Table of Contents

Title Page

Copyright
Dedication

Preface

Part I: Electromagnetic Field Coupling to Thin Wire Configurations of Arbitrary Shape

Chapter 1: Computational Electromagnetics – Introductory Aspects
1. 1.1 The Character of Physical Models Representing Natural Phenomena
2. 1.2 Maxwell's Equations
3. 1.3 The Electromagnetic Wave Equations
4. 1.4 Conservation Laws in the Electromagnetic Field
5. 1.5 Density of Quantity of Movement in the Electromagnetic Field
6. 1.6 Electromagnetic Potentials
7. 1.7 Solution of the Wave Equation and Radiation Arrow of Time
8. 1.8 Complex Phasor Form of Equations in Electromagnetics
9. References
Chapter 2: Antenna Theory versus Transmission Line Approximation – General Considerations
1. 2.1 A Note on EMC Computational Models
2. 2.2 Generalized Telegrapher's Equations for the Field Coupling to Finite Length Wires
3. 2.3 Single Horizontal Wire in the Presence of a Lossy Half-Space: Comparison of Analytical Solution, Numerical Solution, and Transmission Line Approximation
4. 2.4 Single Vertical Wire in the Presence of a Lossy Half-Space: Comparison of Analytical Solution, Numerical Solution, and Transmission Line Approximation
5. 2.5 Magnetic Current Loop Excitation of Thin Wires
6. References
Chapter 3: Electromagnetic Field Coupling to Overhead Wires
1. 3.1 Frequency Domain Models and Methods
2. 3.2 Time Domain Models and Methods
3. 3.3 Applications to Antenna Systems
4. References
Chapter 4: Electromagnetic Field Coupling to Buried Wires
1. 4.1 Frequency Domain Modeling
2. 4.2 Time Domain Modeling
3. References
Chapter 5: Lightning Electromagnetics
1. 5.1 Antenna Model of Lightning Channel
2. 5.2 Vertical Antenna Model of a Lightning Rod
3. 5.3 Antenna Model of a Wind Turbine Exposed to Lightning Strike
4. References
Chapter 6: Transient Analysis of Grounding Systems
1. 6.1 Frequency Domain Analysis of Horizontal Grounding Electrode
2. 6.2 Frequency Domain Analysis of Vertical Grounding Electrode
3. 6.3 Frequency Domain Analysis of Complex Grounding Systems
4. 6.4 Time Domain Analysis of Horizontal Grounding Electrodes
5. References

Part II: Advanced Models in Bioelectromagnetics

Chapter 7: Human Exposure to Electromagnetic Fields – General Aspects
1. 7.1 Dosimetry
2. 7.2 Coupling Mechanisms
3. 7.3 Biological Effects
4. 7.4 Safety Guidelines and Exposure Limits
5. 7.5 Some Remarks
6. References
Chapter 8: Modeling of Human Exposure to Static and Low Frequency Fields
1. 8.1 Exposure to Static Fields
2. 8.2 Exposure to Low Frequency (LF) Fields
3. References
Chapter 9: Modeling of Human Exposure to High Frequency (HF) Electromagnetic Fields
1. 9.1 Internal Electromagnetic Field Dosimetry Methods
2. 9.2 Thermal Dosimetry Procedures
3. References
Chapter 10: Biomedical Applications of Electromagnetic Fields
1. 10.1 Modeling of Induced Fields due to Transcranial Magnetic Stimulation (TMS) Treatment
2. 10.2 Modeling of Nerve Fiber Excitation
3. References
Index

End User License Agreement

List of Illustrations

Chapter 1: Computational Electromagnetics – Introductory Aspects

Figure 1.1 Differential approach concept.
Figure 1.2 Integral approach concept.
Figure 1.3 Configuration of electric and magnetic fields in a cell.
Figure 1.4 Treatment of the air–ground interface by the “the contour integral approach” method.
Figure 1.5 Horizontal grounding electrode in two-layer soil.
Figure 1.6 Transinet current induced at the middle of the buried electrode.
Figure 1.7 Horizontal grounding grid in two-layer soil.
Figure 1.8 Transient currents induced at different points for the horizontal grounding grid (Scenario 1).
Figure 1.9 Transient currents induced at different points for the horizontal grounding grid (Scenario 2).
Figure 1.10 The source point and the observation point.

Chapter 2: Antenna Theory versus Transmission Line Approximation – General Considerations

