A question about the third order distortion of cascaded outputs? Any equations?

I am designing a receiver. In a traditional way, I use two mixers and three ampllifiers. The OIP3 of the amplifiers is +27dBm, and IIP3 of the mixers is about 18dBm. The simple structure of the system is something like the mixer->amplifier->filter->mixer->amplifier->amplifier->filter. The level of the mixers is about -30dBm. So the third order output of the mixer is about (18dBm-(-30dBm))*2=96dBc. As the three amplifiers are of the same gain about +15dB and the mixers are of the same conversion loss about 8dB, the third output of the second amplifier should be (+27dBm-(-30dBm-8dB+15dB))*2=100dBc. In theory, the third output of the third amplifier should be (+27dBm-(-30dBm-8dB+15dB+15dB))=70dBc. Am I right in theory? I just make the calculation of each individual components and I haven't taken the cascaded effect into account. Would anyone like to point me out where I am not right and tell me how to modify my calculations? In which case we should care about the cascaded effect? Is there some equation like the noise figure one? Any reply is appreciated.

There are several free software can calculate the cascade system specifications, you should use software to do it. Such as syscal etc.

The applet below is for 5 stages, but can give you an idea what is going on.

CASCADE08.swf

For more complex analysis you can use the AppCAD from Agilent:

AppCAD

Use the software as described above. Your calculations are way wrong. IP3 is a theoretical point. You will never have your amplifier working in that region because of saturation.

Hey, friends! I use the OIP3 just for the calculations. I don't make the amplifiers work in the IIP3, although I have done it before. The chaos in my spectrum is hard to describe.

The Cascade calculation formula of Gain/NF/OP1dB/OIP3 are:

You can use Cascade or the tool I developed to calculate cascade specifacations.