I see nobody has responded so I'll take a crack at it.
Amplifier directivity is simply the gain or loss when you hook up the amplifier backwards. Loss is the result and it would usually be more than the gain of the amplifier used in the forward direction. Some amplifiers have a frequency selective bypass like those used for cable TV where the cable box might need to send signals back home to momma at a low frequency like 5Mhz or lower and a frequency selective filter will bypass these out of band signals around the amplifier with very little loss.
Before we get to IP3 lets mention IP1 or the 1dB compression point. This is where the amplifier is nearly saturated and cannot put out much more power. To find this point you carefully increase the input signal to the amplifier while monitoring the output signal in 1dB increments and the point where the amplifier is saturating or compressing where a 2dB change at the input results in only 1dB increase at the output is the 1dB compression point. This is not the absolute saturated output but it will be getting very close.
IP3 is a theoretical number that is used to characterize the linearity of an amplifier. All amplifiers will reach a point where they are no longer linear and create distortion and harmonics. When harmonics are produced they increase at a non linear rate compared to the fundamental frequency you are feeding the amplifier. For example you are amplifying a 100MHz signal and you reach the point where the amplifier is producing distortion and harmonics. If you measure the third harmonic then increase the input to the amplifier by 1dB, the fundamental frequency of 100Mhz might go up by 1dB but the harmonics will go up by 2dB. Increase the input by 5dB and the harmonics will go up by 10dB and so on.
The IP3 measurement would be drawn out to show where the fundamental frequency being amplified and the third harmonic will coincide in level if you were to continue raising the signal level into the amplifier since the third harmonic goes up twice as fast in level as the fundamental frequency. The level where the fundamental and third harmonic coincide in level could never be reached in actual practice as it would be way beyond what the amplifier would be capable of producing, but it does provide information on how the amplifier will perform in the presence of strong signals and how it might create Inter Modulation Distortion.
With my past experience using preamplifiers on broad band antennas I now look for the lowest noise figure with moderate gain, and that will be different if your just feeding one receiver or feeding a 16 way divider or how much feedline loss you are trying to overcome or a bunch of other reasons. I think an ideal amplifier that would work for 99% of the general scanning public would cover 30MHz to 1.3GHz, have about 12dB gain, .5dB or less noise figure, a 1dB compression of 30dBm (1 watt!) or greater and an IP3 of 60dBm or greater. However that amplifier does not exist today.
What you will find is amplifiers with similar frequency range, gain and noise figure but a 1dB compression of maybe 22-23dBm and an IP3 of 40dBm or so. That will not work in my area on a Discone or other broad band antenna without creating a ton of IMD which raises the noise floor with hundreds or thousands of ghost signals. Instead I have to trade off noise figure for higher 1dB compression and IP3 numbers like 26-27dBm for 1dB compression, 46dBm for IP3 and live with a higher noise figure of maybe 3.5dB. Not ideal but at least it will not make reception worse as a lower performing amplifier will here.
Now on my various repeaters where there are very narrow band pass filters before the preamps passing only a few hundred KHz of spectrum I might get away with a 15dB gain preamp with a 1dB compression point of only 12dBm, and an IP3 of only 26dBm. This is because the input frequency range of a repeater usually has some mobile radios and hand helds and its not that congested of a spectrum, and I'm filtering out and removing everything I don't need. In this case the preamp is happy and will never see signals that will produce IMD and trash out the receiver downstream. And I would never use the full 15dB of gain to feed just one repeater, I would attenuate its output to 6 or maybe 8dB and carefully measure the receiver sensitivity and limit the gain of the preamp once the sensitivity no longer improves with more gain. A 15dB gain preamp on a repeater system will easily feed an 8-way divider with plenty of gain left over to improve reception for weak hand helds, etc.
