Talk:Impedance matching

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Conjugate Matching and Reflectionless Matching[edit]

THe term 'reflectionless matching' I have not heard before but I think both terms describe the same desireable outcome. That is, when a source and load are matched, no energy whatsoever is reflected. In order to do this with a simple resistive source it only requires that the source and load resistances are made equal.

In the case of complex sources and loads however, it is neccessary to employ the technique of complex conjugate matching to ensure max power transfer. I believe its done all the time to match the output of transmitters to their antennas. If the source reactance is inductive, then the load reactance must be capacitive. etc. This will result again in max power transfer. Whether this power is just as great as if you had purely resistive source and load, I'm not sure without referring to my library articles. This can be seen if you go thro the math. I not going to do that here!! Light current 16:35, 10 August 2005 (UTC)

If you don't understand the difference between them, maybe I shouldn't have directed you here. The "Reflectionless matching or broadband matching" and "Complex conjugate matching" sections describe the difference pretty well.
  • In one, you are matching impedances exactly to prevent reflections down a transmission line. You set the line and load to the same impedance and there will be no reflections at the line-load boundary. You set the source and line to the same impedance so that if there are reflections from the load, they won't reflect back again when they get to the source. If you have a capacitive impedance at the load, you have a capacitive impedance in the source and line, too.
  • The maximum power theorem is entirely different. You match the complex conjugates of the impedances of a source and load so that, if the source has a fixed impedance, you get maximum power dissipation in the load. If your source has a capacitive impedance, you have to "balance it out" with an inductive impedance at the load. I believe this is the same thing as power factor correction, but I could be wrong.
The only thing that this article needs is to be cleaned up and separated into two good articles.
In the case of purely resistive impedances, the two ideas sound like the same thing, which causes a lot of confusion. Please be careful. We're trying to make it less confusing; not mix them up more. - Omegatron 18:28, August 10, 2005 (UTC)
No Im sorry I disagree, I have rewritten the firt half of the article. Please have a look. I dont think it needs separating yet until we see what we have got in total. I am in the process of sorting it. Is it OK by you if I carry on? :-)Light current 19:08, 10 August 2005 (UTC)
It is true that for maximum power transfer from the source to the load, the load impedance should be the conjugate of the source impedance. Now, insert a transmission line between the source and load. What should the load impedance be for maximum power transfer? The answer is that the load impedance should be such that the impedance seen looking into the line from the source is the conjugate of the source impedance. This guarantees that maximum power is delivered to the line and, if the line is lossless, on to the load. Thus, if the load is matched to the line, maximum power transfer from source to load only occurs if the source is also matched to the line. In the general case where the source is not matched to the line, maximum power transfer does not occur from the source to the load even though there is a 'reflectionless' match at the load end of the transmission line. Thus, it seems reasonable that the ideas of matching for zero reflection coefficient (no standing waves) and matching for zero total reactive component (maximum power transfer) are worthy of separate discussions. Alfred Centauri 19:10, 21 August 2005 (UTC)

It is incorrect to say that reflection-less matching is the condition where ZL = ZS. I believe that reflection-less matching is a special case of conjugate matching. I feel the whole theory part of this entry could be better written and here is my suggested wording starting from the beginning. (I have left out any formatting). "For some given complex source impedance Zs, maximum power transfer to a load impedance ZL is attained when ZL=Zs* (1). For a general load impedance ZL, impedance matching is the practice of providing a matching network before the load such that the impedance looking into the matching network and load is Zs*. In many microwave systems the load is connected to the source via a transmission line (TL). For maximum power transfer, (1) is still the necessary condition. (1) is now interpreted such that it applies at any plane between source and load: ZL and Zs are the is impedances looking towards load and source respectively. If (1) is true at any one plane it is true at any plane between source and load. Even under the condition of maximum power transfer (and conjugate matching),in general there is a reflection back from the load towards the source. The presence of forward and reflected waves on the TL results in increased line loss and increased maximum voltage and current on the line, all of which are undesirable. Reflection-less matching eliminates this reflection by providing two matching networks, one at either end of the TL. One matching network matches the source to the characteristic impedance Z0 of the TL and the other matching network matches the load to Z0. All matching is conjugate matching." Jkeevil (talk) 19:17, 23 May 2014 (UTC)

