# Maximum power transfer and minimization of signal reflection: When should what be applied

Impedance matching is the practice of designing the input impedance of an electrical load or the output impedance of its corresponding signal source to maximize the power transfer or minimize signal reflection from the load. In case of maximizing the power transfer the optimal condition we want to archieve is:

$$Z_S=Z^*_L$$

and in case when we want to minimize signal reflection the desired condition is

$$Z_S=Z_L$$

The Question is can we say in in denpendence of given situation how the decide when one wants to maximize the power transfer and when to minimize signal reflection. Are there any creteria know how to decide?

Of course, if we have only a source, no transmission lines, and we want maximize the power transfer, then doubtless maximizing the power transfer is the right choice.

But what what about the case when we have a source, a load and transmission line between them:

Or even a more complicated case we have again source and load, but now two different transmission lines (ie having different impedances, being build of different materials) between them:

Or even more complicated situations which I not want to draw, and so on.

Based on which creteria we can decide with option is more important here?

The maximization of the power transfer (for $$\Z_S\$$ and $$\Z_L\$$ and ignore the $$\Z_0, Z_1\$$ of the transmission lines) or minimization of signal reflection (for $$\Z_S, Z_0\$$ and then for $$\Z_S, Z_1\$$ and then the same story with $$\Z_L\$$ instead of $$\Z_S\$$)? Since the two mathematical conditions on impedances are different we cannot garantee that in general both conditions are satisfied simultaneously (for example when we deal with non trivial reactant components).

How to decide which practice of the two we should do in such case?

Note also that this question is closely related to my Maximum power transfer and minimization of wave reflection: Understanding the difference on intuitive level, but there the focus was on intuitional way to distinguish between maximization the power transfer and minimization of signal reflection, while here I'm interested on understanding when should be applied/prefered what? And how is it possible to decide it?

ADDITIONAL IMPORTANT POINT: ZelmaB noticed in his answer correctly that in my question isn't adressed to a concrete rf system/application. Yes, that's true and this is done intensionally because the main motivation in this question to find out preferably abstract criteria when for a system abstractly given as source, load and transmission line between them our task is to choose a maximization of power transfer and when the minimization of reflexion of signal waves.

If you like thinking in examples, I think ZelmaB gave below two very representative examples which also sprout the the heart of my understand problem in good way as I think, I tried to explain it below:

1. transmitter circuit (as sourse) and output antenna (as load). Between them we assume that the is a transmission line

2. high speed signals running through a transmission line between two ICs, one considered as source, one as load

What follows now is essentially rephrasing my comments below on ZelmaB's answer.

He wrote that for Ex 1) we have to perform maximum power transfer and for Ex 2) the minimization of reflected signal. Clearly, this sounds reasonable from viewpoint of our everyday experience. But what is the precise scientific/formal reason that we chose in these two examples as the matching technique we choose and not respectively the other one.

Let's focuss on Ex 1): Why we not perform on the minimization of signal waves reflexions caused by transmission line between the transmitter circuit and the output antenna, instead of maximizing the power transfer?

Is there a formal reason (not "everyday experience" reason!) why we take here this choice and not the other one? Eg can we argue like that is this case the reflexion effects due to transmission lines are here negligible, because ... (maybe these are to short with respect to wave length of the signal; I don't know, that's just an idea, I'm not sure if that's the correct reason).

But I hope that my last comments help the reader of this question to point out the problem I have and understand for what kind of arguments I'm looking for. As a mathematician I have namely some problems with "everyday experience" arguments, and prefer to see some formal criteria (eg something like "that's the case when the length of transmission line behaves so and so with respect the signal wave length, and so on)

• You need to \ \$ here for math. Nov 17, 2021 at 3:39