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Re: The "second pig" ballast: Questions.

Original poster: "Gerald  Reynolds" <gerryreynolds@xxxxxxxxxxxxx>

Hi Steve,

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

>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.

This is exactly my point when we analyse the ballast limiting current with the pig shorted so the ballast sees the entire line voltage.



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.

Certainly as the gap is added, the current goes up at the same rate as the inductance goes down and I^2 wins out so the energy storage goes up. I'm not sure how you are defining efficiency here but I think of it in the context of power and the power loss in the core is due to the hysterisis of the BH curve (no hysterisis in the gap so no power loss in the gap). As one adds the gap, the power loss in the core (I think) remains constant but now at larger currents. So, yes, the power efficiency would improve relative to the VA of the system.


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.


Yes, isn't that a shame!!  Superconductors saturate too.

Thankyou Steve for your replies. I feel I have a better understanding now and can go and design my ballast :-))

Gerry R.