Brain Scan for Series Pickups???

[ashcatlt]

Is there an easy way to determine the values of 2 pickups and a master volume via the "Brain Scan through a Nostril" method when the switch options are: B, B>N, N?

Let's assume (for reasons detailed over here, for example) that we can't or won't determine the Rmax as detailed in Discerning LP-Type Resistances.

I'd be perfectly happy with a hint or two which might simplify the algebra.

[ChrisK]

The LP method is crucial since it gives two discrete measurements of a function using the same variables of known variation.

Without this variation, one ends up with simultaneous equations of dissimilar variables with only one measurement of each, and none with the exact same variable set.

From the other "ugly" thread;

While I'm turning the pot it reads one thing, occasionally going OL. When I stop turning it, it seems to settle toward a value, but I can never reproduce this value.

Hmmm, ya know, it seems like there may be some capacitive filtering afoot here.

Is the tone control all the way up/off so that the resistance thereof is at its largest?

Does it settle faster if it's at its full on/lower value (take the tone pot resistance out of its maximum reading settling effect)?


I started to run the algebra last night, but my SLU (symbolic logic unit) had already powered down for the night.

The maths are a bit onerous and grow quickly during expansion. Especially at 4 am. Simultaneous linear equations are middle school algebra, simultaneous non-linear ones are not so simple.

I was in no condition to fire up Maple or MathCAD (both of which contain symbolic algebra engines - no numbers required until desired), so cheating was out of the question.


I took another tack and started an iterative interpolating spreadsheet with some seed values. I started with a pickup of 5,000 Ohms and one of 10,000 Ohms, and a volume pot of 500,000 Ohms.

I calculated the measured values of the volume pot in parallel with one pickup, the other pickup, and both in series.

Using these "measured" values I used a differential ratio-metric averaging procedure that after one complete pass came up with 5,002.xxx and 10,011.xxx Ohms for the pickups and around 430,000 and 480,000 Ohms for the volume pot.

This is pretty dang close. These coil values are likely more resolute that one can read with a 3 1/2 digit multi-meter. They are certainly more accurate.

This is why I suggest the use of a multi-meter with enough digits of resolution such that one can use the same resistance range for all measurements. The different ranges are realized with scaling resistors (voltage divider) in the meter, and these are at best +/- 0.1% in accuracy. By using different ranges to gain resolution, one induces a variation of +/- 0.2% or worse in inter-range accuracy.

Using the same range will still be within the meter's absolute (in)accuracy, but at least all readings will be at the same level of ratio-metric accuracy.

If you want to get all of the digits of resolution, for most examples of paralleled pots and coils, you need a 20,000 to 40,000 count meter (4 1/2 to 4 3/4 digit). I use a 6 1/2 digit one of no small cost.


As in the above example, while I got very rapidly very close to the actual coil values, the volume pot values were low. But, so what.

As a bit of insight I tested (in math) the premise that the volume pot resistance span could be ratio-metrically applied to each pickup as a function of its ratio of the total series resistance.

For my test case pickups, I assigned 166,666 Ohms to the 5,000 Ohm coil and 333,333 Ohms to the 10,000 Ohm coil.

As suspected, the parallel values calculated were virtually identical to the "measured" values for my test cases for each pickup selected alone.


This was to be the basis for my second stage interpolation effort, but I haven't done anything with it yet since I'm already close to or better than a +/- 0.1% coil resistance error in my first interpolation stage.

I'll post my spreadsheet later. Let me know if you want me to send it to you after you see the post.

[ashcatlt]

Okay, I think I got it! (WOOT) I'm not going to post the proof here because it goes on for quite a while.

So, we've got 2 pickups and 1 master volume. When both pickups are selected together they are in series. We've measured all 3 meaningful switch positions with the volume at max. This gives us 3 known values:

B = bridge pickup || volume pot
N = neck pickup || volume pot
S = (bridge pickup > neck pickup) || volume pot

We need to find 3 unknown values:
b = bridge pickup DC resistance
n = neck pickup DC resistance
V = volume pot total resistance

First we'll try to figure V. To make things easier, we're going to determine some intermediate values first. I'm just going to choose some letters “randomly”:
W = B*N
X = B + N – S
Y = W squared
Z = X squared

Now the fun part.
V = sqrt ((Y / Z) – (S * W / X)) + W / X
That looks ugly, don't it. It's even worse if you don't do the previous step! Remember, these are all known values at this point. It's just math.

