Dummy Coil Calculations

[jafo]

Strats and Juniors – gotta love the tone, gotta hate the noise. I want to buck some hum without cutting the highs, which means lower inductance: fewer turns of thicker wire; I'd imagine the diameter of the coil also makes a difference. But how does one go about actually working this out? Copper is costly, calculation cheap...

I've run into quotes like "300-400 turns of 34 awg wire should do it," but how large is the coil physically? Is that on a Strat bobbin, or does it require a hole cut in my guitars? Details are always lacking.

[R.G.]

Calculating inductance for many-turn coils in other than simple circular windings gets complicated because the inductance depends on the area of the loop. The same loop of copper in a circular path has a different inductance than the loop on a circular-ended rectangular path like pickup bobbins because the areas are different. I did a quick check and didn't find any of the online calculators that did arbitrary shapes.

A quicker way to do what you are asking is doing a part copper test. Inductance for any given coil form is proportional to the number of turns squared. You might try 100 turns of copper, measure the inductance, and then calculate. Doubling the number of turns gives four times the inductance.  Or, if you can find a pickup winding something or other that tells you the approximate number of turns in a regular-type strat pickup, you could then calculate from that - well, estimate at least. Because of the N-squared nature of coils, half the turns is 1/4 the inductance, all else being equal.

You're also messing with the size of the signal. The voltage output of a pickup is linearly proportional to the number of turns. So starting from a stock strat pickup, cutting the turns in half also cuts the signal voltage in half while the inductance goes down by a factor of four. The lower the signal voltage, the more gain you need in your amplifier to get the same output at the speakers, and the more critical the amplifier's noise performance gets.

I have seen some write ups of single-turn pickups, with copper or aluminum "turns" wrapping once on the pickup bobbin. This required that the turn immediately become the primary of a step-up transformer to get enough signal voltage to run the amplifier.

[PRR]

> buck some hum without cutting the highs, which means lower inductance:

If the windings are not very similar, the hum-cancellation will be insignificant.

> Copper is costly,

A half-pound of fine copper is cheaper than a snazzy playing-out shirt or a couple 6-packs of good-name guitar strings. If you don't wear a nice shirt or change your strings, then I grant your point.

[Rob Strand]

You can calculated the inductance using one of these calculators,

https://coil32.net/

When you place ferromagnetic and non ferromagnetic metals in the field it will change the inductance from the air-core calculations.    A good example of that would be the pickup itself it has pole pieces right in the center of the coil and has surrounding metal.  For that reason the inductance will be higher than an air-core (ie. just the coil and the bobbin).

The main problem in the design of a hum cancelling coil is matching the output of the main pickup so that it does actually cancel.   The area and number of turns both affect the signal level in the dummy coil.  Signal level is proportional to area and to number of turns.   Worry about that well before you worry about inductance.

For best cancellation ideally you want two identical coils at the same point in space.  However if you think of a jazz bass it still works reasonably well when not at the same point in space.   If the coils are dramatically different you might get good cancellation on the axis of the pickups However, the cancellation will degrade off axis as the beam pattern of the pickup and dummy coil will be different and that means the signal from each coil are at different levels and won't cancel.

(Note that the axial depth of the coil is another variable.)

[R.G.]

Neat link, Rob. I didn't run into that one. The rectangular coil section might be a good approximation to the shape of a strat coil.

[Mark Hammer]

Here's a much less theory-informed view.

There are two overarching goals to be met - complete cancellation of hum, or significant reduction of hum that makes the instrument livable - that lend themselves to different methods.