Figure 2.1 Finite length line above a lossy ground.
Figure 2.2 Magnitude of the induced current distribution along the line. L = 5 m, f = 50 MHz. The calculations have been performed using (i) the derived generalized telegrapher's equations and (ii) using NEC-2.
Figure 2.3 Magnitude of the induced current distribution along the line. L = 20 m, f = 300 MHz. The calculations have been performed using (i) the derived generalized telegrapher's equations and (ii) using NEC-2.
Figure 2.4 Induced current distribution along the line. L = 5 m. (a) Real part and (b) imaginary part. The calculations have been performed using (i) the derived generalized telegrapher's equations, (ii) the classical transmission line theory for a perfectly conducting ground (PEC), and (iii) the classical transmission line theory for a lossy ground.
Figure 2.5 Induced current distribution along the line. L = 10 m. (a) Real part and (b) imaginary part. The calculations have been performed using (i) the derived generalized telegrapher's equations, (ii) the classical transmission line theory for a perfectly conducting ground (PEC), and (iii) the classical transmission line theory for a lossy ground.
Figure 2.6 Induced current distribution along the line. L = 20 m. (a) Real part and (b) imaginary part. The calculations have been performed using (i) the derived generalized telegrapher's equations, (ii) the classical transmission line theory for a perfectly conducting ground (PEC), and (iii) the classical transmission line theory for a lossy ground.
Figure 2.7 Induced current distribution along the line. (a) Real part and (b) imaginary part. The calculations have been performed using (i) the derived generalized telegrapher's equations, (ii) the classical transmission line theory for a perfectly conducting ground (PEC), and (iii) the classical transmission line theory for a lossy ground.
Figure 2.8 A straight thin wire buried in lossy earth.
Figure 2.9 Induced current distribution along the wire (f = 1 MHz, L = 20 m, a = 0.01 m, d = 2.5 m, σ = 0.01 S m⁻¹, ϵ_r = 10). (a) Real part and (b) imaginary part. The calculations have been performed using (i) the derived generalized telegrapher's equations, (ii) the NEC-2, (iii) the modified transmission line theory for a lossy ground, and (iv) the classical transmission line theory for a lossy ground.
Figure 2.10 Induced current distribution along the wire (f = 50 MHz, L = 5 m, a = 0.01 m, d = 2.5 m, σ = 0.01 S m⁻¹, ϵ_r = 10). (a) Real part and (b) imaginary part. The calculations have been performed using (i) the derived generalized telegrapher's equations, (ii) the NEC-2, (iii) the modified transmission line theory for a lossy ground, and (iv) the classical transmission line theory for a lossy ground.
Figure 2.11 Induced current distribution along the wire (f = 50 MHz, L = 10 m, a = 0.01 m, d = 2.5 m, σ = 0.01 S m⁻¹, ϵ_r = 10). (a) Real part and (b) imaginary part. The calculations have been performed using (i) the derived generalized telegrapher's equations, (ii) the NEC-2, (iii) the modified transmission line theory for a lossy ground, and (iv) the classical transmission line theory for a lossy ground.
Figure 2.12 Induced current distribution along the wire (f = 50 MHz, L = 20 m, a = 0.01 m, d = 2.5 m, σ = 0.01 S m⁻¹, ϵ_r = 10). (a) Real part and (b) imaginary part and. The calculations have been performed using (i) the derived generalized telegrapher's equations, (ii) the NEC-2, (iii) the modified transmission line theory for a lossy ground, and (iv) the classical transmission line theory for a lossy ground.
Figure 2.13 Finite length line above a lossy ground.
Figure 2.14 Transient current induced at the center of the line with L = 1 m length and a = 2 mm radius above a lossy ground with conductivity of σ = 0.001 S m⁻¹ and relative permittivity of ϵ_r = 10 for three different heights above the ground: (a) h = 0.25 m, (b) h = 0.5 m, and (c) h = 1 m. The calculations have been performed (i) using the GB-IBEM solution of the derived generalized telegrapher's equations, (ii) NEC-4, and (iii) classical TL solution based on the grounding impedance formula proposed by Sunde [15].
Figure 2.15 Transient current induced at the center of the line with L = 1 m length and a = 2 mm radius at height h = 0.1 m above a lossy ground with conductivity of (a) σ = 0.001 S m⁻¹ and (b) σ = 10 S m⁻¹. Therelative permittivity of the ground is ϵ_r = 10. The calculations have been performed (i) using the GB-IBEM solution of the derived generalized telegrapher's equations, (ii) NEC-4, and (iii) classical TL solution based on the grounding impedance formula proposed by Sunde [15].
Figure 2.16 Finite length wire below a lossy ground.
Figure 2.17 Horizontal grounding electrode buried in a lossy medium.
Figure 2.18 Transient current at the center of the straight wire, L = 10 m, d = 4 m. (a) σ = 1 mS m⁻¹. (b) σ = 10 mS m⁻¹.
Figure 2.19 Transient current at the center of the straight wire, L = 50 m, d = 4 m. (a) σ = 1 mS m⁻¹. (b) σ = 10 mS m⁻¹.
Figure 2.20 Transient current at the center of the electrode, L = 10 m, 0.1/1 µs pulse. σ = 1 mS m⁻¹. (b) σ = 10 mS m⁻¹.
Figure 2.21 Transient current at the center of the electrode, L = 50 m, 0.1/1 µs pulse. σ = 1 mS m⁻¹. (b) σ = 10 mS m⁻¹.
Figure 2.22 Finite length line in the presence of a lossy ground. (a) Aboveground line. (b) Belowground line.
Figure 2.23 (a) Real, (b) imaginary, and (c) absolute value of the current distribution along the single wire above a PEC ground: f = 50 MHz, L = 5 m, a = 0.01 m, h = 2.5 m.
Figure 2.24 a) Real, b) imaginary, and c) absolute value of current distribution along the single wire above a PEC ground: f = 50 MHz, L = 10 m, a = 0.01 m, h = 2.5 m.
Figure 2.25 (a) Real, (b) imaginary, and (c) absolute value of current distribution along the single wire above a PEC ground: f = 50 MHz, L = 20 m, a = 0.01 m, h = 2.5 m.
