Circuit-slide-22

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

This preview shows pages 1–13. Sign up to view the full content.

Parallel Plate Waveguide

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Maxwell’s equations

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Wave equation for Transverse Electric (TE) modes
From Wave equation for Transverse Magnetic (TM) modes

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Transverse Electric (TE) modes This solution satisfies the boundary conditions:
We have and from boundary conditions at the conductor plates λ π με ϖ 2 =

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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.
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.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
When the frequency is below the cut-off value The mode attenuates entering the guide as an evanescent wave .
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 34

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

This preview shows document pages 1 - 13. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online