capacitor values & rolloff frequency
 

Some helpful person posted this information - I found it buried in a long thread. I'd like to suggest it be made a sticky:


passive tone control
capacitor values and corresponding frequency rolloffs

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1uf = 200hz (frequencies become bunched together around here)

0.047uf = 300hz

0.022uf = 400hz

0.0047uf = 900hz (nice mids)

0.0022uf = 1.4khz

0.00047uf = 2.9khz

0.1nf/100pf = 4.1khz (that's probably just silly for bass guitar)

It doesn't work that way. Frequency cutoff points are determined, in part, by signal impedance. Those values are based on an unknown impedance.

It is easy enough to back calculate the impedances that give those cutoff frequencies:

796
11288
18086
37625
51674
116768
388183

If the list were to have any utility at all it should at least be based on a consistent impedance. Since the pickup has inductance you would expect the impedance to rise with frequency as this one does but the low frequency impedance should be at least a few kOhms, the pickup winding resistance. This list start at 796 Ohms far too low.

If we could agree on what would be a typical pickup R and L we could put together a list of capacitor values and cutoff frequencies.

Ken

But then you don't know enough about the average pickup to do anything with the numbers.

There is no average pickup so any single list one might compile can only be roughly correct. Even so, roughly correct is more information than no information. Compiling a handful of lists to represent several typical pickup designs would be more helpful. Most helpful of all would be for pickup makers to have their designs characterized for R, L, and C and then publish tables that would be very close for each pickup they make. Dream on, eh?

In any event the list given above seems to have too many issues to be useful, sorry to say. As I mentioned earlier the 200Hz number should be based on a value of at least a few kOhms since that is what the typical pickup resistance is but the back calculated series impedance is only 796 Ohms at 200Hz so it already has a problem. You then should be able to calculate the effective inductance from each pair of frequencies since the increase in impedance is coming from the inductance, the resistance remains constant. When you do that with the table of values given above the inductance is rather large, it changes haphazardly from frequency to frequency and the resistance has to be negative at most frequencies to make the impedance come out right. Clearly the table given above is not based on any real pickup R and L values. One can only imagine where the numbers may have come from.

So, nice try, but no one should rely on that table since it is fraught with errors.

Ken

Did you mean 0.1µF? That can't be 1µF.

Maybe he did, it is an odd tone cap value. The numbers come out a lot better if it is 0.1uF, good catch.

Anyway, the table below is based on a circuit simulation with a pickup inductance of 3H, resistance of 7k, parallel capacitance of 86pF, tone capacitance as given, tone pot resistance setting of 20 Ohms, volume pot of 250k, amplifier input resistance of 1Meg, and no cable capacitance.

C________Fc
1u_______23Hz
100n____313
47n_____563
22n_____892
4.7n____2000
2.2n____2950
470p____5870
100p____9700

I got the pickup model from a University of Illinois professor's web site. It is supposedly correct for a 2001 reissue of a 1961 Jazz Bass neck pickup. One size does not fit all as mentioned above but these numbers are at least based on measurements of a real pickup.

Ken

I guess I haven't been very articulate on this forum lately.
To say that one capacitance value affects one frequency center is to assume known specs about a pickup that are not only subject to wild variation between pickups, but difficult to obtain any accurate measure of. Take any random pickup on the market, and it is unlikely that you will be able to find any more information about it than DCR. Even if you know the inductance or the impedance, the measure is based on a reference frequency that is usually not specified. It would be difficult to lay out a standard of measurement that the average person could use without special measuring instruments and the use of some math. To put it simply, there is simply too much variation in pickup specs, and too many unknowns to do any math for the average person, to try to say what capacitance cuts what frequency center.

0.1µF is a common value for tone caps. 1µF certainly is not! I doubt you would hear very much sound with a 1µF tone cap. Subharmonics I guess!

I guess that's the thing. You have to chose the pickup first, and then you have the frequencies. Hotter pickups will lower the numbers, and under wound pickups will raise them.

It is interesting how we use a few standard values when pickups vary by a fair amount.

There's a weird mentality in the music world as it pertains to tradition. The same mentality is the reason a good number of basses feature four strings, maple necks, and rosewood fingerboards.

Right, and Fender style pickups.