The Pickup Equation: Resistance, Inductance, and Capacitance Demystified

Decoding the science behind pickup performance and tone.

This article serves as an introduction to guitar pickups. The topic has been chosen because I believe that not only are guitar pickups misunderstood, but the industry does an excellent job of exploiting this confusion to sell us all kinds of products.

First and foremost, there are two ways of looking at guitar pickups. From one perspective, they are simple and crude devices—some might even say poorly engineered. From another perspective, guitar pickups are extremely complex and sophisticated, where every detail makes a difference. They represent one of the most crucial components in a guitar player's connection to the rest of their system, meaning even micro-changes in pickups can significantly affect how we feel about creating music.

What’s important to understand here is that, firstly, everything makes a difference, and secondly, some things make a bigger difference than others. In this article, we’ll discuss the aspects that make the biggest difference, so you can use this information to save time and money when selecting a pickup that suits your needs.

Now, I mentioned earlier that the industry uses a confusing approach to market their products. This is, first of all, good for business. Secondly, it creates intrigue around concepts that can actually be explained with little to no effort—again, good for business.

The guitar pickups we’re discussing here are magnetic guitar pickups. These function as part of a larger system comprising four crucial components:

  1. The permanent magnet – This is present in all magnetic guitar pickups and is responsible for creating the magnetic field.
  2. The magnetic field – This field is generated by the permanent magnet and forms the second component of the system.
  3. The coil windings – These generate voltage when the magnetic field is disturbed or excited.
  4. The guitar strings – These are magnetic and reside within the magnetic field. They become part of the magnetic circuit as magnetic flux passes through them.

When a string vibrates, it disturbs the magnetic field, causing its strength to fluctuate relative to the string's position. This fluctuation induces an oscillatory voltage in the pickup coils. Simply put, changes in the magnetic field translate to changes in voltage within the coils. This is how string vibrations are "picked up" and sent to the guitar amplifier.

Now that we understand the main components and how the system works, it’s important to mention that the magnetic field is quite "leaky." This means it isn’t solely focused on the strings but also picks up interference from the surrounding environment, which is why magnetic pickups are prone to noise and hum.

Magnetic fields are also sensitive to their surroundings. Adding any material near the magnetic field alters its shape. This is, for example, how the Telecaster bridge pickup base plate works or why screws made of specific materials can affect a pickup's sound.

Let’s say you’re shopping for a guitar pickup on a popular website. You’ll notice many options available, but how do you differentiate between them? Typically, these websites focus on just one measurement: the DC resistance of the pickup. They might also mention the magnet material, but that’s about it.

Not much is said about the magnets themselves beyond a few popular types and their general characteristics. This leads to the biggest misconception: that DC resistance equals the signal output of a pickup.

To address this, we’ll mention a few other important measurements that aren’t often listed in the specifications on these websites. We’ll explain how these measurements affect the final sound you hear, helping you make a more informed choice

Figure 1 - Parts of a PAF style Humbucker pickup (borrowed from StewMac)

Since we’ve been discussing permanent magnets and magnetic fields extensively, let’s deepen our understanding of permanent magnets a bit more. We all know that the most famous ones are AlNiCo magnets, which are an alloy of aluminum, nickel, and cobalt. These magnets are categorized into different "strength" groups (to put it simply).

For example, there are AlNiCo II magnets and AlNiCo V magnets, with the latter commonly understood to have a "higher output" than the former. While the reality is a bit more nuanced, this generalization is somewhat accurate. AlNiCo V magnets are composed of a slightly different alloy compared to AlNiCo II magnets, resulting in a stronger magnetic field, slightly more string pull, and ultimately a higher output signal.

What’s interesting is that even within the same group, there can be variations between magnets. For instance, an AlNiCo V magnet in one pickup might differ from an AlNiCo V magnet in a different pickup made by another manufacturer. Sometimes, these differences are more significant than you might expect.

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Today, various other alloys are also used for magnetic guitar pickups, including ceramic magnets and even neodymium magnets. While each type of magnet has specific characteristics in the magnetic field it generates, the most notable difference between magnets of varying strengths is that stronger magnets produce stronger magnetic fields. Exciting these fields generates higher voltages in the pickup coils.

This is crucial to understand because using a stronger magnet allows for fewer coil windings while still achieving a comparable output signal to a pickup with a weaker magnet and more windings. The most significant difference in this case isn’t the output but the sound the pickup produces.

