Mutual Inductance in Sidewinders

[fieldwrangler]

Folks -

First, my thanks to the many forum members who have helped deepen my knowledge of this craft. The generally recommended Extech meter has revealed something that seems to have eluded me in the past, which is that the mutual inductance in a conventionally polarized sidewinder seems to be negative! There's always the chance that I've mixed up some lead markings, etc.; I'll check my work again later today. (In fact, there's also a chance that Mike Sulzer may have pointed this out in some way a while back; not sure of that one either.)

However, whether I've screwed up or not this brings up a coupla interesting questions for me:

1. Do y'all think that there are sonic effects of this sort of interaction between the coils (besides the expected effect on resonant frequency of the total inductance)?

2. Would the use of separate center slugs with a bit of a gap in between (and a corresponding repositioning of magnets to allow for normal function) have an effect on this phenomenon? (I s'ppose this would also depend on what the heck I actually do with the mags.)

I'm gonna go back into The Lab and do some empirical dorking around. 'Meantime, if any of you who have a firmer grasp of these kinds of things in principle wanna enlighten us, please do!

Bob Palmieri

[Joe Gwinn]

Inductance (mutual or self) is never negative, as negative inductance would require the storage of negative energy.

The inductance of two inductors in series is Lt = L1 + L2 +/- 2 M12.

The +/- on the mutual inductance term M12 varies with how the two inductors are connected, series aiding or series opposing.

Because series aiding by definition yields the larger total inductance, + 2 M12 is correct for series aiding. If one instead uses minus, M12 will still be correct in size, but the sign will be wrong.

When measuring L1 and L2, make sure that all other coils are open circuited.

[Steve Conner]

In the case of two coupled coils (or one large coil with a 50% tap if you prefer) the total inductance will be four times the inductance from the tap to either end.

When this is plugged into one of the commonly used transformer models (I forget which) you do indeed get an equivalent circuit that contains negative mutual inductances. This is one of the few things I remember from my circuit analysis classes that was actually interesting.

On a related note, if you try to measure the inductance of a pickup above its self-resonant frequency, you may well get a negative answer.

[fieldwrangler]

Fellas -

Thanks for laying this stuff out in this form.

By the way, I've assembled this sidewinder pickup and confirmed that when connected in the usual way (two coils in series / in phase / head-to-head w/ common core) the individual coils measure about 2H and the total inductance measures about 3H.

Bob Palmieri

[Steve Conner]

That sounds quite normal. In order to cancel hum the coils have to be connected in such a way that the total inductance is less than the sum of the individual inductances.

They are in-phase as far as the signal from the strings is concerned, but out of phase as far as mutual coupling and hum pickup are concerned.

Maybe the effect isn't noticeable in regular humbuckers, but sidewinders have stronger coupling?

[fieldwrangler]

Thanks, Steve; I'll look into this more closely when I get back to The Lab tomorrow.

[fieldwrangler]

That sounds quite normal. In order to cancel hum the coils have to be connected in such a way that the total inductance is less than the sum of the individual inductances.

Gee... I never thought that was the case at all. In fact, I seem to recall normal humbuckers having a combined inductance that exceeded the sum of those of the individual coils.

In fact, here's a quote from Joe Gwinn from a coupla days ago:

"Back in November 2004 I measured the coupling between the coils of a Seymour Duncan humbucker (label said "APH1B 0758 IDT72") with side-by-side coils. At 1 KHz, the coupling coefficient K= 0.17. I've tested other humbuckers, and gotten similar values of K.

K is the mutual inductance divided by the square root of the product of the individual inductances of the two coils. One can measure K using an Extech, but it's a multi-step process.

The self inductance of each coil of the Duncan was about 2 Hy, and the inductance when they were connected in series aiding was about 4.8 Hy."

[fieldwrangler]

Also, as "Sweetfinger" pointed out...

"The sidewinder style hum cancelling P-90s I've heard have been surprisingly clean sounding for the DCR and mass of the cores."

