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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Serie: Wiley Series in Microwave and Optical Engineering
- Sprache: Englisch
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.
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Table of Contents
Cover
Title Page
Copyright
About the Authors
Preface
1 Electromagnetics Behind Shielding
1.1 Definitions
1.2 Notation, Symbology, and Acronyms
1.3 Macroscopic Electromagnetism and Maxwell's Equations
1.4 Constitutive Relations
1.5 Discontinuities and Singularities
1.6 Initial Conditions, Boundary Conditions, and Causality
1.7 Poynting's Theorem and Energy Considerations
1.8 Fundamental Theorems
1.9 Wave Equations, Helmholtz's Equations, Potentials, and Green's Functions
1.10 Basic Shielding Mechanisms
1.11 Source Inside or Outside the Shielding Structure and Reciprocity
References
Notes
2 Shielding Materials
2.1 Standard Metallic and Ferromagnetic Materials
2.2 Ferrimagnetic Materials
2.3 Ferroelectric Materials
2.4 Thin Films and Conductive Coatings
2.5 Other Materials Suitable for EM Shielding Applications
2.6 Special Materials
References
3 Figures of Merit for Shielding Configurations
3.1 (Local) Shielding Effectiveness
3.2 The Global Point of View
3.3 Other Proposals of Figures of Merit
3.4 Energy-Based, Content-Oriented Definition
3.5 Performance of Shielded Cables
References
4 Shielding Effectiveness: Plane Waves
4.1 Electromagnetic Plane Waves: Definitions and Properties
4.2 Uniform Plane Waves Incident on a Planar Shield
4.3 Plane Waves Normally Incident on Cylindrical Shielding Surfaces
4.4 Plane Waves Against Spherical Shields
4.5 Extension of the TL Analogy to Near-Field Sources
References
5 Shielding Effectiveness: Near-Field Sources
5.1 Spectral-Domain Approach
5.2 LF Magnetic Shielding of Metal Plates: Parallel Loop
5.3 LF Magnetic Shielding of Metal Plates: Perpendicular Loop
5.4 LF Magnetic Shielding of Metal Plates: Parallel Current Line
References
6 Transient Shielding
6.1 Performance Parameters: Definitions and Properties
6.2 Transient Sources: Plane Waves and Dipoles
6.3 Numerical Solutions via Inverse-Fourier Transform
6.4 Analytical Solutions in Canonical Configurations
References
7 Numerical Methods for Shielding Analyses
7.1 Finite-Element Method
7.2 Method of Moments
7.3 Finite-Difference Time-Domain Method
7.4 Finite Integration Technique
7.5 Transmission-Line Matrix Method
7.6 Partial Element Equivalent Circuit Method
7.7 Test Case for Comparing Numerical Methods
References
8 Apertures in Planar Metal Screens
8.1 Historical Background
8.2 Statement of the Problem
8.3 Low-Frequency Analysis: Transmission Through Small Apertures
8.4 The Small Circular Aperture
8.5 Small Noncircular Apertures
8.6 Finite Number of Small Apertures
8.7 Apertures of Arbitrary Shape: Integral-Equation Formulation
8.8 Rules of Thumb
References
9 Enclosures
9.1 Modal Expansion of Electromagnetic Fields Inside a Metallic Enclosure
9.2 Oscillations Inside an Ideal Source-Free Enclosure
9.3 The Enclosure Dyadic Green Function
9.4 Excitation of a Metallic Enclosure
9.5 Damped Oscillations Inside Enclosures with Lossy Walls and Quality Factor
9.6 Apertures in Perfectly Conducting Enclosures
9.7 Small Loading Effects
9.8 The Rectangular Enclosure
9.9 Shielding Effectiveness of a Rectangular Enclosure with an Aperture
9.10 Case Study: Rectangular Enclosure with a Circular Aperture
9.11 Overall Performance in the Frequency Domain
9.12 Overall Performance in the Time Domain
References
10 Cable Shielding
10.1 Transfer Impedance in Tubular Shielded Cables and Aperture Effects
10.2 Relationship Between Transfer Impedance and Shielding Effectiveness
10.3 Actual Cables and Harnesses
References
11 Components and Installation Guidelines
11.1 Gaskets
11.2 Shielded Windows
11.3 Electromagnetic Absorbers
11.4 Shielded Connectors
11.5 Air-Ventilation Systems
11.6 Fuses, Switches, and Other Similar Components
References
12 Frequency Selective Surfaces
12.1 Analysis of Periodic Structures
12.2 High- and Low-Pass FSSs
12.3 Band-Pass and Band-Stop FSSs
12.4 Recent Trends in FSSs
12.5 Absorbing FSSs
12.6 Modeling and Design of FSSs
References
13 Shielding Design Guidelines
13.1 Establishment of the Shielding Requirements
13.2 Assessment of the Number and Types of Functional Discontinuities
13.3 Assessment of Dimensional Constraints and Non-Electromagnetic Characteristics of Materials
13.4 Estimation of Shielding Performance
References
14 Uncommon Ways of Shielding
14.1 Active Shielding
14.2 Partial Shields
14.3 Chiral Shielding
14.4 Metamaterial Shielding
References
Appendix A: Electrostatic Shielding
A.1 Basic Laws of Electrostatics
A.2 Electrostatic Tools: Electrostatic Potential and Green's Functions
A.3 Electrostatic Shields
References
Appendix B: Magnetic Shielding
B.1 Magnetic Shielding Mechanism
B.2 Calculation Methods
B.3 Boundary-Value Problems
B.4 Ferromagnetic Shields with Hysteresis
References
Appendix C: Statistical Electromagnetics for Shielding Enclosures
C.1 Statistical Analyses
C.2 Examples
References
Appendix D: Standards and Measurement Methods for Shielding Applications
D.1 MIL-STD 285 and IEEE STD-299
D.2 NSA 65-6 and NSA 94-106
D.3 ASTM E1851
D.4 ASTM D4935
D.5 MIL-STD 461G
D.6 Code of Federal Regulations, Title 47, Part 15
D.7 ANSI/SCTE 48-3
D.8 MIL-STD 1377
D.9 IEC Standards
D.10 ITU-T Recommendations
D.11 Automotive Standards
References
Index
End User License Agreement
List of Tables
Chapter 2
Table 2.1 Electrical Conductivity of the Most Common Conductive Materials.
