Electromagnetic Shielding Theory and Applications

Comprehensive Resource for Understanding Electromagnetic Shielding Concepts and Recent Developments in the Field

This book describes the fundamental, theoretical, and practical aspects to approach electromagnetic shielding with a problem-solving mind, either at a design stage or in the context of an issue-fixing analysis of an existing configuration. It examines the main shielding mechanisms and how to analyze any shielding configuration, taking into account all the involved aspects. A detailed discussion on the possible choices of parameters suitable to ascertain the performance of a given shielding structure is also presented by considering either a continuous wave EM field source or a transient one.

To aid in reader comprehension, both a theoretical and a practical engineering point of view are presented with several examples and applications included at the end of main chapters. Sample topics discussed in the book include:

• Concepts in transient shielding including performance parameters and canonical configurations
• Time domain performance of shielding structures, thin shields, and overall performance of shielding enclosures (cavities)
• How to install adequate barriers around the most sensitive components/systems to reduce or eliminate interference
• Details on solving core fundamental issues for electronic and telecommunications systems via electromagnetic shielding

For industrial researchers, telecommunications/electrical engineers, and academics studying the design of EM shielding structures, this book serves as an important resource for understanding both the logistics and practical applications of electromagnetic shielding. It also includes all recent developments in the field to help professionals stay ahead of the curve in their respective disciplines.

Salvatore Celozzi, PhD, is a Professor at the University of Roma "La Sapienza", Italy. He has published more than one hundred and fifty papers in refereed journals or in proceedings of international conferences, mainly in the fields of electromagnetic shielding, transmission lines, and printed circuits.

Rodolfo Araneo, PhD, is a Professor at the University of Roma "La Sapienza", Italy. His fields of expertise are electromagnetic shielding, numerical methods, power systems, and renewable energies.

Paolo Burghignoli, PhD, is an Associate Professor at the University of Roma "La Sapienza", Italy. His research topics are in the areas of antennas, advanced electromagnetic materials, and electromagnetic shielding.

Giampiero Lovat, PhD, is an Assistant Professor at the University of Rome "La Sapienza", Italy. His research encompasses theoretical and numerical studies on electromagnetic shielding, periodic structures, electrodynamics of graphene, leakage phenomena in planar structure, and transient electromagnetics.

Contents

1 Electromagnetics behind Shielding 7

1.1 De_nitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.2 Notation, Symbology, and Acronyms . . . . . . . . . . . . . . . . . . . . . . . . 9

1.3 Macroscopic Electromagnetism and Maxwell's Equations . . . . . . . . . . . . . 9

1.4 Constitutive Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.5 Discontinuities and Singularities . . . . . . . . . . . . . . . . . . . . . . . . . . 15

1.6 Initial Conditions, Boundary Conditions, and Causality . . . . . . . . . . . . . 16

1.7 Poynting's Theorem and Energy Considerations . . . . . . . . . . . . . . . . . . 17

1.8 Fundamental Theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

1.8.1 Uniqueness Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

1.8.2 Reciprocity Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

1.8.3 Equivalence Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

1.8.4 Duality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

1.8.5 Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

1.8.6 Image Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

1.8.7 Babinet's Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

1.9 Wave Equations, Helmholtz's Equations, Potentials, and Green's Functions . . 26

1.10 Basic Shielding Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

1.11 Source Inside or Outside the Shielding Structure and Reciprocity . . . . . . . . 30

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

2 Shielding Materials 33

2.1 Standard Metallic and Ferromagnetic Materials . . . . . . . . . . . . . . . . . . 33

2.2 Ferrimagnetic Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

2.3 Ferroelectric Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

2.4 Thin Films and Conductive Coatings . . . . . . . . . . . . . . . . . . . . . . . . 41

2.5 Other Materials Suitable for EM Shielding Applications . . . . . . . . . . . . . 43

2.5.1 Structural Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

2.5.2 Conductive Polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

2.5.3 Conductive Glasses and Transparent Materials . . . . . . . . . . . . . . 43

2.5.4 Conductive (and Ferromagnetic or Ferrimagnetic) Papers . . . . . . . . 44

2.6 Special Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

2.6.1 Metamaterials and Chiral Materials . . . . . . . . . . . . . . . . . . . . 44

2.6.2 Composite Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

2.6.3 Graphene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

1

2 CONTENTS

2.6.4 Other Nanomaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

2.6.5 High-Temperature Superconductors . . . . . . . . . . . . . . . . . . . . 50

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

3 Figures of Merit for Shielding Con_gurations 57

3.1 (Local) Shielding E_ectiveness . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