Figure 2.26 (a) Real, (b) imaginary, and (c) absolute value of current distribution along the single wire above a PEC ground: f = 1 MHz, L = 20 m, a = 0.01 m, h = 2.5 m.
Figure 2.27 a) Real, b) imaginary, and c) absolute value of current distribution along the single wire above an imperfect ground: f = 50 MHz, L = 5 m, a = 0.01 m, h = 2.5 m, σ = 0.01 S m⁻¹, ϵ_r = 10.
Figure 2.28 (a) Real, (b) imaginary, and (c) absolute value of current distribution along the single wire above an imperfect ground: f = 50 MHz, L = 10 m, a = 0.01 m, h = 2.5 m, σ = 0.01 S m⁻¹, ϵ_r = 10.
Figure 2.29 (a) Real, (b) imaginary, and (c) absolute value of current distribution along the single wire above an imperfect ground: f = 50 MHz, L = 20 m, a = 0.01 m, h = 2.5 m, σ = 0.01 S m⁻¹, ϵ_r = 10.
Figure 2.30 (a) Real, (b) imaginary, and (c) absolute value of current distribution along the single wire above an imperfect ground: f = 1 MHz, L = 20 m, a = 0.01 m, h = 2.5 m, σ = 0.01 S m⁻¹, ϵ_r = 10.
Figure 2.31 (a) Real, (b) imaginary, and (c) absolute value of current distribution along the single wire buried in a lossy ground: f = 50 MHz, L = 5 m, a = 0.01 m, d = 2.5 m, σ = 0.01 S m⁻¹, ϵ_r = 10.
Figure 2.32 (a) Real, (b) imaginary, and (c) absolute value of current distribution along the single wire buried in a lossy ground: f = 50 MHz, L = 10 m, a = 0.01 m, d = 2.5 m, σ = 0.01 S m⁻¹, ϵ_r = 10.
Figure 2.33 a) Real, b) imaginary, and c) absolute value of current distribution along the single wire buried in a lossy ground: f = 50 MHz, L = 20 m, a = 0.01 m, d = 2.5 m, σ = 0.01 S m⁻¹, ϵ_r = 10.
Figure 2.34 (a) Real, (b) imaginary, and (c) absolute value of current distribution along the single wire buried in a lossy ground: f = 1 MHz, L = 20 m, a = 0.01 m, d = 2.5 m, σ = 0.01 S m⁻¹, ϵ_r = 10.
Figure 2.35 GPR dipole antenna above a lossy half-space.
Figure 2.36 Transmitted field (V m⁻¹) into the ground at f = 1 MHz. (a) E_x-component. (b) E_z-component.
Figure 2.37 Transmitted field (V m⁻¹) into the ground at f = 10 MHz. (a) E_x-component. (b) E_z-component.
Figure 2.38 Transmitted field (V m⁻¹) into the ground at f = 100 MHz. (a) E_x-component. (b) E_z-component.
Figure 2.39 Broadside transmitted field (V m⁻¹) into the ground for different frequencies.
Figure 2.40 Vertical straight thin wire above a lossy ground.
Figure 2.41 The geometry of a straight wire and its image.
Figure 2.42 Straight thin wire in free space.
Figure 2.43 Vertical dipole above a PEC ground and its image.
Figure 2.44 The real part of the current distribution (L = 1 m, a = 0.005 m, h = 2 m, σ = 1 mS m⁻¹, ϵ_r = 10, V₀ = 1 V, f = 168.2 MHz).
Figure 2.45 The imaginary part of the current distribution (L = 1 m, a = 0.005 m, h = 2 m, σ = 1 mS m⁻¹, ϵ_r = 10, V₀ = 1 V, f = 168.2 MHz).
Figure 2.46 Resistance of vertical dipole above a real ground (L = 1 m, a/λ = 0.0005 m, σ = 3 mS m⁻¹, ϵ_r = 10, f = 3 MHz).
Figure 2.47 Reactance of vertical dipole above a real ground (L = 1 m, a/λ = 0.0005 m, σ = 3 mS m⁻¹, ϵ_r = 10, f = 3 MHz).
Figure 2.48 The real part of the current distribution (L = 1 m, a = 0.005 m, h = 2 m, E₀ = 1 V m⁻¹, f = 168.2 MHz).
Figure 2.49 The imaginary part of the current distribution (L = 1 m, a = 0.005 m, h = 2 m, E₀ = 1 V m⁻¹, f = 168.2 MHz).
Figure 2.50 The real part of the current distribution (L = 1 m, a = 0.005 m, h=2 m, σ = 1 mS m⁻¹, ϵ_r = 10, E₀ = 1 V m⁻¹, f = 168.2 MHz).
Figure 2.51 The imaginary part of the current distribution (L = 1 m, a = 0.005 m, h = 2 m, σ = 1 mS m⁻¹, ϵ_r = 10, E₀ = 1 V m⁻¹, f = 168.2 MHz).
Figure 2.52 Spectrum of the induced current at the center of the straight wire scatterer (L = 1 m, a = 0.005 m, h = 1 m, σ = 1 mS m⁻¹, ϵ_r = 10, E₀ = 1 V m⁻¹).
Figure 2.53 Tangential field component radiated by the dipole in free space – numerical model.
Figure 2.54 Tangential field component radiated by the dipole in free space – analytical model.
Figure 2.55 Tangential field component radiated by the dipole in free space – comparison of analytical and numerical model at a distance ρ = 0.1 m from the wire.
Figure 2.56 Tangential field component radiated by the dipole in free space – comparison of analytical and numerical model at a distance ρ = 2 m from the wire.
Figure 2.57 Tangential field component radiated by the dipole above a PEC ground – numerical model.
Figure 2.58 Tangential field component radiated by the dipole in free space – analytical model.
Figure 2.59 Tangential field component radiated by the dipole above a PEC ground – comparison of analytical and numerical model at a distance ρ = 0.1 m from the wire.
Figure 2.60 Tangential field component radiated by the dipole above a PEC ground – comparison of analytical and numerical model at a distance ρ = 2 m from the wire.
Figure 2.61 Antenna excitation: (a) delta gap; (b) magnetic frill; (c) magnetic current loop.
Figure 2.62 Delta gap source and simple magnetic current loop.
Figure 2.63 Excitation placement.
Figure 2.64 Antenna input admittance for various number of elements (GB-IBEM ISO2; L = 0.5λ; a = 0.007022λ).
Figure 2.65 Antenna input admittance for various number of elements (GB-IBEM ISO3; L = 0.5λ; a = 0.007022λ).
Figure 2.66 Antenna input admittance for various number of elements (MM; L = 0.5λ; a = 0.007022λ).
Figure 2.67 Antenna input admittance for various number of elements (GB-IBEM ISO2; L = 1.00λ; a = 0.007022λ).
Figure 2.68 Antenna input admittance for various number of elements (GB-IBEM ISO3; L = 1.00λ; a = 0.007022λ).
Figure 2.69 Antenna input admittance for various number of elements (MM; L = 1.00λ; a = 0.007022λ).
Figure 2.70 Antenna input admittance for various number of elements (GB-IBEM ISO2; h = 0.5λ monopole; a = 0.0245λ).
Figure 2.71 Antenna input admittance for various number of elements (GB-IBEM ISO2; h = 0.5λ monopole; a = 0.0509λ).

