This was a posting to RAMPS about "Calculating Intermod Frequencies".

Here's a chance for a 40 page dissertation that I'm not going to take. In the interest of keeping it simple and easy to remember, I'll make some general statements that are 99% true, i.e., errors are 40 dB down and good enough for sound mixers. ;-)

Intermod is calculated in exactly the same way by all the programs and has little or nothing to do with i.f. frequencies.

Odd order intermod (3rd, 5th, etc.) is much more of a problem than even order intermod (2nd, 4th, etc.) because with odd orders it is possible to generate interference that is very close to the receiver frequency. This interference can therefore pass straight through the receiver front end filters. Of the odd orders, third order intermod is of greatest concern because the interference is always at a much higher level than 5th or 7th.

Second and 4th order are of lesser concern because the carriers that generate them cannot be close to the receiver frequency and will be filtered out by the front end. (Our IFB receiver is one of the few receivers for which this statement is not true. The IF is so low, 70 kHz (!!), that the image at 140 kHz from the operating frequency can be generated by 2nd order intermod.)

Intermod due to wireless transmitters getting into the receiver is not a factor if the transmitters are all, repeat ALL, 20 feet or more away from a good quality receiver. Intermod between a transmitter and a TV station does not follow the 20 foot rule for the TV station component obviously, or for two TV stations.

Intermod generation between transmitters is more of a problem in most situations particularly if the transmitters have standard output stages and are closer than 5 feet apart. The intermod frequencies are exactly the same as in receivers and any intermod program will catch them. I have seen fairly strong 5th and 7th order when transmitters are only a few feet apart.

A quick discussion of image frequencies is appropriate here since most programs also calculate images and this is where different brands do have differences. The knowledge of the i.f. frequency is critical in determining where the image frequencies will lie. A first low i.f frequency says the image frequency will be a small distance from the receiver operating frequency. Most modern receivers have a high first i.f. such as 244 MHz. This puts the image at 2 x i.f = 488 MHz away from the tuned frequency. Almost 500 MHz away means the front end filters can strongly suppress it. Generally, with modern i.f.'s, other wireless transmitters don't cause image problems. It's from other high power transmitters in the environment.

If the above is the Reader's Digest version of intermod stuff, here's the Cliff's notes:

1. Third order intermod is the biggie.
2. Any program will calculate third order.
3. Third and higher order between transmitters is usually the main problem.
4. You only need to worry about intermod if the transmitters are close to the receivers (less than 20 feet) or each other (less than 5 feet) or in other words, always.

Since the original question was "Mathematical formula in finding Intermodulation free frequencies" here it is:
1.Find the difference between two transmitter frequencies. 
2.Subtract the difference from the lower frequency and add it to the higher frequency. Those will be the two interfering frequencies, so don't have a receiver on those frequencies.

Example: Transmitter A=525.000 MHz, transmitter B=550 MHz. Difference is 25 MHz. Don't have a system on 500.000 (525-25MHz) or on 575.000 (550+25MHz). Note that you can't screw up the math. Doing it wrong such as 525 +25 and 550-25 gives you the original starting frequencies. Also note that two systems don't have intermod problems. It takes two transmitters to generate garbage on a third frequency and you have to have a third system in order to have something to interfere with. TV stations do count as a transmitter, however, if the signal is strong at the receivers, i.e., equivalent to a wireless transmitter at 20 feet or less.

Well at least I managed to keep it to only one full page (if you use a small font).