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Dealing with impedance matching of RF networks one facing two common techniques: (a) maximize power transfer (b) minimize reflexion of signal waves

In this question I have tried to develop some kind of 'intuition' when I should try to maximize the power transfer in my network and when to minimize the reflexion of signal waves. I think that in such full generality it was a combat with wind mills, so for general networks there is no 'general guide' available, but nevertheless I would like to know if there some 'elementary guide rules' appliable in case of simplified networks. Namely I would like to discuss these three rather elementary cases:

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My question is simply can it for these 3 simple, but didactically interesting cases definitely said if we should apply (a) or (b) in 'guideline manner'? My ideas:

CASE 1: Here is assumed that there is no transmission line between source and load. Or there is a transmission line between them, but is at least assumed that it's length is short compared to the frequences the networks works with.

my guess: If we impose these assumtion, can it be stated as a 'rule' that in this case one should always apply (a), the maximize power transfer archieved by \$Z_S= Z^*_L\$

CASE 2: Here we assume that the source is connected to the transmission line with big length and we don't know what sits behind the transmission line.

Guess: Can for such situations be said that here one should always apply (b), the minimization of the signal waves reflexion, that is \$Z_S= Z_T\$

CASE 3: Assume now that the load is connected to the transmission line and we don't know from whom the signal comes, that is we don't know the source. That means the load sees only the transmission line.

Guess: Does this case obeys the same rule like chase 2, that means here we should always apply (b) for the transmission line and load?

Firstly, are my ideas correct? In other works can it be said that it should be regarded as guideline to apply for cases 1,2,3 (a), (b), (b) and nothing else?

If that's true, can we extract from this a more general principle dealing with multi-staged networks? Say, we have a network consisting of \$k\$ consecutive parts \$P_1=S, P_2,..., P_k=L\$ and we want to know how to match it. As I remarked, in general that's a difficult question. But can we nevertheless state following two principles, which we can consider as rough 'guidelines'?

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  1. the matching should be done successively between direct neighbours. Firstly we match \$P_1\$ to \$P_2\$, then \$P_2\$ to \$P_3\$, and so on. So we can divide the matching problem to \$k-1\$ 'small' matching problems between \$P_i\$ and \$P_{i+1}\$

  2. we want to match \$P_i\$ and \$P_{i+1}\$. Can we consider the following suggestion as a general guideline?

"If \$P_i\$ or \$P_{i+1}\$ is a transmission line, then we always should match \$P_i\$ and \$P_{i+1}\$ by (b): minimization of reflexion, that is our aim is \$Z_i= Z_{i+1}\$?"

and if neither \$P_i\$, nor \$P_{i+1}\$ is a transmission line, then our task is to get (a): \$Z_i= Z^*_{i+1}\$?
Do my considerations make sense? Is there something wrong?

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  • \$\begingroup\$ You are limiting yourself the scenarios that are naive. For instance, you would never ever match a speaker impedance with the output impedance of an amplifier. To do so is missing the point hence, many many times your load is much higher impedance compared with the source impedance and, is done so by choice. \$\endgroup\$
    – Andy aka
    Nov 22, 2021 at 23:23
  • \$\begingroup\$ Most RF circuitry is based on 50 ohm source and load impedances. \$\endgroup\$
    – Barry
    Nov 22, 2021 at 23:36
  • \$\begingroup\$ @Andy: okay, my motivation has pure didactic nature. maybe from practical point of view this approach misses in fact the point, I still have a terrible intuition in this area. I hoped just to understand this field better with this divide and conquer approach. But could you say to me, are my ideas on cases 1-3 at least pure theoretically fine? or is there something that I'm doing conceptually wrong? For example, I'm not sure it I understand how to see when I should try to reach the procedure (a) and when (b). Is there a kind of rough guideline known? \$\endgroup\$
    – user267839
    Nov 23, 2021 at 0:15
  • \$\begingroup\$ I find it hard to answer questions that assert wrong things. Now that's my problem in that I feel disinclined to spend time unwrapping incorrect formed ideas. Sorry. \$\endgroup\$
    – Andy aka
    Nov 23, 2021 at 3:40
  • \$\begingroup\$ @Andy: would you like to point out which of my assertions is wrong? Is there something wrong with cases 1,2,3 I going to discuss in general? Did I make somewhere a false claim in my attepts to solve them? If you if you are not averse, I would like to discuss with you the example with the speaker and amplifier you brought in the conversion. hopefully that will convey your concern to me better. \$\endgroup\$
    – user267839
    Nov 23, 2021 at 14:32

1 Answer 1

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The general rule of thumb for RF circuitry is that inputs and outputs are matched to 50 Ohms, so for Case 2 and Case 3 you would want to have the source and load presenting a 50 Ohm Output / Input impedance respectively. For Multi-staged systems, which Case 1 is a degenerate example, it partially depends on the implementation.For PCB based systems, where you're going to want to be able to probe performance on the board, matching circuit blocks to 50Hms makes the evaluation/optimization easier. If you're implementing the system in a RFIC, then you're free to not match the circuit blocks, and use Voltage/Current/Impedance as needed. Low output impedance/high input impedance is fine there.

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  • \$\begingroup\$ thank you for your answer. these 50 Ohms you introduced, apparently fall from the sky. Does it have any physical background why we choose 50 Ohms and not 10 or 100? or is it a convention? As well, this rule only applies only to cases 2,3, therefore only if one of the components we want to match is a transmission line? \$\endgroup\$
    – user267839
    Nov 23, 2021 at 15:36
  • \$\begingroup\$ As with many things in engineering, the origin story of the convention of 50 Ohms is somewhat unknown. For a coaxial cable, minimum losses are ~ 90 Ohms (Air filled lines) and maximum power handling is ~ 30 to 40 ohms, so 50 Ohms was chosen in WW2 as a compromise, and had developed into an industry standard. As to you second question, many RF circuits (Not just transmission lines) are modeled as a series of 2 port networks, and 50 Ohms is used as the standard impedance, used for Cables/connectors as well as test equipment. \$\endgroup\$
    – rfdave
    Nov 23, 2021 at 16:17
  • \$\begingroup\$ okay, so can we endow this business with 50 Ohm with a model abstraction? suggestion: (Source)- (transmission line with std impedance 50 Ohm) - (Load) and then reduce the problem to two separate problems: 1. match source impedance to the impdance of transmission line (our 50 Ohm) and 2. match tranmission line to load. or does this again miss the point? \$\endgroup\$
    – user267839
    Nov 23, 2021 at 17:22
  • \$\begingroup\$ Yes, typically, you would match a source to 50 ohms, and a load to 50 ohms, and then you could use a 50 Ohm transmission line to connect the two. \$\endgroup\$
    – rfdave
    Nov 23, 2021 at 22:19
  • \$\begingroup\$ but then, what is the difference between this approach you suggesting by introducing this 'virtual' transmission line with \$Z_0=50 Ohm \$ and match separately the source and then the load with it (so you have to archieve \$Z_S= Z_0\$ and \$Z_0= Z_L\$), or alternatively just to match the source with load by maximum power transfer condition \$Z_S= Z^*_L\$? \$\endgroup\$
    – user267839
    Nov 24, 2021 at 22:41

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