Inductance E-Book

Clayton R. Paul

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Serie: Wiley - IEEE
• Sprache: Englisch

Seitenzahl: 372

Veröffentlichungsjahr: 2011

Beschreibung

The only resource devoted Solely to Inductance Inductance is an unprecedented text, thoroughly discussing "loop" inductance as well as the increasingly important "partial" inductance. These concepts and their proper calculation are crucial in designing modern high-speed digital systems. World-renowned leader in electromagnetics Clayton Paul provides the knowledge and tools necessary to understand and calculate inductance. Unlike other texts, Inductance provides all the details about the derivations of the inductances of various inductors, as well as: * Fills the need for practical knowledge of partial inductance, which is essential to the prediction of power rail collapse and ground bounce problems in high-speed digital systems * Provides a needed refresher on the topics of magnetic fields * Addresses a missing link: the calculation of the values of the various physical constructions of inductors--both intentional inductors and unintentional inductors--from basic electromagnetic principles and laws * Features the detailed derivation of the loop and partial inductances of numerous configurations of current-carrying conductors With the present and increasing emphasis on high-speed digital systems and high-frequency analog systems, it is imperative that system designers develop an intimate understanding of the concepts and methods in this book. Inductance is a much-needed textbook designed for senior and graduate-level engineering students, as well as a hands-on guide for working engineers and professionals engaged in the design of high-speed digital and high-frequency analog systems.

Leseprobe

CONTENTS

PREFACE

1: INTRODUCTION

1.1 HISTORICAL BACKGROUND

1.2 FUNDAMENTAL CONCEPTS OF LUMPED CIRCUITS

1.3 OUTLINE OF THE BOOK

1.4 “LOOP” INDUCTANCE VS. “PARTIAL” INDUCTANCE

2: MAGNETIC FIELDS OF DC CURRENTS (STEADY FLOW OF CHARGE)

2.1 MAGNETIC FIELD VECTORS AND PROPERTIES OF MATERIALS

2.2 GAUSS’S LAW FOR THE MAGNETIC FIELD AND THE SURFACE INTEGRAL

2.3 THE BIOT-SAVART LAW

2.4 AMPÈRE’S LAW AND THE LINE INTEGRAL

2.5 VECTOR MAGNETIC POTENTIAL

2.6 DETERMINING THE INDUCTANCE OF A CURRENT LOOP: A PRELIMINARY DISCUSSION

2.7 ENERGY STORED IN THE MAGNETIC FIELD

2.8 THE METHOD OF IMAGES

2.9 STEADY (DC) CURRENTS MUST FORM CLOSED LOOPS

3: FIELDS OF TIME-VARYING CURRENTS (ACCELERATED CHARGE)

3.1 FARADAY’S FUNDAMENTAL LAW OF INDUCTION

3.2 AMPERE’S LAW AND DISPLACEMENT CURRENT

3.3 WAVES, WAVELENGTH, TIME DELAY, AND ELECTRICAL DIMENSIONS

3.4 HOW CAN RESULTS DERIVED USING STATIC (DC) VOLTAGES AND CURRENTS BE USED IN PROBLEMS WHERE THE VOLTAGES AND CURRENTS ARE VARYING WITH TIME?

