Why does ^ reluctance ^ RAC?

[marku52]

I build humbuckers in an unusual configuration. Instead of a single magnet with slugs/screws on either side to complete the magnetic circuit, these have 2 magnets/bobbins that are joined magnetically by a steel baseplate. I wax pot the bobbins/baseplates as an assembly. This is tested for electrical parameters, then the can is soldered onto the baseplate. On retest, one unit had lost about .1H of L, about .2 units of Q, and RAC was up by about 1kohm over expected. What I believe happened was that one or both of the magnets had "floated" off the baseplate during canning/soldering, putting an air gap in the magnetic circuit. I'm pretty sure that *was* what happened, because when I resoldered the can/baseplate, and forced the can down farther than it had been previously, I gained back almost all that had been lost (I always lose a little Q and L from the can).

The images show what the pulse response and numbers looked like. I test Fres using a 10V p-p pulse gen, with 250K series R to mimic the actual R loading the pickup will see in the bass. You can see in image 1 that the response is over damped to the point of not even being able to measure a ring frequency. In the second, the undamped response is back (it looks like all its brothers), and the numbers come out correct.

So the question: I understand that introducing an air gap will reduce the inductance b/c reluctance in the magnetic path is increased. Lower L will reduce XsubL, so that Q drops b/c the resistive portion won't have changed.

Why does measured RAC increase? It is the sum of wire resistance, eddy current losses in the can and magnets and baseplate, and ??????
It doesn't seem that an air gap in the magnetic circuit should affect RAC. But it did, raising it by about 1kohm.

All number measurements done with an extech at 1kHz. And BTW, this pickup (before it was fixed) sounded a little weaker than it should in the test bass. Nothing really dramatic though. Made me feel good that the electrical Q/A was picking up things that were not strongly audible.

[Joe Gwinn]

I don't visualize your design. A diagram and photo would help.

In general, the excess of Rac over Rdc is proportional to eddy current loading. Eddy currents flow to some degree in all nearby pieces of metal.

[big_teee]

It sounds like a full size Humbucker made like a Firebird Mini.
T

[Mike Sulzer]

I don't visualize your design. A diagram and photo would help.

In general, the excess of Rac over Rdc is proportional to eddy current loading. Eddy currents flow to some degree in all nearby pieces of metal.

Then something is wrong. Pulling the magnet off the metal reduces the flux through the metal base plate and the other magnet.

What could it be?

[kg]

since we're talking about non-perfect core materials, depending on where on the "curve" the operating point is, a reduction in flux may either INCREASE or DECREASE inductance.

certainly adding an air gap will reduce overall permeability (increase reluctance)... but it ALSO linearizes that permeability.

since the ferromagnetic core BH characteristic is curved, this "flattening" effect may increase the BH slope at some points, and decrease it at others.

this image from wiki may help:



notice how permeability initially rises with flux (H), then falls. key point: with any non-air core inductor, perm is NOT highest at zero H.

your test for inductance itself (which showed a small drop) may not have shown this due to the level of flux compared to the RAC test (which showed a small rise).

[Mike Sulzer]

since we're talking about non-perfect core materials, depending on where on the "curve" the operating point is, a reduction in flux may either INCREASE or DECREASE inductance.

certainly adding an air gap will reduce overall permeability (increase reluctance)... but it ALSO linearizes that permeability.

You are not saturating or nearly saturating the material.

A pickup always has a huge air gap, at the top, the part that is close to the strings. Yo are not adding an air gap by detaching the magnets from the steel base plate. You are just making an existing huge gap a bit bigger.

[marku52]

Hi, sorry for the delay in getting a picture up. The pickup is sitting on a roll of solder. Each bobbin has its own bar magnet, and their flux is coupled at the bottom through a .030 thick steel baseplate.

I'm kind of glad that no one has posted an obvious answer to my conundrum. Here is my own best guess: introducing a small air gap between the bottom of a magnet and the steel plate changes the flux flow paths in the steel plate, and this (in some fashion I'm having some difficulty in visualizing), increases the eddy current losses in the baseplate.