Table 2.2 Conductivity and Range of the Relative Magnetic Permeability of th...
Table 2.3 Real Part of the Permittivity and Losses of Common Ferroelectric M...
Table 2.4 Surface Resistivity and Thickness of Coatings.
Chapter 7
Table 7.1 Dimensions of Shielding Configuration for Simulation.
Chapter 9
Table 9.1
,
, and
Variables for the Eight Sources of the Unit Cell
Table 9.2
and
Coefficients for the Eight Sources of the Unit Cell
Table 9.3 Values of the Global Shielding Parameters
Table 9.4 Values of the Local (Center) Shielding Parameters
Appendix C
Table C.1 Global TD Shielding Parameters.
Table C.2 Local (Center) TD Shielding Parameters.
Table C.3 Values of Kurtosis and Skewness in the Distributions of the Local ...
Appendix D
Table D.1 MIL-STD 461G Applicable Sections.
Table D.2 FCC-Part 15 Limits for Intentional and Class B Unintentional Radia...
Table D.3 FCC-Part 15 Limits for Class A Unintentional Digital Radiators.
Table D.4 IEC Emission Limits.
Table D.5 ITU-T K.43 Immunity Requirements.
Table D.6 ITU-T K.48 Immunity Requirements.
Table D.7 SAE/ISO EMC Standards.
List of Illustrations
Chapter 1
Figure 1.1 Illustrating the Babinet principle:
(a)
definition of the inciden...
Chapter 2
Figure 2.1 Example of a normalized hysteresis loop.
Chapter 3
Figure 3.1 Configuration with (
a
) and without (
b
) the shield for the evaluat...
Figure 3.2 Geometry of the enclosure with a rectangular aperture illuminated...
Chapter 4
Figure 4.1 Uniform plane wave impinging on a shield of finite thickness
an...
Figure 4.2 Uniform plane wave impinging on a planar multilayer shield and eq...
Figure 4.3 Intrinsic impedance
of three typical shielding materials.
Figure 4.4 Reflection-loss
and absorption-loss
terms as functions of fre...
Figure 4.5 Multiple-reflection-loss term
as a function of frequency for th...
Figure 4.6 Generic
th layer as a length of transmission line and as a two-p...
Figure 4.7 Comparison between the SE of double shields and a single-layer sh...
Figure 4.8 Uniform plane wave incident on an infinitely long cylindrical shi...
Figure 4.9
and
uniform plane waves normally incident on an infinitely lo...
Figure 4.10 SE of a glass cylindrical surface with
cm, and
cm under
(
a
Figure 4.11 Plane-wave incidence on a multilayer spherical shield (
a
) and on...
Figure 4.12 Infinitesimal dipole source arbitrarily oriented illuminating an...
Figure 4.13 Magnitude of the normalized wave impedances as functions of the ...
Figure 4.14 Magnitude of the contributions to the SE of an infinite casting ...
Figure 4.15 Magnitude of the contributions to the SE of an infinite casting ...
Figure 4.16 Basic low-frequency field sources.
Figure 4.17 Comparison among the wave impedances of low-frequency field sour...
Figure 4.18 Frequency trend of the shielding effectiveness achievable by mea...
Figure 4.19 Frequency trend of the shielding effectiveness achievable by mea...
Figure 4.20 Frequency trend of the shielding effectiveness achievable by mea...
Figure 4.21 Frequency trend of the shielding effectiveness achievable by mea...
Chapter 5
Figure 5.1 General multilayered shield excited by electric and magnetic impr...
Figure 5.2 Magnetic-induction distribution in the presence of an infinite pl...
Figure 5.3 Circular current loop parallel to an infinite planar metallic scr...
Figure 5.4 Equivalent networks for the determination of the magnetic field
Figure 5.5 Theoretical
as a function of frequency of an infinite planar me...
Figure 5.6 Circular current loop perpendicular to an infinite planar metalli...
Figure 5.7 Theoretical
as a function of frequency of an infinite planar me...
Figure 5.8 Horizontal current wire parallel to an infinite plate.
Figure 5.9 Theoretical
as a function of frequency for an infinite planar m...
Chapter 6
Figure 6.1 Transient plane-wave incidence upon a single-layer homogeneous, i...
Figure 6.2 A vertical electric or magnetic dipole (VED, VMD) placed in vacuu...
Figure 6.3 Complex plane of the
variable with the integration paths adopte...
Figure 6.4 Peak reduction efficiency
for a slow-transient VED; the insets ...
Figure 6.5 Peak reduction efficiency
for a slow-transient VMD; the insets ...
Chapter 7
Figure 7.1 Electromagnetic sources in an inhomogeneous region
(
a
) and two ...