Whether one directs themselves to the one goal or the other, the critical question becomes one of placement.  As is the case in any sort of anti-phase cancellation, each sensor of EMI has to sense the same amount/amplitude of EMI, in order for their opposite-phase contributions to completely cancel each other out.  In the case of stacked-coil or side-by-side dual-coil pickups, one can pretty much assure that the amount of EMI imposed on each coil will be close to identical, such that cancellation will be maximal, if not complete.  When one or more of the pickups in a dual-SC or triple-SC instrument are RWRP compared to another. one gets hum cancellation (provided the pickups are reasonably matched/balanced).  But if the objective is to supplement existing single-coil PUs with an EMI-only sensor, in order to get cancellation with any individual pickup, where do you put it?  Dummy coils act like antennae, and as most folks will know from futzing around with a radio, reception can vary with where you point the antenna or angle it.  And if I've understood it correctly, "diversity" wireless system receivers effectively track the wireless transmittera on multiple paths and select the one with the strongest signal as the musician moves around.

Alembic's approach was to stick the dummy coil exactly in between the neck and bridge pickups, ostensibly functioning like the 2nd coil of a humbucker for either pickup.  But what if you can't?  The Suhr/Ilitch backplate provided an intriguing solution by having a much larger diameter coil mounted on the backplate, such that it went almost underneath all three pickups.  The sensing of that coil was additionally balanced against what the actual pickups provided, via an adjustment circuit attached to the backplate.

Thirty years ago, I helped out a buddy with the hum in his Telecaster by wiring up a dummy coil.  I used the coil of an old Japanese pickup and installed it in the control cavity of his Tele.  It had many strikes against it.  First, VERY different number of turns and coil shape, none of which was calculated.  Second, it was nowhere near facing the EMI source at the same angle, or from the same distance or orientation as the actual pickups.  Third, I'm pretty sure the control plate provided some shielding and reduced EMI sensitivity.  But it worked.  FAR from complete cancellation, but a big enough reduction in hum, with no complaints from him about tonal change.  This is why I differentiate between the goal of complete hum cancellation, and shaving 12-15db of the existing hum level.

That is not to take a single thing away from doing a precision job of determining desired coil specifications.  But sometimes the goal really is merely "tolerable".  Besides, if you knock off even 6db from hum levels, you've made the job of any noise gate that much easier, such that you can leave the gating threshold so low that it doesn't interfere with gentle string decay.

[R.G.]

But a very practical one, Mark.

The notion that the cheapest and least-difficult dummy coil might just be a used pickup with the magnets pulled out. Good one.

[Mark Hammer]

Thanks, buddy.  I appreciate that.

Some auto repair shops, and especially dealerships, strive to render one's vehicle "as good as new".  The result will be good, but pricey.  Shops where cab and uber drivers go for repairs understand that the objective is to "get me back out on the road as quickly and cheaply as possible".  I respect those who aim for nothing but the best, but there's a whole lot of us out there who find "good enough" to be good enough.

[Rob Strand]

Neat link, Rob. I didn't run into that one. The rectangular coil section might be a good approximation to the shape of a strat coil.

Should be close enough.  These calculators are more an accurate enough, better than 10% that's for sure.

I was thinking about how to minimize the inductance,

L = ue * Ae N^2 / le  proportional to Ae N^2 / le
V = (2*pi*f dB/dt) * Ae*N  proportional to Ae N  ; for a given frequency.

Ae = coil area, le = coil length, N = turns

where we choose V = constant to match existing pickups at low frequencies.

To choose the lowest inductance we want to maximize  V/L

V/L  proportional to Ae N / (Ae N^2 / le) = le / N

Which means choosing a small number of turns.
Since V = constant that means we need larger area.

That conclusion makes sense since  L is proportional to Ae N^2, N has more effect
on the inductance so for low inductance we need to make N small.

We can also make te coil deeper (large le) since that doesn't affect the the pickup *an axis* pickup sensitivity.
However, like I mentioned before if the geometry of the dummy coil differs to much from the
main coil it might not cancel off axis.   I have a feeling a long solenoid act different to a pickup - not to mention it not being practical to put in a guitar  .

[amptramp]

Usually the humbucking coil is in series with the pickup but I have heard of humbucking coils in parallel with the pickup.  Series connection favours low frequencies and is used at the neck where the low frequencies are strongest whereas parallel connection favours high frequencies and gets used at the bridge where treble dominates.  Does anyone do a series-parallel pickup that is more broadband and sounds more like the pickup coil with no humbucking at all?