Welcome to part 2. Let us recap the theories we are testing:
theory 1) (mostly true) – the shape gives more inductance and DCR per turn, which makes for a lower resonant frequency with a lower Q value
theory 2) (partially true) – the additional length of wire used creates a greater capacitance, which shifts the resonant frequency
theory 3) (conditionally true or false) – a wider coil senses a wider string area, which sounds warmer/fatter
In part 1, we tested theory 1 and determined that a shorted+wider coil is a more efficient shape in terms of inductance-per-turn, and less efficient in terms of DCR-per-turn, so an equal number of turns with a shorter+wider shape will result in a frequency response has a with a lower resonant frequency, as well as a flatter frequency peak (lower Q), and a lower high-frequency cutoff. This mostly validates theory 1… but it is not the complete picture. We still have to test the effects of string-sense area and capacitance, which brings us to test #2.
Test #2 – winding-Capacitance:
This batch of tests… sucked. DCR is easy:just stick a meter on it, and even inductance is slightly more complicated… run some tests with a sweep generator and do a bit of math. BUT, capacitance requires a bit of hokey-pokey and hand-wavey math (unless you have fancy-schmancy gear… which I don’t). I ended up building several jigs until I hit on one that gave (relatively) accurate results since my first jig was on a breadboard, which had too much parasitic capacitance to provide useful results. I also had to toss together a small program to do the number crunching because it got quite tedious. I also ended up running each test twice, using a different method each time. The first method was to use the known inductance, find the self-resonance of the coil, and then calculate the capacitance. The second was to resonate the coil at 2 different frequencies and do a bit of math. The results between the two methods were faiiiirly close, but the second method gave more reasonable numbers. They are still not great, but since all the coils tested were with the same jig, at least the general trends should be obvious, if not the definitive numbers.
I will try to touch briefly on all the factors that effect capacitance, but for the sake of comparing just the dimensions (as we are) I tried to isolate the coils’ winding-capacitance as best I could… no hardware, no cores, no shielding, no tape over the coils, no potting, no shielded leads, and with the pickups suspended in air or placed on a wooden slab. I could not isolate the wire from the bobbins’ dielectric constants, but I suppose that could be considered parat of the coil’s capacitance as well (unless you are going for a super-low-capacitance setup like a free-standing/bobbin-less design, or teflon/balsa coil-former or whatever). The other factors will be touched on after the main tests.
To continue with the examples from the last batch of tests (and since these are the two examples I see the most in discussions about coil shape as it related to tone), i will use the strat coil (which tested at 60pF), and the P-90 coil-only (which tested at 119pF). I did not use the mini-coils that I wound for test #1 since the capacitance was too small for me to be confidant in the results with the gear I have.
I don’t know the exact number of turns on each of these coils, but I modeled both pickups using 3 different software tools, and the results are reasonable, so I will mark the simulated parameters as “(sim)” for the physical numbers, and the parameters that were calculated with hand-math are marked “(calc)”. The p-90 is about 9000 turns, and the Strat pickup about 8000 turns. It would be convenient if the turns numbers were the same, but they are close enough for now (consequently, I planned to wind one of each to identical turns counts instead of simulating/calculating the turns… but I ran out of wire of appropriate AWG and I don’t have the cash to get another spool at the moment, so I may revisit these numbers when I get a chance to build another pair to more exacting parameters).
So for general comparison, the coils:
Strat bridge PU (coil only):
-Capacitance = 60pF
-Air inductance = 2.2H
-DCR = 6k ohms
-Turns = 8000 (sim)
-Wire length ~ 3600’ (calc)
-Wire surface area ~ 760” (calc)
-Wire layers ~ 60 (sim)
P-90 neck PU (coil only):
-Capacitance = 119pF
-Air inductance = 4.6H
-DCR = 8k ohms
-Turns = 9000 (sim)
-Wire length ~ 4550’ (calc)
-Wire surface area ~ 960” (calc)
-Wire layers ~ 110 (sim)
(To confirm the result, I also repeated these tests using single humbucker coils with fewer turns using #38 wire, as well as several smaller coils, but I will omit those since the ratios were all very similar, and I would rather stick with a single, real-world example to keep this test less wordy than the last installment.)