Chapter 3: Electromagnetic Field Coupling to Overhead Wires

Figure 3.1 Single wire of arbitrary shape in free space.
Figure 3.2 The wire of arbitrary shape and its image.
Figure 3.3 Horizontal wire above a lossy ground.
Figure 3.4 Horizontal wires above a lossy half-space at different heights.
Figure 3.5 Current induced at the center of the line above a PEC ground versus frequency.
Figure 3.6 Current induced at the center of the line above a lossy ground versus frequency (σ = 0.001 S m⁻¹, ϵ_r = 10).
Figure 3.7 Simple PLC circuit.
Figure 3.8 The current distribution along a simple PLC system.
Figure 3.9 Radiated electric field.
Figure 3.10 Radiated magnetic field.
Figure 3.11 The transient current induced at the center of the line above dielectric half-space (ϵ_r = 10).
Figure 3.12 Transient current at the wire center, L = 1 m, a = 2 mm, h = 0.25, ϵ_r = 10.
Figure 3.13 Geometry No. 1: Two-wire array above a PEC ground (a = 2 cm, L = 10 m, d = 1 m, h₁ = 1 m, and h₂ = 2 m).
Figure 3.14 Geometry No. 2: Two-wire array above a dielectric half-space (ϵ_r = 10, a = 2 cm, L = 10 m, d = 1 m, h₁ = 1.
Figure 3.15 Transient current induced at the center of wire 2 (Geometry No. 1) – comparison between IFFT-NEC2, TD GB-IBEM, and TL results.
Figure 3.16 Transient current induced at the center of wire 2 (Geometry No. 2) – comparison between IFFT-NEC2, TD GB-IBEM, and TL results.
Figure 3.17 Geometry of cylindrical helix.
Figure 3.18 Amplitude of current distribution along cylindrical helix at f = 30 MHz.
Figure 3.19 Amplitude of current distribution along cylindrical helix at f = 750 MHz.
Figure 3.20 Radiation pattern of cylindrical helix at f = 30 MHz. (a) Horizontal plane. (b) Vertical plane.
Figure 3.21 Radiation pattern of cylindrical helix at f = 750 MHz. (a) Horizontal plane. (b) Vertical plane.
Figure 3.22 Geometry of conical helix.
Figure 3.23 Amplitude of current distribution along conical helix at f = 1 GHz.
Figure 3.24 Radiation pattern of conical helix at f = 1 GHz. (a) Horizontal plane. (b) Vertical plane.
Figure 3.25 Geometry of spherical helix.
Figure 3.26 Amplitude of current distribution along the spherical helix at f = 500 MHz.
Figure 3.27 Radiation pattern of spherical helix at f = 500 MHz. (a) Horizontal plane. (b) Vertical plane.
Figure 3.28 System of multiple helical antennas.
Figure 3.29 Amplitude of current distribution along active cylindrical helix at f = 750 MHz.
Figure 3.30 Amplitude of current distribution along passive cylindrical helix at f = 750 MHz.
Figure 3.31 Amplitude of current distribution along conical helix at f = 750 MHz.
Figure 3.32 The localizer antenna element.
Figure 3.33 The absolute values of currents induced along the single LPDA.
Figure 3.34 The single LPDA radiation pattern (lateral view).
Figure 3.35 The single LPDA radiation pattern (top view).
Figure 3.36 Geometry of 14-element LPDA array.
Figure 3.37 The LPDA array radiation pattern (lateral view).
Figure 3.38 The LPDA array radiation pattern (top view).
Figure 3.39 GPR dipole antenna above a dielectric half-space.
Figure 3.40 GPR dipole antenna above a dielectric half-space.
Figure 3.41 The horizontal (E_z) component of the transmitted electric field for penetration depth d = 0.5 m_.
Figure 3.42 The horizontal (E_z) component of transmitted electric field for penetration depth d = 1 m_.
Figure 3.43 The horizontal (E_z) component of transmitted electric field for penetration depth d = 1.5 m_.

Chapter 4: Electromagnetic Field Coupling to Buried Wires

Figure 4.1 The geometry of horizontal buried lines.
Figure 4.2 Configuration No. 1: D = 20.5 mm, d = 106 mm, h = 1 m.
Figure 4.3 The frequency response at the center of the middle wire (configuration No. 1, L = 50 m, σ = 0.001 S m⁻¹).
Figure 4.4 The frequency response at the center of the middle wire (configuration No. 1, L = 50 m, σ = 0.01 S m⁻¹).
Figure 4.5 Configuration No. 2: D = 20.5 mm, d₁ = 36 mm, d₂ = 18 mm, h₁ = 1 m, h₂ = 0.97 m.
Figure 4.6 The frequency response at the center of the middle wire (configuration No. 2, L = 50 m, σ = 0.001 S m⁻¹).
Figure 4.7 The frequency response at the center of the middle wire (configuration No. 3, L = 50 m, σ = 0.01 S m⁻¹).
Figure 4.8 A horizontal thin wire buried in a lossy medium.
Figure 4.9 Transient current at the center of the straight wire, L = 1 m, d = 30 cm. (a) σ = 1 mS m⁻¹. (b) σ = 10 mS m⁻¹. (c) σ = 100 mS m^−1.
Figure 4.10 Transient current at the center of the straight wire, L = 10 m, d = 4 m. (a) σ = 1 mS m⁻¹. (b) σ = 10 mS m⁻¹. (c) σ = 100 mS m⁻¹.

