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This is the first time I write in the forum. I hope to be fully in-topic.

I'm dealing with a rectangular waveguide discontinuity: a perfect-conductor plane orthogonal to the propagation direction, with a circular aperture in the centre of the guide section. The structure is symmetrical along the x axis and the y axis and I drew it in the attachment, where the z axis is outgoing from the screen.

In my note the professor talked about a strange "Edge Theorem" (which we didn't demonstrate and which I can't find in any book). The Theorem says that:

- a field component which is parallel to an edge is diffracted but not folded (and so it doesn't generate any new field component);

- a field component which is orthogonal to an edge is diffracted and folded along the plane perpendicular to the edge (so it could generate a new field component).

The discontinuity is reached by the fundamental TE_{10}mode: in my coordinate system, it has E_{Y}, H_{X}and H_{Z}field components.

According to the Theorem, when E_{Y}reaches the upper and the lower part of the circle (points A and D in the picture) it is orthogonal to the circle edge and it generates an E_{Z}component.

When H_{Z}reaches the left and the right part of the circle (points B and C in the picture) it generates H_{X}; similarly, in those points H_{X}generates H_{Z}.

But what about H_{Y}and E_{X}? I can't see how they are generated, but they are, because I wrote in my notes that the field becomes a 6-components field.

The only electric field component is E_{Y}, but when it reaches the oblique edge between A and B, it generates an E_{Z}again and not an E_{Y}! What is wrong?

Thank you anyway!

Bye,

Emily

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# Waveguide discontinuity with centered circular aperture

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