Inductance: Loop and Partial

Inductance: Loop and Partial

by CLAYTON R. PAUL
Released December 2009
Publisher(s): Wiley-IEEE Press
ISBN: 9780470461884

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Book description

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.

Table of contents

  1. Cover
  2. Title
  3. Copyright
  4. PREFACE
  5. 1: INTRODUCTION
    1. 1.1 HISTORICAL BACKGROUND
    2. 1.2 FUNDAMENTAL CONCEPTS OF LUMPED CIRCUITS
    3. 1.3 OUTLINE OF THE BOOK
    4. 1.4 "LOOP" INDUCTANCE VS. "PARTIAL" INDUCTANCE
  6. 2: MAGNETIC FIELDS OF DC CURRENTS (STEADY FLOW OF CHARGE)
    1. 2.1 MAGNETIC FIELD VECTORS AND PROPERTIES OF MATERIALS
    2. 2.2 GAUSS'S LAW FOR THE MAGNETIC FIELD AND THE SURFACE INTEGRAL
    3. 2.3 THE BIOT-SAVART LAW
    4. 2.4 AMPÈRE'S LAW AND THE LINE INTEGRAL
    5. 2.5 VECTOR MAGNETIC POTENTIAL
    6. 2.6 DETERMINING THE INDUCTANCE OF A CURRENT LOOP: A PRELIMINARY DISCUSSION
    7. 2.7 ENERGY STORED IN THE MAGNETIC FIELD
    8. 2.8 THE METHOD OF IMAGES
    9. 2.9 STEADY (DC) CURRENTS MUST FORM CLOSED LOOPS
  7. 3: FIELDS OF TIME-VARYING CURRENTS (ACCELERATED CHARGE)
    1. 3.1 FARADAY'S FUNDAMENTAL LAW OF INDUCTION
    2. 3.2 AMPERE'S LAW AND DISPLACEMENT CURRENT
    3. 3.3 WAVES, WAVELENGTH, TIME DELAY, AND ELECTRICAL DIMENSIONS
    4. 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?
    5. 3.5 VECTOR MAGNETIC POTENTIAL FOR TIME-VARYING CURRENTS
    6. 3.6 CONSERVATION OF ENERGY AND POYNTING'S THEOREM
    7. 3.7 INDUCTANCE OF A CONDUCTING LOOP
  8. 4: THE CONCEPT OF “LOOP” INDUCTANCE
    1. 4.1 SELF INDUCTANCE OF A CURRENT LOOP FROM FARADAY'S LAW OF INDUCTION
    2. 4.2 THE CONCEPT OF FLUX LINKAGES FOR MULTITURN LOOPS
    3. 4.3 LOOP INDUCTANCE USING THE VECTOR MAGNETIC POTENTIAL
    4. 4.4 NEUMANN INTEGRAL FOR SELF AND MUTUAL INDUCTANCES BETWEEN CURRENT LOOPS
    5. 4.5 INTERNAL INDUCTANCE VS. EXTERNAL INDUCTANCE
    6. 4.6 USE OF FILAMENTARY CURRENTS AND CURRENT REDISTRIBUTION DUE TO THE PROXIMITY EFFECT
    7. 4.7 ENERGY STORAGE METHOD FOR COMPUTING LOOP INDUCTANCE
    8. 4.8 LOOP INDUCTANCE MATRIX FOR COUPLED CURRENT LOOPS
    9. 4.9 LOOP INDUCTANCES OF PRINTED CIRCUIT BOARD LANDS
    10. 4.10 SUMMARY OF METHODS FOR COMPUTING LOOP INDUCTANCE
  9. 5: THE CONCEPT OF “PARTIAL” INDUCTANCE
    1. 5.1 GENERAL MEANING OF PARTIAL INDUCTANCE
    2. 5.2 PHYSICAL MEANING OF PARTIAL INDUCTANCE
