Maximum power gain and maximum stable power

For maximum gain, both input and output ports are conjugately matched
  
Due to the fact that , the output termination affects input termination and vice versa.

Substitute (126) into (125), we have
 

Substitute (125) into (126), we have
 
By the solving (130) and (133), the optimum source termination, , and the optimum load termination, , are found to be

Under the condition that both the input and output termination are conjugated matched, all power gains are equal and they have a value of

It can be shown that

so the maximum stable gain from an amplifier is

Example In a 50 system, a transistor has the following S-parameter at 1.3 GHz. Find the optimum terminations for maximum power gain.

Solution K= 1.032 > 1 , the transistor is unconditionally stable.