In part I, we discussed the construction and basic function of a pickup, along with the implications of the resistance of the coil. In part II, we will discuss pickup inductance in detail, focusing on the electromagnetic properties of the materials that make up the pickup and how they affect pickup performance.
As we discussed last time, we’re going to be looking at all of these physics in terms of how the pickup interacts with the flux generated by the vibrating, magnetized string. We’re basically assuming that the string is magnetized, independent of the pickup. We’ll be talking a lot about magnets and magnet materials, but we’re not really concerned with pickup magnets as magnets at all, we only care about how they behave as conduits for the magnetic flux emanating from the string, at least for most of the analysis.
That’s a good segue, and before we get into inductance proper, let’s talk about pickup construction materials in terms of their role as conduits for magnetic flux. To do that, we have to define something called magnetic permeability. Magnetic permeability can be defined as the ease with which a material can support the development of a magnetic field within itself. The symbol for magnetic permeability is µ (pronounced “/mju/”). Magnetic permeability is analogous to electrical conductivity (conductivity being the inverse of electrical resistance, which we talked about last time), so magnetically permeable materials act as conductors of magnetism. Air is neither a conductor nor a resistor of magnetic flux, it’s basically magnetically transparent, with a relative magnetic permeability, µ, equal to 1. The low carbon steel typically used as humbucker pole pieces may have a relative permeability in the thousands, meaning it is thousands of times more magnetically conductive than air. AlNiCo alloys typically have relative permeabilities in the single digits (but significantly, greater than 1).
Let’s look at an example. Figure 1a shows a small magnetic source in air. There is no preferred path for the magnetic flux (remember that magnetic flux must form closed loops from the north to south poles of the magnet) so it just balloons out in all directions. The flux density is constant at equal distances around the magnet in all directions, but it decays rapidly with distance away from the magnet as it is becomes more and more diluted. Figure 1b shows the same magnetic source, but now with a “C shaped” conduit of highly permeable material (µ = 1000) looping from close to the north pole to close to the south pole of the magnet. Almost all of the magnetic flux is now concentrated in the permeable material. That’s because the magnetic flux will take the easiest path from north to south, and the higher the permeability, the easier the path. The permeable material in effect concentrates the magnetic field within itself. This kind of behavior has a lot to do with how the construction and materials of a pickup affects its performance.
So let’s turn now to inductance. If you look up inductance in the dictionary you’ll find it defined in terms like “the property of an electric conductor or circuit that causes an electromotive force to be generated by a change in the current flowing”. That’s a mouthful. Let’s break down all of those words into some practical examples. One of the simplest inductors is a single layer solenoid, as illustrated in Figure 2. We’re not really going to worry too much about the math, but it is important to understand what inductance depends on, and we get that from the equation. Inductance goes up with the number of turns of wire, N (in fact inductance goes as N, so with every doubling of turns we get 4x the inductance, not just 2 – this is because each turn is feeding off of the other turns based on something called mutual inductance), with the area encompassed by the coil, A, and with the magnetic permeability of what’s in the middle of the coil, µ.
We talked about resistance last time, and R basically tells us about the length of wire used in the pickup, which leads pretty directly to the number of turns on the coil. A pickup wound with the same gauge wire, at the same conditions and on the same size bobbin or support, will have pretty much the same resistance and number of turns. If everything else is the same in a pickup, then that’s all we need to know.
But many times, everything else is not the same. We just looked at an example of the effect of permeability on a magnetic field in Figure 1, and we see from the equation in Figure 2 that inductance increases as the magnetic permeability of the material inside the core (we sometimes refer to the volume encompassed by the coil windings as the “core”) of the coil increases. Basically what happens is that a magnetically permeable material in the core will cause the magnetic flux emanating from the string to concentrate inside itself, increasing the magnetic flux density in the volume encompassed by the pickup coil, hence increasing the electromotive force (or in more straightforward terms: output). Similar to what’s illustrated in Figure 1, a lot of those magnetic flux lines that would balloon out into empty air can be made to concentrate in the area enclosed by the coil where they can contribute to signal generation. So by concentrating the magnetic field lines within itself, and also consequentially within the coil that is wrapped around it, permeable material in the core acts like a multiplier of inductance.
