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)

Clarifications to the L-match section[edit]

While I hesitate to get detailed about the information in the section, I found several statements which are dubious. I believe this info was brought over correctly from the cited reference so it is hard to know who is to blame, presumably the reference. The article states that the L-match is a narrow band solution. In the portion I just added, I compute the circuit Q and find it to be quite small, usually < 3. The bandwidth is approx. 1/3 or more of the operating frequency, which is reasonably wide. And there was a statement mentioning inductor Q as the limiting factor in the use of this circuit but the inductor Q is normally much higher than the circuit Q so it's losses are very small if the circuit is properly built. Therefore, I am unable to verify these statements.

Citations are a sore point with me, especially in fields which are mathematical. When the reference says one thing and the math says another, who am I to believe? And what about "reference unknown," i.e., something I was taught in school or work, a technique that works, and can be shown to be valid mathematically, but the original source is obscure? Isn't the point here to be accurate in the information? Citations are a false god, a form of idolatry. I am all for giving credit to the person who invented/discovered something useful but giving credit doesn't make something useful or accurate.

RDXelectric (talk) 23:36, 27 October 2016 (UTC)RDXelectric (2016/10/27)

The section has problems. The symbols in the figure do not match the symbols in the text. I will add a figure with the same symbols as the text. I'll leave it up to others to decide whether to remove the old figure.Constant314 (talk) 17:52, 28 October 2016 (UTC)
The recently added equations using Q are completely equivalent to the preceding equations and are visually simpler so I subsumed them into the preceding equations. Though it is typical that X1 and X2 are treated as unsigned values, in the references, with the understanding that one of them is a capacitor, the one of them that is a capacitor actually has a negative reactance. To be more mathematically rigorous, I put X1 and X2 inside absolute value signs. I would prefer to treat X1 and X2 as signed values, but that would be a greater departure from the references. Don't like it? Fine. Take away the absolute value signs and add an explanation that X1 and X2 are actually the absolute values of the reactance. Or use the fully signed treatment. I'll be happy to make that change if it is agreeable. Constant314 (talk) 19:34, 28 October 2016 (UTC)
Added reference. Hayward assumes R1 < R2 so the subscripts have to swapped around.Constant314 (talk) 21:21, 28 October 2016 (UTC)
This is better but I suggest the last statement, X_1 approx R_1/R_2 is superfluous, the only time that is true is when the Q is high and that's bad, it is always preferable to keep the Q low for efficiency, even if that means using more than one L-section. That maintains the broadband nature too. — Preceding unsigned comment added by RDXelectric (talkcontribs) 15:20, 29 October 2016 (UTC)
"The L-section is inherently a narrowband matching network with a greater impedance ratio resulting in a larger Q." I must take issue with this line at the end of the first paragraph, it simply is false. We used these networks when I worked at Collins Radio to match the output impedance of a high power transistor amplifier to the antenna (50 ohms) for military UHF radios that covered the 225-400 MHz band which is not narrow. RDXelectric (talk) 15:27, 29 October 2016 (UTC) RDXelectric
I know what you mean. It's only exact at one frequency, but its good enough over a wider band, especially if the impedance ratio is close to one. I have no problem with removing narrow band but there should probably be some statement that it is not broadband like a transformer that might cover three or four decades. Constant314 (talk) 17:20, 29 October 2016 (UTC)
Your example is just a bit less than an octave so requires a fractional bandwidth of 2/3, or a Q < 1.5. Plugging that in to the expression in the article (I'm assuming it's right) gets R1/R2 < 3.25. Should be achievable with a common base amplifier (but you'd be stuffed with common emitter). Filter design becomes difficult at more than an octave bandwidth, and impedance matching is an exercise in filter design, so that example is probably close to the practical limit. Here's a cite: Multi-octave impedance matching is almost exclusively done with transformers, although bandwidths up to 1-2 octaves may be possible with complex LC networks in conjunction with negative feedback etc. SpinningSpark 18:30, 29 October 2016 (UTC)