Electrical Parameters and Pickup Performance, Part II - Inductance

In the first installment of this series I talked about Resistance, one of the most widely used pickup response parameters. Unfortunately, resistance is a parameter that is really only useful in the context of “all other things being equal”. If you change one thing about the design, you could affect pickup response significantly. Alternatively, you could design two pickups with different resistance that could be made to respond similarly.

In this post, I will discuss Inductance, a much more useful parameter than resistance. Inductance is the best descriptor of pickup output. As I demonstrated experimentally in an earlier blog post, How Does a Pickup Really Work?, pickups are after all just inductive sensors – converting the signal from the moving magnet (the vibrating, magnetized string) into an electrical impulse. Inductance is the measure of how effectively the pickup collects and converts that magnetic energy to electrical energy.

Electromagnetic induction is a fairly simple basic concept, the implications of which can get quite complicated. Figure 1 shows a classic example of electromagnetic induction, where the current in a coil produces a magnetic field which may then induce (hence, “Induction”) an electric field in a neighboring body. It is important to remember that magnetism and electricity are intertwined. Maxwell first showed how the two were related and years later Einstein showed that they were actually the same thing, the difference being merely the frame of reference of the observer. This is why with Electromagnetism as one of the 4 basic forces, we do not distinguish between them at the most fundamental level. So, not only will a current in a coil induce a magnetic field associated with the coil as in Figure 1, but a moving magnetic field will induce a current in a coil as well. Think of how electric motors work versus electric generators. They both utilize the same physics, just in reverse compared to each other. An electric motor generates motion through the laws of induction by applying a current, while a generator creates electricity through the laws of induction by harnessing motion.

A basic inductor, along with the governing equation for that inductor, is shown in Figure 2. This type of inductor, called a solenoid, consists of a single layer of conducting wire wrapped around a cylindrical core. The core may be empty (in which case we refer to it as an “air coil”) or it may be filled with, typically, a magnetically permeable material. Inductance is represented by the letter “L” (after Lentz) and is measured in “Henries”. From the equation, you can see that inductance depends linearly on a number of things including; the number of turns of wire that make up the coil (squared, so turns are huge), the area of the coil, the magnetic permeability µ (which we’ll discuss in a moment), and it depends inversely on the length of the coil. Magnetic permeability is a property of materials and it represents the tendency of a material to concentrate magnetic flux. For a material with high permeability, a magnetic field really wants to be in the material and it will basically suck the field in. Magnetic shielding typically has very high permeability and it effectively channels the magnetic field away from the object to be shielded (you can’t block a magnetic field, but you can redirect it). Materials with low permeability don’t tend to concentrate a magnetic field. For convenience, we usually talk about the relative permeability, µr, of a material. Relative permeability is defined such that the relative permeability of empty space (a “vacuum”) = 1. Air basically acts like a vacuum when we consider its magnetic properties, so an air coil is one in which the relative permeability of the core equals 1. A relative permeability of 1 basically does not affect a magnetic field at all, it’s like there is nothing there as far as the magnetic field is concerned. A material with a relative permeability greater than 1 will concentrate a magnetic field. A relative permeability less than 1 will reject a magnetic field.

So from the equation in Figure 2, we can see that relative permeability acts like a multiplier of inductance. A coil with a magnetically permeable core will theoretically have a higher inductance than a coil with a relative magnetic permeability of 1 by a factor of µr. Figure 3 shows what that looks like in terms of a guitar pickup. A guitar pickup is basically an inductor that is configured as a generator. The motion to the generator is supplied by the magnetized string. Remember, that for pickup function the only magnetic field we are concerned with is the field of the moving, magnetized string. The static field of the pickup doesn’t really matter, only that the string becomes magnetized. When plucked, the magnetized string projects a magnetic field that is associated with its vibration, and that vibration carries all of the tonal information of the note being played, the attack with which the note was struck, etc. As that magnetic field interacts with the pickup coil, an electrical signal is induced in the coil which also carries all of the information from the string pluck. That’s how the signal in an electric guitar is generated. As Figure 3 shows, with a low permeability pole piece like AlNiCo5, which has a magnetic permeability barely higher than air and is the most used pole piece in a Strat style single coil pickup, the field of the string is not really affected, it blooms out from the string in a fairly symmetric pattern. With a high permeability pole piece, like the low carbon steel typically used as the screws and slugs in a humbucker, the field from the magnetized string is distorted, and effectively drawn into the pole piece, becoming concentrated in the core of the coil.

Now go back and take a close look at Figure 1. Note that when the magnetic field is created by the current in the coil, the field lines are centered about the coil and are concentrated in the core of the coil. Every field line created by the current in the coil passes through the center of the coil. So for the opposite case, where we want to induce a current in the coil via an external magnetic field, the field lines that will be most efficient in generating that current will be the ones that pass through the core of the coil. This is the physical reason why magnetic permeability is so important in increasing inductance. A permeable material in the core of the coil acts to concentrate the magnetic field exactly where it needs to be in order to make the inductor more efficient.

