pa output

what happens if the RF output of a RF power amp MMIC (3W 2GHZ) is open circuited?(when rf input is applied)

Is the MMIC PA damaged? or have no problem at this power level?

Possibly damaged. It depends on the phase shift between the FET cell and the open. The worst case is an in-phase reflection back to the drain which maximizes gate-drain voltage. A MOSFET will have holes blown in the gate oxide causing either instant or long term failures. A MESFET can have gate metalization melt, or metal migration in the long term. You can just monitor gate-current on a MESFET but MOSFETs you can't easily tell when you are stressing the device. The best case is an out-of-phase reflection which will just cause the FET to get hotter. You need to know the gate-drain breakdown of your process. It needs to be at minimum 2*VDD but more is better since you can have peaking from the harmonics; class A needs less head-room than higher classes.

how to protect it when it is open circuit?
Is there a simple way to protect(protect circuit)
?

There are multiple ways depend on the survival period of the final amplifier.

Let say the amplifier will be damaged immediatly if subjected to poor RL then one can go for isolator model.

If the amplifier sustains few milli seconds then goes bad. Inn this case we can go for sensing the refected power and then cutting the power suppply model.

Some transistors matching is designed such that their reflected energy will be obsorbed by the matching capacitors then they called rugged model.

is there any pdf ,article on methods 2 or 3?

I do not have as they are confidential.
But is the common practice and we need to care care in the initial design and development.