Driving LEDs with a battery pack

Well, I just posted some thoughts and a web site with some nifty equations and addressing itself to the idea that energy is mostly stored in the gaps.. not in the mass of the core, itself. See if it makes any sense.

Jon

So the iron is just shaping/directing the field?

(And holding the wires in place)

Maybe reluctance is what you're looking for?

On Sun, 19 Jul 2009 05:14:10 -0700 (PDT), fungus wrote:

It provides the shorter path, the one taking less energy, so yes. That's kind of the way I like to look at it. Everything in nature appears to choose the path of least energy change. A soap bubble instantly takes up the shape that requires the least energy, regardless of any nearby structures it also clings to. Things like that. So the iron just presents a very low energy path for the field, mostly as I see it because each atom easily aligns if tweaked just a little by the field and provides a near-zero-energy-hop to help the field bridge over all that space it otherwise would need to get through.

The other aspect is that there are an infinite number of 'closed magnetic bubble surfaces', none of which may cross through each other. Each 'surface' is 'looking' for the lowest energy circuit through space, but cannot cross through any other surface. So they 'bunch up' a lot in the iron, which is the way-easy path, but stack. This is why we can usually ignore the air around the core, as almost all of the magnetic bubbles will be found crowded up in the iron core. They pinch together a whole lot and stay nearby, that way. Eventually, enough bubble surface density occurs that the 'lowest energy' path starts to include a little of the space around the iron instead of entirely within in. But for all intents and purposes, we can imagine that all of the magnetic field stays in the iron core because that is far and away the lowest energy pathway for almost every magnetic bubble surface.

These easy paths are easy, though, because the atoms provide free hops. Which means that the effective path length through space (where energy is actually stored) is much shorter. This 'shortness' is what the mu_r measures. The way I see this is that if you have a core material with a typical permeability of 5000, then that means that the vacuum portion in the typical lowest energy pathway through any specific length of it is 5000 times shorter than what you'd measure with a tape measure. Or, if you have 5 inches of the material, then the iron atoms in it provide (5/5000) or 1/1000th of an inch of vacuum that the magnetic field must cross over by force, with 4+999/1000ths inches of free hops across iron atoms. This is why I spoke earlier about my imagination regarding why very high permeability materials tend to also be conductive, as well. On the other hand, there are low perm materials (typically in the low hundreds, so let's use a figure of 250) where you'd get (5/250) or 1/50th of an inch of vacuum and 4+

Another aspect in these iron cores is eddy currents. These are kind of like "electron dogs chasing their tails." Any current flow through the coil induces a magnetic field. But then this magnetic field permeates the area around it (and especially through the iron core because of the easy pathway there.) But just as electron motion sets up a magnetic field, it's also true that any magnetic motion also sets up an electric field. And if there are electrons available in the conduction band (electrons that belong to atoms but where they are just barely attached to the atoms, unlike valence electrons which are firmly held) of atoms where such electric field potentials are set up, they start moving away from the negative potential end and towards the more positive potential, if they can. Iron has lots of electrons in the conduction band, so those electrons want to start moving. If all there is _is_ more iron, then they can move and they do. With very low rates of change in the magnetic field, the electric potentials that are set up are very small and so the electrons do not accelerate very fast and they also have a lot of time to move, as well. All this just means that not very much energy is wasted moving them around (work is force times distance and although they have time to travel some distance there, the force is very very small and the total work is tiny.) When the current through the coil oscillates back and forth fast enough, though, a very strong electric field is also set up and the electrons accelerate quickly. Of course, the field changes quickly, too, and reverses their motion soon after. So the electrons start running around in tiny circles (they'd collide too much if they went in straight lines back and forth, so to avoid that effect they quickly arrange themselves in 'traffic' loops.) That is, if there is a free conduction path for them to do so. If you powder up the iron enough, into bits that are even smaller than the natural loops these electrons would form into, and bind them back together with something that isn't conductive at all, then despite the strong electric field they cannot really move very far. They still move, but then they run up against a barrier and sit and wait for the field to change and go the other way in their tiny little cage. This greatly shortens the net distance they can travel in and despite the strong force their travel distance is forced to be smaller than they'd otherwise do. So the net force times distance shrinks down and the wasted energy in the core is less.

I suppose an optimal core for eddy currents (higher frequencies in the magnetic field induce higher electric potential forces) might set an iron atom forced somehow to be isolated by enough distance that the electrons wouldn't travel across the gap for any particular electric potential (this means separating them further and further apart for higher and higher frequencies.) [Note: This gap might be created by the use of atoms that won't conduct, though their very presence would probably mean more distance is required between the iron atoms.] However, this increasing gap distance would require the magnetic field to place energy in it to hop across, so the iron atoms would represent less and less of a free hop as a net percent of the total distance and eventually you'd be almost as well off with just a vacuum in terms of total size of your inductor.

