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Waveguides may be designed to operate in a mode other than the dominant mode. An example of a fullsine configuration mode is shown in figure 134. The "a" dimension of the waveguide in this figure is one wavelength long. You may assume that the twowire line is 1/4 l from one of the "b" walls, as shown in view (A). The remaining distance to the other "b" wall is 3/4l. The threequarter wavelength section has the same high impedance as the quarterwave section; therefore, the twowire line is properly insulated. The field configuration shows a complete sinewave pattern across the "a" dimension, as illustrated in view (B). Figure 134A.  Waveguide operation in other than dominant mode.
Figure 134B.  Waveguide operation in other than dominant mode.
Circular waveguides are used in specific areas of radar and communications systems, such as rotating joints used at the mechanical point where the antennas rotate. Figure 135 illustrates the dominant mode of a circular waveguide. The cutoff wavelength of a circular guide is 1.71 times the diameter of the waveguide. Since the "a" dimension of a rectangular waveguide is approximately one halfwavelength at the cutoff frequency, the diameter of an equivalent circular waveguide must be 2 / 1.71, or approximately 1.17 times the "a" dimension of a rectangular waveguide. Figure 135.  Dominant mode in a circular waveguide.
MODE NUMBERING SYSTEMS.  So far, only the most basic types of E and H field arrangements have been shown. More complicated arrangements are often necessary to make possible coupling, isolation, or other types of operation. The field arrangements of the various modes of operation are divided into two categories: TRANSVERSE ELECTRIC (TE) and TRANSVERSE MAGNETIC (TM). In the transverse electric (TE) mode, the entire electric field is in the transverse plane, which is perpendicular to the length of the waveguide (direction of energy travel). Part of the magnetic field is parallel to the length axis. In the transverse magnetic (TM) mode, the entire magnetic field is in the erse plane and has no portion parallel to the length axis. Since there are several TE and TM modes, subscripts are used to complete the description of the field pattern. In rectangular waveguides, the first subscript indicates the number of halfwave patterns in the "a" dimension, and the second subscript indicates the number of halfwave patterns in the "b" dimension. The dominant mode for rectangular waveguides is shown in figure 136. It is designated as the TE mode because the E fields are perpendicular to the "a" walls. The first subscript is 1 since there is only one halfwave pattern across the "a" dimension. There are no Efield patterns across the "b" dimension, so the second subscript is 0. The complete mode description of the dominant mode in rectangular waveguides is TE_{1,0}. Subsequent descriptions of waveguide operation in this text will assume the dominant (TE_{1,0}) mode unless otherwise noted. Figure 136.  Dominant mode in a rectangular waveguide.
A similar system is used to identify the modes of circular waveguides. The general classification of TE and TM is true for both circular and rectangular waveguides. In circular waveguides the subscripts have a different meaning. The first subscript indicates the number of fullwave patterns around the circumference of the waveguide. The second subscript indicates the number of halfwave patterns across the diameter. In the circular waveguide in figure 137, the E field is perpendicular to the length of the waveguide with no E lines parallel to the direction of propagation. Thus, it must be classified as operating in the TE mode. If you follow the E line pattern in a counterclockwise direction starting at the top, the E lines go from zero, through maximum positive (tail of arrows), back to zero, through maximum negative (head of arrows), and then back to zero again. This is one full wave, so the first subscript is 1. Along the diameter, the E lines go from zero through maximum and back to zero, making a halfwave variation. The second subscript, therefore, is also 1. TE_{1,1} is the complete mode description of the dominant mode in circular waveguides. Several modes are possible in both circular and rectangular waveguides. Figure 138 illustrates several different modes that can be used to verify the mode numbering system. Figure 137.  Counting wavelengths in a circular waveguide.
Figure 138.  Various modes of operation for rectangular and circular waveguides.

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