Now, let’s introduce another definition and discuss it further:

The output voltage of a pickup is determined by the strength of the magnetic field and the number of coil windings.

In the previous definition, we introduced a new player in the game: the number of windings in the coil. The coil of a magnetic guitar pickup is actually very simple. Wire is wound around the bobbin, and at the center of this winding, we place either a magnet or some type of ferromagnetic material.

The number of turns in the coil determines the strength of the electromagnetic induction that occurs when the magnetic field is excited. Essentially, adding more turns increases the output. However, there are real-world limitations. We cannot add an unlimited number of turns due to the physical properties of the magnet and the limited space on the bobbin.

In cases where space is limited, thinner wire is often used to increase the number of turns. But thinner wire comes with higher resistance per meter. All these parameters—wire thickness, number of turns, and coil size—drastically impact the sound of the pickup. And that’s how this game is played.

Let’s revisit the point where I said that everything makes a difference in a guitar pickup:

  1. Pickup position makes an enormous difference, so it’s pointless to compare two pickups installed in different positions on different guitars.
  2. Pickup design matters just as much, as the shape of the coil dramatically affects the sound (e.g., comparing an AlNiCo V Telecaster bridge pickup to an AlNiCo V P90).

It’s essential to compare apples to apples.

Now, let’s address another crucial factor always present when using guitar pickups: the rest of the guitar electronics.

Guitar electronics come in various forms, sometimes simple, sometimes more complex. Most of the time, they are passive systems, which are inherently imperfect and involve losses. These losses are critical to understanding the sound we ultimately hear.

What do I mean by guitar electronics? This includes everything from the pickup to the first gain stage of an amplifier, pedal, or modeler. It encompasses potentiometers, capacitors, treble-bleed circuits, and even the guitar cable! You’d be surprised by the importance of the guitar cable in the overall sound.

The passive electronics circuit connected to the pickup loads it down and significantly alters the sound. Resonant peaks shift, bandwidth is lost, and various sonic characteristics change. This is why all my measurements are taken as part of the complete circuit—because, honestly, I don’t care how a pickup sounds on its own. I need to know how it sounds in my guitar.

Now, let’s discuss the three main measurable components of a pickup coil: DC Resistance, Inductance, and Capacitance.

  1. DC Resistance is the most familiar parameter, but what is it? Resistance is solely determined by the thickness and length of the wire used. Thicker wire has less resistance per meter, and the longer the wire, the higher the DC resistance of the coil.

Anyone paying close attention will notice that increasing the number of turns in the coil also increases the length of the wire, thereby raising the DC resistance. Pickups with high resistance either have a lot of turns of wire, thinner wire, or both.

  1. Inductance is often overlooked, but it tells us much more about a pickup than DC resistance does. Unfortunately, precise inductance measurement requires more expensive equipment than a simple multimeter.

What determines the inductance of a pickup? This isn’t easy to answer, as inductance depends on several factors, some of which are challenging to measure objectively. Think of inductance as the measurement of a pickup’s efficiency. It’s influenced by:

  • The number of turns in the coil (more turns = higher inductance).
  • The type of core material (e.g., magnet or slug).
  • The shape and size of the coil.

Entire books have been written on this topic, and while it’s possible to measure how each parameter affects inductance, such an analysis is far beyond the scope of this paper—and frankly, a bit boring. The key takeaway is this: inductance is determined by the number of turns, magnet type, and winding quality.

Interestingly, more precise winding (with less scatter) results in higher inductance. But why do we often prefer pickups that are hand-wound with more scatter? The question becomes, do we really want the pickup to be "perfect"? Or is a hand-wound pickup from the '50s actually perfect? This is exactly what we aim to demystify here.

  1. Capacitance is another fascinating component of guitar pickups. It’s also quite difficult to measure precisely without high-end equipment. Whenever you have two conductors separated by insulation, you create a capacitor. In a guitar pickup, thousands of wire turns lie on top of each other, with insulation in between.

The capacitance of a pickup is determined by two factors:

  • Insulation thickness: This depends on the type of wire used (e.g., Heavy Formvar, Plain Enamel).
  • Winding quality: Similar to inductance, the more scatter in the windings, the less capacitance you’ll measure in the end.
Figure 3 - Example of a Plain Enamel insulated guitar pickup wire

Now, finally, we step into the world of: What difference does it make in the sound?