3.5 VECTOR MAGNETIC POTENTIAL FOR TIME-VARYING CURRENTS

3.6 CONSERVATION OF ENERGY AND POYNTING’S THEOREM

3.7 INDUCTANCE OF A CONDUCTING LOOP

4: THE CONCEPT OF “LOOP” INDUCTANCE

4.1 SELF INDUCTANCE OF A CURRENT LOOP FROM FARADAY’S LAW OF INDUCTION

4.2 THE CONCEPT OF FLUX LINKAGES FOR MULTITURN LOOPS

4.3 LOOP INDUCTANCE USING THE VECTOR MAGNETIC POTENTIAL

4.4 NEUMANN INTEGRAL FOR SELF AND MUTUAL INDUCTANCES BETWEEN CURRENT LOOPS

4.5 INTERNAL INDUCTANCE VS. EXTERNAL INDUCTANCE

4.6 USE OF FILAMENTARY CURRENTS AND CURRENT REDISTRIBUTION DUE TO THE PROXIMITY EFFECT

4.7 ENERGY STORAGE METHOD FOR COMPUTING LOOP INDUCTANCE

4.8 LOOP INDUCTANCE MATRIX FOR COUPLED CURRENT LOOPS

4.9 LOOP INDUCTANCES OF PRINTED CIRCUIT BOARD LANDS

4.10 SUMMARY OF METHODS FOR COMPUTING LOOP INDUCTANCE

5: THE CONCEPT OF “PARTIAL” INDUCTANCE

5.1 GENERAL MEANING OF PARTIAL INDUCTANCE

5.2 PHYSICAL MEANING OF PARTIAL INDUCTANCE

5.3 SELF PARTIAL INDUCTANCE OF WIRES

5.4 MUTUAL PARTIAL INDUCTANCE BETWEEN PARALLEL WIRES

5.5 MUTUAL PARTIAL INDUCTANCE BETWEEN PARALLEL WIRES THAT ARE OFFSET

5.6 MUTUAL PARTIAL INDUCTANCE BETWEEN WIRES AT AN ANGLE TO EACH OTHER

5.7 NUMERICAL VALUES OF PARTIAL INDUCTANCES AND SIGNIFICANCE OF INTERNAL INDUCTANCE

5.8 CONSTRUCTING LUMPED EQUIVALENT CIRCUITS WITH PARTIAL INDUCTANCES

6: PARTIAL INDUCTANCES OF CONDUCTORS OF RECTANGULAR CROSS SECTION

6.1 FORMULATION FOR THE COMPUTATION OF THE PARTIAL INDUCTANCES OF PCB LANDS

6.2 SELF PARTIAL INDUCTANCE OF PCB LANDS

6.3 MUTUAL PARTIAL INDUCTANCE BETWEEN PCB LANDS

6.4 CONCEPT OF GEOMETRIC MEAN DISTANCE

6.5 COMPUTING THE HIGH-FREQUENCY PARTIAL INDUCTANCES OF LANDS AND NUMERICAL METHODS

7: “LOOP” INDUCTANCE VS. “PARTIAL” INDUCTANCE

7.1 LOOP INDUCTANCE VS. PARTIAL INDUCTANCE: INTENTIONAL INDUCTORS VS. NONINTENTIONAL INDUCTORS

7.2 TO COMPUTE “LOOP” INDUCTANCE, THE “RETURN PATH” FOR THE CURRENT MUST BE DETERMINED

7.3 GENERALLY, THERE IS NO UNIQUE RETURN PATH FOR ALL FREQUENCIES, THEREBY COMPLICATING THE CALCULATION OF A “LOOP” INDUCTANCE

7.4 COMPUTING THE “GROUND BOUNCE” AND “POWER RAIL COLLAPSE” OF A DIGITAL POWER DISTRIBUTION SYSTEM USING “LOOP” INDUCTANCES

7.5 WHERE SHOULD THE “LOOP” INDUCTANCE OF THE CLOSED CURRENT PATH BE PLACED WHEN DEVELOPING A LUMPED-CIRCUIT MODEL OF A SIGNAL OR POWER DELIVERY PATH?

7.6 HOW CAN A LUMPED-CIRCUIT MODEL OF A COMPLICATED SYSTEM OF A LARGE NUMBER OF TIGHTLY COUPLED CURRENT LOOPS BE CONSTRUCTED USING “LOOP” INDUCTANCE?

7.7 MODELING VIAS ON PCBS

7.8 MODELING PINS IN CONNECTORS

7.9 NET SELF INDUCTANCE OF WIRES IN PARALLEL AND IN SERIES

7.10 COMPUTATION OF LOOP INDUCTANCES FOR VARIOUS LOOP SHAPES

7.11 FINAL EXAMPLE: USE OF LOOP AND PARTIAL INDUCTANCE TO SOLVE A PROBLEM

APPENDIX: FUNDAMENTAL CONCEPTS OF VECTORS

A.1 VECTORS AND COORDINATE SYSTEMS

A.2 LINE INTEGRAL

A.3 SURFACE INTEGRAL

A.4 DIVERGENCE

A.5 CURL

A.6 GRADIENT OF A SCALAR FIELD

A.7 IMPORTANT VECTOR IDENTITIES

A.8 CYLINDRICAL COORDINATE SYSTEM

A.9 SPHERICAL COORDINATE SYSTEM

TABLE OF IDENTITIES, DERIVATIVES, AND INTEGRALS USED IN THIS BOOK

REFERENCES AND FURTHER READINGS

INDEX

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Library of Congress Cataloging-in-Publication Data:

Paul, Clayton R.

Inductance: loop and partial/Clayton R. Paul.

p. cm.

Includes bibliographical references and index.

