A question about P1dB smaller than IIP3

Generally, the IIP3 is about 10dB higher than P1dB value.

However, for the high power input, if the system has loss, (e.g., attenuator) can IIP3 is smaller than P1dB?

Could you provide the material which can explain it?

Thank you very much.

YOu can scan the Razavi's book RF microelectronics on linearity in Chapter 1, I think it is useful.

P1dB is where your non linear is kicking or starting.
ip3 is where non linear products are equal to main signal.
Let say IP3 is lower than P1dB then it means non linear products are equal to input signal and system is still linear. this is not possible right. so IP3 always > P1dB

IIP3 is not a proper definition to compare P1dB..
P1dB is a "1dB Output Compression Point", IIP3 "Input Third order Intercept Point".So, you cannot compare apples and peaches..
If you meant OIP3, in this case OIP3 cannot be smaller than P1dB by theory.