# Equivalent Conditions for Matching Network

#### RobertDa

Joined Dec 24, 2021
2
Assume we want to provide maximal power transfer from a source with
impedance Zs to a load with impedance Zl. The statdard technique to archieve
such impedance match is to place a matching network between source and
load consisting of certain components it can be a L- or T-network or even something
more complicated):

In several books / internet sites it is said that the required condition which
the matching network should satisfy is Zin = Zs^*, in other sources it is
said that the matching network should satisfy Zout= Zl^*. I guess these two
conditions are equivalent.

Problem: I nowhere found a derivation why these conditions are equivalent, ie if Zin = Zs^*
holds, then also Zout= Zl^* and vice versa.

Could anybody give a reference where an explicite derivation of the equivalence of conditions
Zin = Zs^* and Zout= Zl^* can be found?

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#### Papabravo

Joined Feb 24, 2006
20,378
I think you need to match both conditions simultaneously. If Zin ≠ Zout, then the matching network must include an impedance transformation. If on the other hand, Zin = Zout, then no transformation is necessary. In addition, if Z is complex, then you actually want a conjugate match.

#### RobertDa

Joined Dec 24, 2021
2
so you are sure that it might happen that even if one has already matched Zin = Zs^* , the Zout = Zl^* not automatically holds as consequence? see eg 6.4.1 here
https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Electronics/Microwave_and_RF_Design_III_-_Networks_(Steer)/06:_Chapter_6/6.4:_The_L_Matching_Network or the book RF power amplifiers by Michai Albuet, Chap 2.6 (https://digital-library.theiet.org/content/books/ew/sbew030e)
seemingly in both sources one in only interested on reaching the condition Zin = Zs^*. No word on Zout= Zl^*.
BTW: The claim (I still not pretty sure if it's true) that Zin = Zs^* might be equivalent to Zout= Zl^* I found in following attatched file (of course surprise surprise without proof)

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