ISBN 978-0-470-46188-4

1. Inductance. 2. Induction coils. I. Title. QC638.P38 2010

621.37’42-dc22

2009031434

This book is dedicated to the memory of my Father and my Mother

Oscar Paul

and

Louise Paul

PREFACE

This book has been written to provide a thorough and complete discussion of virtually all aspects of inductance: both “loop” and “partial.” There is considerable misunderstanding and misapplication of the important concepts of inductance. Undergraduate electrical engineering curricula generally discuss “loop” inductance only very briefly and only in one undergraduate course at the beginning of the junior year in a four-year curriculum. However, that curriculum is replete with the analysis of electric circuits containing the inductance symbol. In all those electric circuit analysis courses, the values of the inductors are given and are not derived from physical principles. Yet in the world of industry, the analyst must somehow obtain these values as well as construct inductors having the chosen values of inductance used in the circuit analysis. This book addresses that missing link: calculation of the values of the various physical constructions of inductors, both intentional and unintentional, from basic electromagnetic principles and laws.

In addition, today’s high-speed digital systems as well as high-frequency analog systems are using increasingly higher spectral content signals. Numerous “unintended” inductances such as those of the interconnection leads are becoming increasingly important in determining whether these high-speed, high-frequency systems will function properly. This is generally classified as the “signal integrity” of those systems and is an increasingly important aspect of digital system design as clock and data speeds increase at a dramatic rate. Some ten years ago the effects of interconnects such as printed circuit board lands on the function of the modules that lands interconnect were not important and could be ignored. Today, it is critical that circuit models of these interconnects be included in any analysis of the overall system. The concept of “partial inductance” is the critical link in being able to model these interconnects. Partial inductance is not covered in any undergraduate electrical engineering course but is becoming increasingly important in digital system design. A substantial portion of this book is devoted to that topic.

One of the important contributions of this book is the detailed derivation of the loop and partial inductances of numerous configurations of currentcarrying conductors. Although the derivations are sometimes tedious, there is nothing we can do about it because the results are dictated by the laws of electromagnetics, and these can be complicated. Unlike other textbooks, all the details regarding derivations for the inductance of inductors are given. Although these are simplified where possible, only so much simplification can be accepted if the reader is to have a clear and unambiguous view of how the result is obtained.

In Chapter 1 we discuss inductance and show important parallels between inductance and capacitance along with some historical details. All of the derivations of the inductance of various inductors first require that we obtain their magnetic fields. Chapter 2 is devoted to this task. The fundamental laws of Biot-Savart, Gauss, and Ampere are discussed, and numerous calculations of the magnetic fields are obtained from them. In addition, the vector magnetic potential method of computing the magnetic fields is also discussed, along with the method of images and energy stored in the magnetic field. In Chapter 3 we provide a complete explanation of how the inductance, which is computed for dc currents, can be used to characterize the effect of time-varying currents. Maxwell’s equations for time-varying currents are discussed in detail. An iterative solution of them is given which shows why and when the inductor, derived for dc currents, can be used to characterize the effects of time-varying currents.

All aspects of the derivation of the “loop” inductance of various currentcarrying loops are covered in Chapter 4. The flux linkage method, the vector magnetic potential method, and the Neumann integral for determining the “loop” inductance are used, and the “loop” inductances are calculated from all three methods. The proximity effect for closely spaced conductors is discussed along with the loop inductance of various transmission lines.

In Chapter 5 we provide details for computation of the “partial” inductances of wires. Both the self-partial inductance of wires and the mutual partial inductances between wires are derived. These generic results can then be used to “build” a model for other current-carrying structures. Chapter 6 contains all corresponding details about the derivation of the partial inductances of conductors of rectangular cross section, referred to as “lands.” The concept of geometric mean distance as an aid to the calculation of partial inductances is discussed and derived for various structures.

The final chapter of the book, Chapter 7, provides a focus on when one should use “loop” inductance and when one should use “partial” inductance for determining the effect of current-carrying conductors. This chapter is meant to provide a simple discussion of this in order to focus the results of previous chapters. The chapter concludes with the solution of a problem involving coupling between two circuit loops using the “loop” inductance method and then using the “partial” inductance method. Both methods yield the same answer, as expected. This example clearly shows the advantages of using “partial” inductance to characterize “unintentional inductors” such as wires and lands.

With the present and increasing emphasis on high-speed digital systems and high-frequency analog systems, it is imperative that system designers develop an intimate understanding of the concepts and methods in this book. No longer can we rely on low-speed, low-frequency systems to keep us from needing to learn these new concepts and analysis skills.

The author would like to acknowledge Dr. Albert E. Ruehli of the IBM T.J. Watson Research Center for many helpful discussions of partial inductance over the years.

CLAYTON R. PAUL

Macon, Georgia