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.
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.
End View (TE10)
Side View (TE10)
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.
End View (TM11)
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) Mode
The lower cutoff frequency (or wavelength) for a particular TE mode in circular waveguide is determined by the following equation:
(m),
where p'mn is
m
p'm1
p'm2
p'm3
0
3.832
7.016
10.174
1
1.841
5.331
8.536
2
3.054
6.706
9.970
TM (Transverse Magnetic) Mode
The lower cutoff frequency (or wavelength) for a particular TM mode in circular waveguide is determined by the following equation:
(m),
where pmn is
m
pm1
pm2
pm3
0
2.405
5.520
8.654
1
3.832
7.016
10.174
2
5.135
8.417
11.620
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