Let’s go back to our two pickup design examples and see exactly how construction material differences affect the concentration of magnetic flux in the core of the coil, and hence pickup performance. First let’s look at the Strat style single coil and the effect of changes in the pole piece material, as shown in Figure 3. With an air coil, i.e. nothing but air in the core, the field balloons out equally in all directions with nothing to constrain or influence it. Something like AlNiCo 5, with a relative permeability of around 2 will start to concentrate the flux in the core. You can see this in two ways in Figure 3, first by the distortion of the flux contours (remember from last time that a flux contour is a line of constant flux density) deeper into the core and also by the increase in the number of field lines passing through, and deeper into, the core. AlNiCo 2, with a permeability of about 7, increases the effect, concentrating more of the flux from the vibrating string within itself. A steel pole piece, with a permeability of a few thousand, concentrates the flux even more. In Figure 3e, the predicted relative flux density inside the core of the coil is shown (with the flux density at the top of the air coil set equal to 1). If we integrate all of the area under the curves, we find that this model predicts that the total flux density inside the coil increases by about 1.7, 3.2 and 4.9 times for the AlNiCo 5, AlNiCo 2 and steel pole pieces respectively over the air coil. And in fact these levels of multiplicative inductance increases are similar to what we see when we insert these same coil materials in a Zexcoil coil.
But, if you’re really paying attention, you’re probably asking “why isn’t the inductance of the coil with steel thousands of times higher than the air coil as indicated by the equation in Figure 2? Why only about 5 times more?” And, that’s a great question that leads us right into our humbucker example. Basically it has to do with the field’s tendency to expand to fill open space when there is no preferred permeable path to complete the loop. If we had an ideal inductor with a fully closed magnetic path more similar to what’s illustrated in Figure 1b, we would reap the full benefit of the core permeability. But a guitar pickup is more like the system illustrated in Figure 1a with just a short length of a permeable path inserted. In this kind of situation the inductance of the coil can be increased significantly, but nothing close to the ideal case.
Applying this idea of the field’s tendency to fringe out into a non-magnetically permeable region (and conversely to get concentrated in a permeable one), let’s look at the effect of magnet permeability in the classic humbucker pickup design. Figure 4a shows a cut-away view of a typical PAF-style humbucker pickup and Figure 4b shows the 2 dimensional model used to predict the magnetic flux in the pickup circuit. Now, as we’ve been discussing, the conventional way to think about this system is to look at it based on the effect of the magnet as a magnet. Let’s consider that just for second, as it does play into how the string gets magnetized. In a humbucker, the magnet lays at the bottom between the two coils with the north pole facing one row of pole pieces, and the south pole facing the other row of pole pieces. The field from the magnet is concentrated in the highly permeable poles and directed towards the strings (by the same physical mechanism we just discussed), magnetizing them in the region above the poles. Note that since the two rows of pole pieces are magnetized at opposite polarities, the strings also become magnetized at opposite polarities above the poles.
Figure 4c shows the field associated with the magnetized strings, assuming a magnet material with a magnetic permeability of exactly 1, simulating what happens when we use a ceramic magnet. Notice how the field lines emanate from the strings in all directions and how the field lines emanating from the bottom of the string are concentrated in the poles. Also notice that the field lines from one string pass down through the pole piece under the string, across to the other pole piece and up through the other pole piece back to the string. As we discussed above, a permeability of 1 means that the material does not concentrate or reject the magnetic field, it is basically magnetically transparent, so in this case the magnet material has no effect on the field, and in fact if we remove the magnet from this simulation the filed lines look exactly the same. Now again I’ll stress that in this model, we are not considering the magnet as a magnet at all, only as a conductor of the magnetic flux emanating from the string, the string is the magnet in this case, and we assume the same magnetic strength (at the string) in every case. You’ll also notice that the field tends to balloon out from the bottoms of the poles, as well as taking every opportunity to jump straight across from pole to pole.
If we increase the permeability of the magnet material, even by a little bit as in the case of the AlNiCo alloys, we see that just a slight concentration of flux inside the magnet material helps to close the magnetic circuit, affecting the shape of the field lines and the flux density both outside and more importantly inside the boundaries of the coil. Figure 4d shows a magnet material with a permeability of twice that of the ceramic (modelling AlNiCo5 with µ = 2). Figure 4e models a magnet material with µ = 7, similar to AlNiCo2. As the permeability of the magnet material increases, the magnetically conductive bridge between the rows of pole pieces becomes more efficient at closing the magnetic circuit. You can see the effects, not only within the magnet material itself, but everywhere else in the magnetic circuit. Filed lines become more concentrated in the pole pieces (and hence the core of the coil) because they are less inclined to jump across the space between poles or fringe out the bottom of the pole piece and more inclined to stay within the more permeable path down through the entire pole piece and across through the magnet. Figure 4f shows the predicted relative flux density within the core of the slug coil, down the center line of the slug. If we integrate this flux over the whole coil area we see that the flux density in the core is increased 7% with the AlNiCo5 magnet and 30% with the AlNiCo2.
