Someone having fun with magnets

[Mike Sulzer]

Originally Posted by David Schwab

Nice work Mike.



I'm sure it does have an effect, and also the steel poles would increase the inductance, wouldn't you think?

Probably everything that can effect the pickup, does, in some small way. Then you add those changes up and you can hear it.

That is exactly the problem. There are multiple effects from changing a material, and it is really hard to sort them all out.

[Joe Gwinn]

Originally Posted by Mike Sulzer

But for ease of understanding and discussion, it is good that we are in the low frequency limit where the magnetic and electric cases appear so separate and simple.

Actually, in the theory the distinction is between impedances. A magnetic field is low impedance (much less than 377 ohms), a radio wave is 377 ohms, and an electric field is high impedance (much larger than 377 ohms). Frequency is orthogonal to impedance, but both matter.

[Joe Gwinn]

Originally Posted by Mike Sulzer

I have code for doing this kind of thing. It is part of what I do for a living. But to do it efficiently, you want the analytic partial derivatives of the function. This is what I was referring to. Of course in this case there probably is no reason to be efficient. I am just used to doing many thousands of such fits.

Brute force, running overnight if needed. One can do without analytic partials, instead using a numerical approximation.

But is relevant to what you do with the results. At this point it is probably better to investigate how much these effects matter, rather than look for even more subtle effects in the model.

In the lab is where one gets some idea which effects are important and which can be neglected. Without this kind of practical information, modelling physical systems quickly becomes intractable.

Maybe there is. If the scatter means that each pickup has a different sound, one wants to understand even how that happens.

Yes, if it is shown that a particular kind of scatter leads to audible differences of a kind that people care about.

I am not convinced people are hearing the differences if the double blind testing has not been done.

For sure. We have had some threads on just that. And when there is a difference requiring a double-blind approach, most often the purported effect vanishes when subjectivity is excluded.

[Mike Sulzer]

Originally Posted by Joe Gwinn

In the lab is where one gets some idea which effects are important and which can be neglected. Without this kind of practical information, modelling physical systems quickly becomes intractable.

Yes, and this brings up another aspect of modeling, beyond just finding the impedance of the pickup: modeling the frequency response. The obvious way is to use the model found from the impedance and put a voltage source in series with the coil inductance.

There is something missing from this model, and it might be important in the situation discussed concerning eddy currents. The changing flux from the vibrating string induces a voltage around the pole piece. Suppose the pole piece were super-conducting, and let's neglect the leakage flux for the moment. Then we have a resistor of zero ohms appearing across the coil, and the voltage source would make an infinite current. This is not possible. The current in the pole piece induces a magnetic field that cancels the component from the vibrating string, so that there is no voltage around the pole piece.

With a finite load there should be partial cancellation. So the current in the eddy resistor (which is in parallel with the coil) should lower the pickup voltage. With the leakage inductor in series, the effect becomes frequency dependent, and so is a potential issue for determining the pickup frequency response. How does one compute the size of this effect?

[Joe Gwinn]

Originally Posted by Mike Sulzer

Yes, and this brings up another aspect of modeling, beyond just finding the impedance of the pickup: modeling the frequency response. The obvious way is to use the model found from the impedance and put a voltage source in series with the coil inductance.

OK.

There is something missing from this model, and it might be important in the situation discussed concerning eddy currents. The changing flux from the vibrating string induces a voltage around the pole piece. Suppose the pole piece were super-conducting, and let's neglect the leakage flux for the moment. Then we have a resistor of zero ohms appearing across the coil, and the voltage source would make an infinite current. This is not possible. The current in the pole piece induces a magnetic field that cancels the component from the vibrating string, so that there is no voltage around the pole piece.

That doesn't sound quite right. A superconducting slug will exclude magnetic fields. The resulting surface current is not infinite, it's exactly enough to cancel what would have been the internal field, by Lenz's Law. The effect of the zero resistance is not to yield infinite current, it's to ensure that the eddy current never decays.

A good way to keep out of trouble when dealing with actual or modelled zeros and/or infinities is to consider energy, because conservation of energy always applies. An infinite current in a loop (the surface of a slug) would generate an infinite magnetic field containing infinite energy. This may prove hard to arrange. If you succeed in getting this to work, a trip to Stockholm is assured.

By modelled I mean where one has simplified a model by setting some parameter to zero or infinity. If the simplification requires or implies that some kind of energy be infinite, look out. Nonsense results are likely.

With a finite load there should be partial cancellation. So the current in the eddy resistor (which is in parallel with the coil) should lower the pickup voltage. With the leakage inductor in series, the effect becomes frequency dependent, and so is a potential issue for determining the pickup frequency response. How does one compute the size of this effect?

I don't quite picture what you are proposing here, but I will say that one always tries lumped-element circuit models first, because the math is so much simpler. One resorts to distributed-element models only if cornered.

[Mike Sulzer]

Originally Posted by Joe Gwinn

OK.

That doesn't sound quite right. A superconducting slug will exclude magnetic fields. The resulting surface current is not infinite, it's exactly enough to cancel what would have been the internal field, by Lenz's Law. The effect of the zero resistance is not to yield infinite current, it's to ensure that the eddy current never decays.

Exactly. If one considers the model proposed in the preceding paragraph, the voltage source should cause infinite current to flow. If we consider the physics, we see that this cannot be true. Therefore, something is missing from the model.

Originally Posted by Joe Gwinn

I don't quite picture what you are proposing here, but I will say that one always tries lumped-element circuit models first, because the math is so much simpler. One resorts to distributed-element models only if cornered.

I am not proposing that we need distributed elements, but we do need something!