I have a doubt on a step usually performed in matching network design. Consider a load ZL: a method for getting impedance matching (for instance with an amplifier) is that of inserting a transmission line in order to modify its impedance, like in the following picture:
This operation can be seen also in terms of reflection coefficient. Precisely, I found this relation:
where ΓL is the reflection coefficient of the Load. My question is a bout a generic case in which ZL may be also another transmission line, a port etc
where does this relationship come from? Are there any assumption (for instance that the transmission line must have the same characteristic impedance of ZL - in case is a transmission line - , or it must be a no loss line etc) for it?