Radiating Nonuniform Transmission-Line Systems and the Partial Element Equivalent Circuit Method.
Title:
Radiating Nonuniform Transmission-Line Systems and the Partial Element Equivalent Circuit Method.
Author:
Nitsch, Juergen.
ISBN:
9780470682418
Personal Author:
Edition:
1st ed.
Physical Description:
1 online resource (350 pages)
Contents:
RADIATING NONUNIFORM TRANSMISSION-LINE SYSTEMS AND THE PARTIAL ELEMENT EQUIVALENT CIRCUIT METHOD -- Contents -- Preface -- References -- Acknowledgments -- List of Symbols -- Introduction -- References -- 1 Fundamentals of Electrodynamics -- 1.1 Maxwell Equations Derived from Conservation Laws - an Axiomatic Approach -- 1.1.1 Charge Conservation -- 1.1.2 Lorentz Force and Magnetic Flux Conservation -- 1.1.3 Constitutive Relations and the Properties of Spacetime -- 1.1.4 Remarks -- 1.2 The Electromagnetic Field as a Gauge Field - a Gauge Field Approach -- 1.2.1 Differences of Physical Fields that are Described by Reference Systems -- 1.2.2 The Phase of Microscopic Matter Fields -- 1.2.3 The Reference Frame of a Phase -- 1.2.4 The Gauge Fields of a Phase -- 1.2.5 Dynamics of the Gauge Field -- 1.3 The Relation Between the Axiomatic Approach and the Gauge Field Approach -- 1.3.1 Noether Theorem and Electric Charge Conservation -- 1.3.2 Minimal Coupling and the Lorentz Force -- 1.3.3 Bianchi Identity and Magnetic Flux Conservation -- 1.3.4 Gauge Approach and Constitutive Relations -- 1.4 Solutions of Maxwell Equations -- 1.4.1 Wave Equations -- 1.4.1.1 Decoupling of Maxwell Equations -- 1.4.1.2 Equations of Motion for the Electromagnetic Potentials -- 1.4.1.3 Maxwell Equations in the Frequency Domain and Helmholtz Equations -- 1.4.1.4 Maxwell Equations in Reciprocal Space -- 1.4.2 Boundary Conditions at Interfaces -- 1.4.3 Dynamical and Nondynamical Components of the Electromagnetic Field -- 1.4.3.1 Helmholtz's Vector Theorem, Longitudinal and Transverse Fields -- 1.4.3.2 Nondynamical Maxwell Equations as Boundary Conditions in Time -- 1.4.3.3 Longitudinal Part of the Maxwell Equations -- 1.4.3.4 Transverse Part of the Maxwell Equations -- 1.4.4 Electromagnetic Energy and the Singularities of the Electromagnetic Field.
1.4.5 Coulomb Fields and Radiation Fields -- 1.4.6 The Green's Function Method -- 1.4.6.1 Basic Ideas -- 1.4.6.2 Self-Adjointness of Differential Operators and Boundary Conditions -- 1.4.6.3 General Solutions of Maxwell Equations -- 1.4.6.4 Basic Relations Between Electromagnetic Green's Functions -- 1.5 Boundary Value Problems and Integral Equations -- 1.5.1 Surface Integral Equations in Short -- 1.5.2 The Standard Electric Field Integral Equations of Antenna Theory and Radiating Nonuniform Transmission-Line Systems -- 1.5.2.1 Pocklington's Equation -- 1.5.2.2 Hallén's Equation -- 1.5.2.3 Mixed-Potential Integral Equation -- 1.5.2.4 Schelkunoff 's Equation -- References -- 2 Nonuniform Transmission-Line Systems -- 2.1 Multiconductor Transmission Lines: General Equations -- 2.1.1 Geometric Representation of Nonuniform Transmission Lines -- 2.1.1.1 Local Coordinate System -- 2.1.1.2 Tangential Surface Vector -- 2.1.1.3 Volume and Surface Integrals -- 2.1.2 Derivation of Generalized Transmission-Line Equations -- 2.1.2.1 Continuity Equation -- 2.1.2.2 Reconstruction of the Densities -- 2.1.3 Mixed Potential Integral Equation -- 2.1.3.1 Thin-Wire Approximation -- 2.1.3.2 Representation as Matrix Equations -- 2.1.3.3 Current and Charge Trial Function -- 2.1.3.4 Generalized Telegrapher Equations and TLST -- 2.1.4 Computation of Generalized Transmission-Line Parameters -- 2.1.4.1 Parameters -- 2.1.4.2 Source Terms -- 2.1.4.3 Solution of the Extended Telegrapher Equations -- 2.1.4.4 Returning to Voltages? -- 2.1.4.5 Discussion of the New Parameters -- 2.1.4.6 Asymmetric Parameter Matrices -- 2.1.5 Numerical Evaluation of the Parameters -- 2.1.5.1 Starting Values for the Iteration -- 2.1.5.2 First Iteration -- 2.1.5.3 Taylor Series Expansion of the Product Integral -- 2.1.5.4 Eigenvalue Decomposition -- 2.1.5.5 Discussion of the Numerical Methods.