I am probably not qualified (or brave) enough to weigh into the debate about the mechanisms behind it (needless to day: it is not cut and dry), but if you are in the mood for a hoot do some internet searches and it won’t be long before you find mailing lists of engineers clawing each other’s eyes out over the subject of multilayer-coil capacitance… there are many competing mathematical approximations. What I CAN do is lay out sone of the practical considerations.
Firstly, I feel more comfortable calling it ‘parasitic capacitance’, or just ‘winding capacitance’ than ‘self-capacitance’ as that seems to be a bit more accurate since, in our case, it is the mutual capacitance between the pickup’s turns, formed by the differential between them, with respect to their dielectric constant, angle, and spacing, etc: the closer the individual winds, the greater the dielectric constant of the material between the winds, the closer they are to parallel, and the greater the length of the winds = the greater the capacitance. That is why scatter-winding, bank-winding, basket-weave winding, Z-winding, etc lower the winding capacitance (and inductance as well consequently).
Just like the last post, I won’t re-post all the math here (especially since it is quite contentious in terms of multi-layer, irregularly-shaped coils) but the most often used equations were just arrived at by empirical testing and curve fitting, and can be found readily online. There are also quite a few simulators out there which are pretty accurate if you get the proper data inputted, but they are out of my price range. I plan to try fast cap and fast henry in the future though.
In keeping with the traditional empirical+curve-fitting approach, I would like to work up a set of equations for various pickup shapes, but I would like more accurate gear before I would start off on that time-suck of an endeavor. But empirically, the general trend we can see from the tests that the strat coil had about 0.0075 average pF per turn, where the P-90 had about 0.0133, which is about 60% less for the strat coil so from both that data and what we know of the principles behind mutual capacitance, obviously the smaller diameter of the turns has an effect.
‘So why then’, I hear you saying, ‘did you call theory #2 partially true if there is an effect’? Well… it is a matter of the DEGREE of effect. Two reasons:
1) the shape of the coil effects the winding capacitance, which was never over 190pF or under 45pF in any sensible pickup coil I have measured, which in itself would have the effect of only a very small shift in frequency response
2) the winding capacitance is just a small portion of the sum of all the various shunt capacitances before the input stage of an amplifier, so that diminishes the effect even more
I can’t in good conscience call theory #2 false, because there IS an effect there, but it is very minor compared to the effect of inductance and even DCR. Let me illustrate:
Here are some measurements as an example of the complications:
- Pickup coil and bobbin only ~ 100pF
- with 1010 poles ~ 120pF
- with bottom magnets ~ 114pF (dropped here, or I screwed up the readings)
- with foil shield ~ 195pF
- with shielded wire lead ~ 206pF
- with cover ~ 218pF
- with potting/encapsulation ~ 253pF
Let me FURTHER complicate matters: many of the materials used in ‘vintage’ style pickups use materials that are A) particularly controlled in their relevant parameters B) quite susceptible to environmental changes. Let’s consider two pickups:
1) ‘uber-vintage’ pickup: vulcanized fiber bobbin, plain formvar enamel, un-potted, open coil with paper tape or twine, cloth pushback wire, bakelite cover.
2) ‘uber-modern’ pickup: ABS bobbin, modern poly-wire, epoxy-potted, teflon-insulated wire, sealed coil with foil shield and Kapton tape, enclosed plastic cover.
Due to the fact that the modern pickup is enclosed and thus isolated from humidity and temperature changes, it’s capacitance will be the same in a cool, low-humidity environment (like a recording studio or bedroom) as it is in a hot, sweaty, humid environment (like a summer gig at a crowded small club stage in Florida). But the vintage pickup will read entirely differently since the vintage materials and construction allow environmental changes, particularly humidity since dielectric constant of water is orders of magnitude higher than any of the materials used in the pickup, raising it’s capacitance significantly.
