I'm trying to understand general concepts involved in impedance matching and I have question about the conditions which should be satisfied by the matching network. Assume we have in most general setting the classical problem to match impedance between a source S with impedance \$Z_S\$ and load L with impedance \$Z_L\$:
The most general strategy is to put a impedance matching network between source and load (which is a circuit that can be relatively simple like L- or T-network, or a transformator, but even much more complicated in dependence of the actual problem) and the task of the practical impedance matching is then to adapt the parameters of the components in the matching network such that the impedances of source, load and matching network satisfy certain conditions.
Now I read that the conditions on the matching network that is required to be satisfied by involved impedances depend on two auxilary impedances: the input impedance \$Z_{in}\$ and the output impedance \$Z_{out}\$.
These two arise as follows. We can replace the network
Firstly (I) by an equivalent circuit
where \$Z_{in}\$ "summarizes" the impedance of the matching network & load replaced in one common impedance \$Z_{in}\$. In case of L-matching network here Andy aka provided an explicit calculation of \$Z_{in}\$
and secondly (II) we can also replace it by
the generator & the impedance \$Z_{out}\$ replace the source (generator & \$Z_{S}\$) and the matching network.
Note that here the calculation of \$Z_{out}\$ is a bit more subtile because here we have take into account the generator \$V_S\$. But the derivation of \$Z_{out}\$ from given \$Z_{S}\$ and the matching network is not the subject of this question. If one have fixed a matching box there is an arsenal of techniques available to do it, eg by transforming the source & matching network by a sequence of Norton and Theverin transformations until it has the desired shape in the picture above.
My concrete Question is: Assume we can calculate \$Z_{in}\$ and \$Z_{out}\$ as functions of the parameters of the components sitting in the matching network and our goal is to find the optimal parameters for these components in order to archieve an impedance match via maximum power transfer.
Which are in most general setting the conditions on \$Z_{S}\$, \$Z_{L}\$, \$Z_{in}\$ and \$Z_{out}\$ which should be satisfied in order to obtain the impedance match?
Proposal: should always simultaneously satisfied both - (I) \$Z_{S}^*= Z_{in}\$ and (II) \$Z_{out}= Z_{L}^*\$ - or does in suffice only to archieve (I) \$Z_{S}^*= Z_{in}\$?
Why I'm asking this: several times I found in the net tutorials about impedance matching methods that the authors only focus on \$Z_{in}\$ and waive the discussion about \$Z_{out}\$ completely.