antenna-theory.com

[JohnL]

Hello, Thanks for this informative website! I'm looking for an accurate estimate of Total Radiated Power from EIRP measurements. I'm measuring 500 - 1000 points in spherical coordinates, for both horizontal and vertical polarizations.

So far I've been summing all the measurements (horiziontal and vertical) in mW and dividing by the number of measurements taken.

TRP = (EIRP(theta, phi)(Horz) + EIRP(theta, phi)(Vert))/N_points

I've tried equation 4 that you posted here:
http://www.antenna-theory.com/definitions/trp.php

But, because of the sin(theta) part which changes sign, the total adds up to close to zero. So should I be taking the absolute value before summing all the EIRP(theta, phi)*sin(theta)?

I've done that and get a value close to what I've been doing, but don't know if it is correct.

[admin]

theta is the polar angle, measured off the z-axis. So straight up is theta=0, the horizontal plane is theta=90, and straight down is theta=180.

so you should be integrating (or summing) from theta =0 to theta=180, and sin(theta) goes from 0 up to 1 and back to 0. It never goes negative if you measure this way.

[JohnL]

Oh, I see. I actually use the same angle notation a you in my software that controls the DUT rotation. Glad I'm in good company
I followed a RF paper which did the same, but usually see theta used for rotation in the X-Y plane and phi used for angle from the Z axis.

Good to know - that clears it up.

Thanks!
John

[JohnL]

Hi, I tried the equation you provided and was getting strange results. I now see that the equation you provide for TRP (equation 4) indicates the same number of points (M) in rotation around the z-axis, for each theta angle. So at theta near 0 deg or 180 deg you get a lot measured points for a smaller radius, hence the SIN(Theta) scaling factor.

So I had been previously using the following equation for find TRP for points that are equal distance apart on a sphere:

TRP = (1/(2*num_total_points)) * Sum(EIRP_Horizonal + EIRP_Vertical)

Do you know if this is a good approximation for TRP?

In a paper I followed (and later misplaced) it said that is a valid approximation for a large number of points measured. I'm measuring 1000 points for each receiving antenna polarization.

Thanks

[admin]

Yes, total power is Pt = Ph + Pv
if you had measured E-fields it would be Pt is proportional to the square root of (E-horizontal squared + E-vertical squared)

If you had a uniform spacing of points on the sphere, then yes you can directly average them all to get the TRP

[JohnL]

Thank you. Yes, I've been using points equally spaced on a sphere.