Frequency-Domain Characterization of Power Distribution Networks

Frequency-Domain Characterization of Power Distribution Networks

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Frequency-Domain Characterization of Power Distribution Networks Istvan Novak Jason R. Miller

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ISBN-13: 978-1-59693-200-5

Cover design by Yekaterina Ratner

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To our families

Contents Preface

xi

Acknowledgments

xv

CHAPTER 1 Introduction

1

1.1 Evolution of Power Distribution Networks 1.2 The Importance of Frequency Domain 1.3 The Impedance Matrix 1.3.1 Size of the Matrix 1.4 When Time-Domain Characterization Is Useful 1.5 If and When Time-Domain Response Is Needed 1.6 The Characterization Process 1.7 The Modeling Process References

1 2 4 6 8 8 9 10 11

CHAPTER 2 Simulation Methods and Tools

13

2.1 2.2 2.3 2.4

Spreadsheet Calculations SPICE AC MATLAB Field Solvers 2.4.1 Classifications 2.4.2 Convergence 2.4.3 Sources of Simulation Inaccuracies References

13 15 16 17 18 22 25 41

CHAPTER 3 Characterization and Modeling of Vias

43

3.1 Introduction 3.2 Via Partial Inductance 3.3 Via Loop Inductance 3.3.1 Measurement Correlation 3.4 Via Arrays 3.4.1 Measuring Via Arrays 3.4.2 Modeling Via Arrays

43 43 47 54 56 57 60

vii

viii

Contents

3.4.3 Parameterizing Via Arrays 3.4.4 Via Array Summary Points References CHAPTER 4 Characterization and Modeling of Planes and Laminates

61 65 65

67

4.1 Introduction 4.2 Analytical Plane Models 4.2.1 Analytical Models for Rectangular Plane Shapes 4.2.2 Analytical Plane Models for Arbitrary Plane Shapes 4.3 Transmission-Line Models 4.3.1 Transmission-Line Grid Models for Rectangular Plane Shapes 4.3.2 Transmission-Line Grid Models for Arbitrary Plane Shapes 4.3.3 Transmission Matrix Model for Arbitrary Plane Shapes 4.4 Effect of Plane Parameters on Self- and Transfer Impedances 4.4.1 Impact of Dielectric Thickness with Regular Conductors 4.4.2 Impact of Plane Thickness 4.4.3 Parallel Plane Pairs 4.4.4 Impact of Dielectric Constant and Dielectric Losses 4.4.5 Run Time Versus Number of Cells 4.5 Characterization of Plane and Laminate Parameters 4.5.1 DC Resistance of Planes 4.5.2 Measuring DC Resistance of Planes 4.5.3 Effect of Perforations on DC Plane Resistance 4.5.4 Simulating DC Voltage Drop and Effective Plane Resistance 4.5.5 Characterization of Mid- and High-Frequency Plane Parameters References

67 68 68 81 84 84 86 90 92 92 94 96 96 97 98 98 100 101 102 102 120

CHAPTER 5 Impedance Measurements Basics

123

5.1 Selecting the Measurement Concept for PDN Impedance 5.2 The Importance of Two-Port Connections 5.3 Self- and Transfer Impedance 5.4 Transforming Measured S-Parameters 5.4.1 Measuring Self-Impedance with Magnitude |Zx| > W M 1

(2.3)

Inserting the appropriate expressions for the magnetic and electric energy components and simplifying, we obtain: l