But why don’t we get all of the benefit of the magnetic permeability in a guitar pickup? If permeability is a multiplier of inductance, shouldn’t a pickup with a pole piece with 2000 times the permeability of air have an inductance 2000 times the air coil? Why only by a factor of about 6 as shown in Figure 3? First, we have to consider that magnetic energy travels in loops, just like electrical energy. The black lines in Figures 1 and 3 represent the paths taken by representative loops in the magnetic field. The problem with the “magnetic circuit” depicted in Figure 3 is, while the core of the coil is filled with magnetically permeable material, most of the magnetic circuit is air. For the full multiplying potential of the permeable material to be realized, we must construct a closed magnetic loop, as shown at left in Figure 4, where virtually all of the magnetic flux is contained in a closed loop of permeable material. Note that all of the field lines are contained in the rectangular loop of permeable material. Even a fairly short air gap, as shown in the middle of Figure 4, can result in as much as a 99% loss of the native permeability of the core material. Notice how the field lines start fringing out significantly into the low permeability space around the permeable core, even on the opposite side from the air gap. A pickup is basically a completely open magnetic circuit as shown at right in Figure 4, where the field is free to bloom out into the low permeability space. Considering what happens to the field lines in the examples shown in Figure 4, we can start to see how other permeable materials in the pickup, baseplates, covers, etc., might also affect the field and the effective inductance and response of the pickup. Of course, as shown by Figure 1, the most important material is the stuff in the core of the coil.

But what does this mean for pickup design and response? Here’s an example of the effect of the area of the coil coupled with the magnetic permeability of the pole piece material. Figure 5 illustrates the inductance as a function of turn count squared (according to the proportionality shown in the equation in Figure 2) for a range of coils using 41 awg (closed symbols) and 42 awg copper wire. The coils are measured as air coils (i.e. nothing in the core of the coil but air), with an AlNiCo 5 pole piece and with a nickel plated low carbon steel pole piece. As I’ve mentioned a few times, we use a range of coil gauges in Zexcoil® pickups, and we basically use the largest diameter (lowest gauge) wire we can at any given turn count. When we fill up the bobbin we jump to the next wire gauge. So, the highest turn count coil for a given gauge will be as big as the coil can get, we’re basically filling the bobbin up completely. Then the next highest turn count coil, with the next smallest gauge wire, will be significantly smaller and encompass less coil area even though it has more turns. As we can see from Figure 5, with an air coil we can very clearly see this effect. There is a discontinuity in the relationship between turns and inductance every time we “jump” to the next gauge. The larger wire at the highest turn counts is yielding more inductance per turn than the smaller wire. If we put a pole piece in the core of the coil with minimal magnetic permeability, like AlNiCo 5, we still see an area effect but it is reduced. If we put a highly magnetically permeable pole piece in the core, like low carbon steel, the area effect goes away entirely. With a highly permeable core, the magnetic flux becomes so concentrated that it doesn’t really matter exactly how much area the turn encompasses, as long as it’s going around the concentrated flux in the core. The effective area of any given turn becomes the area of the core because that’s where virtually all of the magnetic flux is.

And finally, what does this mean for the player? How can an understanding of inductance help with pickup selection? Well, for one thing since inductance is directly related to how efficient a pickup is in capturing magnetic energy, it is a much better and more direct measure of output than resistance. That’s probably the most important thing for the player to remember, and to try and interpret the number in relation to their known reference points. Table 1 lists some of the typical specifications for a few of the more popular pickup types, representing a range of some of the original designs. With the rise of aftermarket pickup makers, the specification range of all of these designs has expanded considerably from what is represented in the table, which characterizes the “classic” interpretations of these designs. First we have the Stratocaster® pickup. The Strat® pickup uses low permeability AlNiCo 5 pole pieces, and a coil wrapped around those poles consisting of 7500 – 8500 turns. This yields typical resistances in the range of 5500 – 6500 Ohms (5.5 – 6.5 kOhms) and inductances in the range of 2.3 – 3.0 Henries. Next is the PAF. A PAF consists of two coils, roughly the same size as the Strat’s coils, except the PAF uses high permeability steel pole pieces – slugs in one coil, screws in the other. Each coil of the PAF is wound to something in the range of 5500 – 6500 turns yielding a typical resistance of around 7000 – 9000 Ohms with the coils wound in series (resistance adds in series). Even though the PAF is wound only slightly higher than a Strat style single coil, the more permeable steel pole pieces result in a significantly higher inductance, in the range of 4.0 – 5.0 Henries. Finally, the P90 is a single coil design that utilizes steel pole pieces and a shorter and fatter coil than the Strat-style pickup. One thing to keep in mind is that in a conventional pickup design with individual pole pieces much of the core of the coil is air, unlike in a Zexcoil where most of the core is filled with the pole piece. So, as in a P90 where the pole pieces are fairly narrow screws, only about 25% or less of the core is actually occupied by the permeable material, so the effective permeability will be much less than what we would expect based on steel alone. Accordingly, you can see a significant effect of the area of the coil on the P90 response. At a turn count that is more or less the same as a PAF and with a similar (or even lower) effective permeability in the core, the P90 yields a much higher inductance due to the larger area encompassed by the turns. We could also surmise that the area effect would be more significant on a Strat-style pickup than say, a PAF at similar coil dimensions, because of the much lower permeability AlNiCo 5 pole pieces. This is certainly one of the reasons that things like insulation type and winding technique, which one might otherwise assume would be fairly subtle effects, can have an audible impact on the response of these types of designs. Looking again at Figure 4, we can also start to imagine how other permeable masses in the magnetic return path to the string, like the magnets in PAF pickups, have an effect. On that point, I’d like to reiterate, the important field in terms of how a pickup generates signal is the field of the string, not the magnetic field of the pickup itself. The solenoids depicted in Figures 1 and 4 show the field generated by a current in a coil, and because of that the field is necessarily enveloping the coil. While these figures help to understand the basic concepts of inductance and to highlight why pole piece properties are important, and they are not dissimilar to the way you generally see the magnetic field of the pickup depicted in descriptions of electric guitar function, they don’t represent the way signal is generated in a pickup. The way a pickup functions is depicted in Figure 3, as a receiver of the magnetic flux generated by the moving, magnetized string. If this statement causes you pause, I suggest you read this blog post.