Getting back to equation (1) and equation (2):

(1) L = mu_0 * mu_r * N^2 * A_e / l_e (2) L = mu_0 * N^2 * A_e / l_e

Let's assume that all the energy goes into the vacuum, only. We measure, at our macro scale with a tape measure, a loop length (l_e) of 1 and a cross section area (A_e) of 1 and use N=1. But there are two such inductors. One with a true vacuum only, one with an iron core of permeability mu_r=5000. If we used equation (2) on our air core, we get the right figure. But if we used equation (2) on our iron core, we don't because actually all those iron atoms are occupying most of the l_e that we had measured. In fact, 4999/5000ths of it. So the effective l_e that we should have used would have been

Does that make sense?

Jon

What makes you think I'm looking for anything?

Ed

No. The energy is stored in the magnetic field around the wire.

Air has nothing to do with it - the only reason we've used the word air is to differentiate between transformers that are made by wrapping wire around some kind of magnetic material like iron versus those that are not. The latter are commonly called "air core" or "air wound". And sometimes, when you're trying to wind them and the wire won't cooperate, they're called things not suitable for public consumption. :-)

Ed

I suppose that's a fairly accurate picture in the case of something like ferrite or powdered iron, where you have grains of ferromagnetic material separated by something else.

However, I'd hesitate to believe in it too literally as a description of what's physically going on inside solid iron. On the atomic scale, the distinction between "vacuum" and "non-vacuum" is rather unclear. If you consider mass distribution within the atom, then the iron is almost *all* vacuum, even when the atoms are right next to each other.

Another way to look at it is that the magnetic field represents a certain amount of energy per unit volume, but the relevant field is the H field, not the B field. That's because the H field is the only part that's actually generated by the current in the wire. The rest of the B field comes "for free" courtesy of the permanent magnetism of the iron atoms, and as we all know, there ain't no such thing as a free lunch.

The ratio between the B and H fields is the relative permeability of the material, which is just a way of summarising all the complicated interactions going on between the H field and the iron atoms resulting in a certain total field.

And if humans had evolved to live in space rather than an atmosphere, we would probably have called them "vacuum core", with little observable difference in their properties.

While we're on the subject of transformers, there's something that's been bothering me about ordinary (non-flyback) transformers.

Consider an unloaded transformer. We apply an AC voltage to the primary, and a small magnetising current flows, just enough to induce an emf that balances out the primary voltage, and also induces a voltage in the secondary.

Now attach a substantial load to the secondary. The secondary voltage causes a current to flow in the secondary winding. At the same time, a corresponding current flows in the primary winding. The extra magnetic fields from these two currents mostly cancel out (the better the transformer, the closer they come to doing so exactly), leaving just the small magnetising flux to continue producing the secondary voltage.

So the flux in the core is pretty much the same as it was with no load. But now a substantial amount of power is being transmitted from the primary to the secondary.

So there must be *something* different about the state of either the core or the surrounding space between the loaded and non-loaded conditions. But what is it?

The secondary voltage is a little less per turn than the EMF, and the primary voltage is a little more per turn than the EMF. The difference overcomes wire resistance (and any leakage inductance's impedance) to the extent that results in the amount of current in question flowing through the turns of wire.

- Don Klipstein ( snipped-for-privacy@misty.com)

Not at all. I'm familiar with measurements in terms of Barns -- it's an atomic cross-section figure; an abstraction expressing interaction likelihoods. I imagine (or choose to imagine here) a similar idea relative to the passing of a magnetic field loop through space and atoms. For purposes of the iron atom and magnetic field loops (bubble surfaces) passing through them there is some 'size' that I like to consider the permeability figure as an abstraction expressing that.

In any case, it doesn't appear to be inconsistent with the equations.

This doesn't refute what I wrote, though.

I am only just studying the material. As I wrote earlier, all this began for me only a handful of weeks ago, now. So yes, I may yet find a reason to modify the mental model. But so far, it helps me better than other abstractions do.

Jon

This appears to cover it nicely for me:

Jon

I should have added that here I imagine that the mu_r permeability factor merely represents a measured parameter, very much like a cross section in Barns. The cross-section figure isn't fixed for a given atom or particle. It varies quite widely over various energies, too. Although it isn't how things actually work at the quantum level of detail, it remains a very useful concept for practical work. I'm suggesting a similar analog with permeability.

For example, natural Uranium is 0.7% U235 with the rest being U238. The cross section of U235 for thermal energy neutrons is 580 Barns. The cross section of U238 for the same neutrons is effectively 0. So the fission cross section of natural uranium is calculated to be:

Now this doesn't mean, in any way, that the atomic diameters (as measured by different means than slow neutrons) will be the same. It just means this is a useful fiction that allows one to imagine well and also calculate effective values.

I like to imagine permeability in a similar light. The 'cross section' or 'size' from the point of view of the penetrating magnetic field does not in any way have to be related to the size of the atom as measured by other means. Does that make sense?

Jon

Yes, that makes sense.