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Summary

  • A waveguide is a hollow conducting pipe, of uniform cross section, used to transport high-frequency electromagnetic waves (generally, in the microwave band) from one point to another.
  • Waveguides can be generally classified as eithermetal waveguidesordielectric waveguides.
  • There are different modes of wave propagation through a waveguide, e.g., TE mode, TM mode, TEM mode and Hybrid mode.
    • For TE mode, no component of electric field exists in the direction of wave propagation.
    • For TM mode, no component of magnetic field exists in the direction of wave propagation.
    • For TEM mode, no component of either electric or magnetic field exists in the direction of wave propagation.
    • For hybrid mode, both electric and magnetic field exists in the direction of wave propagation.
  • For parallel plane waveguide, consisting of two infinite parallel conducting planes, there exist three modes of wave propagation, e.g., TE mode, TM mode and TEM mode.
  • Different parameters for parallel plane waveguide are given in the table below.

Parameters

TE and TM Modes

TEM Mode

Propagation constant

Description: 49516.png

Description: 49506.png

Cut-off frequency

Description: 49498.png

Description: 49488.png

Cut-off wavelength

Description: 49481.png

Description: 49470.png

Guide wavelength

Description: 49460.png

Description: 49452.png

Phase velocity

Description: 49445.png

Description: 49437.png

Group velocity

Description: 49427.png

Wave impedance

Description: 49420.png;Description: 49411.png

Description: 49404.png

  • A rectangular waveguide is formed by placing four conducting planes.
  • For a rectangular waveguide, four modes of wave propagation, e.g., TE mode, TM mode, TEM mode and hybrid mode, exist. For TEmn mode, m = ;0, 1, 2, …; n = 1, 2, 3, … For TMmn mode, m = 1, 2, 3, …; n = 1, 2, 3,…
  • Different parameters for rectangular waveguides are given in the table below.

Parameters

TE and TM Modes

Propagation constant

Description: 49387.png

Cut-off frequency

Description: 49380.png

Cut-off wavelength

Description: 49370.png

Guide wavelength

Description: 49361.png

Phase velocity

Description: 49352.png

Group velocity

Description: 49345.png

Intrinsic wave impedance

Description: 49337.png;Description: 49328.pngwhere,Description: 49320.png.

  • For TEM mode in rectangular waveguide, Description: 49304.pngDescription: 49297.png, so that Description: 49289.png.
  • A TEM wave cannot exist in a single-conductor waveguide.
  • Cylindrical or circular waveguides are those that maintain a uniform circular cross section along their length. Two modes of propagation, i.e.,TE and TM, exist in circular waveguides.
  • Different parameters for circular waveguides are given in the table below.

Parameters

TE and TM Modes

Propagation constant

Description: 49279.png

where,Description: 49269.png

Phase constant

Description: 49260.png

Cut-off frequency

Description: 49251.png

Cut-off wavelength

Description: 49243.png

Guide wavelength

Description: 49236.png

Phase velocity

Description: 49227.png

Group velocity

Description: 49220.png

Intrinsic wave impedance

Description: 49211.png;Description: 49204.png

where,Description: 49195.png

  • In a waveguide, since the guide walls are not perfectly conducting and the dielectric is lossyDescription: 49181.png,there is a continuous loss of power as a wave propagates through the waveguide. These losses are mainly due to two reasons, represented by two attenuation constants:
     
    Description: 49170.png, attenuation due to dielectric losses
     
    Description: 49161.png, attenuation due to conduction losses
  • The attenuation constants due to conduction losses in a parallel plane waveguide for three different modes are as,
     
    Description: 49151.png,Description: 49144.pngandDescription: 49137.png
  • The attenuation constant due to conduction losses for TEmn waves in a rectangular waveguide is given as,
     
    Description: 49128.png
  • The attenuation constant due to conduction losses for TMmn waves in a rectangular waveguide is given as,
     
    Description: 49121.png
  • The attenuation constant due to conduction losses for TEnm waves in a circular waveguide is given as,
     
    Description: 49111.png
  • The attenuation constant due to conduction losses for TMnm waves in a circular waveguide is given as,
     
    Description: 49103.png
  • A cavity resonator, usually used for energy storage at high frequencies, is one in which the electromagnetic waves exist in a hollow space inside the device.
  • The rectangular waveguide resonator is basically a section of rectangular waveguide which is enclosed on both ends by conducting walls to form an enclosed conducting box.
  • The resonant frequency in a rectangular cavity resonator for TE and TM mode waves is given as,
     
    Description: 49095.png
  • The quality factor of a cavity resonator is defined as,
     
    Description: 49088.png
  • For the dominant mode in a rectangular cavity resonator (i.e.,TE101 mode), the quality factor is given as,
     
    Description: 49078.png
  • The resonant frequency in a circular cavity resonator for TE and TM mode waves is given as,
     
    Description: 49068.png




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