Are you assuming that the characteristic impedance of the transmission line is purely real such as 50 ohms? In that case, at the load end, conjugate matching and reflectionless matching are the same.Constant314 (talk) 22:28, 23 May 2014 (UTC)
I only consider the case when the TL Z0 is real. Complex Z0 is an unnecessary complication. It is also a very unusual case which need not be considered at this level. When the Z0 of the TL is real, conjugate matching and reflection-less matching are not the same. As I state above, reflection-less matching is a special case that uses conjugate matching at both ends of the TL so that there is no reflection on the line. Jkeevil (talk) 14:42, 24 May 2014 (UTC)
The telephone subscriber line is a transmission line with a characteristic impedance that has a substantial imaginary part. There are billions of these. The ordinary RG58 coaxial cable has a characteristic impedance that has a substantial imaginary part at audio. It is still about 10% reactive at 200 kHz. You can try to match it with a resister all day long and you still have a substantial reflection because you didn’t match the imaginary part. So yes, it is important. There is no reason for the article to be incorrect for these cases.
But I think that I am coming to understand what you are saying. Let’s start with a system that has a transmitter, a matching network, a transmission line, a matching network and then a load and consider narrow band situation. Let’s say the impedance of the TL is 50 ohms, the load is 100 -J10 and the source is 10 - J5. So at the load we put +J10 ohms (an inductor) in series with the load and then an ideal matching transformer. So the input to the matching transformer, as seen by the transmission line is 50 ohms. The load sees 100 +J10 so it sees its conjugate impedance. At the source end we put +J5 in series with the source and then an ideal matching transformer. So again the TL sees 50 ohms and the source sees it conjugate impedance. It all goes out the window though if the TL has a characteristic impedance that is not purely real. In that case, if you match for no reflection, the load and source do not see their own conjugate impedance.
The article is about matching whether you match both ends or not. We cannot tell the reader that they aren’t doing matching unless they match at both ends. Still, I think it is an interesting special case and if you want to add it as a special case I would not object.Constant314 (talk) 01:20, 25 May 2014 (UTC)
Consider ZS, ZL and TL Z0 are all complex then. I still don't find ZS=ZL a matched condition. My derivation for the matched case shows zero reflection and maximum power transfer are achieved when ZL=Z0=ZS* for arbitrary lossless TL length. I suggest you try both cases in a reliable circuit simulator and check for yourself. I can email you my derivation if you care to look at it. (It is also satisfying for me to see that if the TL length were reduced to zero and therefore removed from the system that the criterion I found is still ZL=ZS* which of course is the usual maximum power transfer criterion. Jkeevil (talk) 14:55, 25 May 2014 (UTC). Withdrawn.Jkeevil (talk) 14:55, 25 May 2014 (UTC)
That is precisely the arrangement shown in figure 6.30b of the source I linked below. It is still the case that we don't need to consider the matching at both ends simultaneously in the article, but now that we know it is used by practioners of the art, I agree with Constant314 that it could be used as an example of the application of matching. Note that waves returning down the TL in the reverse direction will see a mismatch at the source and will be reflected back towards the load. SpinningSpark 16:09, 25 May 2014 (UTC)
An semi-infinite length of transmission line is reflectionless. The impedance looking into that TL is Z0, the characteristic impedance of the TL. A finite length of TL terminated by an infinite length of the same type TL is also reflectionless. The impedance looking into it is also Z0. But the finite length is terminated by an infinite TL that looks like Z0 so the infinite length can be replaced with an impedance Z0 so you are left with a finite length of LT terminated by Z0 that is reflectionless.Constant314 (talk) 03:25, 26 May 2014 (UTC)
@Jkeevil:. I have restored the post you deleted. Please don't do this after others have replied to it—strike it out instead. SpinningSpark 14:56, 26 May 2014 (UTC)
Consider an infinite line with some complex characteristic impedance Z0. At a plane through some point in the line the impedance looking in either direction is Z0. Thus the join in the line at that point has Z0 facing Z0, not Z0 facing Z0*. Do you suppose that there is a reflection on the line at that point? If so, there will be a reflection at every point on the line. SpinningSpark 23:07, 23 May 2014 (UTC)
I am not familiar with what happens when TL Z0 is complex. I think a better 'thought experiment' is to consider what happens when the TL between the source and load tends to zero length. If ZL=ZS* then maximum power transfer occurs. If (as the entry on Impedance Matching now states) ZL=ZS for reflection-less matching, then max power transfer does not occur, so ZL=ZS for reflection-less matching cannot be correct.Jkeevil (talk) 14:42, 24 May 2014 (UTC)
Termination for max power transfer and termination for reflection-less matching do not mean the same thing.Constant314 (talk) 23:25, 24 May 2014 (UTC)
The concept of "reflection" has no meaning unless a transmission line (or some other object that is distributed through space) is considered. A reflected wave is a wave that travels somewhere. It is meaningless to talk of a reflection at a lumped load connected to a lumped source. By the way, I have corrected your indentation—this is a long and complicated thread so please either indent correctly or just post to the end of the thread to avoid confusion. SpinningSpark 15:59, 24 May 2014 (UTC)
Numerous sources define the reflection coefficient as (ZL-Zs)/(ZL+Zs). This is clearly zero when ZL = Zs and if Zs is complex then the reflection coefficient when ZL=Zs* is not zero.Constant314 (talk) 23:48, 23 May 2014 (UTC)
There is a reflection on the TL even when the system is matched: unless you use reflection-less matching.Jkeevil (talk) 14:42, 24 May 2014 (UTC)
But there is fix up needed on matching for maximum power transfer. ZL=Zs* only applies when Zs is fixed.Constant314 (talk) 23:59, 23 May 2014 (UTC)

