Inductance vs resistance scatter plot comparison

[antigua]

Taking the inductance, resistance and loaded peak frequency from over 200 measured pickups, that can be seen here www.echoesofmars.com/pickup_data/viewer/ , I made a scatter plot that compares inductance (red dots) and resistance (blue dots) in relation to loaded peak frequency, where the load is the usual  200k ohms and 470pF in parallel:



The above is a screen shot, but you can see the dhtml here www.echoesofmars.com/pickup_data/viewer/scatter_L_R.html . 

This shows an inverse relationship between both inductance L and resistance R with respect to peak resonance. I'm surprised by the degree of scatter that is present in the inductance (red), though I was expecting as much for the resistance (blue). You can make out a rather defined curve in the aggregate of the inductance (red) plot points. It's hard to make out, but the resistance (blue) dots form a slightly more linear pattern, which reflects that inductance increases at a greater rate than does wire length, which is partly related to the DC resistance, along with the wire diameter, which varies from 42 to 44 AWG, and anywhere in between.

It's  interesting that the inductance plot points form a curve that is rather well defined along the top curve, but is someone fuzzy below the curve, where as the DC resistance plots points show a relatively equal amount of fuzziness over and under the trend line. 

The resistances points show more outliers than the inductance points, which is to be expected, but I'm rather surprised that it isn't more scattered than it is, seeing as how the resistance has an indirect relationship to peak resonance, where as inductance is literally is half of the equation that determines peak frequency. I suppose this implies that pickup are uniform and predictable to such a degree that even indirect indicators still align somewhat closely with direct indicators. 

[antigua]

This is pretty interesting, here is the same plot, but this time limited to pickups wound with 42 AWG, so that the DC resistance is apples to apples with respect to wire length:



Here is a direct link www.echoesofmars.com/pickup_data/viewer/scatter_L_R.html?42AWG . This is all javascript, so if you're a 1337 hacker, you could download the html and the includes and make your own associative graphs.

The DC resistance is still linear while the inductance is curved, but now the amount of deviation and outliar points is greatly reduced. The two pickups to the far right are Gretsch HiLo trons, bridge and neck, in case you're wondering. 

Note; the reason a loaded resonant peak is used as the baseline instead of the unloaded resonant peak is for two reason: 1) 470pF is typically the added capacitance of a guitar cable, so this peak frequency is more realistic than a no load peak, unless, say, you're using a wireless unit that alleviates that capacitive load. 


Here is the same, but this time just 42AWG Strat pickups:



www.echoesofmars.com/pickup_data/viewer/scatter_L_R.html?strat

Because Strat pickups have such a basic layout, they should be the most consistent sort of pickup, in general, and so the relationship between DC resistance and inductance starts to look almost like a mirror. A few of the plot points to the far left are actually "single coil sized humbuckers" such as the Seymour Duncan Little '59, and are not traditional Strat pickups with AlNiCo rods. 

One thing that causes inductance to vary in Strat pickups is the use of AlNiCo 5 versus A2, A3 and A4 slugs. AlNiCo 5 causes less inductance than the other three. So what does it look like when only AlNiCo 5 pickups are included? 



http://www.echoesofmars.com/pickup_data/viewer/scatter_L_R.html?strat_42awg_a5

The relationship becomes even tighter still. It's also worth noting that the inductance points are much more tightly aligned, showing the stronger relationship between inductance and peak resonance, as compared to DC resistance, even when the pickup design is simple and the wire gauge is controlled. 

Looking at Strat pickups with AlNiCo 2 pole pieces only, shows and even close relationship as well: 





P.A.F.'s are less uniform than Strat pickups, because there are various metal parts involved, but by and large they all share the same dimensions, and most "vintage" style repro's use 42 AWG, they're not really too inconsistent, either. Here is a plot of 42 AWG PAF type pickups:



The two clouds of data points actually look rather similar. 


If PAF type pickups with 43 and 44 AWG are added to the mix, it becomes a lot less coherent:

[Deleted]

hello,

anything about ceramic vs alnico (X) vs neodymium vs ?

[antigua]

Jan 16, 2018 1:06:55 GMT -5 @pyrros said:

hello,

anything about ceramic vs alnico (X) vs neodymium vs ?

If the pickup in question has the magnet in the core of the coil, which is essentially limited to Fender single coils, then the permeability of the magnet will play a role in determining the inductance of the pickup, as well as the overall voltage output. This is true no matter what kind of magnet it is. Therefore, if you select any particular magnet type, then for the set of pickups that uses that particular magnet, the amount of deviation between inductance and DC resistance is made smaller. 

In the case of the PAF style humbucker, the magnet is outside of the core, so it plays a much smaller role in determining the inductance. Therefore, the magnet type can be ignored, and so the only thing worth paying attention to is the wire gauge, and to a lesser extent the shape of the poles and screws, but if we're talking about PAFs, then it's assumed we're limiting the sample to the standard type, with six slugs and six screws that stick out the bottom of the base plate.

[pablogilberto]

For Strat SC pickups, what is the electrical and sonal effect when using A5 or A2 or any other AlNiCo?

I understand that they differ in magnetic strength, A5 being the strongest.
How do this translate to tone?

Do you also mean that since the magnets are the pole itself, changing from A5 to A2 will change the Inductance?
What is the relationship between magnetic permeability and Inductance of the coil?

Thanks

[antigua]

Jun 21, 2020 23:36:05 GMT -5 pablogilberto said:

For Strat SC pickups, what is the electrical and sonal effect when using A5 or A2 or any other AlNiCo?

I understand that they differ in magnetic strength, A5 being the strongest.
How do this translate to tone?

Do you also mean that since the magnets are the pole itself, changing from A5 to A2 will change the Inductance?
What is the relationship between magnetic permeability and Inductance of the coil?

Thanks

Higher permeability means more inductance, and a lower magnetic reluctance. More inductance means lower resonant peak, lower reluctance means more voltage output. 

When the magnets pull on the strings, the strings vibrate asymmetrically, which leads to intermodulations, which is like a mild chorus effect. There might be more subtle consequences that haven't been elaborated on yet, that's something we try to figure out with experiments and models. If you were to ask people to describe the sound difference of pickups close to the strings versus far, or weak magnets versus strong ones, you get a lot of different answers, many of them contradictory.