Guessing inductance from DC R, wire gauge and pickup type

[antigua]

Out of curiosity, I wanted to see how closely inductance correlates with DC resistance for a given pickup type and wire gauge.

I found an average ratio of inductance over DC resistance for a many of the pickups I've measured so far. So if the ratio is 0.44, there was 0.44 henries for every 1k ohms of DC resistance. 

For some combinations I have very few data points, but for others I have a healthy number:

Strat 42 AWG (Fender style only)
0.40
0.38
0.39
0.44
0.42
0.44
0.38
0.36
0.41
0.44
0.44

Strat 43 AWG (Fender style only)
0.35
0.374

PAF 42 AWG
0.61
0.57
0.60
0.56
0.60
0.63
0.58

PAF 43 AWG
0.53

Tele Bridge 42 AWG (Fender style only)
0.52
0.55
0.54
0.47
0.40
0.42
0.38

Tele Bridge 43 AWG  (Fender style only)
(Twisted Tele, Texas Special)
0.35
0.38

Tele Neck 42 AWG (Fender style only)
(Twisted Tele)
0.34

Tele Neck 43 AWG (Fender style only)
0.31
0.30
0.30
0.27
0.27
0.31
0.34
0.27


It appears that these inductance values have a rather wide standard deviation, so that suggests this might not be real accurate, but perhaps it might work better for a given pickup manufacturer. Lollar, Tonerider and sometimes Fender offer inductance values for their pickups, so there are a few sources of raw data out there to be worked with. 

I created a quick and dirty javascript to perform the calculations, and the configuration contains the average ratios:

strat: {
  42: 0.41,
  43: 0.36
},


paf: {
  42: 0.59,
  43: 0.53
},

tele_bridge: {
  42: 0.59,
  43: 0.365
},

tele_neck: {
  42: 0.34,
  43: 0.296
}


jsfiddle.net/thanaton3mix/99zgrt73/6/



This script can be manipulated by anybody, so this could serve as a handy platform for testing out other data sets, or adding additional parameters. 

[antigua]

I believe a part of the reason there is a disparity in the numbers above is because when these pickups are wound with a higher tension, they stretch out, and so the DC resistance rises over what it would have been otherwise. 

If anyone has the time or resources and a pickup winder, what we really need to study is how inductance and DC resistance change depending upon wind tension. Say you wind to coils with 7000 turns of 42 AWG, you'd wind one really loose, and the other really tight, and perhaps make two of each, just to make sure the two of a given type show similar values. Then see how the inductance and resistance differs depending on tighter versus looser wind. The extent to which tension effects both is unknown, but it appears to me that it the DC resistance can increase by at least 200 ohms, and the inductance by 200mH, through higher tension alone. 

Taking it further, the resonant peak will almost certainly be lower for the tighter wind, as the closer winds will have a higher capacitance. This is almost too obvious to bother proving, and the degree of spread has been observed over various single coil pickups, but would be good to document this, for the record. 

It would be valuable to establish that this happens at all, as in the pickup winding community there doesn't seem to be any acknowledgement of how wind tension effects the LCR values of a pickup, so this would be good basic information to have. 

[JohnH]

The dcr vs inductance corellation is interesting, particularly how it varies between pickup types.

But the theory may suggest that as turns and so dcr increases, inductance may increase at a greater % rate, ie, even for similar pickups, the ratio may not be constant.

If this is true, it would be due to extra mutual inductance eg if two similar coils are phyically apart but conected in series, we'd expect 2x dcr and 2x inductance. But if the same total wire was made into one combined coil, we would have 2x dcr but probably more than 2x inductance.

It would be interesting, for the types with a good number of tests, to plot as points on a graph of dcr vs inductance. They may tend to fall more consistently closer to a curve than to a straight line.

[antigua]

That's a good point, though I didn't notice a correlation between the ratios and the ranges of DC resistances, so the non linearity you mention is a factor in the deviation, but unlikely to be the decisive factor. At a later point I'll try reworking this with the values supplied by lollar and Tonerider to see how well it predicts their own pickups.

The calculation probably has to look more like this www.66pacific.com/calculators/coil_calc.aspx :

with DC resistance standing in for turns, and the other values being fixed numbers based on the particular pickup. 

[reTrEaD]

" with DC resistance standing in for turns "

It sorta does. At least more so than it would on a round bobbin. On a round bobbin of small diameter compared to the "thickness" of the wind, the later windings would be much longer than the early winds. In the case of a guitar pickup bobbin, the later winds are only slightly longer than the early winds.

I reckon the SSL-4 you previously evaluated might be worth a closer look? Almost twice the DCR when the full winding is compared to the tapped portion. And you don't add in variables by having different magnets/polepieces/baseplates, etc.

[antigua]

I just discovered for myself that the DiMarzio humbuckers have ferrous slugs buried into their plastic bobbins, which augments the inductance by variable amounts, depending on what and how much metal they stick in there. I just updated this review to discuss the matter a little more guitarnuts2.proboards.com/thread/7765/dimarzio-paf-master-analysis-review 

The embedded slugs, coupled with their patented technique of using different gauges of wire for the two bobbins (which has no technical benefit whatsoever) has two effects 

a) it means their humbuckers can't be guestimated using a technique that assumes they are typical PAF for factors.

b) it makes their pickups harder for Chinese companies to analyze and clone, or at least DiMarzio can legitimately claim that as a selling point, if they wanted to. 

[JohnH]

One series that demonstrates a  steadily increasing ratio of L to R is from a Fender CS69 through to the more overwound but otherwise similar Texas Specials for Strats.

Inductance/resistance


CS69
2.174÷5.36
=0.406

Texas Special - Neck
2.578÷6.12
=0.421

Texas Special -Middle
 2.803÷6.31
=0.444

Texas Special - Bridge
3.171÷6.79
=0.467

[antigua]

That suggests the method might work well for a given manufacturer, at least. I suspect it would also be more reliable the more simplistic the pickup design is. 

[antigua]

Oct 10, 2016 10:35:03 GMT -5 reTrEaD said:

I reckon the SSL-4 you previously evaluated might be worth a closer look? Almost twice the DCR when the full winding is compared to the tapped portion. And you don't add in variables by having different magnets/polepieces/baseplates, etc.

That's a good point. I have some SSL-5's in a guitar that I haven't had time to remove yet that would be even better, as they used a typical Strat style bobbin and pole pieces. 

I had discovered that that SSL-4's outer coil capacitively couples with the inner coil, to the tune of 500 to 600pF, and it's near impossible to fix because the tapped leads that exist the coils are so short, so I'm reluctant to use tapped Seymour Duncans for testing concepts. The also explains why the tapped inner coil is such a low DC resistance, it has to have a low inductance in order to offset the very high capacitance.