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Cutt-off Frequecy of TE and TM mode |
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For both  and  modes the phase constant is given by |
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--------- (6.64 ) |
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For the mode to be travelling  has to be a real quantity. If  becomes imaginary then the fields no more remain travelling but become exponentially decaying |
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The frequency at which changes from real to imaginary is called the cut-off frequency of the mode. At cut-off frequency therefore  giving |
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| --------- (6.65 ) |
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| --------- (6.66 ) |
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The cut-off frequencies for lowest TM and TE modes i.e  can be obtained from eqn. 6.70 as |
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--------- (6.67 ) |
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| --------- (6.68 ) |
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| --------- (6.69) |
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Since by definition we have  we get the frequencies as |
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--------- (6.70) |
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We can make an important observation that if at all the electro magnetic energy travels on a rectangular waveguide its |
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frequency has to be more than the lowest cut-off frequency i.e  . |
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As the order of the mode increases the cut-off frequency also increases i.e with increasing frequency there is possibilty |
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of existence of higher order mode. |
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The very first mode that propagates on the rectangular waveguide is  mode and therefore this mode is called the |
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dominant mode of the rectangular waveguide. The cut-off frequency for the dominant mode is |
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--------- (6.71) |
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The equation suggest that for propagation of an electro magnetic wave inside a rectangular waveguide the width of a |
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waveguide should be greater than half the wave length of the wave. |
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