2.2 General Calculation Methods for the Product Integral/Matrizant -- 2.2.1 Picard Iteration -- 2.2.2 Volterra's Method and the Product Integral -- 2.2.3 Recursion Formulas for Linear Interpolation -- 2.2.4 Approximation by Power Series -- 2.2.5 Interpolation from Diagonalization -- 2.2.6 Numerical Integration -- 2.2.6.1 Euler-Cauchy Method -- 2.2.6.2 Integration by trapezoidal rule -- 2.2.6.3 Explicit Runge-Kutta Method -- 2.2.6.4 Hermite Integration -- 2.2.6.5 Improving Accuracy by the Romberg Method -- 2.2.6.6 Controlling Step Size and Error -- 2.2.7 Remarks on Efficiency and the Choice of an Appropriate Method -- 2.3 Semi-Analytic and Numerical Solutions for Selected Transmission Lines in the TLST -- 2.3.1 The Straight, Finite Length Wire Above Ground -- 2.3.2 The Semi-Infinite Line -- 2.3.3 Field Coupling to an Infinite Line -- 2.3.4 The Skewed Wire Transmission Line -- 2.3.5 The Periodic Transmission Line -- 2.3.6 Cross Talk in a Nonuniform Multiconductor Transmission Line -- 2.4 Analytic Approaches -- 2.4.1 Classical Telegrapher Equations for Nonuniform Transmission Lines -- 2.4.2 Calculation Methods for the General Solution -- 2.4.2.1 The Piecewise-Constant Approximation of the Characteristic Impedance Matrix -- 2.4.2.2 The Continuous Approximation of the Characteristic Impedance Matrix -- 2.4.2.3 Circulant Nonuniform MTLs -- 2.4.2.4 General Approach to Calculate the Matrizant -- 2.4.3 Matrizant Reduction -- References -- 3 Complex Systems and Electromagnetic Topology -- 3.1 The Concept of Electromagnetic Topology -- 3.2 Topological Networks and BLT Equations -- 3.2.1 Wave Quantities -- 3.2.2 BLT 1 Equation -- 3.2.3 BLT 2 Equation -- 3.2.4 Admittance Representation -- 3.3 Transmission Lines and Topological Networks -- 3.3.1 Transformation into a Propagation Matrix -- 3.3.2 Equivalent Scattering Matrices -- 3.3.3 Admittance Matrix.
3.4 Shielding -- 3.4.1 Model for the Transfer Impedance Based on NMTLT -- 3.4.1.1 Transfer Parameters of Cables -- 3.4.1.2 Determination of the Per-unit-length Parameters -- 3.4.1.3 Computation of the Transfer Impedance -- 3.4.2 Shielding of an Anisotropic Spherical Shell -- 3.4.2.1 Shielding of a Plane Wall -- 3.4.2.2 Spherical Shell -- 3.4.2.3 Application to Thin Conductive Shells -- 3.4.2.4 Conclusions -- References -- 4 The Method of Partial Element Equivalent Circuits (PEEC Method) -- 4.1 Fundamental Equations -- 4.1.1 Maxwell Equations and Real Media for Interconnections -- 4.1.2 Mixed Potential Integral Equations (MPIE) -- 4.2 Derivation of the Generalized PEEC Method in the Frequency Domain -- 4.2.1 The PEEC Equation System in the Frequency Domain -- 4.2.2 Generalized Partial Elements and Circuit Interpretation -- 4.3 Classification of PEEC Models -- 4.3.1 Classification in Dependence on Media -- 4.3.1.1 PEEC Models for Conductors -- 4.3.1.2 PEEC Models for Dielectrics -- 4.3.2 Classification in Dependence on the Relation of the Maximum Frequency of Interest to the Discretization Length -- 4.3.2.1 PEEC Models with Generalized Partial Elements -- 4.3.2.2 PEEC Models with Center-to-Center Retardation -- 4.3.2.3 Quasi-Static PEEC Models -- 4.4 PEEC Models for the Plane Half Space -- 4.5 Geometrical Discretization in PEEC Modeling -- 4.5.1 Orthogonal Cells -- 4.5.2 Nonorthogonal Cells -- 4.5.3 Triangular Cells -- 4.6 PEEC Models for the Time Domain and the Stability Issue -- 4.6.1 Standard PEEC Models for the Time Domain -- 4.6.2 General Remarks on Stability of PEEC Model Solutions -- 4.6.3 Stability Improvement of PEEC Models with Center-to-Center Retardation -- 4.6.4 Stable Time Domain PEEC Models by Parametric Macromodeling the Generalized Partial Elements.
