Rectangular & Circular Waveguide: Equations & Fields

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The following equations and images describe electromagnetic waves inside both rectangular waveguide and circular (round) waveguides. Oval waveguide equations are not included due to the mathematical complexity.

See the online cavity resonance calculator here.

Here is a waveguide selection chart.

Click here for a nice waveguide tutorial.

Click here for a transmission lines & waveguide presentation.



Rectangular Waveguide
Click here for a table of TE and TM mode field equations for rectangular waveguides.
Cutoff Frequency
Waveguide equation formula drawingThe lower cutoff frequency (or wavelength) for a particular mode in rectangular waveguide is determined by the following equations: Waveguide equation formula drawing (Hz) Waveguide equation formula drawing (m)
where
a=
b=
m=
n=
ε =
µ = 		Inside width
Inside height
Number of ½-wavelength variations of fields in the "a" direction
Number of ½-wavelength variations of fields in the "b" direction
Permittivity
Permeability
TE (Transverse Electric) Mode
The TE10 mode is the dominant mode of a rectangular waveguide with a>b, since it has the lowest attenuation of all modes. Either m or n can be zero, but not both.
 
Waveguide equation formula drawing fields

End View (TE10)        


 Waveguide equation formula drawing fields

Side View (TE10)


  Waveguide equation formula drawing fields

Top View (TE10)

____ Electric field lines
    _ _ _ Magnetic field lines
 
TM (Transverse Magnetic) Mode
For TM modes, m=0 and n=0 are not possible, thus, TM11 is the lowest possible TM mode.
Waveguide equation formula drawing fields
End View (TM11)


  Waveguide equation formula drawing fields
Side View (TM11)

____ Electric field lines
   _ _ _ Magnetic field lines
 
Circular Waveguide
Click here for a table of TE and TM mode field equations for circular waveguides.
TE (Transverse Electric) ModeWaveguide equation formula drawing fields
The lower cutoff frequency (or wavelength) for a particular TE mode in circular waveguide is determined by the following equation: Waveguide equation formula drawing fields (m), where p'mn is
 
mp'm1p'm2p'm3
03.8327.01610.174
11.8415.3318.536
23.0546.7069.970

TM (Transverse Magnetic) Mode
The lower cutoff frequency (or wavelength) for a particular TM mode in circular waveguide is determined by the following equation: Waveguide equation formula drawing fields (m), where pmn is
 
mpm1pm2pm3
02.4055.5208.654
13.8327.01610.174
25.1358.41711.620




Webmaster: Kirt Blattenberger, BSEE, UVM 1989