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As i know IIP3 is defined by the extrapolation of 1dB and 3dB line, but why the intercept point can determine the linearity of an variable gain amplifier?
Perhaps you can refer to Razavi, "RF Microelectronics".
The gradient set by IIP3 will suffer non-linearity due to compression point. The greater the IIP3, the greater the linearity span or range. No PA or LNA is fully linear, but there is an operational span for linear ampification to eliminate harmonic distortion due to intermodulation product terms.
If the IIP3 is larger, then the amplifier has more linearity.
Because the nonlinearities makes new frequencies. And this causes problem.
The IM3s are very dangerous because they are close to the useful spectrum region.
IIP3 is characterize the third-order intermodulation by a single scalar number, and we like sclara numbers.
The difference betwen 1 dB compression point and IIP3 is approximately 10 dB.
The IIP3 is generally out of the region that you use.
See the picture below.
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