S-matrix normalization

Hi everybody,

I have a generic question about S-parameters...

I know that I can normalize my S matrix using different value of characteristic impedance and I can pass from one to the other using a simple formula:

[S_Zb] = ([S_Za]- Γ[U])*([U]-Γ[S_Za])^-1

where S_Za is the matrix normalized using Za as characteristic impedance, S_Zb is the matrix normalized using Zb as characteristic impedance, U is the unitary matrix and Γ = (Zb-Za)/(Zb+Za).

That's ok to me... but when I want to calculate the "transducer power gain" GT
with source and load impedance matched (Γ_S = 0 , Γ_L = 0), I obtain the formula

GT=│S12│^2

that depend by the normalization

What's wrong ?