Figure 7.2 Subdomain triangular basis functions of the first (
a
) and second ...
Figure 7.3 First-order two-dimensional triangular vector basis function (
a
) ...
Figure 7.4 Three-dimensional FE-BI domain and boundary diagram.
Figure 7.5 Distribution of the FE mesh of the whole model (
a
) and detail of ...
Figure 7.6 Comparison of results between measured SE and simulated GSE of 3D...
Figure 7.7 Geometry in the
-plane of the buried HV cables and the shielding...
Figure 7.8 SE versus thickness (
a
) and total losses (
b
) versus thickness for...
Figure 7.9 Electromagnetic sources radiating in presence of a PEC surface.
Figure 7.10 Triangular rooftop vector RWG basis function.
Figure 7.11 Application of the surface equivalence principle.
Figure 7.12 Shielded box with instrument display window (
); magnitude of th...
Figure 7.13 Resonant PEC box with many apertures on the front plate.
Figure 7.14 Slotted box excited by a monopole antenna with absorbing sheet (
Figure 7.15 The basic geometry illustrating the relationship between the loc...
Figure 7.16 Domain decomposition according to the fast multipole method.
Figure 7.17
computed by means of the MLFMM compared with measured data and...
Figure 7.18 Effect on
due to two wire configurations
Figure 7.19 Time variation of the
-component of electric field for the shie...
Figure 7.20 Transient electric field intensity at the center of the slot for...
Figure 7.21 Electric shielding effectiveness
(
b
) of a rectangular PEC encl...
Figure 7.22 Spatial arrangement of field components in the Yee FDTD grid.
Figure 7.23 Structured mesh (
a
); graded mesh (
b
); mesh with subgrid (
c
).
Figure 7.24 Analysis space used in the cases of the direct strikes and subse...
Figure 7.25 Geometric configurations of the enclosures (
a
) and comparison of...
Figure 7.26 Geometric configuration of the set-up enclosure (
a
) and simulate...
Figure 7.27 Stubbed SCN (
a
); shunt node (
b
); and series node (
c
).
Figure 7.28 Comparison of 10 g SAR at
MHz for
(
a
) and influence of morph...
Figure 7.29 Volume cells for currents and surface cells for charges.
Figure 7.30 Equivalent PEEC circuits: Norton representation (
a
) and Thé veni...
Figure 7.31 Geometric configuration of the enclosures (
a
) and relevant elect...
Figure 7.32 Geometry of the test enclosure (sketch not in scale).
Figure 7.33 Comparison of electric SE results from different codes (
a
); reso...
Chapter 8
Figure 8.1 Transmission of the EM field through a finite aperture
cut in a...
Figure 8.2 TE and TM uniform plane-wave incidence on a perfectly conducting ...
Figure 8.3 Electric and magnetic polarizabilities of an elliptical aperture....
Figure 8.4 Row of
equidistant circular small apertures in a planar perfect...
Figure 8.5 Original problem (
a
); application of equivalence principle (
b
); a...
Figure 8.6 Qualitative effects of apertures on the surface electric current ...
Figure 8.7 SE of a single narrow slot of different lengths
as a function o...
Figure 8.8 SE of
identical narrow slots of length
cm as a function of fr...
Figure 8.9 SE of a single narrow slot of length
cm as a function of freque...
Chapter 9
Figure 9.1 Examples of enclosures: closed region with more than one boundary...
Figure 9.2 Enclosure with an aperture excited by an internal source (
a
) and ...
Figure 9.3 Original problem (
a
) and application of the equivalence principle...
Figure 9.4 Rectangular enclosure.
Figure 9.5 Unit cell of the 3D periodic structure used for the computation o...
Figure 9.6 Uniform plane wave impinging on a rectangular enclosure with a re...
Figure 9.7 Uniform plane wave impinging on a rectangular enclosure with a ci...
Figure 9.8 Electric SE at the center of the enclosure under test for plane-w...
Figure 9.9 Absolute value of the electric field inside the enclosure under
Figure 9.10 Same distribution as in Figure 9.9 at the frequency
MHz. (a)
π
...
Figure 9.11 Elemental electric or magnetic dipole radiating through a circul...
Figure 9.12 Magnitude of the electric field radiated at the point
(
m) by...
Figure 9.13 Same distribution as in Figure 9.12 but with the electric dipole...
Figure 9.14 Same distribution as in Figure 9.12 but with an elemental magnet...
Figure 9.15 Magnitude of the electric field as a function of
(
,
) produc...
Figure 9.16 Same distribution as in Figure 9.15 but with the electric dipole...
Figure 9.17 Enclosure under test.
Figure 9.18 Frequency trends of local and global shielding effectiveness par...
Figure 9.19 Cumulative distributions in case of (empty enclosure): (
a
) incid...
Figure 9.20 Cumulative distributions in case of (loaded enclosure): (
a
) inci...
Figure 9.21 Spectrum of the electric-field source.
Figure 9.22 Spectrum of the classical SE at three different positions.
Figure 9.23 Time trend of the
-component of the electric field without and ...
Figure 9.24 Load positions in the enclosure under test.
Chapter 10
Figure 10.1 Coupling through the shield of a coaxial line.
Figure 10.2 Normalized transfer impedance of tubular and braided shielded ca...
Figure 10.3 Detail of a braided shield surface.
Figure 10.4 Equivalent circuit of an elemental length of coaxial cable.
Chapter 11
Figure 11.1 Different types of shielded gaskets.
Figure 11.2 Equivalent circuit for a portion of a shielded gasket.
