High Frequencies and Microwaves

1. Introduction

1.1. Propagation of electromagnetic waves in uniform waveguides

In a hollow metallic waveguide, electromagnetic field can propagate through some different structures named modes of propagation. The study of these modes involves a specific parameter named the cutoff frequency of the mode, . The theory shows that the propagation of each mode is possible only if the actual frequency of the source is higher than the cutoff frequency of that mode. The cutoff frequencies of different propagation modes depend on the shape and on the transversal dimensions of the guide, and of its dielectric properties.

Among the modes that can propagate in a given waveguide the most important is that which has the lowest cutoff frequency. This mode is named the dominant mode in the waveguide; all other modes are named higher order modes.

Figure 1. Position of different cutoff frequencies on the frequency axis,

the dominant mode and the frequency band of a waveguide

If the actual frequency of the source is higher than the cutoff frequency of the dominant mode but lower than the cutoff frequency of the first higher mode (fig. 1), only the dominant mode can propagate through the waveguide. In practice, this is the usual situation. A simultaneous presence of more than one propagation mode that propagate with different velocities, leads to the apparition of the modal dispersion, degrading the performances of the guide as a transmission channel.

The wavelength in the waveguide differs from the wavelength in free space, . The wavelength in the waveguide depends on the frequency and on the cutoff frequency of the propagation mode , so that it depends on the waveguide, too:

. (1)

Here represents the cutoff wavelength, is the wavelength of the plane wave in free space (or TEM wave), and is the velocity of the light in free space, .

In the ideal rectangular metallic waveguide, the propagation modes can be divided into transverse electric modes, , and transverse magnetic modes, , with some integer values of indexes m, n. The cutoff frequency of the or modes increases with , so that the dominant mode corresponds to the lowest possible combination of and . For the modes, one of the two integers indexes can be zero. Considering – without any loss of generality – that (where and are the height and the width of the transverse section in the rectangular waveguide), one gets the conclusion that in a rectangular waveguide the dominant mode is the mode . The cutoff frequency of the mode depends only on the width of the transverse section,

, (2)

where is the dielectric constant.

For modes, neither index can take the zero value.