Error in Maximum Power Transfer Theorem page

Discussion in 'Feedback and Suggestions' started by Ray A. Rayburn, May 1, 2009.

  1. Ray A. Rayburn

    Thread Starter Guest

    This page states:

    "This is essentially what is aimed for in stereo system design, where speaker “impedance” is matched to amplifier “impedance” for maximum sound power output. Impedance, the overall opposition to AC and DC current, is very similar to resistance, and must be equal between source and load for the greatest amount of power to be transferred to the load. A load impedance that is too high will result in low power output. A load impedance that is too low will not only result in low power output, but possibly overheating of the amplifier due to the power dissipated in its internal (Thevenin or Norton) impedance. "

    This is total nonsense, and harks back to the claims of the "experts" as to why Edison's concept of electrical power distribution could never work. The "experts" assumed that for power transfer the load and source impedances had to be matched which meant half the power was lost at the generating plant. Edison designed a system with a low source impedance and constant voltage independent of load, so each load determined how much power to draw based on its load impedance.

    In exactly the same way a power amplifier has a very low output impedance (small fraction of an ohm), and the loudspeaker impedance determines how much current and therefore power is drawn for a given amplifier output voltage. The ratio of nominal loudspeaker impedance to the output impedance of the power amplifier is called the damping factor, and for typical consumer and professional sound systems is in the range of 100 to 1000.

    It is important to cover the Maximum Power Transfer Theorem, but please use a real example, not this one based on a faulty understanding of audio systems.

    Ray A. Rayburn
    Senior Consultant K2 Audio, LLC
    Fellow of the Audio Engineering Society
    Chairman of the AES Standards Subcommittee on Interconnections
    Ray@SoundFirst.com

    PS: This is the second time I have sent in a correction on this issue. It will be interesting to see if the correction is ignored again.
     
  2. studiot

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    Perhaps if you posted a link to the offending page ?
     
  3. KL7AJ

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    Hi Ray:

    I think we need to address the conjugate match theorem in two parts, since you brought up a controversy that arises in R.F. power amplfiers, as well.

    By definition, the conjugate match will dissipate half the power in the source resistance, and half in the load resistance. This is the condition under which maximum possible power is transferred to the load.

    HOWEVER...this is not necessarily a desirable condition! We need to make this distinction. Power transmission grids are not meant to be run "flat out"....neither are most radio transmitters. In very few applications, actually, are you trying to achieve absolute maximum power transfer...there are often much higher priorities...such as low distortion....audio amplifiers being just one example, as you state.

    I thnk we need to define the conjugate match, and give a proof (which is remarkably simple, by the way), and then go into reasons why and why not to seek a conjugate match.

    By the way....in the telephone company...and broadcast audio chains before the voltage source/bridging model became standard, for example....the conjugate match WAS the norm....but for completely different reasons than maximum power or efficiency. It was much easier to design filters and pads with a conjugate matched system throughout...which generally resulted in a rather low overall efficiency...but very flat.


    Eric
     
  4. Wendy

    Moderator

    Mar 24, 2008
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    I've just completed a through manual search of the entire Feedback and Suggestions Forum, and couldn't find any reference to any other entries. This site is unusual in many ways, we do not delete posts except for spam, and you can edit past posts indefinitely (and I do mean forever), and the ability to upload and store files is astounding.

    By not registering (which is free and has no negatives that I'm aware of) you limit a lot of the abilities. If you had registered the first time I could have clicked on your profile and found every post you ever made. It really is a lot easier if you work with a system, instead of being confrontational with it.

    Could you please point to the previous post where you input this feedback (my curiosity is up)? And it would be most helpful if you point to the problem paragraph, though I'm sure someone has located it by now. Links are OK.

    Thanks.
     
  5. KL7AJ

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    Hi Bill:

    The Wikipedia article on the maximum power theorem is quite good:

    http://en.wikipedia.org/wiki/Maximum_power_theorem

    It is very careful to distinguish between maximum power and maximum efficiency. I'm also glad to see the proof given. (It can also be easily demonstrated with a "thought experiment" using the two extremes....infinite and zero resistance loads, with a finite source resistance.)

    Ray's point is well taken....a modern audio amplfier with essentially zero source resistance driving a very hign impedance load, approaches 100% system efficiency....though the actual power transfer approaches zero. :)

    Walter Maxwell, W2DU, wrote a seminal work on this entire subject as it related to R.F. systems. It was published in QST in the 1970s as a series "Another look at reflections" followed by three editions of a text by the same name. I've corresponded with Walt on several occasions.

