Contrary to popular belief, the pickup tone capacitor does not pass any signal components to the amp or to ground. What the tone capacitor does is shift the resonant peak of the circuit down in frequency as it is brought into the equation. The Q factor (a.k.a. “Q”) of the circuit is also reduced as the tone potentiometer is rolled down because doing so reduces the total resistance of the circuit. In layman's terms, the tone capacitor moves the frequency at which the pickup circuit is loudest down in frequency and flattens the overall frequency response of the circuit.
The pickup coil and the tone capacitor form an inductor-capacitor (LC) network. An LC network is what is known as a "tuned circuit." Every tuned circuit has a resonant frequency F[SUB]0[/SUB], which is equal to 1 / (2 x Pi x SQRT(L x C)), where Pi ~= 3.14, L = inductance in henries, C = capacitance in farads, and SQRT is the square root function. At resonance, a tuned circuit becomes purely resistive. The output amplitude of a tuned circuit is highest at its resonant frequency. This amplitude peak is known as the "resonant peak" of the circuit. The resonant peak is the frequency at which the pickup circuit is loudest.
The value of the volume potentiometer in a guitar sets the Q of the circuit. It does so by combining with the LC network formed by the pickup inductance/self-capacitance and tone capacitor capacitance to form a tuned circuit known as an RLC circuit. The volume potentiometer is wired in parallel with the pickup and the tone capacitor; therefore, we use the formula for a parallel RLC network to determine the Q of the circuit. The Q for a parallel RLC circuit is equal to R x SQRT( L x C), where R = resistance in ohms, L = inductance in henries, C = capacitance in farads, and SQRT is the square root function. As one can clearly see, Q increases as we increase the value of R in parallel a RLC network. Increasing the value of the volume potentiometer increases the amplitude of the resonant peak while narrowing the passband (the range of frequencies that are passed unattenuated), which has the effect of making a dull sounding pickup sound brighter. The upper bound for how bright an increase in the value of the volume control potentiometer can make a pickup sound is set by the resonant frequency of the pickup.
Many people believe that the output of a pickup is determined by its DC resistance. Paraphrasing Bill Lawrence, attempting to determine a pickup's output level by measuring its DC resistance is akin to attempting to determine a person's IQ by measuring the size of his/her feet. The output of a pickup is determined by its coil inductance and the strength and shape of its magnetic field. Pickup inductance is determined by coil dimensions, winding pattern, number of turns, and wire diameter (including insulation). The only time that one can use DC resistance as a measure of output is if both pickups use the same coil form, wire diameter, winding pattern, and magnet structure. Most seriously overwound humbucking pickups are wound using 43 gauge or smaller magnet wire. The resistance per foot rating of any given type of wire increases as its diameter decreases.
Overwound pickups tend to have less sharp resonant peak amplitudes than vintage-wound pickups because a pickup's coil resistance is electrically in series with its inductance; therefore, a pickup by itself is a series RLC network. The Q of a series RLC circuit is equal to (1 / R) x SQRT( L x C), where R = resistance in ohms, L = inductance in henries, C = capacitance in farads, and SQRT is the square root function; hence, the Q of a pickup decreases if coil resistance grows faster than coil inductance. Pickup inductance is primarily determined by the number of turns of wire that one can place on each bobbin. Most pickup makers are dealing with a fixed set of pickup bobbin dimensions; therefore, the only way to increase the number of turns beyond a certain point is to use thinner diameter wire. As mentioned above, thinner diameter wire has a higher per foot resistance rating; therefore, resistance rises faster per turn with thinner wire, which, in turn, lowers pickup Q.
Seymour Duncan is gracious enough to list the resonant frequency of their pickups. Let’s use the ’59 and JB to illustrate what I have outlined above.
DC Resistance:
- '59 Bridge: 8.13Ω
- JB: 16.4kΩ
Resonant Peak
- '59 Bridge: 6kHz
- JB: 5.5kHz
The DC resistance of the ’59 is approximately 50% of the JB's DC resistance; however, the resonant peak is only 500Hz lower. This delta (difference) is much smaller than would be expected if both pickups used the same wire, especially considering that coil inductance is based on the square of the number of turns (i.e., doubling the number of turns quadruples inductance).
Let’s perform a quick and dirty circuit analysis of the '59 and the JB. We are interested in determining if the inductance of the JB is four times that of the ’59. We cannot determine the inductance of either pickup given the information listed above; however, we can calculate the LC product, which will give us a rough idea of how much inductance has increased with respect to resistance.
Re-writing the resonant frequency equation to solve for the LC product gives us:
L x C = (1 / (F x 2 x Pi)) [SUP]2[/SUP], where F = frequency in hertz, Pi ~= 3.14, L = inductance in henries, and C = capacitance in farads
L x C (’59 Bridge) = ( 1 / (6,000 x 6.28)) [SUP]2[/SUP] ~= 0.0000000007
L x C (JB) = ( 1 / (5,500 x 6.28)) [SUP]2[/SUP] ~= 0.00000000084
As one can clearly see, the LC product for the JB is not four times that of the ’59 Bridge, which means that the inductance of the JB is more than likely not four times of that of the ’59 Bridge. The only way that the inductance of the JB could be four times that of the ’59 Bridge is if Seymour Duncan had magically discovered a winding pattern that resulted in an unbelievable reduction in self-capacitance per turn of wire. The small LC product delta combined with a more than two to one delta in DC resistance between the two pickups tells us that the JB is more than likely wound with smaller gauge wire than the ’59 Bridge. The tonal difference between the two pickups is primarily due to the JB having a lower resonant frequency, less pronounced resonant peak spike, and a flatter response curve. The ’59 is brighter than the JB because its resonant peak is higher in frequency and the amplitude spike is more pronounced. The passband of the ’59 is also smaller than that of the JB, which focuses more of the pickup’s output around the resonant frequency.
We can get away with 250K volume potentiometers with vintage-style Fender single coils because they have relatively high resonant frequencies and relatively low DC resistances. The average vintage-style Strat single coil has a resonant frequency in the 9kHz to 10kHz range and a DC resistance in the 5k ohms to 6k ohms range, which means that vintage-syle Strat single coils have sharp resonant peak amplitudes at frequencies that are one and a half to two times higher than the average humbucker.
Finally, I would like to correct an error that was made earlier in this thread. P-90-equipped guitars use 500K volume potentiometers because most P-90s have DC resistances and resonant frequencies that resemble humbucking pickups.
