# Definition of IP3

In response to: Linearity IP3

Can any person tell me if this information is correct: The third intercept point IP3 is equal to the third drift of the drain to source current compared to the third drift of the gate to source voltage i.e. IP3=d3IDS/dVGS3.

If it is correct, please send me the reference of this information.

IP3 is found by approximating a nonlinearity as a third-order polynomial:

y = A×u + C×u3

u is the input (voltage or current) and y is the output (voltage or current). (I omit the B×u2 term for brevity).

As signal increases, A×u increases 1 dB for each dB that u increases.
At the same time, C×u3 increase 3 dB for each dB that u increases.

Generally, A×u starts out much smaller than C×u3 (if it doesn’t, you’ve done something wrong with your amplifier/mixer/etc). However, at some (fictious) point, C×u3 catches up to A×u. This point, where |A×u| = |C×u^3| is the third-order intercept point. You can specify either the input u (input IP3 = IIP3) or the output A×u (output IP3 = OIP3) at this intercept point.

This point may be fictitious because the equation y= A×u + C×u3 is a small-signal (but nonlinear) approximation. In reality, the circuit will clip (saturate). You must ensure you are putting small signals into the circuit to ensure it does not clip. In doing so (inputting small signals), you will find that the polynomial approximation is pretty good.

The effects of third-order distortion (and other nonlinearities) are explained in an article at RF Desgin Line: The need for linear circuits.