Electrical – transmission line theory, complex conjugate matching

impedance-matchingmicrowavetransmission line

Referring to the below output matching network of an amplifier ,in which gamma_out is chosen as the complex conjugate of gamma_l (in the figure Γ and Γ*) in order to achieve maximum power transfer from the output of the amplifier to the network.
Why in this particular case of conjugate matching Γ1 turns out to be 0 ?
Can somebody carefully explains me this perhaps trivial thing?
thank you in advance.

schematic

simulate this circuit – Schematic created using CircuitLab

Best Answer

Since the load exactly 50 ohms, it will have a gamma of zero. You want the gamma looking back into your matching circuit (gamma 1) to also be exactly zero.