A seemingly simple question: what does inductance tell us?

[FunkyKikuchiyo]

So, this is something that gets discussed here and there, but I thought it might be useful to all involved if we tackle the issue head on.

I'm a guitar tech with an Extech meter trying to make/design pickups. A little knowledge is a dangerous thing. I understand the text book definition of inductance as the the ability to create voltage, but since it isn't actually creating a voltage when I read it with my meter, I don't entirely understand what the number could be telling me. If I had true inductance measurements (that is, if we assumed my Extech was perfect), then it would be proportionate to the output of a pickup. But, we don't use inductance to tell us how hot or mellow a pickup is, so it seems few of us see it as being useful for that. I've found it useful in that the resonance seems to be inversely proportionate to inductance readings about 82% of the time and I can get a rough idea of what the "voice" of a pickup will be, but that seems to be more an accidental byproduct.

So I guess the discussion is two part - what things will upset an Extech reading that we could understand better, and what exactly are these readings theoretically? In philosophy it is often advised not to use terms you don't fully understand, and in electronics I feel like I shouldn't use the term "inductance" because I don't completely understand it.

Does anyone have thoughts on this? I have more thoughts, but I'll wait for others to weigh in.

Regarding the inevitable "I just make it and see how it sounds instead of measuring it", I agree mostly. The measurements don't tell me when I have a finished product, but they do help me understand why something isn't behaving the way I want it to. My extech has saved my butt so many times for this... and that is why I want to understand these things more and more.

[Mike Sulzer]

S If I had true inductance measurements (that is, if we assumed my Extech was perfect), then it would be proportionate to the output of a pickup.

No, it is not. How much work are you willing to put into understanding why it is not?

[FunkyKikuchiyo]

No, it is not. How much work are you willing to put into understanding why it is not?

How much snark am I supposed to be reading into this...?

[Mike Sulzer]

How much snark am I supposed to be reading into this...?

None at all. Inductance depends approximately on the square of the number of turns. Output depends approximately linearly on the number of turns. Thye are not proportional to each other. Are you wiling to put in the work to understand why this is so?

[jmaf]

So, this is something that gets discussed here and there, but I thought it might be useful to all involved if we tackle the issue head on.

I'm a guitar tech with an Extech meter trying to make/design pickups. A little knowledge is a dangerous thing. I understand the text book definition of inductance as the the ability to create voltage, but since it isn't actually creating a voltage when I read it with my meter, I don't entirely understand what the number could be telling me. If I had true inductance measurements (that is, if we assumed my Extech was perfect), then it would be proportionate to the output of a pickup. But, we don't use inductance to tell us how hot or mellow a pickup is, so it seems few of us see it as being useful for that. I've found it useful in that the resonance seems to be inversely proportionate to inductance readings about 82% of the time and I can get a rough idea of what the "voice" of a pickup will be, but that seems to be more an accidental byproduct.

So I guess the discussion is two part - what things will upset an Extech reading that we could understand better, and what exactly are these readings theoretically? In philosophy it is often advised not to use terms you don't fully understand, and in electronics I feel like I shouldn't use the term "inductance" because I don't completely understand it.

Does anyone have thoughts on this? I have more thoughts, but I'll wait for others to weigh in.

Regarding the inevitable "I just make it and see how it sounds instead of measuring it", I agree mostly. The measurements don't tell me when I have a finished product, but they do help me understand why something isn't behaving the way I want it to. My extech has saved my butt so many times for this... and that is why I want to understand these things more and more.

Your Extech is applying an AC signal to whatever you're testing and is looking at the disbalance it causes on a "bridge" circuit. Bridges will have a voltage between two legs when at least one of the legs is unbalanced.

Since reactance is proportional to inductance, from the imbalance that the DUT generates on the bridge, the Extech is able to calculate the inductance of that coil. That's what the Extech is, a well calibrated L/C/R bridge. That is all I can contribute to this, as pickup winding and voicing is still a mystery to me

[Steve Conner]

None at all. Inductance depends approximately on the square of the number of turns. Output depends approximately linearly on the number of turns. Thye are not proportional to each other. Are you wiling to put in the work to understand why this is so?

I think this is straining at gnats while swallowing camels. If A varies as the square of B, then I still consider A and B as just two manifestations of the same underlying thing, so one of them can be left out of the problem space. In other words, I can just as easily say that output is proportional to the square root of inductance.

To hint at the camel in the room: A pickup with no magnet could have lots of inductance but no output.

If we assume the pickup geometry constant (let's say a PAF) then a higher inductance reading means there must be more turns of wire, just as a higher DCR reading does.