3.2 The Global Point of View . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

3.3 Other Proposals of Figures of Merit . . . . . . . . . . . . . . . . . . . . . . . . 60

3.4 Energy-Based, Content-Oriented De_nition . . . . . . . . . . . . . . . . . . . . 64

3.5 Performance of Shielded Cables . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

4 Shielding E_ectiveness: Plane Waves 67

4.1 Electromagnetic Plane Waves: De_nitions and Properties . . . . . . . . . . . . 67

4.2 Uniform Plane Waves Incident on a Planar Shield . . . . . . . . . . . . . . . . . 69

4.2.1 Transmission-Line Approach . . . . . . . . . . . . . . . . . . . . . . . . 69

4.2.2 The Single Planar Shield . . . . . . . . . . . . . . . . . . . . . . . . . . 72

4.2.3 Multiple (or Laminated) Shields . . . . . . . . . . . . . . . . . . . . . . 76

4.3 Plane Waves Normally Incident on Cylindrical Shielding Surfaces . . . . . . . . 78

4.4 Plane Waves against Spherical Shields . . . . . . . . . . . . . . . . . . . . . . . 85

4.5 Extension of the TL Analogy to Near-Field Sources . . . . . . . . . . . . . . . . 86

4.5.1 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

5 Shielding E_ectiveness: Near-Field Sources 101

5.1 Spectral-Domain Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

5.1.1 Maxwell's Equations in the Spectral Domain . . . . . . . . . . . . . . . 102

5.1.2 TM/TE Decomposition and Equivalent Transmission Lines . . . . . . . 103

5.1.3 Spectral Dyadic Green's Functions . . . . . . . . . . . . . . . . . . . . . 107

5.1.4 Field Evaluation in the Spatial Domain . . . . . . . . . . . . . . . . . . 110

5.2 LF Magnetic Shielding of Metal Plates: Parallel Loop . . . . . . . . . . . . . . 112

5.2.1 Spectral-Domain Approach . . . . . . . . . . . . . . . . . . . . . . . . . 113

5.2.2 Vector Magnetic-Potential Approach . . . . . . . . . . . . . . . . . . . . 117

5.2.3 Approximate Formulations . . . . . . . . . . . . . . . . . . . . . . . . . 117

5.3 LF Magnetic Shielding of Metal Plates: Perpendicular Loop . . . . . . . . . . . 120

5.4 LF Magnetic Shielding of Metal Plates: Parallel Current Line . . . . . . . . . . 123

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

6 Transient Shielding 131

6.1 Performance Parameters: De_nitions and Properties . . . . . . . . . . . . . . . 131

6.2 Transient Sources: Plane Waves and Dipoles . . . . . . . . . . . . . . . . . . . . 134

6.2.1 Transient Uniform Plane Waves . . . . . . . . . . . . . . . . . . . . . . . 134

6.2.2 Transient Dipoles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

6.3 Numerical Solutions via Inverse-Fourier Transform . . . . . . . . . . . . . . . . 138

6.4 Analytical Solutions in Canonical Con_gurations . . . . . . . . . . . . . . . . . 139

6.4.1 Transient Plane Waves on a Single-Layer Screen . . . . . . . . . . . . . 139

3

6.4.2 Transient Dipoles: The Cagniard{de Hoop Method . . . . . . . . . . . . 143

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

7 Numerical Methods for Shielding Analyses 157

7.1 Finite-Element Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

7.2 Method of Moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172

7.3 Finite-Di_erence Time-Domain Method . . . . . . . . . . . . . . . . . . . . . . 190

7.4 Finite Integration Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201

7.5 Transmission-Line Matrix Method . . . . . . . . . . . . . . . . . . . . . . . . . 206

7.6 Partial Element Equivalent Circuit Method . . . . . . . . . . . . . . . . . . . . 210

7.7 Test Case for Comparing Numerical Methods . . . . . . . . . . . . . . . . . . . 216

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218

8 Apertures in Planar Metal Screens 233

8.1 Historical Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233

8.2 Statement of the Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235

8.3 Low-Frequency Analysis: Transmission through Small Apertures . . . . . . . . 235

8.4 The Small Circular Aperture . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237

8.4.1 Bethe's Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237