Figure 11.3 Different types of shielded windows.
Chapter 12
Figure 12.1 Example of
D array structures of metallic elements (
a
) and of a...
Figure 12.2
D (
a
) and
D (
b
) periodic structures under plane-wave incidence...
Figure 12.3 Multiport network representing a
D periodic structure under pla...
Figure 12.4 Periodical arrangement of infinitely long conducting elements un...
Figure 12.5 Wire-mesh (
a
), its equivalent circuit (
b
), and its transmission ...
Figure 12.6 Array of square patches (
a
), its equivalent circuit (
b
), and its...
Figure 12.7 Examples of center-connected elements: dipole (
a
), tripole (
b
), ...
Figure 12.8 Examples of loop-type elements: four-legged loaded element (
a
), ...
Figure 12.9 Examples of various combined elements.
Figure 12.10 Cascade of FSSs (
a
) and FSSs loaded by dielectric slabs (
b
).
Figure 12.11 Reconfigurable FSS with PIN diodes.
Figure 12.12 Circuit analog absorber (
a
) and its equivalent circuit (
b
).
Chapter 14
Figure 14.1 Three-phase line (conductor
:
m,
m; conductor
:
m,
m; ...
Figure 14.2 Magnetic-induction profiles with and without active shielding at...
Figure 14.3 Three-phase line (conductor
:
m,
m; conductor
:
m,
m; ...
Figure 14.4 Magnetic-induction profiles with and without active shielding at...
Figure 14.5 Wire current near a PEC or PMC shield (
a
) and configuration obta...
Figure 14.6 Split-ring resonator (
a
) and spiral resonator (
b
): transverse vi...
Figure 14.7 (
a
) Metamaterial wire-medium screen; (
b
) transverse view with ge...
Figure 14.8 Comparison between homogenized and full-wave MoM results for the...
Figure 14.9 Sketch of a metamaterial double WM screen.
Appendix A
Figure A.1 Neutral conductor under an external electrostatic field.
Figure A.2 Grounded conductor under an external electrostatic field.
Figure A.3 Conductive shield with no charge inside (
a
), and empty metallic r...
Figure A.4 Conductive shield with a charge inside (
a
), and conductive ground...
Figure A.5 Spherical dielectric shield under an external uniform electrostat...
Figure A.6 Cylindrical dielectric shield under an external uniform electrost...
Figure A.7 Infinitesimally thin, grounded conductive plane with a circular h...
Figure A.8 Spherical conductive shield with a circular aperture under an ext...
Appendix B
Figure B.1 Low-frequency shielding scenario.
Figure B.2 Magnetic-field distribution for cylindrical shields subjected to ...
Figure B.3 Spherical shell placed in a uniform external magnetic field.
Figure B.4 SE of a spherical shell (
cm) compared using different approxima...
Figure B.5 Skin depth
as a function of frequency for the materials conside...
Figure B.6 Cylindrical shell placed in a uniform external “transverse” magne...
Figure B.7 SE of a cylindrical shell (
cm,
mm) under a uniform transverse...
Figure B.8 Cylindrical shell placed in a uniform external “parallel” magneti...
Figure B.9 SE of a cylindrical shell (
cm,
mm) in a transverse uniform ma...
Appendix C
Figure C.1 Shielding enclosure under transient excitation (dimensions are
...
Figure C.2 Electric field
-component with and without the shielding enclosu...
Figure C.3 Frequency spectrum of the classical SE at three different positio...
Figure C.4 Cumulative distribution functions for the peak and derivative red...
Figure C.5 Cumulative distribution functions for the
.
Appendix D
Figure D.1 IEEE Std-299 measurement setup: (
a
) low-frequency range; (
b
) reso...
Figure D.2 NSA 94-106 performance requirements.
Figure D.3 ASTM D4935 measurement setup.
Figure D.4 Scheme for the determination of the scattering parameters (D.U.T....
Figure D.5 MIL-STD 461G basic measurement setups: (
a
) general test setup; (
b
Figure D.6 MIL-STD
emission limits: (
a
) magnetic field; (
b
) electric field...
Figure D.7 RS105 setup (
a
) and pulsed field waveform (
b
).
Figure D.8 ANSI/SCTE48-3 measurement setup.
Figure D.9 MIL-STD 1377 measurement setup: STI low-frequency setup (
a
) and S...
Figure D.10 IEC 61000-4-3 measurement setup for immunity tests.
Figure D.11 IEC 61000-4-21 reverberation chamber setup.
Guide
Cover
Title Page
Copyright
About the Authors
Preface
Table of Contents
Begin Reading
Appendix A: Electrostatic Shielding
Appendix B: Magnetic Shielding
Appendix C: Statistical Electromagnetics for Shielding Enclosures
Appendix D: Standards and Measurement Methods for Shielding Applications
Index
End User License Agreement
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Electromagnetic Shielding
Theory and Applications
Second Edition
Salvatore Celozzi
Rodolfo Araneo
Paolo Burghignoli
Giampiero Lovat
Electrical Engineering Department “La Sapienza” University Rome, Italy
This edition first published 2023© 2023 John Wiley & Sons, Inc. All rights reserved.
Edition HistoryJohn Wiley & Sons, Inc. (1e, 2008)
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Library of Congress Cataloging-in-Publication Data
Names: Celozzi, Salvatore, author.
Title: Electromagnetic shielding : theory and applications / Salvatore Celozzi, Rodolfo Araneo, Paolo Burghignoli, Giampiero Lovat.
