Reflection coefficient for non reciprocal RF elements

Dear all what is the mathematical relation for calculation of reflection coefficient from S-Parameters of a non reciprocal or active RF circuit element
if some could share some paper regarding its derivation İ will be very great-full
Regards

The question little no sense and the answer doesn't depend on reciprocity. Reflection coefficient is S11, presumed the other ports are terminated with Z0.

The Reflection coefficient is S11 when Reflection coefficient Γs is taken as 0 if it will not be zero then reflection coefficient will be different and i am looking for the derivation of this formula Γin=S11+(S12S21Γs)/(1-S22Γs)

O.K., you are asking about S11 of cascaded networks. The only special property of non-reciprocal networks is S12 ≠ S21.

I presume the derivation can be found in RF engineering text books, I didn't yet have a need to verify it myself.