices or machines since it is only by appreciating the functions which they must perform and lhe environment in which they operare that we can assess the properties which will be significant. Electrical devices are required for the following.

1. The proeluction 01' largc amounts 01' c1ectric power from hydraulic or steam turbincs. (Need for thcsc rnachines may be partially superscded in the futurc by the devclopmcnt 01" dircct methods for converting thcrrnal energy to electrical Iorrn.) 2. The transformation of electric energy to a voltage suitable for bulk transmission anel its retransforrnation to voltages suitable for distribution

and use. 3. The conversion of available electric power to other desired forrns involving a change of frequency, source characteristics, etc. 4. The production of mcchanical energy with relatively constant mechanical speed for a majority of the applications of electric motors, large anel srnall.

5. The control, with varying degrees of accuracy, of the speed and position of mechanical systems. 6. The measurcment of mcchanical quantities by the production of proportional electric signals.

If electrical machines predominare in all these roles, it is because they allow economical centralized production of power, relatively simple distribution, economical reconversion to useful form, and a high degrce of control and automation. To contrivc a useful device, various materiais must be assembled in

SOME ENERGY CONVERSION PHENOMENA 3

2 ELECTRIC ENERGY CONVERSlON PROCESSES of that pragmatic approach by which the engineer seeks to obtain the maximum utility in his design and analysis with the minimum expenditure of effort.

such a way as to exploit some physical phenomenon. Chapter I of this book is devoted to a study of some of the basic energy conversion processes on which electrieal devices are based and to an examination of lhe properties of the more important materiaIs that are used.

The concepts of electric and magnetic fields are very useful in reaching an understanding of these basic energy conversion processes. But when these processes are exploited in complex machines, the wealth 01' information contained in the fieId approach generally becomes unwieldy. It is usually possible to extract only a fcw descriptive parameters through whieh the important operational properties of the machine may be adequateJy described. In many instances this extraction results in an equivalent electric circuit; in others, a set of equations is produeed. When making this step from the fieId to the cireuit point of view for purposes of easy analysis, we should keep in mind that the maehine designer must reverse this process, and, starting with the required terminal properties of the maehine, must specify its dimensions. Chapter 2 covers methods by which simple models such as equivalent circuits may be produced for magnetic systems. These models are then used in Chapter 3 to analyze the properties of transformers and some other stationary electrical-toeIectricaI conversion devices.

The remainder of the book is devoted to rotating machines and to systems of these machines. Although these machines are, for convenience, divided into a nurnber of categories, they are ali based on a small and essentially common set of energy conversion phenornena. The appropriate pararnetcrs of these machines are deveIoped frorn a knowIedge of the dimensions and materials, These pararnctcrs are then incorporated into analytieal models, usually in the form of equivalent eircuits. From an analysis of these models, the behavior of these machines may be predicted

and their applications studied. Thus the purposes of this book are to introduce the reader to those physical principIes that have been most widely exploited by engineers to produce electrical devices and maehines, to show how materiaIs are

arranged to produce the device and how the performance is limited by the physical limits of the material properties, to develop means by which the behavior of the machine may be readily predicted in various applications, and to provide some background for the understanding and even for the invention of new devices. Throughout the book, numerous approximations are made to provide the maximum simplicity and yet to retain enough information for the problem under study. Naturally, these approximate analyses neglect various secondary factors which may be significant in certain circumstances. A further purpose of the book is the development

1.2 SOME ENERGY CONVERSION PI-IENOMENA

[1 this section let us examine, in a qualitative manner, some of the elcctrical phenomena that result in the production of mechanicaI force. Figure 1.1 shows lhe familiar forces of repulsion between similarly

Fig. J.1 Force betwecn "electrically charged bodies. (a) Opposite charges. (b) Like charges.

charged bodies. lf in Fig. l.la the two bodies are allowed to move in response to these forces, mechanical work is done. During this motion some of the energy which was originally used to separate the positive charge from the negative is converted to mechanical energy. To pull apart the bodies in Fig. I.la requires an input of mechanical energy that is converted into an electrical formo By generalizing from this simple example, it follows that any system exhibiting mechanical forces of eIectrical origin is capable of hoth electrical-to-rnechanical and mechanicalto-electrical energy conversion.

Figure 1.2a shows the forces that exist on parallelcurrent-carrying

5SOME ENERGY CONVERSION PHENOMENAELECTRIC ENERÇV CONVERSION PROCESSES4 conductors. Displacement of the conductors in the direction of the forces results in conversion 01' energy frorn electrical form to mechanical forrn. The two current-carrying coils 01' Fig. 1.2b exhibit both forces of attraction anel torques tending to align the two coils. The torque produced in this arrangemenl provides ror thc development of mechanical energy in rotary

(Parte **1** de 11)