Description: Second edition. | Hoboken, NJ, USA : Wiley, 2023. | Series: Wiley series in microwave and optical engineering | Includes bibliographical references and index.
Identifiers: LCCN 2022052851 (print) | LCCN 2022052852 (ebook) | ISBN 9781119736288 (hardback) | ISBN 9781119736295 (adobe pdf) | ISBN 9781119736301 (epub)
Subjects: LCSH: Shielding (Electricity) | Magnetic shielding.
Classification: LCC TK454.4.M33 C45 2022 (print) | LCC TK454.4.M33 (ebook) | DDC 621.34--dc23/eng/20221107
LC record available at https://lccn.loc.gov/2022052851
LC ebook record available at https://lccn.loc.gov/2022052852
Cover Design: WileyCover Image: © Zita/Shutterstock
About the Authors
Salvatore Celozzi was born in Rome, Italy, in 1964. He received the Laurea (cum laude) and Ph.D. degrees from La Sapienza University of Rome in 1988 and 1994, respectively.
He is a Full Professor at the University of Rome “La Sapienza” since 2005. He has authored more than 150 papers in international journals or conference proceedings, mainly in the fields of electromagnetic shielding and transmission lines. He is the co-author of the first edition of the book Electromagnetic Shielding (Wiley, 2008).
Prof. Celozzi has been the Chair of the EMC Chapter of the IEEE Central and South Italy Section from 1997 to 2006. He was the recipient of the Best Symposium Paper Award in 1998 and 2011 at the IEEE EMC Conferences. In 2002, he was the recipient of the IEEE EMC Society Award “Certificate of Technical Achievement” for outstanding contributions to the EMC Society, especially in the field of shielding and transmission line theory applied to printed circuit boards. He was serving as an Associate Editor for the IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY from 1995 to 2000 and is serving in the same role since 2016.
Rodolfo Araneo was born in Rome, Italy, in 1975. He received the Laurea (cum laude) and Ph.D. degrees in electrical engineering from La Sapienza University of Rome in 1999 and 2002, respectively. He is Full Professor in the same University since 2021.
In 1999, he was a Visiting Student at the National Institute of Standards and Technology, Boulder, CO, USA, where he was engaged in TEM cells and shielding. In 2000, he was a Visiting Researcher at the Department of Electrical and Computer Engineering, University of Missouri-Rolla (UMR), Rolla, MO, USA, where he was engaged in printed circuit boards and finite-difference time-domain techniques. He is currently a Full Professor at La Sapienza University of Rome. He has authored more than 200 papers in international journals and conference proceedings. He is the co-author of the first edition of the book Electromagnetic Shielding (Wiley, 2008). He serves as a reviewer for several international journals. His research interests include electromagnetic compatibility, energy harvesting, piezotronics based on piezoelectric ZnO nanostructures, graphene electrodynamics, development of numerical and analytical techniques for modeling high-speed printed circuit boards, shielding, transmission lines, periodic structures, and devices based on graphene.
Dr. Araneo was the recipient of the Past President's Memorial Award in 1999 from the IEEE Electromagnetic Compatibility Society. He is currently a General Chair of the IEEE International Conference on Environment and Electrical Engineering. In 2011, he was the recipient of the Best Paper Symposium Award at the 2011 IEEE EMC-S International Symposium on Electromagnetic Compatibility.
Paolo Burghignoli was born in Rome, Italy, in 1973. He received the Laurea degree (cum laude) in electronic engineering and the Ph.D. degree in applied electromagnetics from La Sapienza University of Rome, Rome, Italy, in 1997 and 2001, respectively.
In 1997, he joined the Department of Electronic Engineering, Sapienza University of Rome, where he is currently Associate Professor with the Department of Information Engineering, Electronics and Telecommunications. In 2004, he was a Visiting Research Assistant Professor at the University of Houston, Houston, TX, USA. From 2010 to 2015, he was an Assistant Professor at La Sapienza University of Rome, where he has been an Associate Professor since 2015. In 2017, he received the National Scientific Qualification for the role of a Full Professor of electromagnetic fields at Italian Universities. He is currently teaching courses in electromagnetic fields, advanced antenna engineering, and analytical techniques for wave phenomena for B.Sc., M.Sc., and Ph.D. programs in the ICT area at La Sapienza University of Rome. He has authored about 250 articles in international journals, books, and conference proceedings. His research interests include the analysis and design of planar antennas and arrays, leakage phenomena in uniform and periodic structures, numerical methods for integral equations and periodic structures, propagation and radiation in metamaterials, electromagnetic shielding, transient electromagnetics, and graphene electromagnetics.
Dr. Burghignoli was a recipient of the “Giorgio Barzilai” Laurea Prize in 1996–1997 presented by the former Institute of Electrical and Electronics Engineers (IEEE) Central and South Italy Section, the 2003 IEEE MTT-S Graduate Fellowship, and the 2005 Raj Mittra Travel Grant for junior researchers presented at the IEEE AP-S Symposium on Antennas and Propagation, Washington, DC, USA. He was a Secretary of the 12th European Microwave Week in 2009 and a member of the Scientific Board and the Local Organizing Committee of the 41st Photonics and Electromagnetics Research Symposium in 2019. In 2016 and 2020, the IEEE Antennas and Propagation Society recognized him as an outstanding reviewer for the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION. He is currently an Associate Editor of the Institution of Engineering and Technology (IET) Electronics Letters and the International Journal of Antennas and Propagation (Hindawi). He is a senior member of the IEEE.
