Graph of P1dB, IP2, IP3, and Saturation
See cascade calculations for NF, IP2, IP3, and
P1dB.

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. 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.
Cascading IP3 Values in a Chain of Components
Click here to view an example of a cascaded system. 
Calculating the cascaded values for 3rdorder intercept point (IP3) for the system budget requires use
of ratios for gain and power levels for IP3 (do not use dB and dBm values, respectively). The
standard format for indicating decibel values is to use upper case letters; i.e., IP3 for units of dBm.
The standard format for indicating power values is to use lower case letters; i.e., ip3
for units of mW.
Conversions: ip3 = 10^{IP3/10} ↔ IP3 = 10 * log_{10} (ip3)
where ip3 has units of mW and IP3 has units of dBm
A Typical Chain of Cascaded Components

Combining 2 Stages at a Time for Calculations

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 convenient and efficient to calculate each successive cascaded stage with the one preceding it using
the following format, per the drawing (aboveright).
These formulas are used to convert back and forth between input and outputreferenced IP3 values:
IP3_{Output} = (IP3_{Input} + Gain) {dBm}
IP3_{Input} = (IP3_{Output}  Gain) {dBm}
The following equation is a series expansion of the mixing (multiplying) of two pure tones:
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}
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.