I was beginning to doubt the correctness of the article because I can't get my head around more power being delivered when there is a reflection (I think it is something to do with the power wave having an imaginary part and energy stored on the line but I'm not sure). However, I found this source which pretty much explains the difference of the two matching schemes exactly as in our article. The book is on antenna design and if anyone knows the right answer on reflections it is antenna designers because if they get it wrong their shiny new expensive transmitter goes up in smoke. I think that is pretty much a slam dunk as far as this discussion goes unless someone can come up with an even more authoritative source. SpinningSpark 09:36, 25 May 2014 (UTC)

no authoritative source on my side but just a gut feeling about why more power is being delivered when there is a reflection: aren't the active components introduced by the matching network working in this direction? They are part of a resonant circuit whose frequency is the same as that of the source. — Preceding unsigned comment added by (talk) 16:04, 7 August 2014 (UTC)
2 authoritative sources: link1 and link2
...when the load is equal to the complex conjugate of the source impedance, the reflection coefficient is zero.
It seems "Conjugate matching is not the same as reflectionless matching" as this new link states link3
"Reflectionless matching" refers to matching the load to the line impedance, ZL = Z0, in order to prevent reflections from the load => There are no reflected waves and the source (which is typically designed to operate into Z0) transmits maximum power to the load, as compared to the case when ZS = Z0 but ZL ≠ Z0.
"Conjugate matching" allows absolute maximum power transfer.
So, I deduct they cannot be applied together unless Z0 is real (lossless line).
Some sources are a bit misleading in this respect: link4
-- (talk) 17:54, 7 August 2014 (UTC)

Reflection-less matching should avoid "should"[edit]

I’m generally of the opinion that encyclopedic articles should stick to describing what is and has been and should avoid saying what should be. In particular, the assertion that the characteristic impedance of transmission lines should be resistive is nonsense. There are billions of twisted pair transmission lines connecting telephones to telephone offices. In the voice band the characteristic impedance has a substantial reactive component and it is exactly what it should be. Furthermore, impedance includes a pure resistance and there is no need to justify the use of impedance to refer to a purely real resistance. Accordingly I am removing the comments saying that the impedance should be resistive and the comments that it is conventional to use characteristic impedance even when the impedance is purely real. On the other hand it would be acceptable to post reasons while a pure resistance may be desirable in certain circumstances.Constant314 (talk) 00:27, 15 December 2013 (UTC)

