# Waveguide discontinuity with centered circular aperture

• EmilyRuck
In summary, a rectangular waveguide discontinuity is a perfect-conductor plane orthogonal to the propagation direction with a circular aperture in the center of the guide section. The structure is symmetrical along the x-axis and the y-axis, and the z-axis points outwards from the screen. The Edge Theorem states 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), while 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). However, when EY reaches the oblique edge between A and B, it generates an EZ
EmilyRuck
Hello!
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 TE10 mode: in my coordinate system, it has EY, HX and HZ field components.
According to the Theorem, when EY 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 EZ component.
When HZ reaches the left and the right part of the circle (points B and C in the picture) it generates HX; similarly, in those points HX generates HZ.
But what about HY and EX? 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 EY, but when it reaches the oblique edge between A and B, it generates an EZ again and not an EY! What is wrong?
Thank you anyway!
Bye,

Emily

#### Attachments

• circular_aperture.png
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I don't have a copy of the article, but Hans Bethe wrote a paper during the War on microwave couplers using small holes. These later became referred to as Bethe holes. See http://prola.aps.org/abstract/PR/v66/i7-8/p163_1.
I would also look in Marcuvitz's Microwave Handbook..

Bob S said:
I don't have a copy of the article, but Hans Bethe wrote a paper during the War on microwave couplers using small holes. These later became referred to as Bethe holes.
I would also look in Marcuvitz's Microwave Handbook..

I tried to read the article but it's not available, unfortunately. Thank you anyway for your reference! I read also the Marcuvitz's Microwave Handbook: it deals with such a discontinuity, but it considers just the equivalent circuit (an admittance) and not which field components arise from it.

Emily

## 1. What is a waveguide discontinuity with centered circular aperture?

A waveguide discontinuity with centered circular aperture is a type of waveguide structure that features a circular opening in the center, creating a discontinuity in the flow of electromagnetic waves. It is commonly used in high-frequency applications to couple energy from one waveguide to another.

## 2. How does a waveguide discontinuity with centered circular aperture affect the propagation of electromagnetic waves?

The presence of the aperture causes a change in the electric and magnetic fields of the propagating waves, resulting in diffraction and reflection effects. This can lead to changes in the amplitude, phase, and polarization of the waves as they pass through the discontinuity.

## 3. What factors determine the performance of a waveguide discontinuity with centered circular aperture?

The performance of this type of structure is determined by several factors, including the size and shape of the aperture, the material properties of the waveguide, and the frequency of the incident waves. It is important to carefully design these parameters to achieve optimal performance.

## 4. What are some common applications of waveguide discontinuities with centered circular apertures?

These structures are widely used in microwave and millimeter-wave systems, such as radar, satellite communications, and wireless networks. They can also be found in laboratory equipment for testing and measurement of electromagnetic waves.

## 5. What are some challenges in designing and using waveguide discontinuities with centered circular apertures?

One of the main challenges is achieving a good match between the waveguide modes on either side of the discontinuity. This requires careful design and fabrication to minimize reflections and losses. Another challenge is the potential for interference and unwanted coupling between different apertures in a complex waveguide system.

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