Pickup Physics

First, here is one that I cannot seem to forget. It was made in an article about how guitar pickups work and it goes like this:” Maybe you remember from 5^th grade physics class that if you wrap electric wire around a steel nail and send current through the wire, you have a magnet”. So far true, but he continued: ”Well, that explains about 90% of how a guitar pickup works!” Here is my take on that: It does not explain it at all, but if I should put a percentage to it, I would say less than 1%. Namely, it is insulated wire wrapped around a core of magnetic material. After that the similarities stop.

I will leave it at that, for now, at least. Now it is time to delve into how it really works. Some of this has been likely touched upon from time to time in popular media, but by far it is nothing but hype.

My Cheap Trick Story

This part is inspired by an experience I had back in the 80ies involving the band Cheap Trick which you probably know. I was sitting at the bar in a place owned by a friend who just happened to have gone to school with Rick Nielsen from the band. This was in Rockford IL, where I lived back then. For reasons I do not remember, my friend always had guitars, drums and amplifiers sitting around, not the best instruments at all because they were there for anyone to use. As I am sitting there, the entire band walks in and after a short time they go over and pick up the instruments, not even close to their own, and after some tuning and other preparation they start playing some of their songs. I was quick to get up from the bar and rush to the little area where they were, I was close enough that I could have reached out and touched singer Robin Zander. And the sound, it was like hearing Cheap Trick in concert, something I has done several times, but never like this! After the bar had closed, we sat in the office and my friend said:”Rick invited us to his house afterwards, but I said no thanks”. Boy, I missed the experience of a lifetime, but I got an unforgettable experience in sound and the extreme importance of the player!

As it may seem from the above, just about all people that contribute to the whole discussion about sound (most people use “tone”, a word that is so ambiguous that it in just about meaningless) concentrate on the pickup, just discussing the pickup as it was the only component contributing to the sound. The sound of the pickup, the way they talk about it that is the only thing, as speculated earlier they must be pickup makers.

Now get ready for this: I will go out on a limb here: “The pickup does not have a sound, or “tone”, if you wish”. It does not. Here is why.

The signal transmitted to the pickup from the string depends on: How the string is plucked, where on the string it is plucked, the location of the pickup(s), all typically indicated as a fraction of the string length, L.

The different magnets available and that are typically used in pickups provide a magnetic field, they DO NOT provide any tonal qualities, such as glistering highs, warm lows, mid-scoops and I could continue with the buzz words heard on YouTube and even sadder, in pickup maker’s advertisement. The performance of the magnet is NOT frequency dependent in any way and the magnet CANNOT be de-magnetized to “give you the tone you want”. Basically this goes for slugs and screws used in some pickups. There can be a difference that is material related, that will be discussed below.

Does the magnet wire make a difference, the answer is NO. Nothing meaningful, at least. It can determine how many turns you can place on a given bobbin, and therefore the total resistance of the coil, which is also meaningless, as will become clear later. Also, see the Electronics page.

The sound is created by the guitar player when plucking the string or strings. The way he/she applies the pick to the strings makes a big difference in how the string will react, how it will start and continue to vibrate. This whole process determines the sound, the original sound. In addition to that the sound is textured depending where the string is plucked, measured as the distance from the bridge as a fraction of string length is commonly used. Similarly, it is shaped by which pickup that is in use at the time, same location method as in plucking position. The magnet strength is of less importance in this case, something that will be clear later.

Now, the string vibration starts with a displacement of the point where the pick is applied such that the string takes the shape of a triangle, since it is fixed in both ends and the string being flexible, it will stretch ever so slightly, but it is the triangular shape originally that sets everything in motion. What happens next is fortunately extremely well documented and tested in theory and practice and has been describe by what has become known as the wave equation, not only is the equation known, solutions to it are also known, at least in theory. Various parts of the equation and the solution, the constants and functions are unique to the discipline, whether we are talking about sound waves, radio transmission or in this case string movements. For guitar strings the number of articles out there is very limited, the most concentrate on the part of the process that we call “steady state” where the string is ringing out with a mostly sinusoidal wave shape so the solution would only contain the fundamental frequency and the 2nd harmonic. The first part where the string is initially plucked is far more interesting, but also much harder to describe. It is, however, more or less how the guitar player “sounds”.

