Wave Impedance - Wave Impedance in A Waveguide

Wave Impedance in A Waveguide

For any waveguide in the form of a hollow metal tube, (such as rectangular guide, circular guide, or double-ridge guide), the wave impedance of a travelling wave is dependent on the frequency, but is the same throughout the guide. For transverse electric (TE) modes of propagation the wave impedance is

where f_c is the cut-off frequency of the mode, and for (TM) modes

Above the cut-off (f > f_c), the impedance is real (resistive) and the wave carries energy. Below cut-off the impedance is imaginary (reactive) and the wave is evanescent. These expressions neglect the effect of resistive loss in the walls of the waveguide. For a waveguide entirely filled with a homogeneous dielectric medium, similar expressions apply, but with the wave impedance of the medium replacing Z₀. The presence of the dielectric also modifies the cut-off frequency f_c.

For a waveguide or transmission line containing more than one type of dielectric medium (such as microstrip), the wave impedance will in general vary over the cross-section of the line.