Chapter 5: Lightning Electromagnetics

Figure 5.1 Monopole and dipole representation of the lightning channel energized by current source or voltage source.
Figure 5.2 Antenna model of the lightning channel. (a) ICS model. (b) MCL model.
Figure 5.3 Current waveforms at different heights along the channel.
Figure 5.4 Frequency spectrum of current at height h = 500 m (unit current source) – 2 km channel.
Figure 5.5 Frequency spectrum of current at height h = 500 m (unit voltage source) – 2 km channel.
Figure 5.6 Lightning return stroke channel current versus time for different heights (0, 100 m, 500 m, 1 km, 3 km, 5 km). The channel is considered as a PEC wire. The results at 1 km height are compared with those of [11].
Figure 5.7 Lightning channel current versus time for different heights (0, 100 m, 500 m, 1 km, 3 km, 5 km).
Figure 5.8 Vertical field at 500 m (PEC wire model).
Figure 5.9 Vertical field at 5 km (PEC wire model).
Figure 5.10 Vertical antenna penetrating the ground excited by a voltage source (a) and by a current source (b).
Figure 5.11 Current distribution induced along the vertical wire penetrating a ground for various lengths of ground stake and voltage source at bottom end of the air stake. (a) Real part. (b) Imaginary part.
Figure 5.12 A wire of arbitrary shape and its image.
Figure 5.13 Single wire of an arbitrary shape in a homogeneous medium.
Figure 5.14 Wind turbine struck by lightning and the related wire antenna model.
Figure 5.15 The source current waveform.
Figure 5.16 Characteristic points along the WT.
Figure 5.17 Transient induced at different points along WT for the case of PEC ground.
Figure 5.18 Transient current induced at the strike blade tip.
Figure 5.19 Transient current induced at the middle of the strike blade.
Figure 5.20 Transient current induced at the middle of the side blade.
Figure 5.21 Transient current induced at WT base.

