This post compares two different ways for finding the matchable loads \(Z_L^{'}\) that provide the desired impedance \(Z_G^{*}\) to the generator.
I will show the difference between two approaches, one rigorous and the other approximate, by using a set of S-parameters obtained by a black box network. The only requirement is that the black-box is linear, as the S-parameters requires linearity. For the curious, they are obtained from a binary weighted sweep of a lossy \(LL\) network composed of 1024 states in total from SimSmith.