Lecture 44 : Transverse Electric Mode in Rectangular Waveguide
The analysis of TE mode in a rectangular waveguide can be carried out on the line similar to that of the the TM mode.
For TE mode we have
---------- (6.57 )
The wave equation is solved for in this case.
In the case of TM mode the wave equation was solved for which was tangential to all the four walls of the waveguides. We therefore had boundary conditions on .
In the TE case however the independent component is tangential two the walls of the waveguide which do not impose any boundary conditions on . The tangential component of magnetic field is balanced by the appropriate surface currents on the walls of the waveguides.
The analysis procedure for TE mode therefore is slightly different than that of the TM mode. We have seen in the case of parallel plane waveguide that the tangential component of the magnetic field is maximum at the waveguide walls. Also in Cartesian co-ordinate system the solution to the wave equation are sinosoidal in nature.
One can note that for = , (vertical walls) and for , (horizontal walls) the tangential component of magnetic field is maximum.
Substituting for from
---------- (6.58)
and = 0 in 6.31, 6.32, 6.33 and 6.34, we get the transverse field components as
---------- (6.59)
---------- (6.60)
---------- (6.61)
---------- (6.62)
In this case also we get
---------- (6.63)
Following observations can be made regarding the TE mode :
(1)
The fields for the TE modes have similar behaviour to the fields of the TM modes i.e they exist in the form of discrete pattern, they have sinosoidal variations in and directions, indices and represent number of half cycles of the field amplitudes in and direction respectively and so on.
(2)
Unlike TM mode both indices and need not be non-zero for the existence of the TE mode. However, of both the indices zero makes the magnetic field independent of space and therefore cannot exist. In other words, mode cannot exist but and modes can exist.
(3)
The lowest order mode for the TE case therefore would be and .
in this case. 
which was tangential to all the four walls of the waveguides. We therefore had boundary conditions on 
(vertical walls) and for 
, 
(horizontal walls) the tangential component of magnetic field is maximum. 
directions, indices 
and 
represent number of half cycles of the field amplitudes in 
mode cannot exist but 
and 
modes can exist.
