Available power gain in S-parameters

Thread Starter

xblitz

Joined May 2, 2021
13
Hi!
In these days I'm digging into S parameters. I reading "D.M.Pozar - Microwave Engineering 3 Ed - pp. 538-539" a very good book IMHO... but I'm stuck at this point: according to the book the available power network can be derivated substituting, in the expression of power to the load, \( \Gamma_{out}=\Gamma_{L}^* \) and it's ok for me but in the next step it use the following equivalence
\[ |1-\Gamma_{s}\Gamma_{in}|^2|_{\Gamma_L=\Gamma_{out}^*}=\frac{|{1-S_{11}\Gamma_S|^2|(1-|\Gamma_{out}|^2)^2}}{|1-S_{22}\Gamma_{out}^*|^2} \]
but I'm not able to derive this result (I try to barely substitute the expression of \( \Gamma_{in}\). So can anyone provide an exhaustive demostration of this equivalence?

Best regards
 
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