Giampiero Lovat was born in Rome, Italy, in 1975. He received the Laurea degree (cum laude) in electronic engineering and the Ph.D. degree in electromagnetics in 2001 and in 2005, respectively, both from La Sapienza University of Rome. Since 2010, he is an Assistant Professor in the Astronautical, Electrical, and Energetic Engineering Department (DIAEE) at the same University, and since 2015, he has been qualified for the role of Full Professor in a National Scientific Competition.
He has been doing research activity on leaky waves, periodic structures, electrodynamics of graphene, transient electromagnetics, and electromagnetic shielding. He is the co-author of more than 170 papers on international books, journals, and conference proceedings. He is the co-author of the first edition of the book Electromagnetic Shielding (Wiley, 2008).
In 2005, he was the recipient of the Young Scientist Award at the URSI General Assembly in New Delhi, India. He is the author of Fast Breaking Papers, October 2007 in EE and CS, about metamaterials (a paper that had the highest percentage increase in citations in Essential Science Indicators, ESI). In 2011, he was the recipient of the Best Paper Symposium Award at the 2011 IEEE EMC-S International Symposium on Electromagnetic Compatibility. In 2020, he has been included in the ranking of the top 2% world scientists recently published on Plos One (https://doi.org/10.1371/journal.pbio.3000918). In 2021, he has been selected as a distinguished reviewer of IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY.
Preface
This is the second edition of our book Electromagnetic Shielding. As for the first edition, the assumed background of the reader is limited to standard undergraduate topics in physics and mathematics.
This edition has been completely updated according to theoretical and technological progress in the field of electromagnetic shielding: the book now comprises 14 chapters and 4 appendices; an overview of their content is provided next, highlighting the changes with respect to the first edition. Chapter 1 introduces the basic electromagnetic theory behind electromagnetic shielding; the fundamental theorems are now also presented in the time domain, while symmetry, duality, and Babinet principles have been added for their importance in treating classical shielding problems. An introduction to wave equations and potentials and Green functions in the time domain has also been added to cover all the basic tools to analyze transient shielding problems. Chapter 2 describes the arsenal of conventional and less conventional materials for electromagnetic shielding; an entire new paragraph has been devoted to the electromagnetic description of graphene, a material that has become one of the most attractive materials in the field of electromagnetic loss and absorption. Chapter 3 introduces all the figures of merit for a quantitative analysis of the shielding performance of a given structure. Chapter 4 covers the subject of electromagnetic shielding of planar, cylindrical, and spherical screens against plane waves; an entire new paragraph is devoted to presenting examples that help to understand the extension of the transmission line analogy to near-field sources. Chapters 5 and 6 are entirely new. Chapter 5 considers the important topic of near-field sources in the presence of planar screens and provides an extensive introduction to the spectral domain approach. Chapter 6 introduces the reader to the emergent area of transient shielding analysis offering suitable figures of merit, defining the fundamental transient sources, and describing the numerical and analytical approaches to analyze basic configurations. Chapter 7 is a thorough introduction to the principal numerical methods used in electromagnetics and are here presented in connection with electromagnetic shielding problems; moreover, many illustrative examples have been added to present the characteristics of different numerical approaches with particular reference to the analysis of the shielding characteristics of enclosures. Chapter 8 treats the important topic of electromagnetic penetration through apertures in planar screens; the circular aperture is now analyzed in detail, illustrating the very last developments. Enclosures are considered in Chapter 9: the fundamental case of a rectangular enclosure with a rectangular aperture is now described in detail, considering both a numerical solution based on the Method-of-Moments and approximate analytical approaches. Moreover, two entirely new paragraphs have been added to present the overall performance of an enclosure in both frequency and time domains. Chapter 10 consists in a brief introduction to cable shielding, while Chapter 11 deals with the most common components installed in most of shielding configurations. Chapter 12 introduces the important topic of frequency-selective surfaces; here, the analysis has been extended to include not only a plane wave excitation but also a finite source: for this reason, an integral equation formulation for the solution of the electromagnetic problem is presented together with an introduction to the periodic Green function calculation. The literature on this topic is growing almost exponentially, and a plethora of new structures have been proposed so that some new paragraphs have been added to present some of the most recent developments. Finally, Chapter 13 covers some issues in shielding design procedures, while Chapter 14 introduces to some uncommon ways of shielding: in particular, the use of metamaterials has been extensively reviewed.
As in the first edition, two appendices are devoted to electrostatic and magnetostatic shielding. A new Appendix C has been added, which provides an introduction to the use of statistical electromagnetics in electromagnetic shielding, while the last appendix (Appendix D) covers standards and measurement procedures and has been obviously updated with respect to the first edition.
We would like to acknowledge the support provided within Wiley-Interscience by all the Staff and in particular the patient assistance given by Teresa Netzler.
Rome
29 June 2022
Salvatore Celozzi
Rodolfo Araneo
Paolo Burghignoli
Giampiero Lovat
1Electromagnetics Behind Shielding
Shielding an electromagnetic field is a complex and sometimes formidable task. The reasons are many, since the effectiveness of any strategy or technique aimed at the reduction of the electromagnetic field levels in a prescribed region depends largely upon the source characteristics, the shield geometry, and the involved materials. Moreover, as it often happens when common terms are adopted in a technical context, different definitions of shielding exist. In electromagnetics the shielding effectiveness (SE) is a concise parameter generally applied to quantify shielding performance. However, a variety of standards are adopted for the measurement or the assessment of the performance of a given shielding structure. Unfortunately, they all call for very specific conditions in the measurement setup. The results therefore are often useless if the source or system configurations differ even slightly. Last among the difficulties that arise in the solution of actual shielding problems are the difficulties inherent in both the solution of the boundary value problem and the description of the electromagnetic problem in mathematical form.