I agree with you about "should" but I think you have been overly savage in your trimming of the passage. That a purely resistive characteristic impedance is the ideal is good information. That the ideal case is often assumed in calculation could also be mentioned. SpinningSpark 01:28, 15 December 2013 (UTC)
Yes, I had started out to cut one or two sentences but as I looked at what remained, it also seemed wrong and I cut some more. Here is a sentence by sentence look at what was cut and why:
1. Ideally, the source and load impedances should be purely resistive: in this special case reflection-less matching is the same as maximum power transfer matching. [Retained and modified to eliminate ideally.]
2. A transmission line connecting the source and load together must also be the same impedance: Zload = Zline = Zsource, where Zline is the characteristic impedance of the transmission line. [This is wrong. There are lots of mismatched transmission lines in operation.]
3. The transmission line characteristic impedance should also ideally be purely resistive. [This is wrong in the case of telephone cable where ideal is meeting the primary line parameters as called out by the customer which lead to a substantially reactive component in the characteristic impedance. In fact, the characteristic impedance of most transmission lines is complex for voice band frequencies.]
4. Cable makers try to get as close to this ideal as possible and transmission lines are often assumed to have a purely real characteristic impedance in calculations. [The first clause is definitely wrong for voice band telephone cable. The second clause could be salvaged but would need some qualifying explanation. Is this assumption applied even when it is wrong? Is it true because when the calculations are made the characteristic impedance is almost purely real?]
5.However, it is conventional to still use the term characteristic impedance rather than characteristic resistance. [Unneeded because impedance includes resistance. Wrong because often the characteristic impedance is complex.]Constant314 (talk) 18:26, 15 December 2013 (UTC)
I don't really want to get into a line by line discussion on this. I am happy to see it go, but as I said in my previous post which you deleted for some reason, there are a couple of points that are worth mentioning and you have not really replied to them.
I don't want to argue with you line by line, but I will take up one point. You have made a great deal of telecom analogue twisted pair having a large reactive part to characteristic impedance. This is very true, but that does not mean that this is ideal from the telecom engineers point of view. Trying to correct this is the whole point of line loading which in the era of analogue was pretty ubiquitous. It is also true that telecom designs frequently treated the line characteristic impedance as resistive and terminated it with 600 ohm anyway regardlesss of knowing that there was a reactive component. This situation explains the popularity of Zobel equalizer sections in telecoms: they guaranteee that the equalizer design will precisely equalize the line to the response measured with a 600 ohm test set despite the line not actually being 600 ohms. SpinningSpark 22:53, 15 December 2013 (UTC)
If I deleted your post, it was entirely by accident and I apologize.Constant314 (talk) 05:50, 16 December 2013 (UTC)
The clause I deleted “often assumed to have a purely real characteristic impedance in calculations” almost definitely does not apply to the majority of the subscriber lines. It’s true that if you terminate a subscriber line with 600 ohms, then it looks like 600 ohms at the other end and you can assume 600 ohms in your calculations, but that is not using the characteristic impedance in a calculation. Most people do not even know the value of the characteristic impedance in the voice band (about 1000 + j1000 at 400 Hz for plain 26 AWG air core for example) and fewer actually use it. They are just using the impedance of the terminated line.Constant314 (talk) 01:25, 17 December 2013 (UTC)
Make that 1000 -J1000. Constant314 (talk) 18:58, 17 December 2013 (UTC)

Impedance Matching Devices Sentence Needs A Verb[edit]

Under "Impedance Matching Devices," the following sentence needs a verb or some kind of rework: "Devices intended to present an apparent source resistance as close to zero as possible, or presenting an apparent source voltage as high as possible." Greg J7 (talk) 16:12, 17 June 2014 (UTC)