# Talk:Maximum power transfer theorem

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## impedance matching is not for Maximum Power Transfer at all

This should be merged with impedance matching. - Omegatron 14:38, Jul 29, 2004 (UTC)

I would keep Impedance Matching separated from Maximum Power Transfer Theorem (Jacobi's theorem)

1. Impedance Matching has more to do with camouflage than anything else. For example, if you split an infinit transmission line but do not want the source generator, which feeds that line, to notice that the line is not infinit anymore, one should conceal the line interruption with a device, in this case a resistance equal to Zo (the transmission line characteristic impedance). Someone decided to call this Impedance Matching just because this is obtained by matching the source and load impedances. Incidentally, this happens when there is maximum power transfer. Doing impedance matching, is a way to hide from the signal traveling in the transmission line that that line is not infinit at all. Using analogy, this is exactly what many other creatures (chamaeleon) happen to do to conceal themselves or something, that is Camouflage. Thus, if a transmission line is not infinite but a camouflage impedance can be add to its end, a signal is going to enter smoothily and without return into the device loading the line. That's the same someone driving a car on a long straight motorway would do if they could not tell if the road is infinite or terminated with a nice billboard with a giant paint simulating an extension of the road. Impedance Matching tell what to do to obtain camouflage.

2. The Maximum Power Transfer theorem, as stated by Jacobi, should be well understood not to indicate how to get maximum power transfer but how to obtain maximum efficiency.

3. There is one great example in which Maximum Power Transfer is essencial, i.e. Nyquist theorem, which models thermal noise generated by a resistor. The power generated by thermal noise is proportional to absolute temperature (T) and system bandwidth, Bw. The Boltzman constant completes the equation, i.e. P = k T Bw, where P is the power generated internally in a Resistor, T is the temperature and Bw is the badwidth of the measuring system or amplifier. If the Resistor (a component) is modelled by a Thevenin equivalente circuit, i.e. a noise voltage generator with Vth and Rth (voltage source and its impedance) feeding a matched load impedance R = Rth, results in Maximum power transfer, giving: kTBw = Vth^2/(4Rth). From which the Nyquist equation results as Vth^2 = 4 k T Bw R.

4. In most cases, if not all, one should avoid associating MAximum Power Transfer Theorem with Impedance Matching and threfore avoid very common mistakes and misunderstandings.

Commentator: Anisio R. Braga/ DAEE/CEFETMG/Brazil

"Incidentally, this happens when there is maximum power transfer."

They are the same thing, though, right? I understand that you are saying the purposes are different. Can you give more info about how the "impedance matching theorem" was first conceived, if it originally had nothing to do with the max power theroem? - Omegatron 18:52, May 13, 2005 (UTC)
Here's the historical view. According to Wikipedia, Moritz von Jacobi developed the maximum power theorem between 1837 and 1839 while working on battery-powered electric boats.
Impedance matching for transmission lines originated in the telephone industry, to prevent audible echoes. (Aside: The typical impedance of early telephone lines, which were air-spaced pairs, was 600 ohms, a value that was then copied by the broadcasting industry.) Several Web sources mention the Bell company as the discoverer of this technique. According to James Calvert, the impedance-matching autotransformer was invented by Emil Berliner of Bell and patented on 4 June 1877 as the Bell-Berliner System [1] and first used in 1879 (document in Library of Congress archives). The purpose of Berliner's invention (which he called an induction apparatus) was to match the impedances of the transmitter and receiver to each other, which looks to me like an application of the MPT; it seems that he, like everybody else at that time, was unaware of the need to match the tx/rx unit to the transmission line, although fortuitously his device did that too.
Load coils, first used by Mihajlo Pupin around 1896 but based on earlier work by Oliver Heaviside, were added to long lines to make their impedance more uniform. This, I think, was the true beginning of impedance matching of transmission lines based on a sound theory of electrical impedances.
Conclusion: the MPT was developed first. I can't find a causal link between this and Heaviside's work. There must have been a huge amount of discovery going on in the intervening period, so any link between the two discoveries is likely to be an extremely diffuse one. --Heron 20:44, 13 May 2005 (UTC)
Hmmm... So several different implementations of the same thing were developed for different reasons? I still think they should be part of the same article, with clarification of Anisio's concerns, since most people will think they are the same and won't see the other article. - Omegatron 21:47, May 13, 2005 (UTC)
Not so fast. ;-) I've just found an online textbook (Electromagnetic Waves and Antennas, Rutgers University) that refers to two types of impedance matching: complex conjugate matching and reflectionless matching (see the first two pages of Chapter 11). It states that the first concept is equivalent to the maximum power theorem (Zload = Zsource*, where * means complex conjugate), and the second, not surprisingly, is to prevent reflections (Zload = Zsource). You will notice that these two equations are not equivalent. I'm afraid haven't got time right now to digest the book and explain why they are different, but the equations are all there if you want them. I may try to get my head round this in the next few days. --Heron 22:27, 13 May 2005 (UTC)
Oh! Well that little asterisk is a huge difference. - Omegatron 22:33, May 13, 2005 (UTC)

