TE Modes in Circular Waveguides
It is commonly assumed that the waves in a circular waveguide are propagating in the positive z direction. Figure shows the coordinates of a circular guide.
Figure : Coordinates of a circular waveguide
The TEnp modes in the circular guide are characterized by Ez = O. This means that the z component of the magnetic field Hz must exist in the guide in order to have electromagnetic energy transmission. A Helmholtz equation for Hz in a circular guide is given by :
Its solution is given by :
which is subject to the given boundary conditions.
For a lossless dielectric, Maxwell's curl equations in frequency domain are given by :
In cylindrical coordinates, their components are expressed as :
When the differentiation ∂/∂z is replaced by (-jβg) and the z component of electric field Ez by zero, the TE-mode equations in terms of Hz in a circular waveguide are expressed as :