Is S11 critical for a LNA?
And what about S22?
One of the attributes if LNA is the frequency of operation. Return loss is key for LNA design. Without having proper input impedance matching with desired S11 (at least below -10 dB) in band of interest there is no point in designing LNA. Also,so goes for output matching which refers S22. But, more than that you need to check the stability of your LNA even outside the band of interest , which means checking "K factor".
Why is that?
If the S21, S12, S22 and noise figure are all good (S21 is large enough while S12 and S22 are both close to 0), and Rollett factor K is above one at any frequency, why is the input return loss so critical?
Its better we talk about S parameter in dB scale. You have to clear about S parameters. Lets say S11= b1/a1, where b1 is the reflected and a1 is the incident power. So, if your S11 is high means everything is reflected , so generally it's not possible to have good S21 with bad S11. Particularly, in your frequency of interest with bad S11, everything is reflected, which means your design is already in trouble.
It is difficult to talk in short about LNA noise matching. See a textbook on matching LNAs, the problem is more complex than it can be discussed here.
S11 is critical but only in part- the reactive component of it plays an important role. The matching is not only conjugate for the lowest NF
if you have poor match at input and output, your gain will be reduced. If you have poor match of the LNA, and also have poor match of the other system components (like input antenna, bandpass filter, etc) hooked to the LNA, you can have a VERY LARGE gain ripple.
So good engineering practice is to make the matches good.
The only exception is the S11 when you are looking for the absolute lowest noise figure, sometimes you deliberately mismatch the input port to achieve a lower noise figure.
In my field (MRI hardware), it is common to intentionally design narrowband LNAs where the noise match and power match are very different, so you get a "poor" S11 but an optimal noise figure. Definitely a unique application though.