8.4.2 Spectral-Domain Formulation . . . . . . . . . . . . . . . . . . . . . . . . 242

8.5 Small Noncircular Apertures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243

8.6 Finite Number of Small Apertures . . . . . . . . . . . . . . . . . . . . . . . . . 244

8.7 Apertures of Arbitrary Shape: Integral-Equation Formulation . . . . . . . . . . 246

8.8 Rules of Thumb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251

9 Enclosures 257

9.1 Modal Expansion of Electromagnetic Fields inside a Metallic Enclosure . . . . 258

9.2 Oscillations inside an Ideal Source-Free Enclosure . . . . . . . . . . . . . . . . . 260

9.3 The Enclosure Dyadic Green Function . . . . . . . . . . . . . . . . . . . . . . . 261

9.4 Excitation of a Metallic Enclosure . . . . . . . . . . . . . . . . . . . . . . . . . 264

9.5 Damped Oscillations inside Enclosures with Lossy Walls and Quality Factor . . 265

9.6 Apertures in Perfectly Conducting Enclosures . . . . . . . . . . . . . . . . . . . 267

9.6.1 Small-Aperture Approximation . . . . . . . . . . . . . . . . . . . . . . . 267

9.6.2 Rigorous Analysis: Integral-Equation Formulation . . . . . . . . . . . . 269

9.6.3 Aperture-Cavity Resonances . . . . . . . . . . . . . . . . . . . . . . . . 271

9.7 Small Loading E_ects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273

9.8 The Rectangular Enclosure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274

9.8.1 Symmetry Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . 277

9.9 Shielding E_ectiveness of a Rectangular Enclosure with an Aperture . . . . . . 278

9.9.1 Numerical models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278

9.9.2 Analytical models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282

9.10 Case Study: Rectangular Enclosure with a Circular Aperture . . . . . . . . . . 285

9.10.1 External Sources: Plane-Wave Excitation . . . . . . . . . . . . . . . . . 286

9.10.2 Internal Sources: Electric and Magnetic Dipole Excitations . . . . . . . 288

9.11 Overall Performance in the Frequency Domain . . . . . . . . . . . . . . . . . . 294

4 CONTENTS

9.12 Overall Performance in the Time Domain . . . . . . . . . . . . . . . . . . . . . 297

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299

10 Cable Shielding 309

10.1 Transfer Impedance in Tubular Shielded Cables and Aperture E_ects . . . . . . 310

10.2 Relationship between Transfer Impedance and Shielding E_ectiveness . . . . . 315

10.3 Actual Cables and Harnesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317

11 Components and Installation Guidelines 321

11.1 Gaskets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321

11.2 Shielded Windows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324

11.3 Electromagnetic Absorbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325

11.4 Shielded Connectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327

11.5 Air-Ventilation Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327

11.6 Fuses, Switches, and Other Similar Components . . . . . . . . . . . . . . . . . . 327

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328

12 Frequency Selective Surfaces 331

12.1 Analysis of Periodic Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . 332

12.1.1 Floquet Theorem and Spatial Harmonics . . . . . . . . . . . . . . . . . 332

12.1.2 Plane-Wave Incidence on a Planar 1D Periodic Structure . . . . . . . . 333

12.1.3 Plane-Wave Incidence on a Planar 2D Periodic Structure . . . . . . . . 335

12.1.4 Integral Equation Formulation for Plane-Wave Incidence and Periodic

Green's Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335

12.1.5 Dipole Excitation of Planar 2D Periodic Structure . . . . . . . . . . . . 340

12.2 High- and Low-Pass FSSs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342

12.3 Band-Pass and Band-Stop FSSs . . . . . . . . . . . . . . . . . . . . . . . . . . . 345

12.3.1 Center-Connected Elements or N-Pole Elements . . . . . . . . . . . . . 346

12.3.2 Loop-Type Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347

12.3.3 Solid-Interior-Type Elements . . . . . . . . . . . . . . . . . . . . . . . . 347

12.3.4 Combinations and Fractal Elements . . . . . . . . . . . . . . . . . . . . 347

