confused about S11

There are two amplifiers whose parameters are as follows:S11A=-20dB，S21A=10dB；S11B=-2dB，S21B=10dB.
If they are connected between RF ignal source (if available power equals 0dBm) and Spectrum Analyzer respectively, is 10dBm displayed on Spectrum Analyzer ?(becasuse when Ts=0,TL=0,the GT=S21(dB))
If it happens,when designing an amplifier,why we always care S11 and S22?

Your observation is correct.
Its nothing to do with this amplifier but if you calculate the amopunt of power that is reflecting back to source, you find the 2nd amplifier is reflecting toomuch than the fist one.
If you calculate the same at 40dBmlevel input power then the reflected energy is 38dBm in one case and 20dBm in first amplifier.
The driver is safe if it gets low reflected power.
I hope you understood it, if not pm me.

In the 2nd amplifier, you can add a "matching network" in front of it, and in doing so the "gain" of the amplifier can become much greater than 10 dB. With this higher gain, you can reach the desired 10 dBm output power with a much lower input RF signal.

If you do not fix the 2nd amplifier to have a better input impedance match, then the power reflected from that amplifiers input will reflect back to the source. This reflected power can cause system level problems, like pulling the source off of frequency or causing output power ripple as the frequency is tuned.

if the two amplifiers are both Low noise amplifiers,connected after antenna,will the same power be obtained at the output of low noise amplifier?

Yes of course and there will be back reflections with 2dB RL amplifier. I agree with biff44 that this 2dB amplifier can be tuned to give more than 10dB gain.

But who can tell me whether the second amplifier could be used in real design when it is a LNA connected after antenna with good noise figure and enough gain but bad S11?

Can anyone send me .mdl files of matlab for ask, fsk, psk, qpsk, msk,gmsk, pcm, dm,oqpsk?
plzzzzz.
it is a bit urgent

Hi Basic RF,
if you want help then send us the complete design in the signal path. I will analyze and send you the result.