    3. 5.3 SELF PARTIAL INDUCTANCE OF WIRES
    4. 5.4 MUTUAL PARTIAL INDUCTANCE BETWEEN PARALLEL WIRES
    5. 5.5 MUTUAL PARTIAL INDUCTANCE BETWEEN PARALLEL WIRES THAT ARE OFFSET
    6. 5.6 MUTUAL PARTIAL INDUCTANCE BETWEEN WIRES AT AN ANGLE TO EACH OTHER
    7. 5.7 NUMERICAL VALUES OF PARTIAL INDUCTANCES AND SIGNIFICANCE OF INTERNAL INDUCTANCE
    8. 5.8 CONSTRUCTING LUMPED EQUIVALENT CIRCUITS WITH PARTIAL INDUCTANCES
  10. 6: PARTIAL INDUCTANCES OF CONDUCTORS OF RECTANGULAR CROSS SECTION
    1. 6.1 FORMULATION FOR THE COMPUTATION OF THE PARTIAL INDUCTANCES OF PCB LANDS
    2. 6.2 SELF PARTIAL INDUCTANCE OF PCB LANDS
    3. 6.3 MUTUAL PARTIAL INDUCTANCE BETWEEN PCB LANDS
    4. 6.4 CONCEPT OF GEOMETRIC MEAN DISTANCE
    5. 6.5 COMPUTING THE HIGH-FREQUENCY PARTIAL INDUCTANCES OF LANDS AND NUMERICAL METHODS
  11. 7: "LOOP" INDUCTANCE VS. "PARTIAL" INDUCTANCE
    1. 7.1 LOOP INDUCTANCE VS. PARTIAL INDUCTANCE: INTENTIONAL INDUCTORS VS. NONINTENTIONAL INDUCTORS
    2. 7.2 TO COMPUTE "LOOP" INDUCTANCE, THE "RETURN PATH" FOR THE CURRENT MUST BE DETERMINED
    3. 7.3 GENERALLY, THERE IS NO UNIQUE RETURN PATH FOR ALL FREQUENCIES, THEREBY COMPLICATING THE CALCULATION OF A "LOOP" INDUCTANCE
    4. 7.4 COMPUTING THE "GROUND BOUNCE" AND "POWER RAIL COLLAPSE" OF A DIGITAL POWER DISTRIBUTION SYSTEM USING "LOOP" INDUCTANCES
    5. 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?
    6. 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. 7.7 MODELING VIAS ON PCBS
    8. 7.8 MODELING PINS IN CONNECTORS
    9. 7.9 NET SELF INDUCTANCE OF WIRES IN PARALLEL AND IN SERIES
    10. 7.10 COMPUTATION OF LOOP INDUCTANCES FOR VARIOUS LOOP SHAPES
    11. 7.11 FINAL EXAMPLE: USE OF LOOP AND PARTIAL INDUCTANCE TO SOLVE A PROBLEM
  12. APPENDIX: FUNDAMENTAL CONCEPTS OF VECTORS
    1. A.1 VECTORS AND COORDINATE SYSTEMS
    2. A.2 LINE INTEGRAL
    3. A.3 SURFACE INTEGRAL
    4. A.4 DIVERGENCE
    5. A.5 CURL
    6. A.6 GRADIENT OF A SCALAR FIELD
    7. A.7 IMPORTANT VECTOR IDENTITIES
    8. A.8 CYLINDRICAL COORDINATE SYSTEM
    9. A.9 SPHERICAL COORDINATE SYSTEM
  13. TABLE OF IDENTITIES, DERIVATIVES, AND INTEGRALS USED IN THIS BOOK
  14. REFERENCES AND FURTHER READINGS
  15. INDEX

Product information

  • Title: Inductance: Loop and Partial
  • Author(s): CLAYTON R. PAUL
  • Release date: December 2009
  • Publisher(s): Wiley-IEEE Press
  • ISBN: 9780470461884