4.6.4.1 Stable Time Domain PEEC Models by Full-Spectrum Convolution Macromodeling (FSCM) -- 4.6.4.2 Stable Time Domain PEEC Models by Macromodeling Using Foster's Rational Functions and Circuit Synthesis -- 4.7 Skin Effect in PEEC Models -- 4.7.1 Cross-Sectional Discretization of Wires -- 4.7.2 Skin Effect Modeling by Means of a Global Surface Impedance -- 4.7.3 Skin Effect Modeling by Means of a Local Mean Surface Impedance -- 4.8 PEEC Models Based on Dyadic Green's Functions for Conducting Structures in Layered Media -- 4.8.1 Motivation -- 4.8.2 The DGFLM-PEEC Method -- 4.8.3 DGFLM-PEEC Model for the Stripline Region -- 4.8.3.1 Green's Functions for the Stripline Region -- 4.8.3.2 Discussion of the Behavior of the Green's Functions -- 4.8.3.3 Frequency Domain DGFLM-PEEC Model -- 4.8.3.4 DGFLM-PEEC Models in the Time Domain -- 4.9 PEEC Models and Uniform Transmission Lines -- 4.10 Power Considerations in PEEC Models -- 4.10.1 General Remarks -- 4.10.2 Power Analysis of Magnetic and Electric Couplings -- 4.10.3 Power Analysis of PEEC Models -- References -- Appendix A: Tensor Analysis, Integration and Lie Derivative -- A.1 Integration Over a Curve and Covariant Vectors as Line Integrands -- A.2 Integration Over a Surface and Contravariant Vector Densities as Surface Integrands -- A.3 Integration Over a Volume and Scalar Densities as Volume Integrands -- A.4 Poincar Lemma -- A.5 Stokes' Theorem -- A.6 Lie Derivative -- References -- Appendix B: Elements of Functional Analysis -- B.1 Function Spaces -- B.1.1 Metric Spaces -- B.1.2 Linear Spaces, Vector Spaces -- B.1.3 Normed Spaces -- B.1.4 Inner Product Spaces and Pseudo Inner Product Spaces -- B.1.5 Hilbert Spaces -- B.1.6 Finite Expansions and Best Approximation -- B.1.7 The Projection Theorem -- B.1.8 Basis of a Hilbert Space -- B.2 Linear Operators.
B.2.1 Definition of a Linear Operator, Domain and Range of an Operator.
Abstract:
Preface. References. Acknowledgments. List of Symbols. Introduction. 1 Fundamentals of Electrodynamics. 1.1 Maxwell Equations Derived from Conservation Laws - an Axiomatic Approach. 1.2 The Electromagnetic Field as a Gauge Field - a Gauge Field Approach. 1.3 The Relation Between the Axiomatic Approach and the Gauge Field Approach. 1.4 Solutions of Maxwell Equations. 1.5 Boundary Value Problems and Integral Equations. References. 2 Nonuniform Transmission-Line Systems. 2.1 Multiconductor Transmission Lines: General Equations. 2.2 General Calculation Methods for the Product Integral/Matrizant. 2.3 Semi-Analytic and Numerical Solutions for Selected Transmission Lines in the TLST. 2.4 Analytic Approaches. References. 3 Complex Systems and Electromagnetic Topology. 3.1 The Concept of Electromagnetic Topology. 3.2 Topological Networks and BLT Equations. 3.3 Transmission Lines and Topological Networks. 3.4 Shielding. References. 4 The Method of Partial Element Equivalent Circuits (PEEC Method). 4.1 Fundamental Equations. 4.2 Derivation of the Generalized PEEC Method in the Frequency Domain. 4.3 Classification of PEEC Models. 4.4 PEEC Models for the Plane Half Space. 4.5 Geometrical Discretization in PEEC Modeling. 4.6 PEEC Models for the Time Domain and the Stability Issue. 4.7 Skin Effect in PEEC Models. 4.8 PEEC Models Based on Dyadic Green's Functions for Conducting Structures in Layered Media. 4.9 PEEC Models and Uniform Transmission Lines. 4.10 Power Considerations in PEEC Models. References. Appendix A: Tensor Analysis, Integration and Lie Derivative. A.1 Integration Over a Curve and Covariant Vectors as Line Integrands. A.2 Integration Over a Surface and Contravariant Vector Densities as Surface Integrands. A.3 Integration Over a Volume and Scalar Densities as Volume
Integrands. A.4 Poincaré Lemma. A.5 Stokes' Theorem. A.6 Lie Derivative. References. Appendix B: Elements of Functional Analysis. B.1 Function Spaces. B.2 Linear Operators. B.3 Spectrum of a Linear Operator. B.4 Spectral Expansions and Representations. References. Appendix C: Some Formulas of Vector and Dyadic Calculus. C.1 Vector Identities. C.2 Dyadic Identities. C.3 Integral Identities. Reference. Appendix D: Adaption of the Integral Equations to the Conductor Geometry. Appendix E: The Product Integral/Matrizant. E.1 The Differential Equation and Its Solution. E.2 The Determination of the Product Integral. E.3 Inverse Operation. E.4 Calculation Rules for the Product Integral. References. Appendix F: Solutions for Some Important Integrals. F.1 Integrals Involving Powers of √x2 + b2. F.2 Integrals Involving Exponential and Power Functions. F.3 Integrals Involving Trigonometric and Exponential Functions. Reference. Index.
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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
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