"DC Resistance" as a pickup specification

[antigua]

You might have heard the cliche "resistance doesn't equal output" in discussions where guitarists attempt to judge relative output based on DC resistance figures. 

As a practical matter, if you know the gauge of wire that a pickup was wound with, which is often easy enough to intuit, then the DC resistance can allow you to guess as to the number of windings on the coil, by solving for length using the average resistance per foot, or meter, of copper wire in that particular gauge. 

But as an electrical matter, it's true that DC resistance, at least in the context of pickup measurement, is extremely insignificant.  

If you saw that one humbucker had a DC resistance of 7.62k ohms, and another had a DC resistance of 8.02k ohms, you'd assume that the 8k pickup must be hotter. But that might not be the case. In the demonstration below, 400 ohms is added to a humbucker that reads 7.62k  ohms, and the electrical consequences of that added resistance is measured. 


First we have the DC resistance of a DiMarzio 36th Anniversary humbucker, it reads 7.62k ohms:




Now we add a 400 ohm resistor in series, simulating magnet wire that contains 400 ohms of impurity and/or improper wire tension, and it reads 8.02k ohms:





Now we measure the inductance of the DiMarzio 36th Anniversary, it's 4.135 henry.





Now we add the 400 ohm resistor, and the inductance reads identical at 4.135 henry










And now lets do a bode plot, with and without 400 ohms in series:





And as you can see, the plots overlap, with a difference in unloaded peaks that are no greater than 0.1dB in difference.
It is said that differences that are smaller than 1dB are inaudible to humans, and it would take a substantial amount of series resistance in order to achieve greater than 1dB drop in the Q factor. And if this humbucker were loaded (in a guitar connected to potentiometers), the difference would be even smaller.
 

For more information on how the bode plot is created, see this thread guitarnuts2.proboards.com/thread/7723/measuring-electrical-properties-guitar-pickups

It's interesting to note that, while we rarely see extreme resistance in the copper wire used in guitar pickups, we do see extreme resistance in the form of eddy current losses.  Here is a plot I created comparing a couple covers on a humbucker to no cover. The highest plot line is the "no cover" plot, and the two lower lines are two different covers, whose lines diverge on account of their metallurgical differences:



You can see that at the resonance, the metal cover causes a loss of approximately 3 to 4dBV (after adjusting for the difference in overall output). Someone who is inclined in math could probably even figure out what the equivalent series impedance is added by the cover, but suffice it to say that the eddy losses are far more substantial than 400 ohms, and are very likely to be audible.