Changing the geometry breaks this correlation. For instance, as was pointed out on this forum recently, a sidewinder has less inductance than a regular pickup with the same amount of wire, because the two coils oppose each other.

So, an inductance reading of a pickup tells you roughly what the DCR does, plus some information about the magnetic circuit. If I see a really high inductance, I expect a high output, muddy-sounding distortion humbucker.

Mike may of course wish to add negative space to the debate by demolishing any of the above.

[Mike Sulzer]

I think this is straining at gnats while swallowing camels. If A varies as the square of B, then I still consider A and B as just two manifestations of the same underlying thing,

If you design your house assuming that the destructive power of the wind can be approximated as increasing linearly with its speed, the house will not survive the next hurricane. And you might not either.

That muddy distortion humbucker is another example. Start with a PAF. Now double the number of turns in the same space by using smaller wire. The voltage output doubles at low frequencies into a very high impedance load. Both the resistance and inductance go up a factor of four. Consider the voltage frequency response. If the original peak was at 3.5 KHz, then let's look at what happens to the response at that frequency. The resonance moves down, so you have lost the resonant boost at this frequency. That might be a factor of two. You lost a factor of four due to the increase in inductance. Now you are a factor of eight down. But you have increased the pickup capacitance as well. This actually does not have a huge effect because the cable capacitance dominates, and it has not changed. But we might be up to a factor of 10. That is 20 db. When things multiply together, you can lose a lot. The difference between linear and square is one such multiplication. It matters

[FunkyKikuchiyo]

Steve - that is where I was getting tripped up. If A and B both vary somewhat consistently with C, why couldn't we say that A and B vary consistently with each other? The actual physics say that they vary indirectly, but it could be mathematically written that they DO vary directly.

The magnetless coil is a good example of what I was saying. If I get an inductance reading, that does mean that A) my extech is seriously confused and the coil actually has no inductance (which by my wikipedia understanding of what inductance is would be true), or B) my understanding of inductance is way off?

As an extension of that, what you're saying seems to be that inductance readings across form factors is ultimately meaningless, in the same way that DCR can be ultimately meaningless if you're comparing across bobbin sizes and wire types. Is that about right, or an exaggeration?

jmaf - that was very helpful, thanks!

[Steve Conner]

No, a magnetless coil still has inductance. If you can't see how that is possible, you should definitely ponder the meaning of inductance some more. It is just a way of quantifying the effect researched by Joseph Henry, where a current flowing in a coil of wire gets a kind of inertia. You have to apply voltage for quite some time to get the current going, and then it doesn't want to stop. This sluggishness is what causes inductors to filter out high frequencies, hence the muddy sound of overwound pickups.

I think in the light of what Mike said, the truest underlying basis for it all is the number of turns. This determines the output, and it also determines the inductance according to a square law.

The geometry of the turns affects both inductance and output. A coil all squashed up has less inductance than a big one with lots of loop area. This is why those Suhr type dummy coils need less turns than the pickup.

I will risk getting shot at again here, and say that the geometry affects output and inductance equally, up to the following three factors:

The square law. Except it's not always square. To get the square law, every turn of the coil must have unity coupling to every other one. That is true for regular chokes and transformers with their closed iron cores, but debatable for pickups. Case in point, when the 2 bobbins of a bucker are connected in series, the inductance more than doubles, but it doesn't quite quadruple, either.

The magnet, and the extent to which the field modulated by the strings actually links all of the turns. A dummy coil is an extreme example of this, a completely separate coil that adds inductance but no output.

Taking our gedankenbucker again, the total output is twice the output of either coil, even though the inductance is not quadrupled. This is because the two coils are identical and have equal linkage with the magnetised strings.

I hope this helps to show some of the subtle differences between inductance and output.
I forgot the third one!

[Mike Sulzer]

To get the square law, every turn of the coil must have unity coupling to every other one.

It is the constant geometry that is required for the square law to work, not the degree of flux linkage. That is, if you increase the number of turns from n1 to n2 keeping them in the same space (not so easy!), then the inductance increases by (n2/n1)^2. This follows directly from the fact that the flux in any turn passes through each other turn (to some degree, and by a fractional amount that does not change when the number of turns is changed). That is, the flux from each turn induces voltage in n turns, including itself. There are n turns doing this, so you have n times n. Look at all those inductance equations in your handbook. They all have n^2, but the constants in front are different and depend upon the degree of flux linkage.

