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.

Electrical Parameters and Pickup Performance, Part I - Resistance

In the course of developing the Zexcoil hum canceling format, I was faced with some insurmountable engineering problems with the materials that are conventionally used in Strat-style single coil pickups. As I have been explaining, the pole piece is primarily responsible for defining the timbre of a passive electric guitar pickup, and in the case of single coils it is the electromagnetic properties of AlNiCo alloys (and most specifically AlNiCo 5) that define the classic Strat tone. The problem was, AlNiCo alloys don’t work very well in the Zexcoil format because they can’t effectively close the magnetic dead spot between the D and G strings (where the magnetic polarity flips so we can get hum canceling). So I was forced to develop an understanding of what it was exactly that caused AlNiCo alloys to “sound” like they do and how I could get the same response from different materials, materials capable of closing the magnetic seam.

We think we were successful in solving the problem, but we’ll let you judge that by your impressions of our pickups. What we also got though, was a physical model for the electro-magnetic response of pole piece materials that basically allows us to create a map of tonal characteristics. We use this map in the design of all of our pickups. Since this is a basic model, the general responses are not limited to Zexcoil pickups, and pickup performance in general can be interpreted in the same context.

But we’ve struggled with how to make that information accessible to players to the extent that they can use it to guide their own pickup choices. We’re going to try some new things coupled with the roll out of our Z-Core™ and Z-Series™ models this summer. One of the things we’re going to do is provide a lot of the electrical specs for the various models.

In order for that information to be useful, it’s necessary to place the raw numbers in a tonal context. Resistance, Inductance, Resonant Frequency, Quality Factor, that’s all great: but what does it SOUND like? We’re going to attempt to answer that question, or at least provide some good guidance that might allow players to interpret the electrical specs more easily. We’ll start here by discussing the electrical parameters that we consider critical and describing what they are and what they mean in a terms of pickup performance.

First, the most ubiquitous electrical specification in use today, and by most accounts the most meaningless, Resistance. Electrical resistance is exactly what it sounds like; it’s the tendency of a material to resist electric current. Resistance is measured in Ohms, the symbol for which is “Ω”. Sometimes you’ll see a “k” in front of the“Ω”, and this means multiply by 1,000. So for example, 250 k Ω is the same as 250,000 Ω, it’s just shorthand.  In almost all electric guitar pickups, resistance is a function of only two things; 1) the total length of wire that encompasses the pickup’s coils and 2) the gauge (or more accurately: thickness) of that wire. You can think of resistance like the width and length of a pipe that you are trying to pump water through. The narrower and longer the pipe, the harder it is to push to get the water through. So then, the thicker the wire (or the lower the gauge number), the lower the electrical resistance. The longer the wire, the higher the electrical resistance.

Most Strat style single coil pickups use an identical design and dimensions, the same 42 awg copper wire and similar AlNiCo 5 pole pieces. In this limiting case of “all other things being equal”, resistance actually is a pretty good descriptor of pickup performance. That’s one reason that it has become so widely used. But, change one thing and it starts to get a lot less meaningful. Change the wire gauge, and the resistance for the same length of wire changes. Change the pole piece and the output will change, even at the same resistance (we’ll talk about some of those effects in the next blog post on Inductance). Even change the material used for the wire, say from copper to silver as in the Seymour Duncan Zephyr pickup, and resistance will change at the same length of wire since resistivity (resistance per unit volume) is a property of the material and silver is a better conductor, in that it has inherently lower resistivity than copper.

So, resistance is not a great number as an absolute measure of pickup response. In the Zexcoil format, we pretty much use the fattest wire we can for any given winding level, and we may use 2 or 3 different wire gauges in a single pickup to get them tuned where they need to be given our unconventional magnetics. Resistance also represents a loss of efficiency, and in keeping with our over-arching philosophy of maximizing efficiency, we basically try to keep the resistance as low as possible for any given design.

Pickup Resistance and Pot Values

One place where resistance does become important is in how the pickup interacts with the controls. The simplest way to think about a potentiometer (“pot”) in a guitar is as a gate. A typical guitar control is just a variable resistor in a circular format. The knob turns a wiper that is contacting a semi-circular resistive strip, with one end of the strip connected to ground. When on “10”, the full resistance of the pot blocks the path to ground.  When the pot is set to “0” that block is removed, and pretty much all of the signal goes to ground and we get no volume. When the pot is on “10”, most of the signal is retained, but some of the higher frequencies can manage to sneak through the pot and get lost to ground. The higher the value of the pot, relative to the pickup, the less high end is lost. Go back to the water analogy. Think about the volume pot/pickup system as a garden hose with a pin hole in it. The water coming out of the nozzle at the end of the hose is like the signal going out to the amp. With a small pin hole in the hose, almost all of the water in the hose still comes out the nozzle, but just a little bit of spray will escape through the pin hole. That spray is like the high end being lost through the volume pot. A 250 k pot versus a 500 k pot is like a bigger hole in the hose so more spray is lost. A volume pot on zero is like a hole in the hose big enough so that all of the water comes out the hole and none makes it to the nozzle. Strat style single coils, with resistances on the order of 5,000 Ohms or so, generally use 250 kΩ pots. Hum buckers, which typically have higher resistance than single coils – approaching 10,000 Ω, are usually better balanced with 500 kΩ pots. A good rule of thumb is that the pot value should be 25-50x the value of the pickup.

We refer to this scenario of attaching a resistance along with the pickup as “loading”. Tone pots (at “10” anyway, when you start dialing down the resistance of the tone pot, the tone capacitor comes in to play and things get a lot more complicated) represent a similar “load” on the pickup as a volume pot. In fact, when you have both a 250 kΩ volume and tone pot connected the effective resistance to ground is only 125 kΩ, so more signal (highs go first remember) can bleed over the lower barrier. A “No Load” tone pot is one in which there is a physical break in the resistive strip just below “10” on the dial. When the wiper is in the “10” position then, the pot is disconnected from ground and the load is removed. With a no load tone pot on “10” the only path to ground is through the volume pot. This has the audible effect of maintaining more of the high end “air”, and the tone will darken up noticeably when the tone pot is engaged just below “10”, especially through a clean amp. Go back again to the water analogy. A no load pot is like putting a bandage over the pin hole when the pot is on “10”, so the hole in the hose is plugged up and the spray is not allowed to escape. Just below “10”, as the resistive strip is engaged, it’s like the bandage has been removed and the spray through the pin hole is allowed out. We like to use no load pots on the neck and bridge positions, and we especially like the way they open up the “in between” positions. For most typical control layouts, the bridge pickup can benefit from tone pot loading, so we don’t use them much there. One exception would be the Convertible for Bridge where we like to use the no load tone as a “load toggle” between the two modes; unloaded for the higher resistance series mode to let all of the power come through and loaded down a bit more to attenuate the highs on the lower resistance parallel mode.