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Transmission Lines and Lumped Circuits

  • Introduction
  • Transmission Line Equations and Properties
    • Transmission Line Model
    • Two-Conductor Transmission Line Equations
      • Ideal Transmission Lines
      • Lossy Transmission Lines
      • Nonuniform Transmission Lines
      • Transmission Lines with Distributed Sources
      • Transmission Lines with Frequency-Dependent Parameters
    • Multiconductor Transmission Line Equations
      • Ideal Multiconductor Transmission Lines
      • Lossy Multiconductor Transmission Lines
      • Multiconductor Transmission Lines with Distributed Sources
      • Multiconductor Transmission Lines with Frequency-Dependent Parameters
    • Poynting’s Theorem for Lines with Frequency Independent Parameters
      • Two-Conductor Transmission Lines
      • Multiconductor Transmission Lines
      • Equations
    • Uniqueness of the Solution of Transmission Line
      • Two-Conductor Transmission Lines
      • Multiconductor Transmission Lines
    • Transmission Line Equations in the Laplacde Domain
    • Reciprocity Theorems for Two-Conductor Transmission Lines
      • The First Form of the Reciprocity Theorem
      • The Second Form of the Reciprocity Theorem
      • The Third Form of the Reciprocity Theorem
      • Reciprocity Theorems for Multiconductor Transmission Lines
        • The First Form of the Reciprocity Theorem
        • The Second Form of the Reciprocity Theorem
        • The Third Form of the Reciprocity Theorem
        • Reciprocity Theorem for a Semi-infinite Transmission Line
  • Ideal Two-Conductor Transmission Lines Connected to Lumped Circuits
    • d’Alembert Solution of Two-Conductor Transmission Line Equations
    • Some Elementary Networks
      • An Infinite Line
      • A Semi-infinite Line Connected to an Ideal Current Source
      • A Semi-infinite Line Connected to a Linear Resistor; Reflection Coefficient
      • A Semi-infinite Line Connected to a Linear Capacitor
      • A Semi-infinite Line Connected to a Nonlinear Resistor
      • Semi-infinite Line Connected to a Nonlinear Resistor in Parallel with a Linear Capacitor
    • Natural Frequencies of a Finite Length Transmission Line Connected to Short Circuits
    • Two-Conductor Transmission Lines as Two-Ports
      • State Variables of the Line
      • Transmission Line Behaviour at the Ends
    • The Input-Output Description
    • The Input-State-Output Description, and
    • Lines Connected to Linear Lumped Circuits
      • State Equations in Normal Form
      • Natural Frequencies of the Network
      • Solution in the Laplace Domain
    • A Glimpse at a Transmission Line Connected to a Nonlinear One-Port: State Equations in Normal Form
      • A Line Connected to a Nonlinear Resistor
      • A Line Connected to a Nonlinear Resistor in Parallel with a Linear Capacitor
    • Ideal Two-Conductor Transmission Lines with Distributed Sources
      • A Particular Solution of the Line Equations With Distributed Sources
      • Characterization as Two-Ports
  • Ideal Multiconductor Transmission Lines
    • d’Alembert Solution for Ideal Multiconductor Transmission Lines
      • Properties and Diagonalization of the Matrices LC and CL
      • Characteristic Resistance and Conductance Matrices
      • Natural Modes of Propagation
    • Infinite Multiconductor Transmission Lines
    • Semi-infinite Multiconductor Transmission Lines and Equivalent Circuits
    • Ideal Multiconductor Transmission Lines as Multiports
      • Characterization of the Transmission Line Behavior at the Ends
    • Multiconductor Lines with Homogeneous Dielectric
      • Characterization of the Transmission Line Behavior at the Ends
    • Multiconductor Transmission Line Connected to Linear Resistive Multiports
      • Natural Frequencies of the Network
    • A Particular Solution of the Ideal Multiconductor Transmission Line Equations with Distributed Sources
      • Transversally Homogeneous Lines
    • Properties of the Characteristic Conductance Matrix G, and Resistance Matrix R,
  • Lossy Two-Conductor Transmission Lines
    • Lossy Transmission Lines are Dispersive
      • The Heaviside Condition
    • Solution of the Lossy Transmission Line Equations in the Laplace Domain
    • The Propagation Along a Lossy Transmission Line
    • Semi-infinite Lossy Line Connected to an Ideal Current Source
  • Lossy Multiconductor Transmission Lines
  • Nonuniform Transmission Lines
  • Transmission Line Equations in Characteristic Form
  • Lumped Nonlinear Networks Interconnected by Transmission Lines
  • Qualitative Analysis of an Ideal Two-Conductor Line Connected to Nonlinear Resistors: Periodic Solutions, Bifurcations and Chaos
  • Appendix A Some Useful Notes on the Matrix Operators
    • Preliminary Definitions
    • The Eigenvalue Problem Au = Au
    • The Generalized Eigenvalue Problem Au = lambdaBu
    • Function of a Matrix Operator
    • Perturbation of a Matrix Operator: Asymptotic Behavior of the Eigenvalues
  • Appendix B Some Useful Notes on the Laplace Transformation
  • Appendix C Some a-priori Estimates
  • Appendix D Tables of Equivalent Representations of Transmission Lines