I've done exactly that using MS-Excel.

You bring in the Az/El gain pattern data and you can graph it as a colourful Mercator projection.

To integrate it you need to remember that the 'north and south poles' (zenith and nadir) are over-represented in your data set and so you need to cosine weight the data set according to elevation. That cosine weighting is really the only complication, the rest is very simple.

So, here are the steps that I used:

1) Import the data in to MS-Excel
2) Graph it so that you can see that it makes sense
3) Calculate the average weighted by cosine(el).

Triple check to make sure that the average is close to zero dBi for some ideal examples.  Real world data should be slightly less than zero dBi.  Manufacture's brochure data might be more than zero dBi <smirk>.

Further to previous, you should prepare some ideal antenna data on one worksheet with facilities for setting the gain and aiming Az and El. Then you can make sure that your ideal antenna always integrates to something very close to 0 dBi no matter how you set the gain and no matter where you aim it.

The aiming checks are to ensure that your el weighting is being done properly.  If the average gain varies with elevation aim, then the weighting for the Mercator data set isn't being done properly.

I found that Az and El steps of 2 degrees were sufficient for my purposes.  I tried 1 degree, but the volume of data was a bit overwhelming.  5 degrees was too rough.  YMMV.

Directivity vs. Gain;

When you integrate antenna patterns, you are calculating "Directivity".

"Directivity" is not the same as "Gain". Gain includes losses. Directivity justs shows you how focused the beam pattern is, i.e. the shape of the antenna pattern.

To arrive at the peak "Gain" value of the antenna you need to measure/calculate/estimate the antenna losses, such as VSWR loss, power divider loss, and loss due to crosspole components from the antenna. Or, since that's such a headache to get good accuracy, it's most common to a known good gain standard to reference your measurements, (horns and dipoles primarily.

Check your result compared to this approximate formula.

Directivity = 41,000/(Azimuth beamwidth x Elevation beamwidth),      -  beamwidths in degrees.

To estimate the gain, often 34,000/AZ*EL beamwidths is used.

One note of caution I've learned the hardware using this simple formula, it can be inaccurate;
While measuring a 6-18 ghz ridged horn antenna for beam patterns and gain, I compared it to an accurate gain standard horn.
I had 4 dB lower measured gain when using an accurate horn antenna gain standard than I expected when I compared the gain to calcuated using the above simple formula 34,000/Az*El beamwidths. i.e it was way way off, and below spec. The VSWR was good, so I was puzzled.
An odd mode was generated in the antenna resulting in the antenna pattern being weaker at boresight and stronger in the intercardinal planes, or the corners top left, top right, bottom left, bottom right and boresight became the weak point. Since I used the E and H plane antenna beamwidths instead of the intercardinal plane beamwidths, that was my error.
The horror, it took a month to fix the problem.
 
kch

I'm currently going through a similar problem with a center feed axial-symmetric antenna.  The issue is that gain calculated using 3dB and 10dB beamwidth (AZ,EL cuts in E and H-planes) are 1.0 to 2.0 dB higher than boresight gain referenced using a std. gain horn.  I've taken the antenna to a far-field, ground reflection and a compact range all will similar results.  In the gain beamwidth calculation, I've taken out the appropriate loss for the manufacture provided feed loss and reflector surface error losses.  I've even had the surface measured and measured insertion loss, with no evident problems.  VSWR is also better than 1.9:1.  I've relied upon the std. gain horn comparison method as being more accurate than the 3/10dB beamwidth calculation because surface and feed loss are included in the measurement.  However, I had a recent conversation with a antenna engineer whose experience has been that gain measured by comparison to a Std.Gain horn is often unreliable when the AUT and the Std.Gain differ by 20dB or more.  In his experience, ground reflection was the culprit.  He typical integrates the pattern and subtracts feed loss to arrive at gain.

If this a high gain reflector antenna with a primary feed, then the feed losses you refer to must also include "spillover loss", i.e. the energy that misses the reflector from the feed?

I think the closed form solution for Directivity 41,000/AZ*El beamwidths will always be higher by at least one dB than your measured Gains for most simple antennas. The best efficiency for a reflector antenna is often 60% which is 2 dB lower than you'd get using the simple directivity formula 41,000/Az*EL. So if you haven't added in the Spillover loss from the feed, that might answer the loss question.

If you have already taken into accout spillover loss, have you also taken patterns in other planes? i.e. rotate your UUT +/-45 degrees from it's E plane orientation and look at those antenna pattern cuts?. Also, take cross-pole antenna patterns, you never know about the gain loss until all the data is looked at.

kch

Yes, thanks for the suggestions.  Primary pattens of the feed horn show 10-12dB edge taper at the half angle.  Just what you expect.  I haven't look at the intercardinal planes but that's a good idea.  Did you determine how the "odd mode" was generated in your antenna?  When you say "odd mode" do you mean overmoding of higher frequeincies with in feed?  