Oliver Heaviside (See Oliver Heaviside: The Life, Work, and Times of an Electrical Genius of the Victorian Age by Paul J. Nahin) is to be credited with the Matching Impedance idea, something Oliver discovered around 1880's. By the way, Heaviside was the guy who coined the terms Impedance and helped us all, without complicated math's (operational calculus) to solve dynamical circuits using algebraic equations in the frequency domain (i.e. in the complex domain). Nowadays it is understood that systems of all kinds, e.g. hydraulic, Thermal, pneumatic, besides electric, requires Matching generalized impedance to avoid reflections. For example, a soil pressure cell should have the same soil impedance (mechanical stiffiness) to avoid reflections of pressure waves. That has nothing to do with MTP but a lot to do with Matching Impedance, which I preffer to call system camouflage. (Anisio)

I started to clarify the differences and split up the attentions of both articles, but they still need a lot of work. - Omegatron 17:44, May 22, 2005 (UTC)

--

Omegatron, when you wrote:

(though typically, more of an impedance bridging connection is used, to maximize control of the cone and lower distortion).

were you referring to valve amplifiers or to transistor amplifiers? I thought that valve amplifiers were an example of where transformers were used to match the hi-Z output to the low-Z speaker, but I could have been wrong. I can see the relevance of your statement to solid-state amplifiers - if that is what you meant, then please let me know and I will make it clearer in the text. Thanks. --Heron 22:52, 9 July 2005 (UTC) P.S. Thanks for spotting my equal/opposite reactance mistake - oops!

Yes, that's for transistor amps. I don't know much about tube amps, but this paper says:
"Older valve amplifiers needed a different form of impedance matching, because output valves generally had a fairly fixed and relatively high output impedance, so they couldn?t deliver audio energy efficiently into the low load impedance of a typical speaker. So an output transformer had to be used, to produce a closer impedance match. The transformer ?stepped up? the impedance of the speaker, so that it gave the output valve an effective load of a few thousand ohms; this was at least comparable with the valve?s own output impedance, so only a small amount of energy was wasted as heat in the valve." - Omegatron 05:09, August 13, 2005 (UTC)

## Does it make Sense Now?

Rewritten most of intro. Can people say whether it now makes adequate sense to them?Light current 01:14, 14 August 2005 (UTC)

I'm sorry, I just don't understand one thing : if you augmented the internal resistance of the generator with something useful such as light bulbs than couldn't you augment efficiency too ? If you were to make additional internal resistance to the generator useful then you could get more power for the other components couldn't you ? I doubt I just discovered a miracle theory to make 100 per cent efficiency, there's something I didn't understand I just can't see what. Stevenjlm (talk) 17:20, 8 April 2008 (UTC)

## Jacobis Theorem

I dont think the description of Jabobis theorem is totally correct yet. Will attempt to fix later.Light current 11:08, 14 August 2005 (UTC)

WE seem only to have one reference to this theorem being called 'Jacobis' theorem. I personally have never heard it called this, neither is Jacobi mentioned in any of my books as the originator of this theoerm. Does anyone have any more evidence that it was in fact Professor Jacobi' theorem?? Light current 21:39, 14 August 2005 (UTC)
Google search "Jacobi's theorem power". Note that there are two Jacobi's theorems. This is one, and the other is over here: Skew-symmetric matrix. - Omegatron 22:46, August 14, 2005 (UTC)
Yes thats correct. I have seen the link but all references to Jacobis Max power theorem stem from a single web article (His biographical notes). Is it safe to assume the validity of this single article? Light current 23:10, 14 August 2005 (UTC)
Can you link to that article? - Omegatron 23:19, August 14, 2005 (UTC)
Nice clean up job there 'O'. Not sure what you mean. I am able to link to it but I dont think the link goes directly the biography. Or did you mean 'could I put the correct link into the article'?? Light current 02:55, 15 August 2005 (UTC)
I just meant "you said 'all references to Jacobis Max power theorem stem from a single web article'. what is that article?" - Omegatron 03:06, August 15, 2005 (UTC)
Its here [2] Light current 03:17, 15 August 2005 (UTC)
Yeah, I found that, too. Looks like we need to recruit a Russian to check out the sources for us. - Omegatron 03:26, August 15, 2005 (UTC)
I have looked through the references, the reference http://www.kurierweb.com/81-100(2)/90(190)kurier/articles/academic.htm does not work (the site looks like an e-zine, there only latest issue is available). The other three references have nice biography of Jacobi but no mention of the theorem.
On the other hand simple search on "maximal power theorem" and Jacobi brings 132 google references, among them http://www.absoluteastronomy.com/encyclopedia/m/ma/maximum_power_theorem.htm http://web.linix.ca/pedia/index.php/Maximum_power_theorem
Those are just mirrors of this article!  :-) - Omegatron 05:59, August 15, 2005 (UTC)
Yep, they are verly close and many refer to Wikipedia. But 136 mirrors, wow!

