How Does the Antenna Imaging Effect Influence Radiation Patterns?

[JamesGoh]

Hi everyone

Currently I am reading through antenna imaging effect. I am aware of positive and negative imagaing (essentially the polarity of the antenna is constant/reversed depending on the antenna orientation)

However the illustrative example my lecturer has given me has caused quite a bit of confusion. For the curious, I have attached it as 2 separate doucments, however I will now try to describe it.

1) He has a vertically oriented dipole situated $$\lambda/2$$ above the ground plane. Due to the imaging effect, a positive image of this antenna is produced $$\lambda/2$$ below the ground plane.

2) The dipoles are replaced by point sources (shown as dots in the attachments)

3) From the dots he draws rays being emitted at an angle of $$\theta$$ to the horizontal. He also draws an imaginary line from the origin parallel to both rays. This creates a scenario whereby the ray from the topmost point leads the origin by a distance of $$\(lambda/2)*sin(theta)$$and the ray from the bottmomost point lags the origin by the same distance

4) Now at the far-field point, he converts the lagging and leading distances to angles by multiplying them by $$(2*pi)/lambda$$ and subsequently adding the field vectors. From this he gets his result as $$(2*cos(pi*sin(\theta))$$, however I have no idea how this arises, due to the orthogonal nature of the vectors (as seen in the attachment)

Once again, the attachments show the problem in better detail. Any help on how he gets the result would be highly appreciated

regards

 

[eljose79]

Hello,

Thank you for bringing this confusion to our attention. The example you have described is a common one used to illustrate the imaging effect. To better understand how the lecturer arrived at the result of (2*cos(pi*sin(theta)), let's break down the steps.

1) The first step is to understand that when an antenna is placed above a conducting ground plane, an image of the antenna is produced below the ground plane. This is known as the imaging effect.

2) In the example, the antenna is replaced by two point sources, one at the top and one at the bottom. These point sources represent the positive and negative images of the original antenna.

3) The rays being emitted from these point sources are at an angle of θ to the horizontal. This means that they are not parallel to each other. This is where the confusion may arise.

4) However, the key is to remember that the imaginary line connecting the two point sources is parallel to both rays. This line is essentially the "axis" of the antenna. So, while the rays may not be parallel to each other, they are both parallel to this imaginary line.

5) Now, at the far-field point, the lagging and leading distances are converted to angles by multiplying them by (2*pi)/lambda. This is done to account for the phase difference between the two point sources.

6) Finally, the field vectors are added together to get the total field at that point. Since the vectors are orthogonal to each other, they can be added together using vector addition. This results in the expression (2*cos(pi*sin(theta)).

I hope this helps clarify the confusion. It's important to remember that in antenna imaging, the key is to consider the imaginary line connecting the positive and negative images, rather than just the individual rays themselves. Let me know if you have any further questions or need more clarification. Best of luck with your studies!

 

[charng]

Hello,

Thank you for sharing your question about the antenna imaging effect. I can provide some insight into this concept.

The antenna imaging effect is a phenomenon that occurs when an antenna is placed above a ground plane. As you mentioned, this can result in a positive and negative image of the antenna, depending on its orientation.

In the example provided by your lecturer, it seems that they are using the point source model to illustrate the concept. The point sources represent the dipole antennas, and the rays being emitted at an angle of θ represent the radiation pattern of the antenna.

At the far-field point, the lagging and leading distances are converted to angles using the equation (2π/λ)*d, where d is the distance. This is based on the principle that the phase difference between two points on a wavefront is equivalent to the difference in their distance from the source.

By adding the field vectors from the two point sources, your lecturer is essentially combining the radiation patterns of the two dipole antennas. The resulting equation, 2*cos(π*sin(θ)), is based on the mathematical representation of the radiation pattern of a dipole antenna.

I hope this helps to clarify the example provided by your lecturer. If you have any further questions, please don't hesitate to ask. Good luck with your studies!