[bbsailor]

It is the constant geometry that is required for the square law to work, not the degree of flux linkage. That is, if you increase the number of turns from n1 to n2 keeping them in the same space (not so easy!), then the inductance increases by (n2/n1)^2. This follows directly from the fact that the flux in any turn passes through each other turn (to some degree, and by a fractional amount that does not change when the number of turns is changed). That is, the flux from each turn induces voltage in n turns, including itself. There are n turns doing this, so you have n times n. Look at all those inductance equations in your handbook. They all have n^2, but the constants in front are different and depend upon the degree of flux linkage.

Mike, and all interested

On strat type pickups with a center set of magnets, the coil turns closer to the magnets produce a higher output than the outer turns that are in a weaker magnetic field. Theory tells us that the strength of the magnetic field falls off to the inverse cube of the distance. If the magnetic field, M has a value of X at distance D then at twice the distance, 2D the magnetic field, M will be X/8 or the inverse of 2 cubed. What this says is that the outer turns add increased output but the added output diminishes quickly as the distance of the outer turns gets farther from the magnet cores. By putting a ferrous metal plate on the underside of the pickup, the underside of the pickup's magnetic field is reflected back up to the strings and helps to increase the flux density in those outer turns which then increases the output in those outer turns. I find through experimental tests that adding a ferrous plate on the underside of the pickup adds about 25 percent to the output level. Mike, would your magnetic models verify my findings?

Another geometry issue is that the upper turns, that are closer to the vibrating string, produce more output than the lower turns which are farther from the vibrating string. Adding coils turns is the easiest way to change the output and tonal characteristic of a pickup but altering the geometry of where the coil turns are located in relation to the string location also has an effect on output level and tone. The unfortunate side effect of adding more turns is the additional resistance of the outer turns, lower turns and the added winding capacitance which alters the main tonal character of any particular pickup design geometry.

Joseph Rogowski

[Mike Sulzer]

Mike, and all interested

On strat type pickups with a center set of magnets, the coil turns closer to the magnets produce a higher output than the outer turns that are in a weaker magnetic field. Theory tells us that the strength of the magnetic field falls off to the inverse cube of the distance. If the magnetic field, M has a value of X at distance D then at twice the distance, 2D the magnetic field, M will be X/8 or the inverse of 2 cubed. What this says is that the outer turns add increased output but the added output diminishes quickly as the distance of the outer turns gets farther from the magnet cores.

Here is one example of why it is so important to use the law of magnetic induction to understand a pickup, rather than, for example, using variable reluctance as method for understanding the physics, rather than as a mere mathematical analogy, which is all it is. What you say seems to make sense, but it is not correct. The law of magnetic induction states that all changing flux inside the closed path contributes. The outer turn contains all the flux that the inner one does, and more. Now it is true that the outer turn does contribute less, but not as much less as you are implying. The reason that it contributes less is that in contains flux with the opposite sign returning up to the string after passing down through the coil. (It points in the opposite direction, and so a line going up cancels the effect of a line coming down.)

Note on variation of magnetic field with distance: It is cubic for a dipole. All magnetic field sources look like dipoles if you get far enough away. But up close the field does not fall off with the cube.

By putting a ferrous metal plate on the underside of the pickup, the underside of the pickup's magnetic field is reflected back up to the strings and helps to increase the flux density in those outer turns which then increases the output in those outer turns. I find through experimental tests that adding a ferrous plate on the underside of the pickup adds about 25 percent to the output level. Mike, would your magnetic models verify my findings?

I think the plate helps a bit because it provides a somewhat shorter path for flux to return to the string after passing through the coil.

Another geometry issue is that the upper turns, that are closer to the vibrating string, produce more output than the lower turns which are farther from the vibrating string. Adding coils turns is the easiest way to change the output and tonal characteristic of a pickup but altering the geometry of where the coil turns are located in relation to the string location also has an effect on output level and tone. The unfortunate side effect of adding more turns is the additional resistance of the outer turns and the added winding capacitance which alters the main tonal character of any particular pickup design geometry.

Joseph Rogowski

Yes, the flux coming from the string diverges, even with a core present, and so turns farther down contain less flux. (Do not forget that adding more turns also increases the inductance!)

[FunkyKikuchiyo]

Steve - thanks for that. I have 4 or 5 resources where I've been reading about inductance, but none of them properly explain it. My erroneous statement that inductance is the potential to output in fact came from one of them. It seems they are more interested in giving short answers to move on to the next chapter or something. You've given me some good clues to find better resources, though.

[David Schwab]

I think in the light of what Mike said, the truest underlying basis for it all is the number of turns. This determines the output, and it also determines the inductance according to a square law.

Don't forget the affect of a steel core.