With a solid understanding of how a pickup works and the measurable elements in the pickup coil, we can now explore practical examples and examine frequency response plots. Remember, though, that frequency response is just one way to analyze how a pickup sounds.

But don’t forget the golden rule—what? Everything makes a difference.
The differences may not just affect what we hear but also what we feel. And let’s face it—the best measurement device for feel is a very mentally stable, experienced guitar player who genuinely tries to give an objective opinion. But good luck finding that, because this topic is just far too subjective.

For now, let’s stick with what we can measure.
\[L = 4H\]

\[R = 8k\Omega\]

\[C = 250pF\]

And we will assume that in the circuit, we have 2x 250kΩ potentiometers for tone and volume, both turned fully open, including a 5m cable connecting the system to the amp. The cable essentially adds capacitance in parallel to the entire circuit, cutting some high end. It’s a typical situation we would encounter in a Tele-type guitar.

Take a good look at Figure 3:

Figure 3 - A plot showing the frequency response of a guitar pickup with all the real world electronic losses approximated

Each line in Figure 3 represents the frequency response of a pickup with a certain component changed. Obviously, it is almost practically impossible to increase the inductance without affecting the resistance, but I have created these plots just to illustrate how each of these parameters impacts the sound.

If you look at the green line, this is our reference, corresponding to the values I mentioned earlier. We will compare all the other lines to the green one.

The blue line represents the frequency response when only the resistance is increased to 16kΩ. Not a big difference, right? It actually loses some output and makes the resonant peak a bit smoother.

If we look at the dark yellow line, this is achieved by increasing the capacitance to 800pF. Increasing the capacitance results in a loss of high-end frequencies, but it also changes the Q factor of the filter that creates the resonant peak. In practice, this makes the sound more "quacky," which is not always a bad thing. In music, you can find many examples of a similar sound because a very similar effect happens when you use a longer cable or turn down the tone pot.

Now, if we take a look at the red and pink lines, these are the "most different" compared to where we started. The red line represents the pickup with an inductance of 10H, while the pink line represents the pickup with an inductance of 2H. What does this tell us?

The sound of the pickup is GREATLY affected by its inductance.

From this plot, we can infer that making the pickup "better" or "more perfect" (increasing the inductance) will make it highly susceptible to treble loss due to guitar electronics losses (mainly cable capacitance). If you were paying close attention, you will quickly realize that if you wind many turns on a coil, you will not only increase the output but also increase inductance and resistance. The pickup will not only be hotter, but it will also be darker. This is a very important point.

So, what if we wanted to increase the output but keep the pickup nice and open? Well, normally we would use a stronger magnet that generates a stronger magnetic field. This way, we could keep the same number of windings or even use fewer windings. This is a generalization, of course; it’s not that simple. Many engineers throughout the years have implemented different strategies to create higher-output pickups, and they’ve achieved different results. Starting with the DiMarzio Super Distortion and continuing with the work of people like Bill Lawrence, we’ve seen many different solutions to the same problem—each of them interesting and inspiring for making music.

There are examples like the one with Paul Reed Smith's 513/509 pickups. Paul and his partner (whose name I do not recall) wanted to create a very efficient pickup. They created a special coil shape, used special magnet shapes, and reduced the distance between the wire and the magnet to make a very efficient pickup. Efficient equals inductive. However, that pickup was just too dark for me, and it had a resonant peak around 1.5kHz, which made it very nasal. But, as I said, this is all subjective. I’m sure it worked for someone.

One more thing I’d like to touch on: since many people associate resistance with output, yet Slash has a signature set with Alnico II magnets and a DC resistance of about 16kΩ, which is still considered vintage. That’s because Alnico II magnets are a bit weaker than their more popular counterpart, the Alnico V, so more turns of wire are needed for these pickups to have a similar output. So basically, if you want a bit darker and smoother pickup, go with the Alnico II, or if you want a more punchy and open sound, go with an Alnico V with a DC resistance of about 8kΩ. This is really just a rough example to prove a point.

So, that’s basically it. A not-so-short, but I think comprehensive introduction to guitar pickups and some practical things to look out for. I’m going to be writing more about this. Until then, happy pickin’.

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