The triangular shape will with time develop into a standing wave that behaves in accordance with a list of parameters, first the point where the string was plucked, the length of the string, the weight of the string (diameter), tension and not to forget, the end points, in this case nut and bridge. No, I did not forget the wood species, wood has no influence on the string behavior and thereby the resulting sound. We are talking about electric guitars here, not acoustic guitars where wood has an influence. Not with electrics, at least no bearing on the sound. I am amazed that this is still being discussed!

Now, as mentioned, the string behavior is very well know and predictable. We do need, however, to take a closer look at the endpoints of a string. There are some, unfortunately contradicting requirements to a nut and a bridge. If the string ends had been clamped to a body of considerable mass connecting the end supports, the resulting wave equation for the string movement would be easy to solve. That is not reality, however, because we need ease of changing strings, we need to be able to tune the strings without changing the length, e.g. the distance between endpoints needs to be constant (scale length).

If the situation is as first described the string would vibrate forever, well there would be some air resistance (friction) that would result in the string losing energy and at some point come to a rest as it started. In order to continue to vibrate, the standing wave would require that there would be perfect reflection of the wave at the endpoints. With what we have to accommodate with the real necessities as mentioned, the string will have to move at the endpoints and the guitar will have to be carried by a single person, sometimes for hours. So the conclusion is that the reflection of the wave at the endpoints is not perfect so there will be losses since vibration is transferred to the rest of the guitar resulting in a much faster decay of the standing wave, a considerable reduction in time before the string comes to a rest. Now the question will come up, what about “sustain”. I would say, what about it? Name me one place in electric guitar music where sustain matters. Just perform a simple test, say you pluck an open A string and let us say that you record the sound without any effects, dry recording. If you record at a tempo of 60 bpm, the sound will ring for 20 bars at least, all notes we play are much, much shorter than that! You do not need that kind of sustain, any kind of sustain, but if you do purchase an effects pedal or processor there are about a million of them out there! I think that “sustain” of a guitar is another irrelevant buzzword that has stuck, sorry to say.

Sustain

The only contributor to a note’s sustain is the string, for ease of understanding, we will expand this to from the point of plucking until the sound has dropped to a level of say -60dB, picking with the same applied force every time. The only component of the guitar that determines sustain is the string, most important parameter, the string diameter, everything else subtracts from the total sustain. If a string was mounted in a way that would ensure perfect reflection at the end points (nut and bridge), the string would almost ring forever. I say almost because internal friction (stiffness) will be the only damping on the vibration. That would be if both the nut and bridge would mechanically clamp the string end to the supports and that these would be clamped to a body of great mass and density. If you have seen the Les Paul experiment with a rail track with a string clamped to it will know what I am referring to. Good example of a substantial mass where nothing moves! It is totally impractical, of course, to make a guitar out of a rail track. Any practical wood for guitar bodies and necks are so close in density so there will be no difference in how the vibration is affected. I will mention information available in literature on the subject of string vibration a few times during this, especially (1) which has a superior but very high level way mathematically to present the various aspects of string behavior by examine the excitement of the string (plucking), the end support problem by nut and bridge, the effects of string stiffness and much more. It is all in chapter 2, Vibes. I have been wanting to include a condensed version of this here, but it is a subject that requires a deep treatment, so I have kept it to a minimum. This section is about pickups after all. I must stress the fact that string vibration is of extreme importance to understand because it is essential to the player’s sound. The next few paragraphs will deal with the subject.

Fortunately, we have a little bit of a choice here, We can use an analogy that most people know that when we are talking sound, a soft material will absorb sound whereas a wall made out of hard material will reflect the sound extremely well. The same goes for a vibrating string, harder material will reflect the string movement better and greatly aid in the strings movement. Also harder material makes the string slide easier, making it stay it tune. This is mainly aimed at the nut, the bridge for electric guitars is already made out of a hard material, metal.

Well, let us get back to the string vibration. As mentioned earlier the location of the plucking has an influence of the string vibration, more specifically the harmonic content of the wave. So far we are only discussing the string, so the pickup location does not come in to play just yet, that will become clear when we talk pickup later. Here are more factors that matter when it comes to the harmonic content of the string vibration, the force applied by the picker, the pick width and stiffness, the direction of the pick movement (plucking angle). The string movement is, if we include all, three dimensional, but since we later on will include the pickup, it is enough to consider the movement in two dimensions, parallel to the guitar body and perpendicular to the body. The steady movement of the string can be described as a double circular movement (in two dimensions). This accounts for the fundamental note plus the harmonics. There is literature out there performing an in depth analysis of guitar string motion (Ref 1), as mentioned earlier, if you are interested in a detailed evaluation of string theory, read the section called Vibes. 

