Hi Angel,
> I guess that microwave oven transformers designers also try to use as
> little copper as possible, because of its high price.
Yes, of course they do! This approach generally leads to rather longish
transformers (laminastion stack much taller than the with of the center
leg). Also, such transformers are more suited to low copper loss and
high iron loss - exactly what is needed for a transformer that will work
at full load whenever it's plugged in. On this topic, it's interesting
to note that a transformer with a rather square center leg tends to be
better suited for intermittent or low load, while one with a tall stack
(highly rectangular center leg) is more suited for full load.
> When I measured the curent across the primary of the microwave oven
> transformers, I increased the voltage gradually.
> From 0 to about 110 V, the curve voltage / current was straight
> (linear). But from 110 to 220V, the curve is not linear any more, it is
> definitely parabolic. Exactly as predicted:
>
>> At the same time, iron loss will be higher, also roughly to the square
>> of flux density.
This "parabolic" curve has nothing to do with the losses! It's simply a
copy of the magnetization curve of the iron. This curve tends to be
roughly linear up to about 0.8 Tesla, then it starts bending to a
flatter slope as its permeability decreases due to the increased
magnetization. The curve will eventually get essentially horizontal at
something above 2 Tesla, a level at which you are left with the
permeability of air, and thus an immense primary current!
The fact that you see the current curve starting to bend at about 110V
means that at this voltage the transformer is working at about 0.8
Tesla. So, at 220V it's working at around 1.6 Tesla - a pretty usual
figure for such transformers that are run at full load for a minute and
then switched off.
Note that the exact values, which I gave as 0.8, 1.6 and 2 Tesla, change
according to the exact steel alloy used, but these values are quite
typical.
That the losses also change roughly to the square of the flux density
and thus to the voltage, is merely incidental. To really measure the
losses, you would have to measure the real part of the primary current,
either by using a real power meter, or by measuring the magnitude and
phase angle of the current against the voltage on a scope, and
calculating the real part in the current. This can be hard and
imprecise, because the real part is usually much smaller than the
reactive part.
> If we had only de-watted current here, I guess that the current increase
> would be linear:
No. Even with lossless iron, the curve still would be nonlinear, rising
fast as the iron approaches saturation.
> voltage across an impedance means a current is
> circulating. It's the Ohm's law. So it should be linear.
Ohm's law is linear, but the impedance in this case is not constant. As
you increase the voltage, and the iron gets closer to saturation, the
impedance goes down. That's why the current increases more than
proportionally to the voltage.
> I did not leave the transformer on long enough, so I didn't notice any
> heating.
In a transformer that size, thermal stabilization will probably occur
only after two hours or so.
> So knowing all this, what I am going to try is this: two microwave ovens
> with their primaries in series. This will decrease magnetic flux. With
> both transformers about the same size, voltage should divide evenly
> between the two primaries.
> The secondaries will also be wired in series, so the total secondary
> voltage should remain around 2200 V.
That's correct. Or if you need half the voltage, you can connect the
secondaries in parallel, which would force a better sharing between the
transformers.
> These ovens are about 800 W units,
> so using 2 transformers would be just right for maximum legal power.
Big mistake! By using the transformers in this way, you will have twice
the resistance, so the voltage drop with load current will be twice as
much as that of a single transformer. On the modulation peaks you should
be able to overload the transformers by perhaps 30% or so, but running
at half voltage, this still means just about 550W from each, or slightly
over 1 kW from the pair - enough for a 700W output amp, but not for
legal limit!
The problem is that running these transformers at half their voltage is
going too far! Running them at about 170V instead of 220V should be
about optimal for amp use. But who has that line voltage...?
If they were mine, I would probably rip them apart and rewind them for
the exact specs I need! On the other hand, that isn't much economy,
because the wire can't really be re-used, and the iron is cheap. The
only sense is in actually getting a usable core, because it can be hard
to locate a source that sells transformer laminations in small quantities.
I bought material for two 10kVA transformers a few weeks ago, and the
wire was almost 70% of the total bill, with the iron being just 20%! The
remaining 10% was for insulating material, impregnating varnish, and
other odds and ends. Copper is becoming excruciatingly expensive!
Manfred.
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