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Transformer efficiency

Discussion in 'Electronic Design' started by Danny, Oct 18, 2003.

  1. Danny

    Danny Guest


    What would the maximum feasible transformer efficiency achieved in a
    relitavly primative laboratory, by that i mean high-school type laboratory.
  2. Mathew Orman

    Mathew Orman Guest

  3. Steve

    Steve Guest

    depends on transformer size and rating. Larger transformers are usually
    more efficient than smaller ones.

  4. Is Metglass easy to work with , What are the typical Flux Densities that the material runs at??

  5. Roy McCammon

    Roy McCammon Guest

    I've worked with some met-glass torroids. They have sharp edges.
    I handle them with cotton gloves until I get them completely wrapped
    with tape.
  6. I read in that Roy McCammon
    Isn't it very costly? The OP is asking about work in a high-school lab,
    and the question is not very sophisticated. I think there is a risk of
    'blinding with science'.

    There are two sources of energy loss in a transformer - the electrical
    resistance of the windings and the hysteresis loss in the iron core. The
    physical shape of the core affects the ratio of these losses, and
    efficiency is at a maximum when the two losses are equal (this is an
    example of an important theorem, with many applications).

    You could get a slight improvement in efficiency by using silver wire
    instead of copper, but the improvement doesn't justify the cost. The
    type of core material affects the hysteresis loss. Plain silicon-iron
    (there are several grades) has more loss than grain-oriented silicon
    iron. There are nickel-iron alloys that have yet lower losses, but most
    of them have rather low saturation induction ('induction' is now the
    proper name for 'flux density'). They are also very costly. Metglas has
    even lower losses but also is very costly.

    For a high-school lab, you should probably go for a grain-oriented
    silicon-iron toroid, but you'll have 'great fun' putting the windings
    on. You would increase your chances of success if you used a laminated
    ('E-I') core of grain-oriented silicon iron, with a plastic bobbin to
    put the windings on. The core volume controls the power rating of the
    transformer. For anything above about 100 W, you should be able to get
    95% efficiency at 60 Hz.
  7. Mathew Orman

    Mathew Orman Guest

  8. Tom Bruhns

    Tom Bruhns Guest

    Um, John, how do you arrive at that conclusion?? (It seems to me that
    I can think of several rather different counterexamples if the problem
    isn't somehow constrained, but maybe I'm not looking at it right.)

  9. It's true in the common case where two loss curves intersect at
    only one point where they have derivatives of opposite sign, such
    as a 1/(x^n) curve intersecting a 1/(N-x^m) curve or similar.
    Moving either side of the intersection increases the sum (total
    loss), because you necessarily move up one curve more than you
    move down the other. There are obviously other curves that also
    satisfy the requirements, and as Tom points out, there are also
    curves that don't!

  10. It's a text-book result. You can constrain the problem so that either
    the copper loss or the iron loss is fixed and the other is variable.
    It's then just a matter of finding the minimum of the total loss by
    differential calculus. The resulting condition is 'fixed loss = variable
  11. Roy McCammon

    Roy McCammon Guest

    I think there is a tacit assumption of 50/60 Hz operation.
  12. Glen Walpert

    Glen Walpert Guest

    The unstated assumption here is that the cost of copper efficiency is
    the same as the cost of core efficiency, which is essentially never
    the case, so that in fully optimized transformer designs core loss and
    copper loss are almost never the same. Yes, it is a text-book result,
    but you will not find it in any decent text on transformer design,
    because it is not useful except as a crude first order approximation.

    A good text that discusses real transformer optimization is "Magnetic
    Components, Design and Application" by Steve Smith.
  13. I read in that Glen Walpert <>
    The OP asked for 'maximum efficiency' in a *high-school* context. Not
    for a fully-optimized design, based on post-graduate concepts.

    Equal losses DOES give maximum efficiency. It doesn't necessarily give
    lowest product cost, although for small transformers, the differences
    are very small.
  14. Tom Bruhns

    Tom Bruhns Guest

    Presumably under the constraint that a loss component can't go
    negative. But if, for example, I say the core loss is fixed and the
    conductor loss is variable, would the minimum not be with zero
    conductor loss? If I have zero conductor loss, and fix that, how am I
    to get to zero core loss if I have lossy core material? Or if I have
    zero core loss (an air core), but lossy condutors, how could I make
    them equal? I'm still thinking that you're probably seeing the
    problem in a certain clear light in your mind but not stating all the
    constraints implicit in that, and I'm seeing it differently in mine.
    (That seemed to be a common problem with calculus texts, too, as I
    recall! If you started thinking outside the box the author had not
    properly defined, you could come up with other answers...) I suppose
    ultimately, you're right and we could all agree: minimum loss is when
    the core loss and the conductor loss are equal and both zero. But I
    didn't need calculus to find that answer.