1.1 Definitions
To establish a common ground, we will begin with some useful definitions. An electromagnetic shield can be defined as [1]:
[A] housing, screen, or other object, usually conducting, that substantially reduces the effect of electric or magnetic fields on one side thereof, upon devices or circuits on the other side.
This definition is restrictive because it implicitly assumes the presence of a “victim.” The definition is also based on the misconception that the source and observation points are in opposite positions with respect to the shield, and it includes the word “substantially” whose meaning is obscure and introduces an unacceptable level of arbitrariness.
Another definition of electromagnetic shielding even more restrictive is [2]:
[A] means of preventing two circuits from electromagnetic coupling by placing at least one of the circuits in a grounded enclosure of magnetic conductive material.
The most appropriate definition entails a broad view of the phenomenon:
[A]ny means used for the reduction of the electromagnetic field in a prescribed region.
Notice that no reference to shape, material, and grounding of the shield is necessary to define its purpose.
In general, electromagnetic shielding represents a way toward the improvement of the electromagnetic-compatibility (EMC) (defined as the capability of electronic equipment or systems to be operated in the intended electromagnetic environment at design levels of efficiency) performance of single devices, apparatus, or systems. Biological systems are included, for which it is correct to talk about health rather than EMC. Electromagnetic shielding is also used to prevent sensitive information from being intercepted, that is, to guarantee communication security.
Electromagnetic shielding is not implemented only for such purposes. Some sort of electromagnetic shielding is almost always used in electrical and electronic systems to reduce their electromagnetic emissions and to increase their electromagnetic immunity against external fields. In cases where the available methodologies for reducing the source levels of electromagnetic emission or strengthening the victim immunity are not available or are not sufficient to ensure the correct operation of devices or systems, a reduction of the coupling between the source and the victim (either present or only potentially present) is often the preferred choice.
The immunity of the victims is generally obtained by means of filters that are analogous to electromagnetic shielding with respect to conducted emissions and immunity. The main advantage of filters is that they are “local” devices. Thus, where the number of sensitive components to be protected is limited, the cost of filtering may be much lower than that of shielding. The main disadvantage of using a filter is that it is able to arrest only interferences whose characteristics (e.g., level or mode of transmission) are different from those of the device, so the correct operation in the presence of some types of interference is not guaranteed. Another serious disadvantage of the filter is its inadequacy or its low efficiency for the prevention of data detection.
In general, designing a filter is much simpler than designing a shield. The filter designer has only to consider the waveform of the interference (in terms of voltage or current) and the values of the input and output impedance [3], whereas the shield designer must include a large amount of input information and constraints, as it will be discussed throughout the book.
Any shielding analysis begins by an accurate examination of the shield geometry [4–7]. Although the identification of the coupling paths between the main space regions is often trivial, sometimes it deserves more care, especially in complex configurations. The complexity of a shield is associated with its shape, apertures, the components identified as the most susceptible, the source characteristics, and so forth. Subdividing its configuration into several subsystems (each simpler than the original one and interacting with the others in a definite way) is always a useful approach to identify critical problems and find ways to fix and improve the overall performance [5]. This approach is based on the assumption that each subsystem can be analyzed, and hence its behavior can be characterized, independently of the others components/subsystems. For instance, in the frequency domain and for a linear subsystem, for each coupling path and for each susceptible element, it is possible to investigate the transfer function relating the external source input and the victim output characteristics as , where represents the subsystem output in the absence of external-source excitation. In the presence of multilevel barriers, the transfer function may ensue from the product of the transfer functions associated with each barrier level.
The foregoing approach can be generalized for a better understanding of the shielding problem in complex configurations. However, it is often sufficient to consider only the most critical subsystems and components, on one hand, and the most important coupling paths, on the other hand, in order to solve the principal shielding problems and thus improve the overall performance [8]. The general approach is obviously suitable in a design context. A complete analysis of the relations between shielding and grounding is left to the specific literature [4, 9–11].
1.2 Notation, Symbology, and Acronyms
The abbreviations and symbols used throughout the book are briefly summarized here in order to make clear the standard we have chosen to adopt. Of course, we will warn the reader anytime an exception occurs.
Scalar quantities are shown in italic type (e.g., and , while vectors are shown in boldface (e.g., and ); dyadics are shown in boldface with an underbar (e.g., and ). A physical quantity that depends on time and space variables is indicated with a lowercase letter (e.g., for the electric field). The Fourier transform with respect to the time variable is indicated with the corresponding uppercase letter (e.g., while the Fourier transform with respect to the spatial variables is indicated by a tilde (e.g., ); when the Fourier transform with respect to both time and spatial variables is considered, the two symbologies are combined (e.g., ).
The sets of spatial variables in rectangular, cylindrical, and spherical coordinates are denoted by , , and , respectively. The boldface Latin letter is used to indicate a unit vector and a subscript is used to indicate its direction: for instance, , , and denote the unit vectors in the rectangular, cylindrical, and spherical coordinate system, respectively.
We will use the “del” notation with the suitable product type to indicate gradient (), curl () and divergence operators (); the Laplacian operator is indicated as . The imaginary unit is denoted with and the asterisk as a superscript of a complex quantity denotes its complex conjugate. The real and imaginary parts of a complex quantity are indicated by and , respectively, while the principal argument is indicated by the function . The base-10 logarithm and the natural logarithm are indicated by means of the and functions, respectively.
