Time-Domain Electromagnetic Reciprocity in Antenna Modeling

MARTIN STUMPF, PhD, is an Associate Professor of Electromagnetic Theory at Brno University of Technology, Brno, The Czech Republic. His research interests include analytical and numerical modeling of wave and diffusive field phenomena with an emphasis on electromagnetic compatibility and antenna engineering. He is a member of the IEEE and the IEEE Antennas and Propagation and Electromagnetic Compatibility Societies.

• Preface xiiiAcronyms xv1 Introduction 11.1 Synopsis 21.2 Prerequisites 51.2.1 One-Sided Laplace Transformation 61.2.2 Lorentz's Reciprocity Theorem 82 Cagniard-Dehoop Method of Moments for Thin-Wire Antennas 152.1 Problem Description 152.2 Problem Formulation 162.3 Problem Solution 182.4 Antenna Excitation 202.4.1 Plane-Wave Excitation 202.4.2 Delta-Gap Excitation 21Illustrative Example 223 Pulsed EM Mutual Coupling Between Parallel Wire Antennas 253.1 Problem Description 253.2 Problem Formulation 263.3 Problem Solution 274 Incorporating Wire-Antenna Losses 294.1 Modification of the Impedance Matrix 305 Connecting a Lumped Element to The Wire Antenna 315.1 Modification of the Impedance Matrix 326 Pulsed EM Radiation from a Straight Wire Antenna 356.1 Problem Description 356.2 Source-Type Representations for the TD Radiated EM Fields 366.3 Far-Field TD Radiation Characteristics 387 EM Reciprocity Based Calculation of Td Radiation Characteristics 417.1 Problem Description 417.2 Problem Solution 42Illustrative Numerical Example 438 Influence of a Wire Scatterer on a Transmitting Wire Antenna 478.1 Problem Description 478.2 Problem Solution 48Illustrative Numerical Example 499 Influence of a Lumped Load on EM Scattering of a Receiving Wire Antenna 539.1 Problem Description 539.2 Problem Solution 54Illustrative Numerical Example 5510 Influence of a Wire Scatterer on a Receiving Wire Antenna 5910.1 Problem Description 5910.2 Problem Solution 59Illustrative Numerical Example 6111 EM-Field Coupling to Transmission Lines 6511.1 Introduction 6511.2 Problem Description 6811.3 EM-Field-To-Line Interaction 6811.4 Relation to Agrawal Coupling Model 7111.5 Alternative Coupling Models Based on EM Reciprocity 7311.5.1 EM Plane-Wave Incidence 7311.5.2 Known EM Source Distribution 7412 EM Plane-Wave Induced Thévenin's Voltage on Transmission Lines 7712.1 Transmission Line Above the Perfect Ground 7712.1.1 Thévenin's Voltage at x = x1 7812.1.2 Thévenin's Voltage at x = x2 8112.2 Narrow Trace on a Grounded Slab 8312.2.1 Thévenin's Voltage at x = x1 8512.2.2 Thévenin's Voltage at x = x2 88Illustrative Numerical Example 8913 VED-Induced Thévenin's Voltage on Transmission Lines 9313.1 Transmission Line Above the Perfect Ground 9313.1.1 Excitation EM Fields 9413.1.2 Thévenin’s Voltage at x = x1 9713.1.3 Thévenin’s Voltage at x = x2 9813.2 Influence of Finite Ground Conductivity 9813.2.1 Excitation EM Fields 9813.2.2 Correction to Thévenin’s Voltage at x = x1 10013.2.3 Correction to Thévenin’s Voltage at x = x2 101Illustrative Numerical Example 10114 Cagniard-Dehoop Method of Moments for Planar-Strip Antennas 10314.1 Problem Description 10514.2 Problem Formulation 10614.3 Problem Solution 10714.4 Antenna Excitation 10914.4.1 Plane-Wave Excitation 11014.4.2 Delta-Gap Excitation 11114.5 Extension to a Wide-Strip Antenna 111Illustrative Numerical Example 11715 Incorporating Strip-Antenna Losses 12115.1 Modification of the Impeditivity Matrix 12215.1.1 Strip with Conductive Properties 12315.1.2 Strip with Dielectric Properties 12315.1.3 Strip with Conductive and Dielectric Properties 12415.1.4 Strip with Drude-Type Dispersion 12416 Connecting a Lumped Element to The Strip Antenna 12516.1 Modification of the Impeditivity Matrix 12617 Including a Pec Ground Plane 12917.1 Problem Description 12917.2 Problem Formulation 13017.3 Problem Solution 13117.4 Antenna Excitation 132Illustrative Numerical Example 133A Green's Function Representation in an Unbounded, Homogeneous, and Isotropic Medium 137B Time-Domain Response of an Infinite Cylindrical Antenna 141B.1 Transform-Domain Solution 141B.2 Time-Domain Solution 143C Impedance Matrix 147C.1 Generic Integral IA 147C.2 Generic Integral IB 149C.3 TD Impedance Matrix Elements 150D Mutual-Impedance Matrix 151D.1 Generic Integral JA 151D.2 Generic Integral JB 153D.3 TD Mutual-Impedance Matrix Elements 154E Internal Impedance of a Solid Wire 157F VED-Induced EM Coupling to Transmission Lines — Generic Integrals 159F.1 Generic Integral I 159F.2 Generic Integral J 163F.3 Generic Integral K 165G Impeditivity Matrix 169G.1 Generic Integral J 169G.1.1 Generic Integral JA 171G.1.2 Generic Integral JB 175H A Recursive Convolution Method and Its Implementation 177H.1 Convolution-Integral Representation 177H.2 Illustrative Example 179H.3 Implementation of the Recursive Convolution Method 180I Conductance and Capacitance of a Thin High-Contrast Layer 183J Ground-Plane Impeditivity Matrix 187J.1 Generic Integral I 187J.1.1 Generic Integral IA 189J.1.2 Generic Integral IB 193K Implementation of CDH-Mom for Thin-Wire Antennas 195K.1 Setting Space-time Input Parameters 195K.2 Antenna Excitation 197K.2.1 Plane-Wave Excitation 197K.2.2 Delta-Gap Excitation 199K.3 Impedance Matrix 200K.4 Marching-on-in-Time Solution Procedure 202K.5 Calculation of Far-Field TD Radiation Characteristics 203L Implementation of VED-Induced Thévenin’s Voltages on a Transmission Line 205L.1 Setting Space-Time Input Parameters 205L.2 Setting Excitation Parameters 206L.3 Calculating Thévenin’s Voltages 207L.4 Incorporating Ground Losses 211M Implementation of CDH-Mom for Narrow-Strip Antennas 215M.1 Setting Space-Time Input Parameters 215M.2 Delta-Gap Antenna Excitation 217M.3 Impeditivity Matrix 217M.4 Marching-on-in-Time Solution Procedure 200References 223Index 227