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 fc is the cut-off frequency of the mode, and for (TM) modes
Above the cut-off (f > fc), 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 fc.
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.
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