When a string is plucked, an amount of energy is transferred to the string, after that the only thing that happens is that the total energy of the system will decrease as the string is transferring its energy to the rest of the system through the nut and bridge that will vibrate and transfer energy to the neck and body where the energy is lost through vibration of the body and neck. The rate of energy loss is related to the string reflection at the ends, the higher the rate, the shorter the sustain time. No wood, neck or body, no bolted or glued joints will have any effect on the sound that is any different from any other. If you hear the comment:”hey, this type of wood sounds louder than that type of wood” or that “this fix to the neck-body joint has massive influence on sustain”, it is 100% false. If someone tells you that the nut material or the bridge have influence you can be sure they are correct! There are a few other things that matter, but we will leave these to a different forum.

Letting the string ring, the triangular shape will morph into a more sinusoidal oscillation, as the amplitude becomes smaller, that is consistent with the string length, this a natural process for the string, because the original triangular shape is considered unstable whereas the sinusoidal vibration is the natural behavior of the string left to its own devices, the vibration assumes a steady state. How long this will be audible, depends on the inertia of the string, in other words, the larger the diameter the longer it will be in motion. The higher the frequency the shorter the duration of sound.

So the amplitudes of all the harmonics will decrease, the higher the faster. The process has been described mathematically with equations, that we will look at towards the end, that will include the amplitudes of the frequencies, the harmonics or as they are also called, the partials. Having discussed harmonics, we know that the position where the string is plucked has an influence on the amplitudes of the harmonics. Let us say that we pluck the string in a distance of L/6 from the bridge, working out the math determines that the harmonic number 6 will have amplitude A = 0, so will number 12, 18, 24 and so on. L/6 is not taken out of the blue, if you think about it, it is a very common plucking position, for me and many other guitar players. One more thing before we get into how the pickup handles the string motion, it should be mentioned that the string motion depends on how far we pull the string when plucking and to some extent in what direction, since this will affect how the pickup “sees” the string motion. As I have mentioned before, the sound depends a lot on these factors, in other words, on the player and thereby the unique way the string is plucked. That is the sound of the guitar player, it is not very dependent on his equipment. The physics of a vibrating string is very elaborate and complicated mathematically. I would love to get into it a lot more, but the subject is described elsewhere, see Ref 1. This is after all about pickups and electronics. There is a website that is quite interesting concerning the effects of pickup placement, including the comb filter effect. I will add a link when I locate the website again.

Pickup Specifics

Now it is time to look at the pickup and how the string vibrations get transferred to an electric voltage and later on how this signal from the pickup gets handled through the processing to the input of the amplifier. Now, up to this point we have been looking at a string and how it behaves as a string over its entire length, we add a pickup and the whole spectacle changes since we are now only looking at how the string behaves in this particular point of the string’s length. This is very important to keep in mind!

The pickup is a collection of cylindrical magnets, one (or two) under each string OR a number of pole pieces of ferromagnetic material, likewise placed under the strings, magnetized by one bar magnet. Both the single magnets or the bar magnet can be made out of different alloys giving them residual magnetic fields varying in strength which with a given number of turns of wire in the coil that surrounds the magnets or pole pieces will result in a voltage output that will reflect the strength of the magnets. The strings on the guitar must be of a ferromagnetic material in order to have a significant influence on the magnetic field created by magnets or poles that is directed at the strings. There are variations of the described constructions, but that will not affect the basic operation of the magnetic pickup. Just to be complete, there are other types of pickups such as optic sensors and piezo electric pickups. These work in different ways than the magnetic pickup which is by far the most common for electric guitars and that is what we will concentrate on for now. Some piezo pickups, however, come in the form of string saddles, a thing that we will get back to later.