And it is this increase in eddy losses that shows up in the RAC measurement. Of course, it is also possible that there is some error in the RAC measurement by the Extech that this particular test shows up. All the other stuff (decrease in L causes a corresponding decrease in Q b/c the R losses are held roughly constant) seems to hang together on its own.

Thanks for the comments.

[Mike Sulzer]

Of course, it is also possible that there is some error in the RAC measurement by the Extech that this particular test shows up. All the other stuff (decrease in L causes a corresponding decrease in Q b/c the R losses are held roughly constant) seems to hang together on its own.

Thanks for the comments.[ATTACH=CONFIG]15017[/ATTACH][ATTACH=CONFIG]15018[/ATTACH]

That's right. The Extech works by measuring the complex impedance R + jX. In the series mode, R is interpreted as Rac. That is what you use because you do indeed have a coil with a series resistance. However, the load caused by currents in nearby pieces of metal is in parallel. The simplest that can be is an R and L in series. The size of the L is related to how much of the flux does not go through the metal. So when you detach the megnet from the base plate, you increase the size of that L. The R is series is significant and the effect on R +jX is complicated. You can figure out what it does if you really want to. The Extech is not intended to handle this situation; it just does what it does.

[marku52]

"The Extech is not intended to handle this situation; it just does what it does. "

That explanation makes a lot of sense, thanks! Poor machine is trying to model a complex series-parallel network as just R + jX, with the occasional odd result.

[kg]

You are not saturating or nearly saturating the material.

huh? i never mentioned saturation, so this statement confuses me.

A pickup always has a huge air gap, at the top, the part that is close to the strings. Yo are not adding an air gap by detaching the magnets from the steel base plate. You are just making an existing huge gap a bit bigger.

are we arguing semantics?

[Mike Sulzer]

huh? i never mentioned saturation, so this statement confuses me.



are we arguing semantics?

You wrote previously: "...key point: with any non-air core inductor, perm is NOT highest at zero H". Are you sure that this is always true? True for typical materials used in pickups?

This data (steel_bh.zip):


File: steel1008_permag.dat
* Field Precision, Albuquerque NM
* Field Precision LLC: Finite-element Software for Electromagnetics
* Table extension using Bs = 2.10 tesla
*
* Converted quantities
* B0 (tesla) B (tesla)
* =============================
* 0.000000 0.000000
* 0.000817 1.000000
* 0.001382 1.200000
* 0.002262 1.400000
* 0.003116 1.500000
* 0.004549 1.600000
* 0.005781 1.650000
* 0.007351 1.700000
* 0.009299 1.750000
* 0.011750 1.800000
* 0.014828 1.850000
* 0.018812 1.900000
* 0.023876 1.950000
* 0.030373 2.000000
* 0.038780 2.050000
* 0.050002 2.100000
* 0.115007 2.200000
* 0.209984 2.300000
* 0.299959 2.400000
* 0.399988 2.500000
* 0.849989 2.850000

* Data values
* B (tesla) MuR
* ============================
0.000000 1486.691188
1.000000 1224.268853
1.200000 868.117914
1.400000 618.935920
1.500000 481.315376
1.600000 351.723648
1.650000 285.440945
1.700000 231.250783
1.750000 188.189976
1.800000 153.197279
1.850000 124.761296
1.900000 101.000136
1.950000 81.671620
2.000000 65.848139
2.050000 52.862548
2.100000 41.998668
2.200000 19.129201
2.300000 10.953213
2.400000 8.001087
2.500000 6.250194
2.850000 3.352984
* Extension
3.00000 3.33333
4.00000 2.10526
5.00000 1.72414
10.00000 1.26582
20.00000 1.11732
ENDFILE


would seem to indicate otherwise. It looks like permeability decreases towards saturation without dips in the middle.

If we already have a circuit with a large air gap, I do not expect an additional small gap to have much effect.

Remember also that very large values of permeability do not do much over moderate values when you have a large gap. Changing the permeability from 1000 to 100 is not a huge effect.

[kg]

i will find out if all non-air core materials exhibit this effect... already sent an email out...

[CRU JONES]

Here is my theory:

the bladed humbucker is a very efficient design in that it contains it's magnetic flux much more than the standard PAF style design. Could it be that all of a sudden with the air gap, the magnetic flux path is no longer tightly coupled and is directed, increasingly through the baseplate as leakage flux? The rise in Rac is then from eddy currents. You could test this by measuring Gauss levels on the Bottom of your pickup.

