RE: The "second pig" ballast: Questions.

["Tesla list" <tesla@xxxxxxxxxx>]

Original poster: "Steve Conner" <steve.conner@xxxxxxxxxxx>

>This is the very subject Ive been trying to learn about recently and I'm a
>little confused as to what you mean by  "it impossible to make an efficient
>ballast no matter what number of turns you use".

Hi Gerry,

I found it very difficult back when I was learning too. I had to experiment
with using old transformers as ballasts to convince myself. I seem to
remember I was trying to use them as ballasts for fluorescent tubes. What I
found was that as the number of turns was decreased, they went straight from
drawing a tiny current that hardly lit the tube at all, to saturating and
destroying the tube.


>Seems
>like the flux density in the core is a function of the cross sectional
>area. the volts per turn and frequency, and not dependent on the presence
>of an airgap.  Would this be correct??

I think this is true, but only if the coil were driven from a constant
voltage source, like a transformer primary connected to the mains. The
reason is that the Faraday's law induced EMF must always be equal to the
drive voltage (if the coil is an ideal one with zero resistance) and hence
the constant voltage forces constant flux density.

In this case, as the airgap was widened, the flux density would stay
constant but the magnetizing current would go up. As the reluctance of the
magnetic path is increased, it takes more magnetomotive force to produce a
given flux density.

If you think about it, this line of thought proves the efficiency of the
airgap. Widening the airgap will not cause saturation since the flux density
stays constant. But it will decrease L, and I will increase in proportion
(since with the constant voltage drive, I=V/X_L)

But the energy storage in the core is proportional to L*I^2. If we assume
that L goes down as I goes up (so L=some constant/I) then the equation turns
out as energy storage=some constant*I.

This proves that as the airgap is widened the energy storage capability of
the core increases even though the maximum flux density stays constant.

Now taking this to its logical conclusion, you might think that the best
inductor is a completely air cored one because it would be able to store
infinite energy. But the resistance of the coil (which we ignored in this
analysis) messes things up. So it turns out that adding some iron usually
makes a more efficient coil, as it gives more inductance for a given length
of wire (and hence resistance)

As an interesting aside- Superconducting air cored coils can in fact store
colossal amounts of energy. The amounts would be infinite except there is a
critical flux density beyond which the superconductor loses its magic
properties.

Steve C.