I did find the solution to my gain problem and the cause. The double ridged horn was sealed electrically around its' perimeter with conducting epoxy. With a perfect electrical seal, the boresight dip occurred. Removing the conductive epoxy mostly removed the problem. i.e. just letting the rf leak out a bit.

I found on the web that 60% efficient reflector antennas are uncommon and that 50% efficient ones are the norm.

That means that if you assume 50% efficient and allow 1 dB loss in transmission lines, VSWR, polarization loss, etc. then you have 2 dB loss in spillover. I'd bet that's where your 2 dB extra loss went to, over the side. A feed antenna pattern is about -6 dB towards the edge of your reflector which produces about -11 dB illumination at the edge since the edge is farther away than the center of the reflector. That says that your reflector captures 75% of the energy you send out and you lose 25% of the energy, which is 1.3 dB (10 log 0.75)loss already. Add the 0.5 dB VSWR loss for 2:1 VSWR and you're at 1.8 dB down from the calculated gain based on antenna pattern shape.

You can't look at the antenna pattern and see this loss since the boresight gain is very high and sidelobes in the back hemisphere look extremely low compared to the front lobe. Seems like an invisible loss, but take the reflector out of the equation and then think about it your feed radiates energy that isn't hitting the reflector and all of that missed energy is equal to loss for your antenna.

kch

Higgler: "Directivity vs. Gain: When you integrate antenna patterns, you are calculating Directivity. Directivity is not the same as Gain. Gain includes losses."

Actually, if your antenna pattern data is from real world measurements, and depending on how you've calibrated the entire system, then you might well be calculating Gain.

I had already touched on this issue with this ending note on my first post:

"Triple check to make sure that the average is close to zero dBi for some ideal examples.  Real world data should be slightly less than zero dBi.  Manufacture's brochure data might be more than zero dBi <smirk>."

Ideally, the loss number will fall out when you integrate the whole pattern (again, depending on how you calibrate the whole thing).

The process is the same in any case. The big issue is calibrating the amplitude scale - ie. the difference between gain and directivity. That's actually the hardest part - patterns are easy compared to making sure that they're calibrated.

With respect to 'invisible loss' (like dish spill-over), and if you're doing everything in dB [of course], then you really shouldn't misplace anything worth accounting for.

For a typical dish, optimally illuminated, the edge is typically -10dB down from the middle. Hopefully your equipment is adjusted so that you have at least 40dB SNR from the boresight to the noise floor. This should be more than sufficient to capture all significant parts of the pattern (unless you're dealing with a laser beam with a lot of widely distributed leakage).

If you're not capturing at least two complete slices (360 degrees each), then you might miss somthing. I've taken two slices and 'spun them around' in MS-Excel to prepare an estimated complete pattern (the whole sphere, Mercator style).

Higher gain antenas benefit from more data (obviously) - so that you don't miss some important aspect of the pattern (massive sidelobes somewhere odd - as per Higgler's nightmare example).

Personally, I don't like using simplified formulas for gain versus beamwidth. Complications (side lobes) can render them very misleading.

If you have enough data, then everything should fall into place.

In my case, I was able to go back to the OEM and ask if the peak gain was really 6.3 dBi, or more like 8.0 dBi. They provided more data and confirmed that I was correct. The 6.3dBi was nominal and an understatement.

All done with MS-Excel.

What if you integrate your antenna pattern data and get a result. Then you put a 10 dB pad on your antenna, take data again and the antenna pattern is identical.
 
I think the integrating the pattern idea includes the assumption that you don't really have any gain reference point in the data to get a peak value.

The integration technique is one way to get real antenna efficiency too. If directivity from integration and gain from a calibrated reference are 1 dB apart, your antenna is 80% efficient.

kch

I think that we're in agreement, if perhaps putting in different ways.

I've used manufacturer's data that provided a couple of poorly calibrated slices AND a supposedly accurate boresight gain. The integration proved that one manufacturer was understating the gain, and that the other manufacturer didn't have a clue.


"...1 dB apart, your antenna is 80% efficient."

Or, 1dB apart in the other direction, 125.9% efficient(*).

(*Yes, I know... )

I guess my main point was that this sort of analysis can be done using MS-Excel fairly easily. One can take a single slice and spin it in 3D, create a complete Mercator data set, integrate it all, and so on. If the antenna is low gain and with a smooth well-behaved pattern, the results can be a reasonably accurate extrapolation of the available data (enough to detect errors in the original data).