Chapter 6: Transient Analysis of Grounding Systems

Figure 6.1 Horizontal grounding wire excited by a current generator I_g.
Figure 6.2 Current induced at the center of the grounding wire versus frequency (L = 20 m, d = 1 m, a = 5 mm, σ = 0.1 S m⁻¹, ϵ_r = 10).
Figure 6.3 Current induced at the center of the grounding wire versus frequency (L = 20 m, d = 1 m, a = 5 mm, σ = 0.01 S m⁻¹, ϵ_r = 10).
Figure 6.4 Current induced at the center of the grounding wire versus frequency (L = 20 m, d = 1 m, a = 5 mm, σ = 0.001 S m⁻¹, ϵ_r = 10).
Figure 6.5 Voltage spectrum at the grounding electrode driving point (L = 10m, d = 1 m, a = 5 mm, σ = 0.01 S m⁻¹, ϵ_r = 10).
Figure 6.6 Current distribution along the horizontal electrode (f = 1 MHz, L = 10 m, a = 0.005 m, d = 0.3 m, σ = 0.01 S m⁻¹, ϵ_r = 10). (a) Real part, (b) imaginary part, (c) absolute value.
Figure 6.7 Current distribution along the horizontal electrode (f = 1 MHz, L = 10 m, a = 0.005 m, d = 0.3 m, σ = 0.001 S m⁻¹, ϵ_r = 10). (a) Real part, (b) Imaginary part, (c) absolute value.
Figure 6.8 Current distribution along the horizontal electrode (f = 10 MHz, L = 10 m, a = 0.005 m, d = 0.3 m, σ = 0.01 S m⁻¹, ϵ_r = 10). (a) Real part, (b) imaginary part, (c) absolute value.
Figure 6.9 Current distribution along the horizontal electrode (f = 10 MHz, L = 10 m, a = 0.005 m, d = 0.3 m, σ = 0.001 S m⁻¹, ϵ_r = 10). (a) Real part, (b) imaginary part, (c) absolute value.
Figure 6.10 Scattered voltage distribution along the horizontal electrode (f = 1 MHz, L = 10 m, a = 0.005 m, d = 0.3 m, σ = 0.01 S m⁻¹, ϵ_r = 10). (a) Real part, (b) imaginary part, (c) absolute value.
Figure 6.11 Scattered voltage distribution along the horizontal electrode (f = 1 MHz, L = 10 m, a = 0.005 m, d = 0.3 m, σ = 0.001 S m⁻¹, ϵ_r = 10). (a) Real part, (b) imaginary part, (c) absolute value.
Figure 6.12 Scattered voltage distribution along the horizontal electrode (f = 10 MHz, L = 10 m, a = 0.005 m, d = 0.3 m, σ = 0.01 S m⁻¹, ϵ_r = 10). (a) Real part, (b) imaginary part, (c) absolute value.
Figure 6.13 Scattered voltage distribution along the horizontal electrode (f = 10 MHz, L = 10 m, a = 0.005 m, d = 0.3 m, σ = 0.001 S m⁻¹, ϵ_r = 10). (a) Real part, (b) imaginary part, (c) absolute value.
Figure 6.14 Real part, imaginary part, and absolute value of the current induced along the electrode (σ = 1 mS m⁻¹, f = 1 MHz).
Figure 6.15 Real part, imaginary part and absolute value of the current induced along the electrode (σ = 10 mS m⁻¹, f = 1 MHz).
Figure 6.16 Real part, imagin ary part, and absolute value of the current induced along the electrode (σ = 1 mS m⁻¹, f = 10 MHz).
Figure 6.17 Real part, imaginary part, and absolute value of the current induced along the electrode (σ = 10 mS m⁻¹, f = 10 MHz).
Figure 6.18 Frequency spectrum of the current induced at the center of the grounding electrode (L = 1 m, σ = 1 mS m⁻¹).
Figure 6.19 Frequency spectrum of the current induced at the center of the grounding electrode (L = 1 m, σ = 10 mS m⁻¹).
Figure 6.20 Frequency spectrum of the current induced at the center of the grounding electrode (L = 10 m, σ = 1 mS m⁻¹).
Figure 6.21 Frequency spectrum of the current induced at the center of the grounding electrode (L = 10 m, σ = 10 mS m⁻¹).
Figure 6.22 Transient current at the center of the electrode, L = 1 m, σ = 1 mS m⁻¹, 1/10 µs pulse.
Figure 6.23 Transient current at the center of the electrode, L = 1 m, σ = 10 mS m⁻¹, 1/10 µs pulse.
Figure 6.24 Transient current at the center of the electrode, L = 10 m, σ = 1 mS m⁻¹, 1/10 µs pulse.
Figure 6.25 Transient current at the center of the electrode, L = 5 m, σ = 1 mS m⁻¹, 0.1/1 µs pulse.
Figure 6.26 Transient current at the center of the electrode, L = 5 m, σ = 10 mS m⁻¹, 0.1/1 µs pulse.
Figure 6.27 Transient current at the center of the electrode, L = 10 m, σ = 1 mS m⁻¹, 0.1/1 µs pulse.
Figure 6.29 Transient impedance of the grounding electrode (1/10 µs pulse, L = 10 m, σ = 1 mS m⁻¹).
Figure 6.28 Transient impedance of the grounding electrode (1/10 µs pulse, L = 10 m, σ = 10 mS m⁻¹).
Figure 6.30 Transient impedance of the grounding electrode (1/10 µs pulse, L = 1 m, σ = 0.19 mS m⁻¹).
Figure 6.31 Transient impedance of the grounding electrode (1/10 µs pulse, L = 10 m, σ = 0.19 mS m⁻¹).
Figure 6.32 Transient impedance of the grounding electrode (1/10 µs pulse, L = 30 m, σ = 0.19 mS m⁻¹).
Figure 6.33 Transient impedance of the grounding electrode (0.1/1 µs pulse, L = 10 m, σ = 10 mS m⁻¹).
Figure 6.34 Transient impedance of the grounding electrode (0.1/1 µs pulse, L = 10 m, σ = 1 mS m⁻¹).
Figure 6.35 ICS, MF, and MCL source at the open wire end.
Figure 6.36 Percentage difference from ICS (L = 10 m; a = 0.005 m; σ = 0.001 S m⁻¹).
Figure 6.37 Percentage difference from ICS (L = 50 m; a = 0.005 m; σ = 0.001 S m⁻¹).
Figure 6.38 Current at the center of grounding wire (L = 50 m; a = 0.01 m; σ = 0.001 S m⁻¹).
Figure 6.39 Percentage difference (MF results with respect to ICS results; L = 20 m).
Figure 6.40 Percentage difference (with respect to ICS results; L = 20 m, b/a = 3, a = 0.001 m).
Figure 6.41 Vertical grounding electrode excited by the current source.
Figure 6.42 Real and imaginary parts of the current and voltage along the electrode (f = 1 MHz and σ = 0.01 S m⁻¹).
Figure 6.43 Absolute value of current distribution along the electrode (f = 10 MHz and σ = 0.01 S m⁻¹).
Figure 6.44 Absolute value of current distribution along the electrode (f = 10 MHz and σ = 0.001 S m⁻¹).
Figure 6.45 Absolute value of the scattered voltage along the electrode (f = 10 MHz and σ = 0.01 S m⁻¹).
Figure 6.46 Absolute value of the scattered voltage along the electrode (f = 10 MHz and σ = 0.001 S m⁻¹).
Figure 6.47 Transient current at the center of the grounding electrode, L = 1 m, σ = 10 mS m⁻¹.
Figure 6.48 Transient current at the center of the grounding electrode, L = 10 m, σ = 1 mS m⁻¹.
Figure 6.49 Square grounding grid subjected to a lightning stroke.
Figure 6.50 Different grounding grid configurations.
Figure 6.51 Spatial discretization of the square grid.
Figure 6.52 (a) Conditions at the grid edges; (b) equivalent electrical network of grounding grid.
Figure 6.53 Transient feeding point voltage for dry soil.
Figure 6.54 Transient impedance for dry soil.
Figure 6.55 Transient feeding point voltage for wet soil.
Figure 6.56 Transient impedance for wet soil.
Figure 6.57 The impedance spectrum for σ₂ = 0.01 S m⁻¹.
Figure 6.58 The impedance spectrum for σ₁ = 0.001 S m⁻¹.
Figure 6.59 Grounding grid under central injection of the current source (double exponential excitation).
Figure 6.60 Spatial distribution of the voltage induced along the grounding grid (center injection) at T = 0.5 µs computed via (a) AT approach; (b) FDTD–TL approach.
Figure 6.61 Spatial distribution of the voltage induced along the grounding grid at T = 0.5 µs computed via (a) AT approach (b) FDTD–TL approach; corner injection.
Figure 6.62 Ring grounding system energized by a current source I_g.
Figure 6.63 Transient impedance of ring electrode calculated for various ring radiuses.
Figure 6.64 WT subjected to a lightning strike.
Figure 6.65 Typical WT grounding system arrangement.
Figure 6.66 Transient behavior of the basic grounding system.
Figure 6.67 Additional horizontal electrodes on WT grounding system.
Figure 6.68 Induced feeding point transient voltage for different lengths of additional horizontal electrodes.
Figure 6.69 Transient impedance for different lengths of additional horizontal electrodes.
Figure 6.70 Additional vertical electrodes on WT grounding system.
Figure 6.71 Induced feeding point transient voltage for different lengths of additional vertical electrodes.
Figure 6.72 Transient impedance for different lengths of additional vertical electrodes.
Figure 6.73 Comparison of the induced feeding point transient voltage in the case of added 15 m horizontal or vertical electrodes, respectively.
Figure 6.74 Comparison of transient in the case of added 15 m horizontal or vertical electrodes, respectively.
Figure 6.75 Influence of grounding wire in a cable trench on the induced feeding point transient voltage.
Figure 6.76 Influence of the grounding wire in a cable trench on the transient impedance.
Figure 6.77 Horizontal grounding electrode buried in a lossy medium.
Figure 6.78 Transient current induced at the center of the grounding electrode.
Figure 6.79 The leakage current density.
Figure 6.80 Transient current at the center of the electrode, L = 1 m, σ = 10 mS m⁻¹. 0.1/1 µs pulse.
Figure 6.81 Transient current at the center of the electrode, L = 10 m, σ = 1 mS m⁻¹. 0.1/1 µs pulse.
Figure 6.82 Transient current at the center of the electrode, L = 10 m, σ = 10 mS m⁻¹. 0.1/1 µs pulse.
Figure 6.83 Transient current at the center of the electrode, L = 20 m, σ = 1 mS m⁻¹. 0.1/1 µs pulse.
Figure 6.84 Total leakage current versus time. (a) σ = 0.1 mS m⁻¹. (b) σ = 1 mS m⁻¹. (c) σ = 10 mS m⁻¹.

