![]() ![]() This implies that any larger free-space wavelength certainly cannot propagate, but that all smaller ones can. The free-space wavelength at which this takes place is called the cutoff wavelength and is defined as the smallest free-space wavelength that is just unable to propagate in the waveguide under given conditions. We then haveįrom Equation (10-10), it is easy to see that as the free-space wavelength is increased, there comes a point beyond which the wave can no longer propagate in a waveguide with fixed a and m. It is now possible to use Equation (10-9) to eliminate λ n from Equation (10-3), giving a more useful expression for λ p, the wavelength of the traveling wave which propagates down the waveguide. The previous statements are now seen in their proper perspective: Equation (10-9) shows that for a given wall separation, the angle of incidence is determined by the free-space wavelength of the signal, the integer m and the distance between the walls. Substituting for λ n from Equation (10-4) gives M = number of half-wavelengths of electric intensity to be established between the walls (an integer) Λ n = wavelength in a direction normal to both walls If a second wall is added to the first at a distance a from it, then it must be placed at a point where the electric intensity due to the first wall is zero, i.e., at an integral number of half-wavelengths away. Another important difference is that instead of saying that “the second wall is placed at a distance that is a multiple of half-wavelengths,” we should say that “the signal arranges itself so that the distance between the walls becomes an integral number of half-wavelengths, if this is possible.” The arrangement is accomplished by a change in the angle of incidence, which is possible so long as this angle is not required to be “more perpendicular than 90 °.” Before we begin a mathematical investigation, it is important to point out that the second wall might have been placed (as indicated) so that a′ = 2λ n/2, or a″ = λ n/2, without upsetting the pattern created by the first wall. A major difference from the behavior of transmission lines is that in Parallel Plane Waveguide the wavelength normal to the walls is not the same as in free space, and thus a = 3λ n/2 here, as indicated. ![]()
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