When two or more tones are present in a nonlinear device, intermodulation products are created as a result. A power
series describes all of the possible combinations of generated frequencies. 3rdorder products lie near in frequency
to the two input tones and are therefore very likely to fall inband at the output. As a device is driven farther into
its nonlinear region, the amplitudes of the third order products increase while the powers of the input tones decrease.
If the device was not limited in output power, then the powers of the intermodulation products would increase in power
until they were eventually equal in power with the input tones at the output.
Assuming a gain of 1 (0 dB) the slope of the fundamental gain line would be 1:1; the slope of the 3rdorder gain
line would be 3:1. The slope of the 3rdorder product line is 2:1 relative to the fundamental gain line. Accordingly,
the 3rdorder products increase in power at twice the rate of the input tones and are always three times farther away
from the IP3 than the input tones when not near saturation.
The power of the 3rdorder products can be predicted when the IP3 is known, or the IP3 can be predicted when the
relative amplitudes of the 3rdorder tones and the input tones are known.
Equal Input
Powers (see below for unequal powers)

P_{3rdorder products} = P_{input tones@output}  2 · (IP3  P_{input tones@output})
{dBm}

P_{3rdorder products} = 3 · P_{input tones@output}  2 · IP3 {dBm}

IP3 =3/2 · P_{input tones@output}  1/2 P_{3rdorder products}
{dBm}


Here's
a great
link to a paper on intermod frequency prediction for any number of tones.

Cascading IP3
Values in a Chain of Components

Calculating the cascaded values for IP3 for the system budget
requires the following operation based upon ratios for gain and IP3 (do not use decibel values). The standard
format for indicating decibel values is to use upper case letters, i.e., OIP3 for units of dBm. The standard
format for indicating watt values is to use lower case letters, i.e., oip3 for units of mW or W.
A Typical Chain of Cascaded Components

This equation gives the method for calculating cascaded output
IP3 (oip3) values based on the oip3 and gain of each stage. When using the formula in a software program or
in a spreadsheet, it is more convenience and efficient to calculate each successive cascaded stage with the
one preceding it using the following format:


Conversion of the IP3 and IP2 reference may be accomplished with the following
equations:

IP3_{OUTPUT} = (IP3_{INPUT} + Gain) {dBm}

or

IP3_{INPUT} = (IP3_{OUTPUT}  Gain) {dBm}


The following equation is a series expansion of the mixing (multiplying) of two pure tones:

Unequal
Input Powers
P_{L} = P_{2}  2*(IP3  P_{1})
P_{U} = P_{1}  2*(IP3  P_{2})
Where power units are kept constant in dBm or dBW