This is the final way I got the concept of IP3 using equations.
y(t) = k1 x(t) + k2 x(t)62 + k3 x(t)^3 + HOT
IMD3 = k3 x(t)^ 3 + HOT
For an sinusoid input of amplitude 2A (and doing a bunch of math to
find how two sinusoids look like when they are added and raised to the
power of three), we get:
P_IMD3 = k3 A ^3 + HOT

In the log scale

Log(IM3) = log k3 + 3 * log (A)

This gives the slope of 3 on the IIP3 Pin Pout graph. The coefficient
k3 decides where the IM3 line intersects the y axis. The more linear
the analog stage, the smaller k3 is and the more negative log (k3) is.

Frank

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