    It's important to not let practical or desirable application become confused with definition. A conjugate match is a conjugate match. It doesn't necessarily mean it's a good thing, however!

    Eric
     
  6. Wendy

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    Mar 24, 2008
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    Oh, I knew most of that. A power supply with much more than a ohm is not too useful. RF need maximum matching to prevent reflections. In the scheme of things an audio amplifier is closer to a power supply than a transmitter.

    Just curious, have you located the problem paragraph yet?
     
  7. studiot

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    I couldn't find it either. That's why I asked for the link.

    Seems to me that the theorem is taught cursorily at relatively junior level in electrical engineering, and often not at all in electronics and then forgotten about. Explanations as to why we use other arrangements are in scant supply. You are correct to assert the validity of the theorem.

    However I do agree with Ray that the originally presented text is rather wooly and could benefit from revision.
     
  8. Ray A. Rayburn

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    Jun 29, 2009
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  9. Ray A. Rayburn

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    I have now registered.

    Don't recall seeing the forum when I made my first comment on this issue. (It was a couple of years ago.) I believe I sent in an email.

    http://www.allaboutcircuits.com/vol_1/chpt_10/12.html

    Still not fixed.
     
  10. Ray A. Rayburn

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    Professional or consumer audio has not used matched interfaces for at least 35 years at mic and line level, and I don't believe has ever commonly used matching at speaker level which was the claim made in that page.
     
  11. Ray A. Rayburn

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    What you say is true for mic and line level interfaces where the load impedance is at least 10 times the source and at times is much higher.

    Speaker loads, however, do get significant amounts of power from the output of the power amplifier. The typical loudspeaker is in the 4 to 16 ohm nominal impedance range (but varies a lot with frequency), but the power amplifier output impedance driving the loudspeaker usually has a source impedance 100 to 1000 times lower than the speaker load impedance. For the loudspeaker case the actual power transfer does not approach zero.
     
  12. studiot

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    We've all agreed the page needs revision.

    So now dazzle us with your version Ray.
     
  13. Dcrunkilton

    E-book Co-ordinator

    Jul 31, 2004
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    This is my proposed revision; red is changed text; blue is new text. I have replaced the reference to an audio amplifier with a reference to an RF amp final driving a transmission-line/antenna. I would have serious doubts about including the following passage below the last red text:
    or electric vehicle design (seeking to maximize power delivered to drive motor).
    I am not convinced that this is valid-- maybe, maybe not. Any opinions?

    Proposed test follows:



    The Maximum Power Transfer Theorem is not so much a means of analysis as it is an aid to system design. Simply stated, the maximum amount of power will be dissipated by a load resistance when that load resistance is equal to the Thevenin/Norton resistance of the network supplying the power. If the load resistance is lower or higher than the Thevenin/Norton resistance of the source network, its dissipated power will be less than maximum.

    This is essentially what is aimed for in radio transmitter deisgn , where the antenna or transmission line impedance is matched to final power amplifier impedance for maximum radio frequency power output. Impedance, the overall opposition to AC and DC current, is very similar to resistance, and must be equal between source and load for the greatest amount of power to be transferred to the load. A load impedance that is too high will result in low power output. A load impedance that is too low will not only result in low power output, but possibly overheating of the amplifier due to the power dissipated in its internal (Thevenin or Norton) impedance.

    Taking our Thevenin equivalent example circuit, the Maximum Power Transfer Theorem tells us that the load resistance resulting in greatest power dissipation is equal in value to the Thevenin resistance (in this case, 0.8 Ω):

    figure
    http://sub.allaboutcircuits.com/images/00249.png


    With this value of load resistance, the dissipated power will be 39.2 watts:
    figure
    http://sub.allaboutcircuits.com/images/10204.png

    If we were to try a lower value for the load resistance (0.5 Ω instead of 0.8 Ω, for example), our power dissipated by the load resistance would decrease:

    figure
    http://sub.allaboutcircuits.com/images/10205.png

    Power dissipation increased for both the Thevenin resistance and the total circuit, but it decreased for the load resistor. Likewise, if we increase the load resistance (1.1 Ω instead of 0.8 Ω, for example), power dissipation will also be less than it was at 0.8 Ω exactly:

    figure
    http://sub.allaboutcircuits.com/images/10206.png

    If you were designing a circuit for maximum power dissipation at the load resistance, this theorem would be very useful. Having reduced a network down to a Thevenin voltage and resistance (or Norton current and resistance), you simply set the load resistance equal to that Thevenin or Norton equivalent (or vice versa) to ensure maximum power dissipation at the load. Practical applications of this might include a radio transmitter (seeking to maximize power delivered to the antenna, or electric vehicle design (seeking to maximize power delivered to drive motor). Another example is a grid-tied solar inverter which adjusts its load on a solar power array to achieve maximum power transfer as insolation varies.