I'm thinking that this intrinsic property of the whole-is-less-than-the-sum-of-the-parts as regards inductance is a large part of the explanation for the above observation.

Also, it could account for why there's so much wire on those EB-O pickups...

[Steve Conner]

Gee... I never thought that was the case at all. In fact, I seem to recall normal humbuckers having a combined inductance that exceeded the sum of those of the individual coils.

Maybe it only happens with sidewinders, then.

Joe never specified whether "series aiding" is the way that the pickup is supposed to be used in the guitar, though. Maybe he tested it the wrong way round.

Maybe you're testing yours the wrong way round.

[fieldwrangler]

Maybe you're testing yours the wrong way round.

I assembled the pickup and tested it for conventional in-phase operation as regards its response to string motion.

I also recall that my measurements on conventional side-by-side humbuckers agrees with Joe's in that the overall series impedance exceeds the sum of that of each of the coils added together.

So, I still don't think that hum cancellation depends on whether the overall inductance is more or less than the sum.

[Mike Sulzer]

I assembled the pickup and tested it for conventional in-phase operation as regards its response to string motion.

I also recall that my measurements on conventional side-by-side humbuckers agrees with Joe's in that the overall series impedance exceeds the sum of that of each of the coils added together.

So, I still don't think that hum cancellation depends on whether the overall inductance is more or less than the sum.

I think fw (Bob) is right. In the sidewinder flux from the vibrating string passes down and bends in each direction to pass through the two coils. Consider winding one long coil continuously and separating it into two parts. Obviously these two coils would have high positive mutual inductance since they are wound like one coil. But this would cancel the signal coming from the strings since one of the ends facing in is + and the other -. So you have to reverse one, and this makes the sign in front of the mutual inductance negative.

In a regular humbucker the two coils must have opposite electrical polarity in order to add string signals that have opposite magnetization. In side by side coils, the mutual effect happens when a field line from one coil is pointing up (for example), and then enters the other coil going down. This is reversed by the opposite polarity, and so the sign in front of the mutual inductance is positive.

[Steve Conner]

Ah, makes sense! Sorry for adding to the confusion earlier.

So, the mutual inductance is positive in regular humbuckers and negative in sidewinders.

It makes sense that a sidewinder would have more high end per turn, but the EB-0 wasn't exactly noted for its high end. It sounded somewhat like a fart at the bottom of a 200 foot well.

[fieldwrangler]

the EB-0 wasn't exactly noted for its high end. It sounded somewhat like a fart at the bottom of a 200 foot well.

Indeed; I think many of us agree that they really took it Too Far in that case.

[Joe Gwinn]

When this is plugged into one of the commonly used transformer models (I forget which) you do indeed get an equivalent circuit that contains negative mutual inductances. This is one of the few things I remember from my circuit analysis classes that was actually interesting.

I can see this happening in a transformer with a turns ratio different from 1:1, because the inductances of the windings will be different, perhaps ver different.

The mutual inductance M isn't negative (as stored energy must be positive), but M enters with a sign depending on how the transformer is connected into the circuit.

On a related note, if you try to measure the inductance of a pickup above its self-resonant frequency, you may well get a negative answer.

Because a resonant circuit above resonance appears as a capacitor, and if one fits the resulting complex impedance to a RL circuit, the inductance will surely come out negative.

[Mike Sulzer]

Ah, makes sense! Sorry for adding to the confusion earlier.

So, the mutual inductance is positive in regular humbuckers and negative in sidewinders.

It makes sense that a sidewinder would have more high end per turn, but the EB-0 wasn't exactly noted for its high end. It sounded somewhat like a fart at the bottom of a 200 foot well.

Steve,

Just to avoid confusion in the future: The mutual inductance is positive by definition. As Joe said above, this makes energy relationships work out. But the sign in front of the mutual inductance in an equation involving it and other inductances (or other impedances) can be either sign.