Since there is no significant difference, at least in principle, between magnet pole pieces and regular pole pieces “powered” by a single bar magnet, we will look at the operational details using a magnet. Since the strings at rest are placed in the field created by the magnets at a specific distance from the face of the magnet, something will change when the string moves away from the rest position. What changes is the field that the coil that surrounds the magnet senses, this change in magnetic field will induce a voltage in the coil creating the signal that the pickup transmits to the signal path. Earlier we looked at the vibration of a string an how the parts of the string would move around in space, the description was indicating the location of the string in space with respect to a resting in position and we saw how the position where we hit the string with the pick has an influence on the resulting way the string moves. Mounting the pickup under the string a distance from the bridge, the pickup will react to what the string movement is at that spot only and that will also influence the voltage output from the pickup. And here is the important part, the pickup signal will be proportional to the speed at which the string changes position creating a change in the magnetic field, not on the actual location of the string. This has a significant influence on the harmonics in the signal and how the higher harmonics decay in amplitude with the harmonic number compared to equivalent amplitude for the vibrating string. Looking at it in a little different way, earlier we concentrated on describing how the string behaved over the entire length (L) of the string when plucked at a certain point (p) on the string. Moving on to adding a magnetic pickup under the string at a position (P), we completely have to change focus to describing how the string is moving in that narrow spot on the string in that vertical plane over the pickup magnet and not only that, we have to extract the speed at which this point of the string moves in time and from that find how this movement changes how fast the magnetic field changes with time at the surface of the magnet.

This was a mouthful to take in, so let us look at it in a different way. The string is located in a magnetic field, the strength of the field depends of the location of the string with respect to say the top surface of the magnet. The further the distance the weaker the field and the function of field strength (B, magnetic flux density) with distance is not a linear relationship which means that the output signal from the pickup coil is a distorted version of the actual string motion. This is the first stage of distortion, but there will be more in this process.

To have a point of origin, we select the center of the top magnet surface and we have the string placed a distance above the center of the magnet, we can think of the string moving with respect to this point, part of the movement will be vertical and part will be horizontal with respect to the point on the top surface of the magnet. How the string moves depends on how it was plucked (the player), where on the string it was plucked and finally, when we consider the voltage output of the pickup, on the location of the magnet (the pickup). When we look at the B-field from the magnet we see that it varies significantly in the vertical direction and very little in the horizontal direction.

String Geometry

Let us look at an example where the string after it is plucked at position p and the pickup is located at position P, both normally indicated as a fraction of the open string length L, all used to describe the movement of the string and especially the resulting harmonics of the resulting movement on string speed and pickup output. If we take a string movement that is circular, meaning that the point of interest to the creation of a pickup output voltage is moving around in a circle above the pole piece in a distance, r, from the surface of the pickup, when at rest (sometimes referred to as h). This is a situation that is easily simulated on the bench, so this is something we will look at later as part of the experimental phase of this effort. Now, from what we have just seen, the pickup reaction to vertical movement of the string is much stronger than the horizontal movement, so if we use a picture analogy, the string movement will look like a perfect circle where the output of the pickup will look like a circle that is flat (ellipsis), deformed in the horizontal direction elongated in the vertical direction. This simple analogy is showing one part of the distortion of the signal.

Next step is to look at how the output signal of the pickup is developed from string movement through magnetic field changes to electric induced signal and therefore voltage output of the pickup. A good way of looking at this is in two steps, number one, the signal creation that is purely based on physics and number two, the signal processing that based on electronics and regarding the pickup as components in an electric circuit or equivalent diagram. All this is happening even before we get to the output jack of the guitar! At this point I have to warn the reader that the two parts cannot be mixed up because that will royally screw things up. This has been seen in many explanations given on YouTube and in popular magazines. Beware!

Physics

A magnet is characterized by size, material and magnetization and before we add a winding around the magnet and add a string above the magnet we will look at how the magnetic field behaves at some distance from the magnet top surface. The field strength at the center of the top surface of the magnet we will call Bo and consider this our point of origin for the determination of the magnetic field strength, B, at a distance from this point. Now, some will say that I keep talking about the B field, but we know what causes an output of the coil around the magnet is magnetic flux, or more correctly, the flux change with time. The fact is that there is a simple relationship between the flux and the B field (often referred to as the flux density) and if you are familiar with the physics you will know that there is not much sense in talking about flux before we have the coil around the pickup defined.

As we move on, Fig. A shown a cylindrical magnet and the B-field the magnet creates around it in a plane going through the center point of the magnet where the field strength is Bo, we can call this our yz plane, if we add a string on the z-axis going through the center of the magnet, Fig. B, the string will be parallel to the x-axis of the xyz coordinate system, where y is now representing the string movement in the horizontal direction where the z-axis represents the movement in the vertical direction. Depending how the string is plucked, it will move around the rest point, r, on the z-axis in a rotating figure. In this case, we show a circular motion for simplicity, as indicated in Fig. C. Notice the magnetic field lines are closed curves which is characteristic for magnetic field lines, they never end anywhere.

