IMPEDANCE BOUNDARY CONDITIONS IN

ELECTROMAGNETICS

Daniel Jay Hoppe, Ph.D.

Yahya Rahmat-Samii, Ph.D.

University of California at Los Angeles

A SUMMA Book

Taylor &Francis ' Publishers since 179H

Contents

Preface ix

Nomenclature xi

Abbreviations xvi

1 Introduction 1 1.1 Background 1 1.2 Scattering by Conducting Bodies 3 1.3 Scattering by Coated Conducting Bodies 4 1.4 Approximate Boundary Conditions 7 1.5 A Bit of History 8 1.6 Organization of This Book 9

2 Spectral Domain Theory of Higher Order Impedance Boundary Conditions 15 2.1 Step 1: Exact Spectral Domain Boundary Conditions 16 2.2 Step 2: Polynomial Approximations 19 2.3 Step 3: Coefficient Determination 20 2.4 Step 4: Construction of the Spatial Domain Equations 22 2.5 Special Cases 23

2.5.1 TIBC 24 2.5.2 SIBC . 24 2.5.3 GIBC 24

2.6 Conclusions 25

3 Planar Higher Order Impedance Boundary Conditions 27 3.1 Planar Dielectric Coatings 27

3.1.1 Exact Spectral Domain Boundary Conditions 28 3.1.2 Higher Order Impedance Boundary Conditions 30 3.1.3 Examples 33

3.2 Corrugated Conductors 38 3.3 Planar Chiral Coatings 40

3.3.1 Exact Spectral Domain Boundary Conditions 40

v

CONTENTS

3.3.2 Higher Order Impedance Boundary Conditions 43 3.3.3 Examples 43

3.4 Conclusions 46

Boundary Conditions for Curved Dielectric and Chiral Coatings 47 4.1 Scattering by Dielectric Coated Circular Cylinders using Planar

HOIBC 47 4.2 Higher Order Impedance Boundary Conditions for Curved Coat­

ings 57 4.2.1 Exact Spectral Domain Boundary Conditions 57 4.2.2 Higher Order Impedance Boundary Conditions 59 4.2.3 Examples 60

4.3 Conclusions 65

Scattering by a Dielectric-Filled Groove in a Ground Plane 67 5.1 Higher Order Impedance Boundary Condition Solution 68

5.1.1 Exterior Region 68 5.1.2 Interior Region 70 5.1.3 Edge Conditions 73

5.2 Exact Formulation: A Mode Matching Approach 77 5.3 Examples 83

5.3.1 Rectangular Grooves 83 5.3.2 Rectangular Groove: Lossy Dielectric 89 5.3.3 Asymmetrie Groove 89 5.3.4 Tapered Groove: Two-Layer Dielectric 92

5.4 Conclusions 94

Scattering by Two-Dimensional Dielectric-Coated Cylinders 97 6.1 HOIBC Solution of the Scattering Problem 98

6.1.1 Exterior Problem 98 6.1.2 Interior Problem 100 6.1.3 Method of Moments Solution 101

6.2 Exact Solution 104 6.3 Superquadric Cylinders 104 6.4 Examples 104

6.4.1 Impedance Approximation 105 6.4.2 Circular Cylinder: Bistatic RCS 106 6.4.3 Superquadric Cylinders: Bistatic RCS 108 6.4.4 Superquadric Cylinders: Monostatic RCS 110 6.4.5 Superquadric Cylinder: Magnetic Coating 112

6.5 Conclusions 113

CONTENTS vii

7 Scattering by Dielectric-Coated Bodies of Revolution 115 7.1 Problem Geometry 116 7.2 Fourier Series Decomposition 116 7.3 Exact Solution 118 7.4 HOIBC Solution 121

7.4.1 Exterior Region 121 7.4.2 Interior Region 122

7.5 Examples 126 7.5.1 Coated Sphere: Validation 127 7.5.2 Superquadric Cylinders: Curvature Effects 128 7.5.3 Spheroid: Monostatic RCS 132 7.5.4 Superquadric Cylinder: Magnetic Coating 132

7.6 Conclusions 134

Appendixes

A Properties of Exact Impedance Tensors 135 A.l Impedance Matrices for Lossless Boundaries 135 A.2 Impedance Matrices for Reciprocal Boundaries 137

B Symmetry Properties of the Polynomials P^ — Pg 139

C Surface Waves on Impedance Surfaces 143

D Plane Wave Scattering at an Impedance Plane 147

E Plane Wave Scattering at an Impedance Cylinder 151

F Matrix Elements for the CFIE Portion of the BOR Solution 155

G Transformation of the HOIBC onto the BOR 159

H Matrix Elements for the HOIBC Portion of the BOR 167

Solution

Bibliography 169

Index 173