I've done this a few times. You can plot the stability circles and then adjust the transmission line length between the amplifiers to avoid the unstable region. So you'll end up with a forbidden length. Just watch it as things become more unstable as they get cold.

Of course with that much gain, just put a 3 dB pad between the two, to accomplish the same regardless of phase. With 30 dB gain in the first stage, that will dominate the noise.

What do you mean by "large noise"? If you terminate the input with 50 Ohms, do you get the expected -174 dBm/Hz + 60 dB at the output? Is the antenna impedance making the first stage oscillate?

Ignore this advice if the amplifiers are in coax packages....If you are talking about cascading MMIC chip amplifiers, 60 dB gain is enough so that a little radiation from wirebonds or microstrip can cause positive feedback and then oscillations (You need to have some space between them and preferably channelize the signal path with small enough cross-section to cut off any waveguide mode where gain is available (not a problem when you are at 2 GHz!) In a pinch some RF absorber over the top of the MMICs can do wonders, but I believe that if you put absorber over the first MMIC you might degrade the noise figure. Good luck and let us know how you solved this issue... even better if you supply some photos and text for a Microwaves101 page!

I was able to cascade two high gain amplifiers, one with a gain of 20 with a noise figure of 0.5 db and the 2nd stage with a gain of 55 and a noise figure of 5 db. Both amplifiers were obtained from EBay for less than $30. The problem I had regarding stability and oscillations were removed using a 3 dB attenuator between them. However, I found a problem after connecting a dual-Schottky diode envelope detector ( obtained also from EBay) to the 2nd stage amplifier. Unfortunately, output from the higher gain amplifier produced oscillations again. Fortunately, however, this problem was resolved after using a tunnel diode detector.

I was able to cascade two high gain amplifiers, one with a gain of 20 with a noise figure of 0.5 db and the 2nd stage with a gain of 55 and a noise figure of 5 db. Both amplifiers were obtained from EBay for less than $30. The problem I had regarding stability and oscillations were removed using a 3 dB attenuator between them. However, I found a problem after connecting a dual-Schottky diode envelope detector ( obtained also from EBay) to the 2nd stage amplifier. Unfortunately, output from the higher gain amplifier produced oscillations again. Fortunately, however, this problem was resolved after using a tunnel diode detector. I wish I knew why the use of the 3 dB attenuator and tunnel diode approach worked.