  15. Glen Walpert

    Glen Walpert Guest

    OK, I will accept the "equal loss" rule as a useful first-order
    approximation to get in the ball-park of optimum with only a high
    school level analysis. But I think it should be identified as a first
    order approximation, even to a high school student.
    Equal losses DOES NOT give maximum efficiency, even if it does
    minimize losses per a particular simplistic design equation. Given
    any transformer with equal losses, I can design a more efficient
    transformer within the same size, cost and weight constraints, or a
    less expensive, smaller or lighter transformer with the same
    efficiency. So how can you continue to claim that equal losses gives
    maximum efficiency, while apparently admitting that efficiency per
    unit of cost, weight or volume is not optimized (which is the case
    wether you admit it or not). What exactly are you optimizing for -
    effeciency per minute of design time perhaps?

    I thought we had established that the equal-loss rule was a crude
    approximation and not in any way a true optimization last time we
    discussed this a few years ago, but perhaps one or both of us has a
    faulty memory here!

  16. I read in that Glen Walpert <>
    Because you have simply asserted the contrary, not very politely,
    without any attempt to show where the 'simplistic' analysis is wrong.
    No, watts out/ watts in, the definition of electrical efficiency.
    I don't recall any such discussion. But I don't subscribe for 24/7/365/4
  17. Yes, but with real, resistive conductors you would need an infinite
    winding space.
    You would need some way of getting close coupling between the windings.
    With an air core, that difficult!

    The fact that 'fixed loss = variable loss' gives minimum total loss
    doesn't imply that the condition can be satisfied in every conceivable
    case. For example, I have a laminated transformer whose core stack is 5
    tongue-widths deep, giving a huge mean-turn length and far from optimum
    electrical efficiency. It's like that because of a very severe core
    height constraint, and a misguided cost restraint that prevented the
    specification of a toroidal unit. Revision 1 substituted the toroid and
    solved the overheating problem.
    You don't need the 'both zero' condition to *minimise* the total loss,
    using real conductors and core materials.

    OK, I AM considering 'power' transformers, not Tesla coils or 35 MHz IF
    transformers. But for those beast, no-one ever looks at electrical
    efficiency. And simple 'power' transformer theory works up to a
    frequency limit where capacitances become significant, which, for small
    transformers, is often above 1 kHz.
  18. Roy McCammon

    Roy McCammon Guest

    I don't think that you can make it zero, but you reduce it
    with more turns (assuming a voltage transformer). If your
    copper loss is not zero, then more turns means more copper
    loss. So one goes up as the other goes down, it is plausible
    that the minimum would include a balance between the core loss
    and copper loss. Its not obvious to me that it would be one to one.
    Perhaps its a fluke of typical core material constants.
  19. Tom Bruhns

    Tom Bruhns Guest

    Superconductors aren't real? There are companies now who have
    commercialized them, so they aren't even just lab curiosities.
    Hmmm...not so! Folk have been making very efficient air-core RF
    transformers for quite some time. Really tight coupling isn't a
    requirement for good efficiency. And transmission-line transformers
    do achieve very close coupling in any event.

    I suspect folk who design megawatt, and even smaller, transmitters do
    indeed look very closely at efficiency in inductively coupled
    circuits. Usually they call them "tanks," and they may be resonated,
    but the coupling is still transformer-type inductive coupling (in some
    cases). And having seen how rabid some of the Tesla coil folk get, I
    would not be surprised to find that they consider efficiency. I know
    for sure they consider how to wind coils to get the biggest voltages
    for a given input power, and somewhere along that path efficiency is
    likely to creep into their thoughts.

    OK, so I've been thinking well outside your box here, and I readily
    admit it, but partly that's been in an effort to find out just what
    the box is supposed to be in this case. I don't think it's completely
    defined yet, but at least a few of the sides are in place.

  20. Of course they are real. But they are not 'real, resistive'. Please
    remember the context here is 'high school'. Transformers with
    superconducting windings are well outside the scope.
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