Coordinate system transform for antenna measuring system

In summary, the conversation is about converting coordinates in a positioning system for an antenna from a great circle coordinate system to a spherical coordinate system. The speaker is asking for help with the conversion process and has found online formulas but is having trouble implementing them in MATLAB. They also mention the possibility of using high school trigonometry to solve the problem.
  • #1
squalho
11
0
Hello,

I have a question related to coordinate transform. If this is not the right section please feel free to move this thread.

My problem is the following: I have a positioning system to move an antenna, that allows me to perform scans according to a great circle coordinate system. Check this link out to get an idea of what I'm talking about:

http://www.ce-mag.com/archive/02/Spring/fogelle1.html

(Check "great-circle method", figures 5 and 8(a))

As you can see, the sphere surrounding the antenna being measured is scanned by controlling two angles: one is the azimuthal angle and the other is a roll angle. Therefore this coordinate system is equivalent to an equatorial coordinate system, where the roll angle represents how much every great circle is rotated with respect to the "equator", and the azimuthal angle represents one position on a given great circle. Therefore I think that the roll angle has a meaning of "altitude" and the azimuth angle has a meaning of "hour angle". Fell free to correct me if you think I am wrong.

My problem is to convert these two angles to the classical theta and phi angles of a spherical coordinates system, to map the same points on the sphere surrounding the antenna. If theta (or 90-theta) is the latitude and phi is the longitude, I want to pass from azimuth and roll to theta and phi.

I have found online formulas to convert between the two coordinate systems, but when I plug them in MATLAB they don't work quite right. In particular I am having problem figuring out what declination, right ascension, and all these sort of things are in my case. I think that in the general astronomical problems there are more variables than the ones involved in my case.

Can anybody help? I hope I explained my problem clearly enough, let me know! Thanks!
 
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  • #2
This is simply spherical transformed to spherical. Just a matter of rotations and scalings. High school trig, at worst. You could back into it using cartesian-to-spherical transform identities combined with linear transform between the coordinate frames.
 

1. What is a coordinate system transform for an antenna measuring system?

A coordinate system transform is a mathematical process that converts the coordinates of a point from one coordinate system to another. In the context of an antenna measuring system, it is used to transform the measurement data from one coordinate system (such as Cartesian) to another (such as spherical or cylindrical) to better analyze and understand the performance of the antenna.

2. Why is a coordinate system transform necessary for an antenna measuring system?

An antenna measuring system typically involves measuring the radiation pattern of an antenna in one or more coordinate systems. However, different coordinate systems may provide different insights into the antenna's performance. A coordinate system transform allows for a more comprehensive analysis of the antenna's behavior.

3. How is a coordinate system transform performed in an antenna measuring system?

A coordinate system transform is typically performed using mathematical formulas or algorithms. The specific method used may vary depending on the type of coordinate system being transformed and the software or equipment being used for the measurement.

4. Are there any limitations to using a coordinate system transform in an antenna measuring system?

While a coordinate system transform can provide valuable insights into the performance of an antenna, it is important to note that it is not a perfect solution. The transformation process may introduce some errors or inaccuracies, particularly if the original measurement data is not precise or if the transformation is complex.

5. Can a coordinate system transform be applied to any type of antenna?

Yes, a coordinate system transform can be applied to any type of antenna as long as the measurement data is available in the original coordinate system. However, the complexity of the transform may vary depending on the shape and orientation of the antenna.

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