The gain of a microwave component is a function of the generator and load impedance. There are a number of specific gains that are of special interest to RF / microwave engineers.

Associated Gain (G_A)
The tuned gain of a device when it is matched on the input for optimum noise figure and matched on the output for minimum reflection.
G_A = { (1-|_opt|²)|S₂₁|²} / {|(1-S_11opt)|²}

Maximum Available Gain (G_max or MAG)
The tuned gain of an unconditionally stable device when it is matched for minimal reflection (conjugately matched) at both the input and the output.
G_max = |S₂₁/S₁₂| (k - SQR[k²-1])

Maximum Stable Gain (G_ms or MSG)
The gain that would be achieved if a conditionally stable device were first terminated with resistors to the point that it was unconditionally stable, and then conjugately matched at both the input and the output.
G_ms = |S₂₁| / |S₁₂|

Power gain (G_P)
The tuned gain of a device when the output is presented with the appropriate loadline _L to produce some specified output power, and the input is matched for minimal reflection.
G_P = |S₂₁|² (1-|_L|²) / |1-S_22L|²

Small signal gain (G_ss, or loosely, "Gain")
The gain measured with an amplifier operating in the linear region, and with source and load impedances of 50 ohms. Small signal gain is normally measured a minimum of 10 dB below the 1 dB gain compression point.

Transducer power gain (G_T)
The unmatched gain in a 50 ohm system. It corresponds to the S-parameter S₂₁, and can be calculated from
G_T = |S₂₁|².

Unilateral power gain (U)
The gain that would be achieved if the transistor were "unilateralized" (feedback set to zero) and conjugately matched.
U = {1/2|S₂₁/S₁₂ - 1|²}/ {k |S₂₁/S₁₂| - Re(S₂₁/S₁₂)}

See also:
Generator Impedance, Impedance, Impedance Matching, Load Impedance, Reflection Coefficient, S-Parameters