    The Maximum Power Transfer Theorem is not: Maximum power transfer does not coincide with maximum efficiency. Application of The Maximum Power Transfer theorem to AC power distribution will not result in maximum or even high thermodynamic efficiency. The goal for AC power distribution is high efficiency. This dictates a relatively low generator impedance and relatively high load impedance.


    Similar to AC power distribution, Audio amplifiers are designed for a relatively low output impedance and a relatively high speaker load impedance. As a ratio, "load impdances" : "amplifier output impedance" is known as damping factor, typically in the range of 100 to 1000. [rar] [dfd]


    Maximum power transfer does not coincide with the goal of lowest noise. For example, the low-level radio frequency amplifier between the antenna and a radio receiver is often designed for lowest possible noise. This often requires a mismatch of the amplifier input impdeance to the antenna as compared with that dictated by the maximum power transfer theorem.

    • REVIEW:
    • The Maximum Power Transfer Theorem states that the maximum amount of power will be dissipated by a load resistance if it is equal to the Thevenin or Norton resistance of the network supplying power.
    • The Maximum Power Transfer Theorem does not satisfy the goals of maximum efficiency or lowest noise.


    (at end of chapter at ibiblio)

    Bibliography



    1. [rar]Ray A. Rayburn , private communications, Senior Consultant K2 Audio, LLC; Fellow of the Audio Engineering Society, (6/29/2009).
    2. [dfd]Damping Factor De-Mystified , at http://www.sweetwater.com/shop/live-sound/power-amplifiers/buying-guide.php#2
     
    Last edited: Jun 30, 2009
  14. studiot

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    Can we hold any revision until the discussion is complete please?

    I don't see the proposal as being helpful, quite the reverse as it simply piles on more flannel to obscure the subject even further.

    Sorry.
     
  15. Dcrunkilton

    E-book Co-ordinator

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    Yes, we need to hold it until it is in a satisfactory state.

    An audio amplifier driving a loud speaker is not a correct example of the application of the Maximum Power Transfer Theroem. At a minimum, if we do nothing else, that example has to go. A 0.04 to 0.004 Ohm generator driving a 4 Ohm speaker is not the MPTT (100 to 1000 damping ratio). I replaced the audio amp and speaker example with the RF transmitter example.

    If the section "The Maximum Power Transfer Theorem is not:" is out of place, out of context, we can drop it.
     
  16. R!f@@

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    Why all the fighting guys.
    I think Ray is trying to be noticed.
    For what it is worth ..I DO NOT BELIEVE RAY
    Cause I have verified the maximum power transfer for audio in both theory and practical during my study years. I my self wanted to see if it is true or not and it is true that the impedance has to be matched in audio power amplification.
    If Ray could not give definite proof in practical application a lot of us don't think will believe him

    Rifaa
     
  17. Wendy

    Moderator

    Mar 24, 2008
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    If you read the early part of this thread you would see what the issue is. No fighting, but we want to get it right the second time. No one is arguing the theory of maximum power transfer, but it only applies in special cases, and stereo audio isn't one of them.

    When you enter the realm of RF, where signals can bounce hither and dither, it becomes extremely important, and has several different measurements to describe it, including return loss, and SWR. Cables and network theory also become important in this arena.

    I like where part of the article has gone, where it focuses on the RF and reflections aspect.

    Let me repost the same article with the illustrations intact. I'm not judging at this point, but I am spellchecking and more. For example, what is the correct work for "insolation", shown in red?

    Also, what is the [rar] signify?

    ********************************************

    The Maximum Power Transfer Theorem is not so much a means of analysis as it is an aid to system design. Simply stated, the maximum amount of power will be dissipated by a load resistance when that load resistance is equal to the Thevenin/Norton resistance of the network supplying the power. If the load resistance is lower or higher than the Thevenin/Norton resistance of the source network, its dissipated power will be less than maximum.