I've read your links and there's no mention of any theorem or such. The articles give some info on Jacobi's researches in the field of electromagnetism in partnership with Heinrich Lenz, but he's mostly attributed for his works in galvanoplastics (Electroplating).

I think someone confused him with his brother Carl Gustav Jakob Jacobi who researched rational mechanics and invented Hamilton-Jacobi theory, studied by math students. He is most known for his Jacobi's theorem and it's the only meaning of the name known in Russia, contrary to what the article says (see search results on the web portal of Ministry of Education).

Yes there's a maximum power transfer rule in Russian physics courses, known as согласование нагрузки, but it's derived as a general rule from the formula for electromotive force that takes into account internal resistance of a cell or a generator. There's no mention of the theorem in physics courses for high education. --DmitryKo 16:07, 15 August 2005 (UTC)

Oh Dear!! Does this mean we will have to remove the ref to Jacobi from this page??Light current 16:22, 15 August 2005 (UTC)
I think calling it Jacobi's theorem is simply confusing people and may not even be correct (according to the view of our Russian user). Why dont we delete ref to Jacobi to play safe?Light current 23:52, 15 August 2005 (UTC)
We shouldn't delete it, but explain the origin of the term. It seems a lot of websites talk about him, so if it's not true, we should say so in this article. User:Heron started the article. We can start with him. ;-) - Omegatron 23:57, August 15, 2005 (UTC)
Sorry . my last edit comment should have read 'fraternal' not 'filial'. Im forgetting my LatinLight current 00:10, 16 August 2005 (UTC)

All right, all right. I admit I started the Jacobi thing. I had never heard it called Jacobi's Law until I read James Calvert's article [3], and I was convinced because it seemed to be corroborated by the biography that you mentioned above. If you want me to sort it out, then my solution will be to remove the reference to Jacobi until we find some proof. It's only a couple of sentences, so it will be easy to reinstate later. --Heron 19:55, 16 August 2005 (UTC)

Ooh, ooh, I just found a reference to Jacobi's theorem that seems to be independent of Wikipedia and the sources we have already mentioned. It's here, on the Oregon Public Education Network, and claims to be based on a Dictionary For The Electrician with Formulas, Tom Henry, Copyright 1997 (a later edition is ISBN 0945495099). All we have to do is find the electrician with formulas, and ask to see his dictionary. --Heron 20:17, 19 August 2005 (UTC)

## PFC

"Power factor correction(where an inductive reactance is used to "balance out" a capacitive one), is essentially the same idea as conjugate impedance matching although it is done for entirely different reasons."

How is it "essentially the same idea"? - Omegatron 23:13, August 18, 2005 (UTC)
Makes the over all impedance look resistive and hence near to unity PF Light current 23:39, 18 August 2005 (UTC)

## RE Merge: Ecological application of maximum power as a principle of energetics

There has been something of a hoo haa over my article on Maximum power. Some have suggested that it be merged with this article. The maximum power article was meant to document the use of maximum power in ecology by H.T.Odum, who considered maximum power the 4th principle of energetics (following on from the first 4 laws of thermodynamics). I suggest that this article be merged with the maximum power article including the history of the development of the theorem, together with a section applications such as those in systems ecology, and biology for example. Also...this article current could do with some more specific and authoritative references. Sholto Maud 07:31, 2 December 2005 (UTC) Post script: I also added the table and graph to try and demonstrate the concept of maximum powe efficiency more effectively.

