**Subject :**Microwave Engineering

## TE modes in Rectangular Waveguides

**Introduction : -**

** ** The section explains the propagation of TE mode in a recangular waveguide, cut-off frequency, propagation constant and group velocity.

**Explanation : -
**

It isassumed that the waves are propagating in the positive z direction in the waveguide.Figure shows the coordinates of a rectangular

waveguide.

**Figure : Coordinates of a rectangular waveguide
**

The TE_{mn} modes in a rectangular guide are characterized by E_{z} = O. In other words, the z component of the magnetic field, H_{z}, must exist in order to have energy transmission in the guide. Consequently, from a given Helmholtz equation,

--------(1)

a solution in the form of

.........(2)

will be determined in accordance with the given boundary conditions, where kx = mπ/a and ky = nπ/b are replaced. For a lossless dielectric, Maxwell's curl equations in frequency domain are

.........(3)

In rectangular coordinates, their components are :

..........(4)

With the substitution ∂/∂z = - jβ_{z} and E_{z }= 0, the foregoing equations are simplified to