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  • A transmission line is a device used for transmission of electromagnetic energy guided by two conductors in a dielectric medium.
  • Transmission-line mode is the distinct pattern of electric and magnetic field induced on a transmission line under source excitation.
    Three types of transmission line modes are
    1. Transverse ElectroMagnetic (TEM) mode
    2. Quasi-TEM mode
    3. Waveguide mode
  • A transmission line can be characterized by four distributed parameters: resistance (in Ω/m), inductance (in H/m), capacitance (in F/m), and conductance (in S/m). These four distributed parameters are constant for a particular transmission line and are known as primary line constants of a transmission line.
  • Apart from these primary line constants, there are few other constants related to a transmission line. These include the characteristic impedance (Z0), the propagation constant (γ), attenuation constant (α), and phase constant (β). These constants are known as the secondary line constants.
  • Transmission line voltage and current equations, known as telegrapher’s equations, are given as,
    Description: Description: 101799.png and Description: Description: 101808.png
    where Description: Description: 101817.png is the complex propagation constant. 
  • Characteristic impedance of a transmission line is defined as the ratio of positively travelling voltage wave to current wave at any point on the line. It is given as,
    Description: Description: 101827.png
  • A transmission line is said to be lossless if
    • the conductors of the line are perfect, i.e., the conductors have infinite conductivity and zero resistance (σ = ∞, R = 0), and
    • the dielectric medium between the conductors is ideal, i.e., the medium has zero conductivity and infinite resistance (σ = 0, G = 0).
      For a lossless line, Description: Description: 101836.png
  • A transmission line is said to be distortionless if it has no frequency and phase distortions.
    The condition for a line to be distortionless is written as, Description: Description: 101846.png.
    For a distortionless line, Description: Description: 101853.png.
  • The input impedance at any point on the transmission line is given by the ratio of voltage to current at that point.
    Input impedance for different types of transmission lines are given as follows.
    For finite lossy transmission line,
    Description: Description: 101861.png
    For finite lossless high-frequency transmission line,
    Description: Description: 101870.png
    For infinite (lossy and lossless) transmission line,
    Description: Description: 101880.png
  • Reflection coefficient of a transmission line is the ratio of the reflected voltage (or current) to the incident voltage (or current), when a transmission line is terminated in an impedance (ZR) not equal to the characteristic impedance (Z0) of the line. The reflection coefficient as a function of position can be written as,
    Description: Description: 101891.png
  • The reflection coefficient at the load (z = l) is,
    Description: Description: 101900.png
  • Standing wave ratio in a transmission line is defined as the ratio of the maximum voltage (or current) to the minimum voltage (or current) of a line having standing waves.
    Description: Description: 101908.png
  • The input impedance as a function of position at any point along a general transmission line is given as,
    Description: Description: 101917.png
  • A Smith chart is a useful graphical tool used to calculate the reflection coefficient and impedance at various points on a (lossless) transmission line system.
    A Smith chart can be used for different purposes, such as, to find the normalised admittance from normalised impedance and vice versa, to find the parameters of mismatched transmission lines, to find the VSWR for a given load impedance, to find the reflection coefficient, to find the input impedance of a transmission line, to locate a voltage maximum on a transmission line, and to design stubs for impedance matching.

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