## Waveguide Modes

Waveguide modes of operation will be covered in this tutorial.The waveguide analyzed in the previous paragraphs yields an electric field configuration known as the half-sine electric distribution. This configuration, called a MODE OF OPERATION, is shown in the figure below.

Recall that the strength of the field is indicated by the spacing of the lines; that is, the closer the lines, the stronger the field. The regions of maximum voltage in this field move continuously down the waveguide in a sine-wave pattern. To meet boundary conditions, the field must always be zero at the "b" walls.

The half-sine field is only one of many field configurations, or waveguide modes , that can exist in a rectangular waveguide. A full-sine field can also exist in a rectangular waveguide because, as shown in the second figure below, the field is zero at the "b" walls.

Similarly, a 1 1/2 sine-wave field can exist in a rectangular waveguide because this field also meets the boundary conditions. As shown in the last figure, the field is perpendicular to any conducting surface it touches and is zero along the "b" walls. Half sine E field distribution. Full sine E field distribution. One and one half sine E field distribution.

The magnetic field in a rectangular waveguide is in the form of closed loops parallel to the surface of the conductors. The strength of the magnetic field is proportional to the electric field. The next figure illustrates the magnetic field pattern associated with a half-sine electric field distribution. The magnitude of the magnetic field varies in a sine-wave pattern down the center of the waveguide in "time phase" with the electric field. TIME PHASE means that the peak H lines and peak E lines occur at the same instant in time, although not necessarily at the same point along the length of the waveguide. Magnetic field caused by a half sine E field.

An electric field in a sine-wave pattern also exists down the center of a waveguide. In the figure below, view (A), consider the two wavefronts, C and D. Assume that they are positive at point 1 and negative at point 2. When the wavefronts cross at points 1 and 2, each field is at its maximum strength. At these points, the fields combine, further increasing their strength. This action is continuous because each wave is always followed by a replacement wave.

View (B), illustrates the resultant sine configuration of the electric field at the center of the waveguide. This configuration is only one of the many field patterns that can exist in a waveguide. Each configuration forms a separate mode of operation. The easiest mode to produce is called the DOMINANT MODE. Other modes with different field configurations may occur accidentally or may be caused deliberately Crisscrossing wavefronts and the resultant E field.

The dominant waveguide modes are the most efficient mode. Waveguides are normally designed so that only dominant waveguide modes will be used. To operate in dominant waveguide modes, a waveguide must have an "a" (wide) dimension of at least one half-wavelength of the frequency to be propagated. The "a" dimension of the waveguide must be kept near the minimum allowable value to ensure that only the dominant mode will exist. In practice, this dimension is usually 0.7 wavelength.

Of the possible waveguide modes of operation available for a given waveguide, the dominant mode has the lowest cutoff frequency. The high-frequency limit of a rectangular waveguide is a frequency at which its "a" dimension becomes large enough to allow operation in a mode higher than that for which the waveguide has been designed.

Waveguides may be designed to operate in a mode other than the dominant mode. An example of a full-sine configuration mode is shown in the next figures view A and view B respectively. The "a" dimension of the waveguide in this figure is one wavelength long. You may assume that the two-wire line is 1/4! from one of the "b" walls, as shown in view A.

The remaining distance to the other "b" wall is 3/4 wavelength. The three-quarter wavelength section has the same high impedance as the quarter-wave section; therefore, the two-wire line is properly insulated. The field configuration shows a complete sine-wave pattern across the "a" dimension, as illustrated in view B. Waveguide operation in other than dominant mode. 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. The last figure below 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 half-wavelength 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. Dominant mode in a circular waveguide.

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