I suggest that the Maximum power article be renamed to Maximum power principle and this article on Max power theorem be left un-altered. A short redirect page under Maximum power could point to both and clear the confusion. They have absolutle nothing to do with each other. --Pfafrich 22:49, 30 December 2005 (UTC)

Don't merge. That article is about something completely different (though I'm not sure what, exactly...) — Omegatron 23:44, 30 December 2005 (UTC)

## RE Maximising power transfer versus power efficiency

Does the maximum power transfer theorem apply when we convert from the electrical form of energy into the mechanical form of energy? That is, does maximum power transfer only apply when we restrict the power transfer to the electrical form of energy, and NOT when we are converting from electrical to other forms of energy like mechanical, heat, light etc.? It seems to me that the article has some confusion about this point. Sholto Maud 02:19, 3 May 2006 (UTC)

The maximum power theorem is about altering the load impedance to obtain maximum power at the load (not maximum efficiency). Converting from one form of power to another is concerned with efficiency. — Omegatron 13:46, 3 May 2006 (UTC)

Agreed. Maximum power theorem is not about maximum efficiency. However the article states that the theorem can be "sidestepped". What does this mean to sidestep a theorem? Is it that the theorem does not apply in cases where energy is converted from one form to another? Further discussion about analogous application of the theorem in mechanical systems is currently taking place on impedance matching talk. Sholto Maud 03:14, 4 May 2006 (UTC)

The only meaning I can think of for "sidestepping" a theorem is violating the assumptions of the theorem. For instance, Earnshaw's theorem conclusively proves that there is no way to stably levitate an object using classical unmoving magnets. It is certainly possible to levitate things, though, and it's done by using moving magnets or diamagnets. — Omegatron 23:37, 4 May 2006 (UTC)

## Rename article

I believe "Maximum power transfer theorem" is the more common name for this theorem. I propose renaming the article accordingly. -Roger (talk) 19:54, 18 January 2009 (UTC)

Correct: I was taught it as the 'Maximum power transfer theorem'. I have even taught it as the 'Maximum power transfer theorem'. Every electrical text book that I have used refers to it as the 'Maximum power transfer theorem'. Ergo, the article name is cutrrently incorrect. Sadly, I don't know how to rename an article, otherwise I would do it. 86.179.167.116 (talk) 16:08, 22 December 2010 (UTC)

Something does not make sense in the equation with multiplying by RL and RS. I think they get switched by accident too early. —Preceding unsigned comment added by 139.140.167.192 (talk) 10:38, 28 October 2010 (UTC)

What does that have to do with renaming the article? 86.179.167.116 (talk) 16:08, 22 December 2010 (UTC)
Renamed, using the confusingly-named "move" button; oh well, we're all used to clicking on "start" to shutdown a computer. --Wtshymanski (talk) 16:31, 22 December 2010 (UTC)
What 'Move' button would that be? I don't seem to have one. 86.179.167.116 (talk) 15:21, 26 December 2010 (UTC)

## The step by step through the equation has a problem.

When we decide to only find the minimum of the denominator, RL gets put in the denominator of R^2 when it should be in the numerator. When we switch everything, then RL goes in the denominator (which we have right). —Preceding unsigned comment added by 139.140.167.192 (talk) 10:44, 28 October 2010 (UTC)

## Maximum power transfer for current source

My suggestion is to also include the equivalent circuit and equations for maximum power transfer if source is a pure current source (Norton equivalent circuit). 128.104.199.64 (talk) 18:09, 19 October 2012 (UTC)

## Merging MPPT and power optmizer

These are just other names for variations of devices that present itself to the power source as a resistance value that provides the most power transfer. Instead of wasting our research effort on redundant information, I suggest we combine them so that we can consolidate all the good stuff. I also have some materials I researched and added to solar inverter and solar micro inverter. I am thinking combining all of the discussion that has to do with V/I conversion device here and move solar specific discussions to one of PV articles. thoughts? Cantaloupe2 (talk) 06:51, 2 September 2013 (UTC)

Well first off, the article on power transfer is related to this one, but certainly not the "same thing" by any definition or stretch of the imagination. Moreover, an optimizer may or may not use MPPT, the Tigo is a counterexample. I really don't see any logic behind this merge. If there's too much duplication of content between the articles we can fix that, but merging them is wrong. Maury Markowitz (talk) 12:16, 11 April 2014 (UTC)
'Oppose merge - theorem is not the same as hardware. We wouldn't merge Ohm's law and resistor, either. --Wtshymanski (talk) 13:36, 11 April 2014 (UTC)
Just because you opppose (sic) the merge, that does not give you the right to delete the merge tag from the article. Especially as you left the tags on the two source articles. Once this discussion has run its course and there is a reasonable concensus, then the merge can be closed. And unlike you, someone else will probably do it correctly. DieSwartzPunkt (talk) 14:35, 11 April 2014 (UTC)
I have cleaned up the stale tags on the other articles. --Wtshymanski (talk) 16:10, 11 April 2014 (UTC)
Oppose: Not sufficiently closely related. DieSwartzPunkt (talk) 14:35, 11 April 2014 (UTC)