Finally, throughout the book, the international system of units SI is adopted, electromagnetic is abbreviated as EM, and shielding effectiveness as SE.
1.3 Macroscopic Electromagnetism and Maxwell's Equations
A complete description of the macroscopic electromagnetism is provided by Maxwell's equations whose validity is taken as a postulate. Maxwell's equations can be used either in a differential (local) form or in an integral (global) form, and there has been a long debate over which is the best representation (e.g., David Hilbert preferred the integral form whereas Arnold Sommerfeld found more suitable the differential form, from which special relativity follows more naturally [12]). When stationary media are considered, the main difference between the two representations consists in how they account for discontinuities of materials and/or sources. Basically, if one adopts the differential form, some boundary conditions at surface discontinuities must be postulated; on the other hand, if the integral forms are chosen, one must postulate their validity across such discontinuities [13, 14].
Maxwell's equations can be expressed in scalar, vector, or tensor form, and different vector fields can be considered as fundamental. A full description of all these details can be found, e.g., in [12]. In this book we assume the following differential form of the Maxwell equations:
From these equations the continuity equation can be derived as
In this framework the EM field—described by vectors (electric field, unit of measure V/m), (magnetic field, unit of measure A/m), (electric displacement, unit of measure C/m), and (magnetic induction, unit of measure Wb/m or T)—arises from sources (electric current density, unit of measure A/m) and (electric charge density, unit of measure C/m. Further, except for static fields, if a time can be found before which all the fields and sources are identically zero, the divergence equations in (1.1) are a consequence of the curl equations [12], so under this assumption the curl equations can be taken as independent.
It can be useful to make the Maxwell equations symmetric by introducing fictitious magnetic current and charge densities and (units of measure V/m and Wb/m, respectively), which satisfy a continuity equation similar to (1.2) so that (1.1) can be rewritten as
As it will be shown later, the equivalence principle indeed requires the introduction of such fictitious quantities.
It is also useful to identify in Maxwell's equations some “impressed” source terms, which are independent of the unknown fields and are instead due to other external sources (magnetic sources can be only of this type). Such “impressed” sources are considered as known terms in Maxwell's differential equations and indicated by the subscript “i.” In this connection, (1.3) can be expressed as
The impressed-source concept is well known in circuit theory. For example, independent voltage sources are voltage excitations that are independent of possible loads.
Although both the sources and the fields cannot have true spatial discontinuities, from a modeling point of view, it is useful to consider additionally sources in one or two dimensions: surface- and line-source densities can be introduced in terms of the Dirac delta distribution , as (singular) idealizations of actual continuous volume densities [12, 15].
Finally, in the frequency domain, Maxwell's curl equations are expressed as
where the uppercase quantities indicate either the Fourier transform or the phasors associated with the corresponding time-domain fields. Note that in this text the following definition of temporal Fourier transform will be adopted:
with the corresponding inverse Fourier transform:
whereas in the phasor domain a time-harmonic dependence is assumed:
where and is the phasor associated with . The same definitions also apply for vector functions.
1.4 Constitutive Relations
By direct inspection of Maxwell's curl equations in (1.1), it is immediately clear that they represent six scalar equations with 15 unknown quantities. With fewer equations than unknowns no unique solution can be identified (the problem is said to be indefinite). The additional equations required to make the problem definite are those that describe the relations among the field quantities , and , enforced by the medium filling the region where the EM phenomena occur. Such relations are called constitutive relations, and they depend on the properties of the medium supporting the EM field.
In non-moving media, with the exclusion of magnetoelectric and chiral materials, the field depends only on the field, depends only on , and depends only on . These dependences are expressed as constitutive relations, with the and fields regarded as causes and the , , and fields as effects.
If a linear combination of causes (with given coefficients) produces a linear combination of effects (with the same coefficients), the medium is said to be linear (otherwise nonlinear). In general, the constitutive relations are described by a set of constitutive parameters and a set of constitutive operators that relate the above-mentioned fields inside a region of space. The constitutive parameters can be constants of proportionality between the fields (the medium is thus said isotropic), or they can be components in a tensor relationship (the medium is said anisotropic). If the constitutive parameters are constant within a certain region of space, the medium is said homogeneous in that region (otherwise, the medium is inhomogeneous). If the constitutive parameters are constant with time, the medium is said stationary (otherwise, the medium is nonstationary).
If the constitutive operators are expressed in terms of time integrals, the medium is said to be temporally dispersive. If these operators involve space integrals, the medium is said to be spatially dispersive. Finally, we note that the constitutive parameters may depend on other nonelectromagnetic properties of the material and external conditions (temperature, pressure, etc.).
The simplest medium is vacuum. In vacuum the following constitutive relations hold:
The quantities H/m1 and F/m are the free-space magnetic permeability and dielectric permittivity, respectively. Their values are related to the speed of light in free space through , whose exact value is m/s; the above two values for correspond to approximating m/s and m/s, respectively.
For a linear, homogeneous, isotropic, and nondispersive material, the constitutive relations can be expressed as
where and are the magnetic permeability and dielectric permittivity of the medium, respectively. These quantities can be related to the corresponding free-space quantities through the dimensionless relative permeability and relative permittivity , such that and . The dimensionless quantities and (known as magnetic and electric susceptibilities, respectively) are also used. The third equation of (1.10) expresses the Ohm law in local form, and is the conductivity of the medium (unit of measure S/m).
For such a simple medium, thanks to (1.10), Maxwell's equations (1.4) can be rewritten as