Here is an example. I took a vintage-style single coil and ran self-resonance sweeps at room humidity, then higher humidity, and then after being held over a steaming pot of water for a few minutes to represent the change in frequency response from moisture content. Unfortunately, it is very humid here today, so I could not get readings on a very dry vintage coil, but you can still see the general trend:
The difference is significant, relatively speaking. I re-created the response difference by adding shunt capacitance, and the change from the humidity — in this case — was the equivalent of adding 147pF to the winding-capacitance (and a big more resistance our to the heat) in the worst case scenario. Considering that the coil itself measures around 60pF under dry conditions, even if we knock the numbers down to HALF the worst case humidity scenario capacitance (the steam) and say we added around 75pF to our coil, we effectively double the capacitance, which puts us comfortably over the winding-capacitance of our short+wide coil (in it’s cool, dry state), which would essentially nullify theory #2 in certain situations.
(As an aside, while ‘vintage-recreation’ is fantastic for controlled situations, in terms of consistency of tone it may be more useful to go with a pickup with more modern construction and materials that has been voiced similarly to whatever vintage pickup you are trying to emulate… just food for thought if you are obsessive about consistency of tone.)
SO you can see how complex it can get. Ironically, calculating the capacitance of shielding, cover, potting, bobbin, etc is simpler than the coil’s winding-capacitance, but keep those figures in mind: the total capacitance, in this case, is 2.5x higher than the winding capacitance. Since our pickup’s shunt capacitances are in parallel with load shunt capacitance, we also have to add those in order to get the total frequency response (I know this ha nothing to do with winding-capacitance of coil shape, but stick with me, it will be relevant). So we have to consider everything else that will be parallel. these include possible additional shunt capacitance from:
- cable capacitance
- Miller capacitance of the amp/pedal’s input stage
- proximity to shielding in guitar cavity
- any shunt capacitance from either the amp/pedal’s wiring shield, resistor-to-board, PCB trace-to-groundplane
- from the guitar’s output jack to the cable jack
- between selector switch contacts
- mounting hardware
- from any RF noise input filter
- carbon resistor self-capacitance
- amp/pedal input emi shielding
- environmental conditions such as humidity and condensation
That can all add up to pF values in the 4-digits, which easily swamps a change of 50-70pF or so in winding capacitance. For example, 20 feet of Mogami Gold ‘low capacitance’ guitar patch wire (@ 39.7pF/foot) plus 2 Switchraft 1/4” jacks (@ 12.5pF each) = 819pF, so even JUST the cable is more than 10x our change in pickup capacitance from a tall+narrow shape to a short+wide shape… and I have measured cheap cables with capacitance-per-foot up over 100.
BUT TAKE HEART: Winding capacitance is just a small part of the overall sound. Here is a sweep of a strat coil, with another sweep overlaid where the pickup’s capacitance is doubled:
So you can see that even DOUBLING the winding-capacitance (which is a reasonable possibility) was only a shift of the resonant peak from 4.45kHz to 4.28kHz, and a change in cutoff frequency from 5.7kHz to 5.5kHz, both of which are barely noticeable… not COMPLETELY unnoticeable because people can hear a slight difference, but if you recall, doubling our inductance shifted the peak from 3.1kHz to 1.9kHz, which is a WORLD of difference compared to doubling the capacitance and going from 4.45kHz to 4.28kHz.
Compare that to this graph, which is the complete coil electrical spice model equivalent of a strat vs a p90 coil (in-circuit with full amp and cable load, not counting eddy-current loss, flux, etc) and you can see how small a difference that additional capacitance makes relative to the inductance and loading shunt capacitance:
Conclusion of TEST #2:
A shorter+wider coil with the same number of turns as a taller+narrow coil will use more wire with a wider combined surface area, resulting in higher winding-capacitance (about the equivalent of using a cable that is a few feet longer), which will SLIGHTLY lower the resonant frequency and cutoff frequency, contributing to a SLIGHTLY darker/warmer tone. This equates to about 4% change in resonant frequency (under the specific conditions of this test) compared to 39% change in frequency from the inductance test, so the change is barely significant compared to the test #1. Additionally, the change in capacitance will not really effect the Q of the peak, whereas the DCR will.