12.4 Recent Trends in FSSs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348

12.4.1 Multilayer and Cascaded FSSs . . . . . . . . . . . . . . . . . . . . . . . 348

12.4.2 3-D FSSs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349

12.4.3 2.5-D FSSs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351

12.4.4 Recon_gurable and Active FSSs . . . . . . . . . . . . . . . . . . . . . . 351

12.5 Absorbing FSSs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353

12.5.1 Circuit analog absorbers . . . . . . . . . . . . . . . . . . . . . . . . . . . 353

12.5.2 Absorptive Frequency Selective Reection/Transmission Structures . . . 354

12.6 Modeling and Design of FSSs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357

5

13 Shielding Design Guidelines 373

13.1 Establishment of the Shielding Requirements . . . . . . . . . . . . . . . . . . . 374

13.2 Assessment of the Number and Types of Functional Discontinuities . . . . . . . 375

13.3 Assessment of Dimensional Constraints and Non-Electromagnetic Characteristics

of Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376

13.4 Estimation of Shielding Performance . . . . . . . . . . . . . . . . . . . . . . . . 376

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377

14 Uncommon Ways of Shielding 379

14.1 Active Shielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379

14.2 Partial Shields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384

14.3 Chiral Shielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 386

14.4 Metamaterial Shielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391

A Electrostatic Shielding 399

A.1 Basic Laws of Electrostatics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399

A.2 Electrostatic Tools: Electrostatic Potential and Green's Functions . . . . . . . 402

A.3 Electrostatic Shields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405

A.3.1 Conductive Electrostatic Shields . . . . . . . . . . . . . . . . . . . . . . 405

A.3.2 Dielectric Electrostatic Shields . . . . . . . . . . . . . . . . . . . . . . . 409

A.3.3 Aperture E_ects in Conductive Shields . . . . . . . . . . . . . . . . . . . 414

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416

B Magnetic Shielding 417

B.1 Magnetic Shielding Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . 418

B.2 Calculation Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 421

B.3 Boundary-Value Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422

B.3.1 Spherical Magnetic Conducting Shield . . . . . . . . . . . . . . . . . . . 423

B.3.2 Cylindrical Magnetic Conducting Shield in a Transverse Magnetic Field 426

B.3.3 Cylindrical Magnetic Conducting Shield in a Parallel Magnetic Field . . 431

B.4 Ferromagnetic Shields with Hysteresis . . . . . . . . . . . . . . . . . . . . . . . 434

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434

C Statistical Electromagnetics for Shielding Enclosures 439

C.1 Statistical Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442

C.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 448

D Standards and Measurement Methods for Shielding Applications 453

D.1 MIL-STD 285 and IEEE STD-299 . . . . . . . . . . . . . . . . . . . . . . . . . 454

D.2 NSA 65-6 and NSA 94-106 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 459

D.3 ASTM E1851 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 459

D.4 ASTM D4935 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 460

D.5 MIL-STD 461G . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 462

D.6 Code of Federal Regulations, Title 47, Part 15 . . . . . . . . . . . . . . . . . . . 468

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D.7 ANSInSCTE 48-3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 471

D.8 MIL-STD 1377 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 472

D.9 IEC Standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473

D.10 ITU-T Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479

D.11 Automotive Standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484

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