Circuit-slide-22

Circuit-slide-22 - Parallel Plate Waveguide Maxwell's...

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Parallel Plate Waveguide
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Maxwell’s equations
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Wave equation for Transverse Electric (TE) modes
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From Wave equation for Transverse Magnetic (TM) modes
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Transverse Electric (TE) modes This solution satisfies the boundary conditions:
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We have and from boundary conditions at the conductor plates λ π με ϖ 2 =
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For each possible index m we have a mode of propagation . Modes are labeled TE 10 , TE 20 , TE 30 , …. The first index gives the periodicity (number of half sinusoidal oscillations) between the plates, along the x-direction . The second index is zero to indicate uniform solution along the y-direction. Note that the solution m = 0 (or mode TE 00 ) is not acceptable, because it would require a field configuration with uniform electric field tangent to the metal plates. This is an unphysical boundary condition , which is possible only for the case of trivial solution of zero field everywhere.
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A mode can propagate only if the frequency is sufficiently high, so that β z > 0. We have the cut-off condition when Exactly at cut-off the wave would bounce between the plates, without propagation along the wave guide axis.
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When the frequency is below the cut-off value The mode attenuates entering the guide as an evanescent wave .
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The magnetic field can be tangent to the conductor plates. In fact, it is maximum at the plates, since the reflection coefficient is Γ H = 1. The solution is of the form: Transverse Magnetic (TM) modes
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Note that the solution m = 0 (or mode TM 00 ) is acceptable , because the magnetic field can be uniform and tangent to the metal plates. Modes are labeled TM
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Circuit-slide-22 - Parallel Plate Waveguide Maxwell's...

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