Since there are many factors effecting capacitance, it is not as cut and dry as DCR or even inductance. I will have to spin-off a separate blog about all the factors effecting winding-capacitance, but a few (of many) things to consider, just with the wire and bobbin (meaning: disregarding external shunt capacitance, cover, etc), in addition to our tall+narrow/short+wide test are:
- -dielectric constant of the wire
- -dielectric constant of the bobbin material
- -amount of surface contact between the ends of the coil and the top/bottom of the bobbin
- -which end of the wire is grounded
- -dielectric constant of potting/encapsulating material
- -degree of potting material penetration
- -whether the shape of the bobbin causes the windings to ‘flare out’ and increase the distance between turns at various points in the coil
- -winding tension combined with wire (and insulation) stretch factor, elasticity, friction coefficient
- -winding pattern and spacing
BUT, remember that the effect of all that will be fairly small compared to external shunt capacitance… it WILL have an effect though, which can be important if you are trying to duplicate an out-of-production pickup exactly, etc.
NOW onto test #3 where we look at the third theory about the effect of the shorter+wider coil windings sensing a wider area of string area. See you there!
NOTE: I plan to eventually cover all the factors that effect the capacitance of a complete pickup (wire dielectric constant, winding pattern, bobbin material, shielding, grounding, covers, etc), but it did not relate directly to the general concepts that we are exploring here, so I will leave that until a later date. I will include an appendix of some dielectric constants for reference, and I will flesh that out in a future post.
A few relevant dielectric constant values (measured between 50Hz-1kHz — I used the 60-100Hz when I could since the value decreases at higher frequencies and throws off the comparison)
(Remember that the dielectric constant of a combination/layering of materials is an average figure based on the cross-sectional area of each material)
Commonly-used guitar magnet Wire coatings (abbreviated designations vary across countries) in descending order:
- alkyd enamel/resin/varnish = 4.9 – 6.9
- solderable polyurethane /w polyamide-nylon, plain enamel (PE/PN/NT – NyTemp, Nyleze, etc) =5.7- 6.3
- Polyester-Amide-Imide (MT – Magnetemp200) = 4.6
- modified polyurethane (PU – Polysol) = 4.0
- solderable polyester(-imide) = 3.93
- Aromatic polyimide (ML – PyraML) = 3.9
- acetal polyvinyl formal /w epoxy coating (FE – coated Formel epoxy) = 3.86
- acetal polyvinyl formal (F – plain Formvar/Vinylec/Formel) = 3.72
- Vulcanized fiber = 5-7.5
- Nylon = 4-6
- Bakelite = 3.7-5.0
- Glass epoxy PC board = 5.5
- FR-4/G-10 = 4.2-4.9
- Maple wood = 4.5
- rubber = 3-4
- press-board = 4
- Delrin (acetal resin) = 3.6
- ABS = 2.5-3.3
- PVC = 3.2
- balsa wood= 1.5
- air ~ 1.0
- Epoxy = 4.0
- Bee’s Wax = 2.7-3.3
- Paraffin Wax = 2.3-2.9
NOTE: It is worth mentioning again that water has a dielectric constant of 80 at room temperature, so any of these materials that can become saturated by humidity will see their dielectric constant rise (dramatically in some cases) with humidity as the water displaces the air in the material. This can cause some interesting dilemmas, as in a potted pickup will have a higher dielectric constant (and hence higher capacitance) than an identical un-potted pickup UNLESS it is humid, in which case the un-potted pickup has the potential for it’s capacitance to rise somewhat dramatically. So measuring an un-potted pickup on your workbench may be a poor indicator of it’s parameters onstage in a hot, sweaty club. The same goes for cloth wire vs rubber wire, twine vs tape, vulcanized flatwork vs plastic flatwork, bakelite vs ABS, wood, and susceptible magnet wire coatings (like plain, uncoated Formvar for example).