Now one thing to keep in mind is that the way we’re looking at these cases, a 2 dimensional model centered on the pole piece, is inflating the effect that would be observed in most conventional pickups. I said earlier that the inductance increases we see in a Zexcoil pole piece are similar to the 2d model predictions of core magnetic flux density increases for the Strat geometry. This is true, and it’s true because in a Zexcoil coil, the pole piece fills most of the core of the coil taking more advantage of the permeable material. In conventional single coil and hum bucker designs, the pole pieces are discrete cylinders under each string and a large portion of the space in the core is occupied by air. In a vintage style Strat pickup, with the coil wound directly on the pole pieces, the core of the coil is about 40% pole piece/60% air, with a bobbin that ratio is more like 30/70. So the effective permeability of the core will be some weighted average of the pole piece material and air, with the flux field being concentrated through the poles and fringing out in the area between poles. But still, these cases show directly how the properties of the permeable materials in the core, and elsewhere, affect the performance and function of the pickup. Considering the more dramatic effects of something like a steel pole piece, with 5 times the flux concentration of air in this kind of geometry (and 3 times the flux concentration of AlNiCo5), even at only 30% fraction of the core – you’re going to notice that difference as plain as day. Even with more subtle effects like the difference between AlNiCo5 and AlNiCo2 in a humbucker, magnet swappers know there is a difference because they can hear it, and here we demonstrate a solid physical basis to ascribe it to as well as a model in which to interpret design changes and material effects in pickups.
We’ll look at one final example that shows the interaction between core permeability and coil dimensions. Figure 5 gives the inductance of a series of individual Zexcoil coils, illustrating the effect of coil dimensions on inductance. In this example, we are looking at coils with successively higher winds of larger gauge coil wire (41 awg) until the bobbin is full, then we jump to the next smaller wire (42 gauge) and continue the sequence. [Keep in mind that as we add turns with the same gauge, the added turns encompass a larger area. Because of this, additional turns wound on the outside tend to yield more inductance per turn than the smaller area turns on the inside.] When we jump to the smaller gauge wire inductance is less at the same number of turns because the coil is physically smaller, encompassing less area with the same number of turns. We see this effect clearly with the air coil, where the magnetic field is unaffected by the core and is free to bloom out into space. In this case, the inductance is directly related to the real area encompassed by the coil as added area means more magnetic field lines passing through that area. But, as we increase the magnetic permeability of the core by adding first AlNiCo 5 we see less of an effect, and with a highly permeable steel core we see no effect at all. The reason is, with a very permeable core like steel, virtually all of the magnetic flux becomes concentrated in the steel itself. So, the marginal area increase of the added winds does not add to the number of field lines encompassed by the coil because they’re all already concentrated in the highly permeable steel core. At high permeability every wind acts like it has the area of the perimeter of the pole piece where the flux is concentrated.
Tying this back to understanding pickup function as it relates to construction and electrical specifications, we can see that the physical structure of the coil is much more important as the permeability of the core of the coil is reduced. We would expect the structure of the coil to be most important in a conventional Stratocaster say, where the pole piece has very low magnetic permeability and most of the core is air. And considering that the outermost wind on a Strat pickup can encompass more than 3 times as much area as the innermost wind one could envision how variations in wind pattern might build up to have not-so-subtle effects. In pickups made up largely of more permeable materials, like PAF humbuckers, we might expect material effects to start to become more dominant in the pickup behavior and performance.
So that’s another big dose of information to chew on, but it’s not the end of the story. Our treatment of these pickup materials based solely on their magnetic permeability is an oversimplification. It turns out that these materials affect not just how much magnetic field gets concentrated within them, but they also act to filter that flux as it passes through. The mechanism of this flux filtering is the degree to which eddy currents in the materials act to oppose the flux that is trying to pass through them. Eddy current opposition in the materials acts to dampen the magnetic flux that is passing through them, and thus has a damping effect on the frequency response, lowering the Q value of the pickup. But that’s going too deep already. We’ll talk about these physics in detail in the final installment, along with a discussion of pickup resonance and frequency response.