Chapter 8: Modeling of Human Exposure to Static and Low Frequency Fields

Figure 8.1 Geometry and boundary conditions for numerical 3D model of a human seated in front of a VDU.
Figure 8.2 Head models: (a) person 1; (b) person 2.
Figure 8.3 Electrostatic field on the female face: (a) FEM solution; (b) BEM solution.
Figure 8.4 Electrostatic field at the specific locations of the female face.
Figure 8.5 Lateral view of the pregnant woman at 26th gestational week: (a) fetus in the cephalic presentation; (b) fetus in the breach presentation.

Chapter 9: Modeling of Human Exposure to High Frequency (HF) Electromagnetic Fields

Figure 9.1 Cross section of the human eye (a) and various eye tissues (b) from the compound and the extracted eye model.
Figure 9.2 Model of the human head (a), and the overlay depicting various head tissues; (b), surrounding the compound eye model.
Figure 9.3 Induced electric field due to 1 GHz vertically polarized plane wave in the transverse cross section of (a) the extracted eye model and (b) the compound eye model.
Figure 9.4 Induced electric field due to 1 GHz vertically polarized plane wave on the surface of the eye. Anterior view (a) and (b), and top view (c) and (d), of extracted and compound eye model, respectively.
Figure 9.5 Induced SAR due to 1 GHz vertically polarized plane wave in the transverse cross section of the (a) extracted eye model and (b) compound eye model.
Figure 9.6 Model of the human head with different subdomains (tissues).
Figure 9.7 Electric field induced on the surface of the human head model due to 900 MHz horizontally polarized plane wave: (a) field magnitude and (b) field direction.
Figure 9.8 Induced electric field in the sagittal cross section of the head due to (a) 900 MHz HP, (b) 900 MHz VP, (c) 1800 MHz HP, (d) 1800 MHz VP.
Figure 9.9 Induced electric field in the coronal cross section of the head due to (a) 900 MHz HP, (b) 900 MHz VP, (c) 1800 MHz HP, (d) 1800 MHz VP.
Figure 9.10 Induced electric field in the transverse cross section of the head due to (a) 900 MHz HP, (b) 900 MHz VP, (c) 1800 MHz HP, (d) 1800 MHz VP.
Figure 9.11 The brain represented by a lossy homogeneous dielectric.
Figure 9.12 Triangular mesh of the homogeneous brain model.
Figure 9.13 SAR distribution in the brain at f = 900 MHz.
Figure 9.14 (a) Model of the eye exposed to plane wave. (b) Meshing detail.
Figure 9.15 SAR in the eye exposed to plane wave of power density 10 W m⁻² at frequency (a) 1 GHz, (b) 2 GHz.
Figure 9.16 Temperature increase in the eye exposed to plane wave of power density P = 10 W m⁻² at frequency (a) 1 GHz, (b) 2 GHz.