Physics describe how the B-field changes with the distance from the surface of the magnet and if we concentrate on the change in the z-direction from the origin where the field is Bo, the field in a distance, r, on the z-axis will be B_z = Bo/r², looking at Fig. C, it appears that the field does not change much in the horizontal direction, that is how we arrive at the odd transformation shown in Fig. D. The influence the string has on the magnetic field lines is not shown here (Fig C), the significance will be shown in a later figure This is, however, not the whole story, if we go back to how B_z is behaving with distance, we detect an obvious change in magnetic field strength which is indicated by how dense the lines are at a particular point because lines start “swinging around”. From the given formula, we can see that this is what we call a non-linear behavior which is best illustrated with a graph of the function, Fig. E. This is somewhat representative of a magnet found in a guitar pickup. We can also see that if we move in the horizontal or y-direction, the field does not change a lot, actually quite a bit less than in the z-direction. The change is indicated in Fig. F that also indicates that the field is symmetrical around the string’s resting point. Even though the field change with distance is not linear, harmonics will be created, but an interesting part of the symmetry manifests itself in which harmonics will be created. An example is if we have a string movement that only contains the fundamental and no harmonics, the horizontal string movement will just contain the even harmonics, which creates the unusual situation that the fundamental disappears and the 2^nd harmonic will be the dominant followed by the 4^th and so on.

Back to our assumed circular motion, and if we look closer at the figures E and F, we see that the indications on these represents field strength B for the two directions with the same amplitude which is picked to be a realistic string displacement, 1.6 mm, and we immediately realize that vertical field is varying very differently depending on the string location, 225 Gauss is the string is below the rest position and only 72 Gauss if the string is above rest by the same amount. The situation is in the horizontal direction is much less, 11 Gauss. Please remember that the “string” mentioned is imaginary, at this point we are looking at the magnetic field in the positions where the string would be, why we do this will become clear later.

Now the situation in the vertical z-direction is quite different, we get a fairly large change in field from top to bottom position by it is uneven in magnitude which is basically what makes it non-linear. In a real situation, this gives rise to a number of harmonics besides the harmonics already created by the string. Not much point to go any further with the actual field strength B measured at different points around the magnet, but what we have talked about will actually be a big help when we start to add a coil of wire around the magnet and place a string at its rest position, r, above the magnet. Consider this an example of how the interaction works, sort of an appetizer for when we go to the next step. One thing before we leave this, please point your attention to the second set of numbers in Fig. E, 53 and 36 gauss, these represent a smaller amplitude of string vibration, .6 mm to be exact, This brings us to realizing that the smaller the amplitude of the string vibration, the better the linearity and therefore a smaller number of harmonics, more and more towards a simple sinusoidal oscillation where the only frequency present is the fundamental. Another interesting observation when looking at Fig. E is if you move upwards on the curve towards larger z, you get a flatter curve which means less difference in B between “top” and “bottom” which means less unlinearity for the same vibration amplitude, less distortion!

Shifting focus a little bit now, we will move to looking at the field as it is measured at the top center of the magnet, indicated in the above figures as B₀ when no string is present. What we are interested in is how the magnetic field at the place where B₀ was measured reacts to adding a string and the changes in location of the string, the string vibration around the resting position.

The field strength B₀s with the string present will be different than the field strength, B₀ without the string, measured on the top surface of the magnetic pole piece. If we assume that the magnetic field without the string is constant which will be the case if a magnet has been left undisturbed for long enough for it to be in equilibrium, we can continue with developing the theory of how we get to the output voltage of the pickup coil. If we say B₀s is the flux density measured with the string in its rest position located over the pole piece at distance r as indicated in Fig C, I should probably mention that this distance r = h, where h is the normal constant for string height that will also be used later on. We can summarize that in the following equation by stating that the string location including the string height can be written as follows, where the function B(t) is the function that actually determines the output voltage:

This equation will be our start to a new chapter concerning the voltage induced in the coil surrounding the magnet. In this case g is a function of the string location.

This approach is often seen in theoretical work for developing equations for flux and coil voltage, but as mentioned in some literature, these equations do not have a mathematical solution so numerical methods must be employed to calculate a solution. We will take a different approach by measuring the B field at the center top surface of the magnet with the string present, moving or static. That should make things easier and more accurate. One of the many interesting things that we will get into later as this page develops with additional test results, the value if B₀s does change with magnetic material, it can be 4000 G for Neodymium and below 1000 G for AlNiCo and the magnetic field measured on the top surface of a non-magnet slug with a ceramic magnet in the bottom will give surprisingly different results in output voltage for the pickup that is not related to the strength of the magnet, which means that if you replace an AlNiCo magnet with a Neodymium magnet of 4 times the “strength”, you do not get 4 times the output voltage. Sorry!

