But then I found some small tiny inductors on
Mouser.ca...
I thought I found the jackpot, but then I faced it... 3.7 kOhms for the 960 mH, 2.15 kOhm for the 370 mH. It makes sense... they are like tiny pickup coils with hair like strands of copper to compensate for their small size to get a high inductance. But that's too much series resistance to be negligible. Is the non negligible series resistance of an inductor such a problem though? Can we reduce this resistance, or rather re-use it as series resistance on the bridge pickup?
If my initial thought of the bridge pickup being so much louder that it needed both the extra resistance and the extra inductance it wouldn't have been an issue — we could just subtract the inductor's resistance from the extra resistance (and hope the result is still non-negative). As that likely isn't the situation we have, the inductor being for the middle instead, we have to do something else. Can we reduce the inductor's intrinsic series resistance? No, not really. However we can do what we've been doing all along, mirror this difference to the other pickup — add even more resistance in series with the bridge. There is a cost to pay the extra resistance on both pickups will lower the amplitude of the resonant peak, but after running a sim it's not as bad as I thought it could be — around only half a decibel, so inaudible.
Not with a fixed inductor, no. If given a choice between two equally incorrect values I'd probably pick the smaller, so as to be closer to the 'natural' sound of the pickup, less augmented.
To that end I'd also second
gckelloch's suggestion to at least temporarily try it with a blend pot, before getting out-of pocket for an inductor. Assuming a 250k 10%-log taper wired such that lugs 1 & 2 are connected between the middle & bridge hot leads 0-10k will be at around 0-30% of rotation. (In position 3 you'll be adding the resistance in series with the bridge, and position 1 adding it in series with the middle).
Returning to your question of variable inductance, looking back at
antigua's
investigation of the Q-filter note that the assembly is held together via a steel screw. With this in place the inductance is 2.18H, when removed it drops to only 630mH. This change in inductance being because we've changed the permeability of the inductor's core (replaced the high permeability steel with air). We can take advantage of this to produce a variable inductor, below is a snippet from a TDK data sheet showing the exploded view of the typical construction:
Here the purpose of the adjusting screw is not to affix the halves of the core together, rather it is to enable incremental adjustment of the permeability of the core. The majority of the screw's body is non-ferrous, whereas the upper wider section consists of a ferrite bead — therefore by adjusting it's position we alter the total amount of high permeability material contained within the centre of the inductor's core, thereby changing its inductance. Although having seen adjusting screws possessing differing grades of ferrite (presumably for differing ranges of adjustment), I've yet to see any mention of what the approximate adjustment ranges are.
I basically covered this in my previous post, but I'll answer it here too: if the voltage-to-inductance ratio of the two pickups is already equal then, yes, you wouldn't need the additional inductor.
It's mostly irrelevant, but it does save us from thinking about how the addition of series impedance would affect the tone control.
Yep, well close enough, maybe a couple of frames out.
If the Strat in question has virtually identical pickups, and we're driving the pickups via a flat frequency response (i.e. ignoring comb filtering effects from the strings), then yes to the congruence, but note that we're not quite there in terms of the overall output. Observe in the plot above that the amplitude before the resonant peak is approximately -3.8dB or 0.65 times the level of the middle pickup alone, whereas if we were combining identical pickups this would be exactly half (−6dB) — meaning that the the combined output is also louder, at approx. 1.3 times or 2.3dB. Additionally although the resonant peak of the bridge's response is shifted significantly, the peak of the combined pickups still isn't quite as high as it would be for two typical Strat pickups.
Below is a plot comparing the combined output (the sum of the above red & yellow traces) coloured in orange against the output if we had two pickups identical to the middle (plus an extra 250k of loading, representing the tone pot that would usually be present) coloured in green:
As long as you're consistently plugging into a reasonably high input impedance (and that there's space on the superswitch) we can further correct the combined SC & S90 output via the use of a bass cut. This is the third blue trace: the output though a 1nF cap and 71k5 resistor in parallel.
Pretty much. Whatever your inductor ends up being it will have some damping from its own intrinsic equivalent parallel resistance but that'll likely be quite a bit higher. Although, I am really only basing that on a couple of data points: the much larger 7.5H inductor used in the Gibson Blueshawk appears to have EPR of around 300k; and
antigua's measurement of the Q-filter puts its EPR at over 5Meg.
Yes.
I have a plan if I don't want to jack up the bridge pickup by 2.5 db (see Yogi's post for context--2.5 db louder than the middle pickup prevents me from using the inductor altogether)
Just to be perfectly clear that's an extra 2.5dB assuming it's already 6dB louder, which it may not be.
I take it that knowing the volume difference between both pickups is very important. What I could do, is first put the middle pickup at the middle pickup position on the pickguard, put it at a set height and remember that height, and then plug it into the computer to see how loud it is. Then I put the bridge pickup in the middle position spot, put it at the same height, and then record the decibel loudness levels there too.
Firstly, I'm including pickup-to-string distance within the measurement, so when placing the bridge pickup in the middle position you'd want to set it at the same height as it was when in the bridge position.
Admittedly there's likely still going to be quite a wide error margin, though it should still be more accurate since a variable has been eliminated. Of course, assuming that the effect of magnetism of middle pickup upon the strings is negligible, at the very least that should have lesser impact than disparate pickup positions, so still a net win. (And such magnetic effects should be further reduced by measuring the loudness close by to the initial attack of the note.)
+4dB & +9dB are not necessarily the minimum & maximum, just interesting special cases — that being said I do think +4dB is a reasonable absolute minimum, the maximum I'm less sure about. Above 9dB you'd be adding the inductor the bridge pickup, and worse scaling: e.g. at +12dB you'd need a 3H—4H inductor.
