1. Every wire has inductance, because it causes a magnetic field to exist circularly around it when current flows. Mother Nature said that any flowing current causes a magnetic field, and so it is. The field has a direction around the axis of the wire. Mother Nature's Rules of electromagnetic induction were discovered independently by Michael Faraday and Joseph Henry in 1831. [... Henry? Yep, that's where it comes from.] If you grasp your right hand on a wire, with your fingers wrapped around the wire and your thumb along the wire, then current in the direction your thumb is pointing makes M-field flow circularly in the direction your fingers are wrapped around the wire. This is called (oddly enough
) the Right Hand Rule
2. The inductance can be computed from the physical size and materials of the conductor. However, for the wires we would ever deal with, the variations from physical size of just the wire can be ignored.
3. When you coil a wire, the fields cancel between adjacent wires, and combine along the axis of the coil. The field strength per ampere per length of the wire becomes transformed into the inductance per turn.
4. Inductance per turn
depends on the physical setup, notably the area of the wire coil loops.
5. Inductance is proportional to the *square* of the number of turns
. Double the turns, 4x the inductance. Half the turns, 1/4 the inductance.
6. Inductance is also proportional to the material the M-field flows in. The property of space which affects inductance and M-field flow is called "permeability
". The actual units of permeability are computable, and complex, but useless for effects hackers. Instead, we can just say that a coil has an inductance of whatever it has in a vacuum (and in fact, in most other materials, notably air), but if you stick ferromagnetic materials into the coil, the inductance goes up. Ferromagnetic materials (essentially, iron, cobalt, and nickel) have a relative permeability
that can be many times that of free space. Some varieties and mixes of these three materials and a spicing of other stuff can make for permeabilities of hundreds of thousands of times more than free space. The down side of this is that ferromagnetic materials do their trick by having each atom be like a little bar magnet, and aligning with the M-field going through it. When all the bar magnets are aligned, that's all the more it can do, and the material is saturated. Each increase of current/M-field beyond that acts like the material was free space again. This is what "saturation" is.
With that as background, you can now talk about how to make a wah inductor.
The simple way is to get a bunch of wire and wind turns, measuring the resulting inductance til you get to 500mH. The only down side to that is that the number of turns and physical size is HUGE. You'll have more wire in there than would fit in a wah pedal, or bigger turns (like, a meter in diameter) which would also pick up incredible amounts of interference junk noise.
So the clever trick is to use some kind of ferromagnetic core. Iron has permeabilities on the order of 10,000 without even breaking a sweat. So an iron core reduces that coil-too-huge-to-wind down to something as small as a cube 0.5"/1.3mm on a side with a hundred turns, more or less. This is the primary of the Xicon transformer sometimes used. Another alternative is to use a ferrite core, as in most all commercial wah inductors. "Ferrite" is a composition of magnetic iron oxides, cobalt, barium, oxygen, cinnamon and coriander. (I made up that cinnamon and coriander.
) It has a modest relative permeability (maybe 3000 instead of 10,000) but corrects other flaws in iron that I haven't talked about.
Ferrite cores solve the issues of size by high permeability, and noise pickup by being physically formed so the ferrite material wraps around the coil, shielding it from external magnetic fields.
Once you get to here, you know in theory at least how to design a wah inductor. (1) Pick a physical size ferrite core; (2) look up the manufacturers' data on permeability, inductance factor Al
, and (3) compute the needed number of turns. From that, (4) calculate from the physical space inside the core what wire diameter will fit, (5) look up the wire size in a wire table and pick one small enough to get that number of turns in the space available.
When you do this, you will find that (6) it won't fit without insanely small wires (7) the cores which will give you what you want are not available in ones; ( 8 ) cores which you can get have Al
which is too small, and ( 9 ) you can't get either insanely small wire or the right core.
You then start again at (1) and iterate until you find some combination of core you can get, wire you can get, and physical/magnetic properties which give you a working inductor. This is what the poor schmuck in the basement office back at the inductor company does all day long.
To answer your question directly:
Has anyone taken wah inductors apart to discover their anatomy?
Yes. All of the people selling replacement wah inductors have, or they buy from people who have. I do know one guy who made almost a life's-calling out of finding vintage wah inductors and replicating them. He spent years on it, and is understandably reluctant to tell anyone how it was done, as he feeds his family on that information. There are others who may be more (or less) inclined to share.
I'm interested in how they achieve the inductance while keeping the resistance low in such a small package.
They use special high Al
cores which are also small. These are competing requirements, as you can appreciate. They also have access to any wire, no matter how fine. And they pay that poor schmuck to keep tinkering til he gets it right or gets fired, whichever comes first. The "poor schmuck" probably has at least a master's degree and does magnetic design 8-10 hours a day forever, so he has some experience by now. He's forgotten more than I personally know about magnetics and I used to make a living doing transformer design.
Resistance is ((rho)*l)/A, where rho is resistivity of the material, l is the length, and A is the area. In copper wire, this reduces to a resistance per foot/meter for a given wire size. Zillions of turns = high resistance because length is long. High Al
means not only fewer turns, but probably shorter length per turn because you get the same inductance in a smaller size core.
So - the resulting answer is: the use high Al
cores to get fewer turns, allowing thicker wire and hence low resistance from both shorter total length and thicker wire.
I have also wondered if maybe these inductors use a torroidal core.
Some of them are. Toroidal cores are the ne plus ultra of a magnetic core, as this completely eliminates any air gap
in the M-field path, resulting in absolutely highest Al
. Also easiest saturation, but that's not a huge factor in low-signal inductors.
I have read that the original Fasels weren't torroidal.
To the best of my knowledge, this is correct.
This is another of those issues where if it was easy, everyone would already be doing it.
That's not what you're looking for, but it's the right background information. It's where to dig.