So now we know the total resistance of our master volume pot. Let's figure out the pickups:
b = (B * V) / (V - B)
n = (N * V) / (V – N)
Notice that these formulas are the same?

Please don't ask me to try this with 3 pickups!

I've tried this with two sets of “measured”* values and both came out correct. That's proof enough for me that it works. If anybody wants to verify, though, be my guest!


*”measured” = pulled out my...

[ChrisK]

ashcatlt,

Your algorithm works correctly. I've run a number of seed value data sets and all are correct.

Congratulations, this was not simple.

Please don't ask me to try this with 3 pickups!

I will as a matter of course ask you to do this.

However, operating on the premise that any (or all) of three pickups can be shorted by the switching mechanism, one only has to measure two of the single pickup positions and one of those two in series (all sharing the common volume pot) to determine the volume pot's value.

After that is known, any single pickup's DC resistance (a) is child's play after one measures it alone in parallel with the volume pot,

a = (A * V) / (V – A)

just as it was for your solution.


2, 3, 4, 5 coils, whatever.

[ashcatlt]

Jan 26, 2009 16:55:03 GMT -5 ChrisK said:

ashcatlt,

Your algorithm works correctly. I've run a number of seed value data sets and all are correct.

Congratulations, this was not simple.

Thanks.

I was actually kind of disappointed in how long it took me. It's not so much that there was anything super tough in the algebraic manipulation, just a whole lot of it. The hardest part was completing the square in the final stretch. I'm sure that my first attempts ended in ruin thanks to a missed - sign, a transposed letter, or something silly like that.

2, 3, 4, 5 coils, whatever.

Yeah, that makes sense.

[ChrisK]

Now, can you do this by measuring one of the single pickup positions and the two in series (both sharing the common volume pot) to determine the volume pot's value?

[ashcatlt]

Why would you do such a thing to me? And on the eve of my day off! I had such big plans. I was gonna...

I'm pretty sure it can be done. Gonna hafta wait till my body metabolizes an as of yet undetermined amount of alcohol.

[ashcatlt]

The fact that you asked the question led me to believe that this would be possible by way of algebraic manipulation. I tried all kind of different ways. I've come to the conclusion that it is, in fact, not possible given the two measurements to find the values for any of the 3 variables.

I did, however, come up with a way to find the answer. Maybe you'll call it cheating, but it works. In fact I think this method (with the application of proper formulas) will work for most, if not all, brain-scan procedures regardless of pickup/switching/control variations.

The question at hand is that we've got 2 coils and a master volume. When selected together, both coils are in series. We are only capable of measuring one of the coils independently. I figure this will be most often encountered when we've got a single HB with a switch to split off one of the coils, so I've chosen my variable "names" with that in mind.

We want to find the value of the DC resistance for the humbucker and for the split coil, such that

h = humbucker DC resistance
s = split coil DC resistance

from these we can figure the other coil's resistance if we want it:

o = other coil DC resistance = h - s

Along the way we will (have to) find the exact value of the volume pot's resistance:

V = volume pot resistance.

It's easy enough to measure the DC resistance across the jack in humbucker mode:

H = h||V

and in split mode:

S = s||V

...but that's not enough information. We've got 3 unknowns and only 2 equations, giving an infinite number of valid results.

We'll have to manufacture a third equation without creating another unknown variable. The LP version of the Brain-Scan technique works in theory, but for reasons I've detailed above is not guaranteed to be effective in practice.

On the other hand, if we can find something, anything, with a measurable DC resistance - a resistor, pot, screwdriver...- and wire it in into the circuit, things become a lot easier. I've chose to wire it in series, because it seemed like it would make the algebra a little easier to navigate.

Due to the limitations of accuracy in our instruments of measurement, it will help if this new resistance is closer in value to the expected value for the pickup we're measuring. A spare pickup would be ideal!

So measure you're external resistance and call it

k = external known resistance

Now wire it in series with the either the sleeve or tip of the jack while one of the pickups (I'll use the full humbucker) is selected, and measure across the jack. This gives us

K = (h>k)||V

And now we have plenty of information.

h = sqrt( ( (KHk) / (K-H) ) + ( K² / 4 ) ) - (k/2)

V = Hh / (h-H)

s = SV / (V - S)

and, as mentioned above:

o = h - s

Like I said, this works for LPs, it works for single pickup guitars (!), and most other pickup combinations.

Does that count?