Chapter 10: Biomedical Applications of Electromagnetic Fields

Figure 10.1 The lossy homogeneous dielectric brain model.
Figure 10.2 The human brain model for SIE formulation. (a) Detailed 3-D model from Google Sketchup. (b) Final model discretized using the triangular elements.
Figure 10.3 Equivalent electric current density for (a) circular coil, (b) figure-8 coil.
Figure 10.4 Equivalent magnetic current density for (a) circular coil, (b) figure-8 coil.
Figure 10.5 Sagittal cross section of the electric field induced in the brain model by (a) circular coil, (b) figure-8 coil. Coils not shown.
Figure 10.6 Transversal cross section of the electric field induced in the brain model by (a) circular coil, (b) figure-8 coil. Coils not shown.
Figure 10.7 Thin wire antenna model of the myelinated nerve fiber.
Figure 10.8 Passive nerve fiber model.
Figure 10.9 Rectangular subthreshold current pulse.
Figure 10.10 Intracellular current along the passive nerve fiber, t = 1 ms, L = 2 cm.
Figure 10.11 Intracellular current in the passive Ranvier's node 2, L = 2 cm.
Figure 10.12 Intracellular current in the passive Ranvier's node 6, L = 2 cm
Figure 10.13 Active nerve fiber model.
Figure 10.14 Ionic current of activated node of Ranvier.
Figure 10.15 Two wire junction representation of the active node.
Figure 10.16 Rectangular superthreshold current pulse.
Figure 10.17 Intracellular current in the active Ranvier's node 2, L = 2 cm.
Figure 10.18 Intracellular current in the active Ranvier's node 6, L = 2 cm.
Figure 10.19 Intracellular current along the active nerve fiber, t = 0.2 ms, L = 2 cm.

List of Tables

Chapter 2: Antenna Theory versus Transmission Line Approximation – General Considerations

Table 2.1 Admittance of dipoles calculated by different numerical techniques
Table 2.2 Admittance of monopoles calculated using different excitation (GB-IBEM ISO2)

Chapter 3: Electromagnetic Field Coupling to Overhead Wires

Table 3.1 Maximum values of the radiated electric field at the 30 m distance
Table 3.2 LPDA parameters

Chapter 7: Human Exposure to Electromagnetic Fields – General Aspects

Table 7.1 Basic restrictions for SAR according to the ICNIRP guidelines

Chapter 9: Modeling of Human Exposure to High Frequency (HF) Electromagnetic Fields

Table 9.1 Tissue parameters [12]
Table 9.2 Tissue dielectric parameters according to the 4-Cole–Cole model described in [15]

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Preface

Electromagnetic Compatibility (EMC) as a topic has become very important in the last few decades. The vitality of EMC nowadays can be seen in many academic activities, as there are many universities worldwide offering undergraduate or graduate EMC courses, either obligatory or optional. Moreover, today, in the world of wireless communication and Internet of Things (IoT), many electronic products, devices, or systems are required to pass immunity and emission testing regarding EMC standards. Accordingly, there are dozens of books related to various EMC aspects currently available from major scientific publishers. Nevertheless, books rarely deal with EMC computational models and related numerical methods.

The previous book by Dragan Poljak, Advanced Modeling in Computational Electromagnetic Compatibility, was published by Wiley in February 2007. The present book authored by Dragan Poljak and Khalil El Khamlichi Drissi provides an overview of the further advances in the area of computational electromagnetics arising from a decade of very close and highly intensive collaboration between the Dragan research group from the University of Split, Croatia, and the Khalil group from Universitė Clermont Auvergne, France.

This rather fruitful collaboration resulted in successful joint projects and numerous journal and conference papers. The beauty of this collaboration reflects in merging two research teams tackling similar problems with different approaches related to antenna theory models (Dragan group) and transmission line methods (Khalil group). Furthermore, there is the benefit of discussing different solution methods related to boundary integral equation techniques and finite difference techniques. Moreover, throughout the book a trade-off between the different formulations and numerical solution methods is provided.

While the previous Wiley book by Dragan was primarily focused on academic examples, the present book by Dragan and Khalil deals with many practical engineering problems. The most significant topics covered in the book are related to realistic antenna systems, such as antennas for air traffic control or ground penetrating radar (GPR) antennas, grounding systems, such as grounding systems for wind turbines and biomedical applications of electromagnetic fields, such as transcranial magnetic stimulation. The book includes a large number of illustrative computational examples and reference list at the end of each chapter. Rigorous theoretical background and mathematical details of various formulations and solution methods being used throughout the book are presented in detail.

The authors hope that the present book gives not only a useful description of their expertise related to computational EMC but also updated information on the latest advances in this area.

The book is divided in two parts. The first part deals with electromagnetic field coupling to thin wire configurations of an arbitrary shape covering the following topics: introductory aspects of computational electromagnetics, antenna theory versus transmission line approximation, electromagnetic field coupling to overhead and buried wires, transient analysis of grounding systems and lightning channel modeling. An important goal of this part of the book is to provide a trade-off between a highly efficient transmission line approach, rather widely used by EMC community researchers and engineers, and antenna theory models providing the most rigorous analysis of high frequency (HF) and transient phenomena.

The second part of the book deals with advanced modeling of bioelectromagnetics phenomena featuring the method of moments (MoM), boundary element method (BEM) and hybrid finite element method (FEM)/ BEM, respectively. Of particular interest is not only human exposure to low frequency (LF) and HF electromagnetic fields but also some biomedical applications of electromagnetic fields.

We hope that this book will be useful material for undergraduate, graduate and postdoc students to learn about advanced EMC computational models and that it will also enable engineers in industry to solve some demanding practical problems. We also think that the book could be used for various university courses involving not only computational EMC models but also computational electromagnetics in general or numerical modeling in engineering itself.

The book requires a general background in electrical engineering, involving mainly basic electromagnetics. Fundamental EMC concepts such as numerical modeling principles are given in this book. Thus, the book is convenient for students, specialists, researchers and engineers.

To sum up, we are glad we have managed to compose this material stemming from more than a decade of very intensive collaboration in the areas of EMC and bioelectromagnetics. Of course, there are many rather challenging problems we plan to deal with together in days to come.

Split, Croatia–Clermont-Ferrand

France, June 2017

Dragan Poljak

Khalil El Khamlichi Drissi