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Cylindrical or Circular Waveguides

Cylindrical or circular waveguides are those that maintain a uniform circular cross section along their length.

The method of solution of the electromagnetic field equations for circular waveguides is similar to that for rectangular waveguides. However, in order to simplify the application of the boundary conditions that the tangential component of the electric field be zero, we convert all field equations in cylindrical coordinate systems.
 
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Cylindrical or circular waveguide

Properties of TE and TM Waves in Circular Waveguides

We find the following quantities for TE and TM mode waves in circular waveguides:
  1. Propagation Constant (γ)
     
    It is given as,
     
    Description: 20758.png 
     
    where, the value of hnm is obtained from Tables  for TE and TM waves, respectively.
     
    Here also, wave propagation will occur only when Description: 21081.png in which case the propagation is entirely imaginary.
  2. Phase Constant (β)
     
    From Eq. the phase constant in the propagation mode is obtained as,
     
    or, Description: 20696.png
     
    Description: 26586.png  
  3. Cut-off Frequency (fc)
     
    The cut-off frequency below which the wave is attenuated and above which the wave is propagated through the guide is obtained as,
     
    Description: 63757.png 
     
    Description: 28984.png
     
    where Description: 29276.png is the phase velocity of a uniform plane wave in a lossless dielectric medium.
     
    Description: 28276.png
     
    From Eq. and from Tables. we see that the lowest cut-off frequency is with TE11 mode, the next higher modes being TM01, TE21, TE01.
  4. Cut-off Wavelength (λc)
     
    Corresponding to every cut-off frequency, there will be a cut-off wavelength given as,
     
    Description: 24297.png
     
    where, Description: 28651.png is the phase velocity of a uniform plane wave in a lossless dielectric medium inside the guide.
  5. Phase Velocity (vp)
     
    The phase velocity of the wave propagation is given by,
     
    Description: 21234.png  
     
    Description: 24616.png is the phase velocity of uniform plane waves in a lossless dielectric medium inside the waveguide.
     
    Equation  indicates that the phase velocity of wave propagation in the circular waveguide is greater than the phase velocity of a uniform plane wave.
  6. Group Velocity (vg)
     
    From the relation that Description: 23617.png, the group velocity is obtained as,
     
    Description: 20427.png
     
    Description: 35908.png  
     
    This shows that the group velocity in the guide is less than that in free space.
  7. Guide Wavelength (λg)
     
    The wavelength in the circular waveguide is given as,
     
    Description: 22956.png  
     
    where Description: 26141.png is the wavelength of the uniform plane wave in the lossless dielectric medium inside the guide.
  8. Intrinsic Wave Impedance (η)
     
    As for rectangular waveguides, for circular waveguides too, the intrinsic wave impedance will be different for TE and TM modes.
    1. Intrinsic Wave Impedance for TE Modes in Circular Waveguides For TE waves, from Eq., it is given as,
       
      Description: 24501.png
       
      where Description: 28136.png is the intrinsic impedance of a uniform plane wave in a lossless dielectric medium.
       
      Description: 25383.png
    2. Intrinsic Wave Impedance for TM Modes in Circular Waveguides For TM waves, from Eq., it is given as,
       
      Description: 28659.png
       
      where Description: 23849.png is the intrinsic impedance of a uniform plane wave in a lossless dielectric medium.
       
      Description: 26486.png





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