# Transformer efficiency

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

1. ### DannyGuest

Hi

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

3. ### SteveGuest

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

Steve

4. ### Martin RiddleGuest

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

Cheers

5. ### Roy McCammonGuest

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. ### John WoodgateGuest

I read in sci.electronics.design 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.

8. ### Tom BruhnsGuest

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.)

Cheers,
Tom

9. ### Clifford HeathGuest

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!

Clifford.

10. ### John WoodgateGuest

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
loss'.

11. ### Roy McCammonGuest

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

12. ### Glen WalpertGuest

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. ### John WoodgateGuest

I read in sci.electronics.design 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 BruhnsGuest

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.

Cheers,
Tom

15. ### Glen WalpertGuest

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!

Regards,
Glen

16. ### John WoodgateGuest

I read in sci.electronics.design 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
billion.

17. ### John WoodgateGuest

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 McCammonGuest

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 BruhnsGuest

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.

Cheers,
Tom

20. ### John WoodgateGuest

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.