I have a lot of GSM and WiFi antennas of various lengths and shapes with SMA connector.
I know of the antenna length relation with wavelength, but in some cases it is difficult or impossible to determine the length of the antenna (weird shape, there is some housing etc.)
Can I determine antenna band without very expensive equipment and knowing antenna length?
Actually I just need differentiate 900/1800MHz antennas from 2.4/5GHz antennas.
The equipment can be quite affordable. The simplest way to test such antennas is with a VNA, like a NanoVNA. There probably are YouTube tutorials about how to do it. All you need to see is at what frequency the antenna has the best SWR - that will usually be the representative of the operating band.
That's going to be hard. For example, I have a lot of "rubber" antennas that have small coils integrated into them for electrical lengthening purposes. Heck, I have 433 MHz antennas that work reasonably well, less than 7cm long! If I had guess their frequency from their dimension, I'd have assumed them to be "naive" \$\lambda/2\$ dipoles (coax to the middle of the antenna, outer conductor folded back to the bottom, inner conductor to the top) and put them more into the 2.4 GHz category than 433 MHz!
Unless you can literally see the conductors, don't trust the plastic shape! A lot "higher-end" consumer wifi access points, for example, come with screw-on (RP-)SMA antennas that look a lot bigger than their insides are – because many sharp-edged antennas look very "pro gamer" or something.
So, aside from simply testing with reference devices (if it works well for wifi reception, it's probably at least a wifi antenna, could still be a multi-band-antenna), I'd say it's hard to get anywhere just from looking at external dimensions.
The closest you can get without equipment, is to use simulator programs for RF simulation. So build the antenna in the simulator (length of antenna, width of the antenna wire etc) and running the simulator, should give you some results that will be close to real life.
I cannot suggest any program here due to policy of the site, but you can find such programs if you look it up.
Like others have said, you need use a 3-D field solver like HFSS or CST Microwave to model and analyze the antenna, or antenna element. But you have to get all the bits and pieces correct (conductor lengths, widths, bends), along with any passive conductors and dielectric involved.
This is one of the reasons that when you see a picture of the antenna for a modern day fighter radar such as the F-22 or F-35, the individual elements are slightly blurred. Doing so makes it harder for an adversary to reverse engineer and analyse the performance of the elements, which has a large impact on the radar's performance.
Image source: Aviation Today - F-35 AESA: The Most Advanced Jet’s Biggest Antenna
