Calculating TRP from measurement data

Foregive me if this question has been answered in a different thread, however I have been searching and not found it. I think it should be an easy question, but my theoretical knowledge in the area has obviously become a bit fuzzy!

Problem
I have measured the radiated power of a device using R&S AMS32 in a shielded chamber and exported my data, which is a dBm value for each position θ=0°...360° and Φ=0°...360° in a certain resolution. I would then like to analyze the data in Matlab and among other things calculate the total radiated power (TRP), but how is this done? My measuring software is able to calculate this value, but I have not been able to get the same value in Matlab

The total radiated power is theoretically given as

but since I don't have a function for the radiation intensity U I guess I have to do some sort of numerical integration.

These are the posts I have found with some semblance to my question:
https://www.edaboard.com/threads/145135/
https://www.edaboard.com/threads/130910/

Example
The following is a coarse example of an exported measurement that should result in TRP=-4.03dBm.

Hopefully you are able to help!

Thank you for a great electronic community!

1 "0,00" "-2,71" "0,18" "4,52" "-6,53" "0,02"
2 "90,00" "-2,71" "-0,50" "5,76" "-0,54" "-5,13"
3 "180,00" "-2,71" "-1,29" "5,05" "-6,94" "-6,48"
4 "270,00" "-2,71" "0,35" "5,50" "-3,58" "-3,14"
5 "360,00" "-2,71" "0,19" "4,50" "-6,52" "-2,70"

I don't know what software you used, and I am not familiar with TRP formula you posted.
A first impression looking to the dBm values you posted, and averaging all of them somehow, the TRP should be about -1.2dBm.

Thank you for your reply vfone.

AMS32 by Rohde & Schwarz is measurement software used for automating measurements, but I don't think it is so important. The main thing is how I calculate the TRP from the exported data. Since the radiated power components of the file is in dB it is not correct just calculating the average without further to -1.2dBm. You can then convert dBm to W do averaging and then convert back, but this is not correct either as this gives 0.5dBm.

The total radiated power is the total amount of power that my product is able to radiate into the air. Intuitively it makes good sense that in mathematics you have to integrate the power in each unit solid angle over the entire sphere. However, in practice where I have measured power values in different positions on the sphere I'm not sure what to do. The definition I used on TRP can be found here: Antenna gain - Wikipedia, the free encyclopedia

Nobody who's able to help?

I have come a bit further after contacting the support of my measurement software. They said that the TRP was calculated in nearly the same way as NHRP45 and gave the following definition:

Also I found **broken link removed**.

However, no matter how I use the formula the result is never -4.03 dBm. I'm a bit frustrated, bacause I don't think it should be that difficult.

I do not have any concrete equations to give you. But have used a GTEM cell once to calculate total radiated power. You measure the power in 3 discrete orthogonal axes, and then you can calculate the TRP. There was a canned program to do the math.

First convert dBm measurement results to linear numbers before averaging and that will result in TRP, so that part is ok.
A problem is that you are measuring same vector several times, 0 and 360 degrees is for example same angle and if you check your formula does it not say [0-360°]:[0-360°].
I do usually measure [0-359°]:[- 89° - +89°]:[Horizontal/Vertical] as that makes it more easy to understand what vector it corresponds to (assuming stepping resolution is 1°).

Hi
I have same problem with calculating the TRP from the measured power date at vertical and horizontal plan around the antenna each 15 degree.
Can you plz. Help me???

Check the pictures.