3 GHz Signal Propagate in a Circular Waveguide?

Consider a circular waveguide having a radius of \(2\,\text{cm}\). Determine whether a signal with a frequency of \(3\,\text{GHz}\) can propagate through the waveguide.

Solution

The dominant mode of a circular waveguide is \(TE_{11}\). From the previous calculation, the cutoff frequency for the \(TE_{11}\) mode is:

$ f_{c,11}^{TE}=4.39\,\text{GHz} $

The given operating frequency is:

$ f=3\,\text{GHz} $

For a wave to propagate through a waveguide, the operating frequency must be greater than the cutoff frequency:

$ f>f_c $

Here:

$ 3\,\text{GHz}<4.39\,\text{GHz} $

Since the operating frequency is below the cutoff frequency of the dominant mode, the \(3\,\text{GHz}\) signal cannot propagate through the circular waveguide.

$ \boxed{ 3\,\text{GHz}<4.39\,\text{GHz} } $

$ \boxed{ \text{The 3 GHz signal does not propagate.} } $

The waveguide therefore operates below cutoff at \(3\,\text{GHz}\), and the signal becomes an evanescent wave rather than a propagating wave.