That is a cool pickup, Marku52!

Cheers,
Ethan

[marku52]

I was trying to visualize the change in flux paths through the base plate with, and without an air gap, and not having a lot of luck. I suppose, if I had all the time in the world, I could sim it in FEMM and get some idea, but that "time" thing is a bit of a problem.

Are you suspecting that the measured flux below the baseplate would increase because of the air gap? Can you explain further?

[CRU JONES]

I was trying to visualize the change in flux paths through the base plate with, and without an air gap, and not having a lot of luck. I suppose, if I had all the time in the world, I could sim it in FEMM and get some idea, but that "time" thing is a bit of a problem.

Are you suspecting that the measured flux below the baseplate would increase because of the air gap? Can you explain further?

FEMM! You and I both need to learn how to use it!

Leakage flux/ eddy currents was just an idea i was throwing out, really. As far as measuring increased flux below; I reconsider and think you will NOT measure increased field strength below the plate. I was imagining a steel plate between your magnets and that the plate we all see was a further base plate below your magnetic circuit. Now, I realize the base plate IS your .030" steel plate. Furthermore, I was imagining the air gap to be at 90 degrees of what it actually is. Still... It is a possibility of increased eddy losses due to the air gap as I will try to explain at the end... But first, I think the permeability curve of your plate may be most promising or maybe just more interesting.


Permeability:
Is it possible that your .030" steel plate is being SATURATED? Magnetic saturation is simply when the material cannot have any more flux going through it. A thin sheet of steel cannot hold as much flux as a thick sheet. Once the magnet is lifted off, permeability goes up increasing inductance and thus reducing the Q at resonance.

The other possibility is the 10 Vp-p impulse signal may provide enough of a coercive force to change the perceived readings if, for instance, the steel plate retains any REMNANT MAGNETIZATION. i.e. the impulse charges the steel plate and the plate is magnetized for any portion or the entirety of your reading. So possibly that. Neither Mike Sulzer or Ken Gilbert are putting forth that the plate is saturated. And that may be, those guys are smart and may have experience to have a good idea if the flux through .030" steel could be saturated by the field strength of your magnets. What are your magnets/ field strength by the way? I am interested in what they may have to say about the non-linear slope that permeability has... But since we haven't heard from them yet ;-), I am putting it forth that your base plate COULD be saturated.

I will also put forth, and support what Ken Gilbert was saying, that possibly your steel plate is no where near to saturation and is in the region of the B-H curve where the coercive force is near zero and the slope of permeability is still low. the graph of permeability for many metals has two knees (non-linear) one at near zero and one at near saturation... At least the high grade stuff I buy for transformers does... Oh wait, I don't buy the high grade stuff... I recycle the " who knows what grade stuff". But the B-H curves I derive show low permeabilty at near zero coercive force and at near saturation. So... Your plate could be at the edge of either of these "knees" and an air gap could put your working point on a new slope of permeability. I think it is possible.

Flux paths:

If you just look at the two magnets, the flux will flow form North pole to South pole by path of LEAST RELUCTANCE and path of LEAST DISTANCE. The flux path will travel from North pole to either its own South pole or the South pole of the other magnet. Without the plate; the flux will travel to the closest South pole. With the steel plate; the flux will travel the path of least reluctance (greatest permeability). Leakage flux is defined as any flux that doesn't travel in a straight line across your air gap. Since, in your case, the the air gap is created at a right angle to your poles... Maybe it's all leakage flux? Possibly the field pattern is now following the path of LEAST Distance and is returning to its own South pole. So now, instead of flux running the length in the same direction of the plate of steel, flux is now entering the plate increasingly perpendicularly. Thus creating eddy currents at right angles to the flux lines. As noted above, I was imagining your magnetic circuit incorrectly, so this possibility is less exciting to me.

I do think what you are observing is quite intriguing! Thank you for sharing it! I do hope Mike and KG chime in again as both have very interesting ideas and definitely a great understanding of this stuff.

take care,
Ethan