    This is essentially what is aimed for in radio transmitter design, where the antenna or transmission line impedance is matched to final power amplifier impedance for maximum radio frequency power output. Impedance, the overall opposition to AC and DC current, is very similar to resistance, and must be equal between source and load for the greatest amount of power to be transferred to the load. A load impedance that is too high will result in low power output. A load impedance that is too low will not only result in low power output, but possibly overheating of the amplifier due to the power dissipated in its internal (Thevenin or Norton) impedance.

    Taking our Thevenin equivalent example circuit, the Maximum Power Transfer Theorem tells us that the load resistance resulting in greatest power dissipation is equal in value to the Thevenin resistance (in this case, 0.8 I(c)):

    [​IMG]


    With this value of load resistance, the dissipated power will be 39.2 watts:

    [​IMG]


    If we were to try a lower value for the load resistance (0.5 Ω instead of 0.8 Ω, for example), our power dissipated by the load resistance would decrease:

    [​IMG]


    Power dissipation increased for both the Thevenin resistance and the total circuit, but it decreased for the load resistor. Likewise, if we increase the load resistance (1.1 Ω instead of 0.8 Ω, for example), power dissipation will also be less than it was at 0.8 Ω exactly:

    [​IMG]

    If you were designing a circuit for maximum power dissipation at the load resistance, this theorem would be very useful. Having reduced a network down to a Thevenin voltage and resistance (or Norton current and resistance), you simply set the load resistance equal to that Thevenin or Norton equivalent (or vice versa) to ensure maximum power dissipation at the load. Practical applications of this might include a radio transmitter (seeking to maximize power delivered to the antenna, or electric vehicle design (seeking to maximize power delivered to drive motor). Another example is a grid-tied solar inverter, which adjusts its load on a solar power array to achieve maximum power transfer as insolation varies.


    The Maximum Power Transfer Theorem is not: Maximum power transfer does not coincide with maximum efficiency. Application of The Maximum Power Transfer theorem to AC power distribution will not result in maximum or even high thermodynamic efficiency. The goal for AC power distribution is high efficiency. This dictates a relatively low generator impedance and relatively high load impedance.


    Similar to AC power distribution, Audio amplifiers are designed for a relatively low output impedance and a relatively high speaker load impedance. As a ratio, "output impedances" : "load impedance" is known as damping factor, typically in the range of 100 to 1000. [rar]


    Maximum power transfer does not coincide with the goal of lowest noise. For example, the low-level radio frequency amplifier between the antenna and a radio receiver is often designed for lowest possible noise. This often requires a mismatch of the amplifier input impedance to the antenna as compared with that dictated by the maximum power transfer theorem.





    REVIEW:
    • The Maximum Power Transfer Theorem states that the maximum amount of power will be dissipated by a load resistance if it is equal to the Thevenin or Norton resistance of the network supplying power.
    • The Maximum Power Transfer Theorem does not satisfy the goals of maximum efficiency or lowest noise.
    (at end of chapter at ibiblio)

    Bibliography


    1. [rar]Ray A. Rayburn , private communications, Senior Consultant K2 Audio, LLC; Fellow of the Audio Engineering Society, (6/29/2009).
     
    Last edited: Jun 30, 2009
  18. Dcrunkilton

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  19. studiot

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    I don't see the relevance. Loudspeakers are not resistors. They are not even purely electric/electronic devices. As such their impedance contains terms which are not normally included in the statement that they are 4ohm, 8ohm or whatever. Strictly these terms reflect back into and modify the electrical component of impedance they possess and should be included in any network analysis that includes them.

    Another way of viewing this is to say that modelling a loudspeaker as an equivalent resistor will get you the wrong answer. You have to use the correct model, just as with ac analysis of transistors you need the appropriate model.

    I did publish the appropriate equations back along I will try to find the thread.
     
  20. Dcrunkilton

    E-book Co-ordinator

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    in⋅so⋅la⋅tion

    –noun Meteorology.
    solar radiation received at the earth's surface.

    See Bibliography

    1. [rar]Ray A. Rayburn , private communications, Senior Consultant K2 Audio, LLC; Fellow of the Audio Engineering Society,

    If you find mispelled words let me know. If for any reason you want to work on the .sml , I can attach that.
     
    Last edited: Jun 30, 2009
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