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Is there an antenna supplier out there that is particularly well known for publishing enough data on their antennas that one can model their antennas' transmission fields in spherical or cylindrical coordinates?

I'd like to make mathematical models of several antennas in three-dimensions, using whatever coordinate system, and then use level curves of those equations to calculate power density at various points in space given an input wattage to the antenna.

These systems will be using 2.4 GHz and 5.0 GHz to transmit ( and receive ).

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Most antenna manufacturers will supply you with measurement data of how much power is radiated in which direction. That is a perfectly normal thing to do, and it's much more likely you'll get one of these measurements that fully describe the far field of your antenna then measurements that suffice to do a simulation. For example, something like:

Radiation pattern, wikimedia, from https://upload.wikimedia.org/wikipedia/commons/a/ae/Patch_antenna_pattern.gif

for both the E- and the H-Plane. Having two orthogonal cross-sections of the amount of power radiated in the respective angles fully describes your antenna's directivity. Nothing to simulate.

These are called radiation patterns. When buying non-trivial antennas for use cases where approximate knowledge of the directivity isn't enough, it's expected that the manufacturer has done the measurements necessary to generate them – it's practically impossible to do this at home, without an anechoic chamber and calibrated reference antennas.

You probably won't get exact fabrication data of what you can buy as patch antennas, but you can simply measure them with a ruler – so PCB type antennas should be OK, too, assuming the substrate is well-known (for cost reasons, and because at these frequencies it still works great, it'll be FR-4, anyway).

What you're describing is antenna simulation. Such simulations are usually rather complex finite element method simulations, that, by decomposing the antenna geometry and the time or frequency domain into small enough parts can mathematically approximate the antenna's fields well enough. You don't have to re-invent the wheel. There's software out there that does that.

As a free software, have a lookt at OpenEMS.

By the way, if you're really experienced, then your simulations are meaningful. I've rarely seen someone generate a simulation that is closer to measured reality than an educated guess at the first try.

So if your goal is to learn how to simulate antennas, start with very basic ones. A dipole, then a rectangular patch, then a patch with receded feedline etc, not with something as overwhelmingly complex to simulate as real-world 3D aperture antennas.

If your goal is to get a very good impression of what an antenna will behave like in usage before buying it, than the manufacturer's measurements are way more useful than a simulation.

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For wire antennas I do mathematical modeling using NEC4. NEC4 is version 4 of the National Electromagnetics Code. It must be licensed from Lawrence Livermore Labs. I have a licensed copy and the cost was $300 when I obtained my copy 4 years ago. There is a public free version, older and less accurate with less features known as NEC2.

NEC2 and NEC4 are batch programs (written in Fortran, NEC4 is Fortran 90+) and they accept an input antenna description with execution commands dictating the desired simulation and output. The output is printed numbers, not graphs. To obtain graphs of output you need to post-process the output data and draw the graphs yourself or use some of the freely available software that does that for you such as 4NEC2, CocoaNET (for Mac computers), and EZNEC (licensed, not free).

I use the Wolfram Mathematica application to produce all my graphic output. This is far more powerful than any of the above cited software but you need Mathematica (Home Edition about 200 or maybe 300 US dollars). And, you need to learn Mathematica which to some people is a bit of a learning curve to overcome. But, I create functional representations of all of the output data that not only allows me to plot graphs nicely but I can do Calculus on the functions for finding minimums and maximums or working to do other extended calculations.

Note that NEC2 and NEC4 are useful for wire antennas only or antennas using linear conductors such as aluminum tubing on Yagi antennas. You can do some mesh network modeling and try your hand at simulating a dish antenna but that is stretching the accuracy depending on the work you are doing.

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