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. 2ndorder products lie far in frequency to the
two input tones and are therefore not very likely to fall inband at the output in a narrow band system. As a device
is driven farther into its nonlinear region, the amplitudes of the 2ndorder 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 2ndorder gain line would
be 2:1. The slope of the 2ndorder product line is 1:1 relative to the fundamental gain line. Accordingly, the 2ndorder
products increase in power at the same rate as the input tones and are always twice times farther away from the IP2
than the input tones when not near saturation.
The power of the 2ndorder products can be predicted when the
IP2 is known, or the IP2 can be predicted when the relative amplitudes of the 2ndorder tones and the input tones
are known.
P_{2ndorder products} = 2 · P_{input tones@output}  IP2 {dBm}

IP2 =2 · P_{input tones@output}  P2_{ndorder products} {dBm}

Cascading IP2 Values in a Chain of Components 
Calculating the cascaded values for IP2 for the system budget requires the following operation based upon
ratios for gain and IP2 (do not use decibel values). The standard format for indicating decibel values is to
use upper case letters, i.e., OIP2 for units of dBm. The standard format for indicating watt values is to use
lower case letters, i.e., oip2 for units of mW or W.
A Typical Chain of Cascaded Components
This equation gives the method for calculating cascaded output
ip2 (oip2) values based on the oip2 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:

IP2_{OUTPUT} = (IP2_{INPUT} + Gain) {dBm}

or

IP2_{INPUT} = (IP2_{OUTPUT}  Gain) {dBm}

Thanks to Bernard R. for pointing out the missing square in
the denominators.