When the string is located in a magnetic field, it will cause a change in the magnetic field measured at the top surface of the magnet as we have mentioned above. We have also seen that the vibration and harmonics of the string itself depends on how and where on the string it is plucked, the outcome of the pickup signal also depends on where on the string the signal, the string movement, is sensed by the magnet(s). From the magnetic field descriptions above we know that the string movement in the magnetic field is a non-linear function that will add more distortion to our final product, the output voltage of the pickup coil surrounding the magnet.

In physics, the determination of the induced voltage (EMF, called e) in the coil is based on what is known as Faraday’s Law and it is stated as follows, the induced EMF (voltage) is proportional to the change of the magnetic flux (Φ) in the coil with time:

e = – dΦ/dt                            [2]

That is if we only have a single loop around the magnet, 1 turn. A pickup coil has thousands of turns, normally named N, so our voltage will be as follows:

V = -N _* dΦ /dt                    [3]

Earlier, we have mentioned that the magnetic field is indicated by B, the magnetic flux density, which means that the flux Φ can be calculated as this:

Φ(t) = B(t) _* A_c                          [4]

Where A_c is the area of the coil that surrounds the magnet and B(t) is the magnetic flux density at the top surface of the magnet as a function of time. Remember that this B field is dependent on the string movement at the point on the string where the pickup is located so the string movement creates the change in time of B. If we go back to the voltage induced in the pickup coil, we can see that this voltage will depend on the magnetic field change with time, going a little further that this depends on the movement of that point on the string that the pickup “sees”, the point that is in its magnetic field. The string movement, position change with time and how it affects the magnetic field, B(t), is what we are interested in because that is the parameter that shapes out output voltage:

V = -N _* A_{c *} dB(t)/dt                   [5]

Now, N is pretty straight forward so is A_c, the area. Well, maybe not completely straight forward, but they do not vary with time. Right now, you might argue that a coil wire can move a little with pickup vibration, that maybe true, but it does NOT change the coil area or the number of turns, so the change caused by these is ZERO.

It has been discussed what exactly the coil area, A_c, is. It could be the cross section area inside the coil or based on some center line in the coil, see figures. One thing is certain, Ac is constant with respect to time so is the function mentioned earlier that determined the change in B when a string is introduced, B₀s at the surface of the magnet. Since the determination of the flux relative change is independent of the constants all we need to know is that they are constants where time is concerned. The last term in the equation for V is the important one and it indicates the Gauss per second change in magnetic field caused by the string movement. Anything that is expressed as a change with time is essentially speed, in this case it is how the magnetic field changes with time and since the area of the coil is also involved it is the flux but does not change in time. Again, this change is triggered by the string movement. The term is known as the differential of, in this case, the B field and it is a mathematical operation used frequently in physics and is part of a larger subject in math known as calculus.

Longwinded, I know, but I hope it makes sense to everyone. One thing that needs to be made clear again, the change in magnetic field is not related to the absolute value of the magnetic field, something that will be discussed later, including some examples based on actual measurements.

Summary

Let us stop for a minute and summarize what we have been through so far.

If we start with the strings, it is clear that the string material matters, it has to be ferromagnetic to have any influence on the magnetic field. At the same time, the thickness, or diameter, and the tension matter. Next step is to determine how the string is plucked and where on the length of the string it takes place will determine the initial harmonics of the string vibration. This will be the main characteristic of the sound of the string for a short amount of time right after you hit the string with a pick. Assuming the string is left untouched, the shape of the string and the amplitude of the string vibration will change, the shape will gravitate towards a more sinusoidal shape as the higher harmonics die out as the amplitudes get smaller.

The interesting part of the initial string shape and its richness in harmonics is that, if you think about it, the most notes we play are of relatively short duration, so most notes that we play are rich in harmonics which is the reason why it is so important and so dependent on our playing style what sound comes out of the speaker in the end. There is a long way to that point and many things happen to the note played through that path.

Next step, we introduce the magnetic pickup and we have seen that sound changes “through” the pickup in a few ways, the first being the difference it makes on the harmonic content on where the pickup is located  in the space available to it between the bridge and the neck. The big difference is made when we see that the magnetic pickup induces a voltage in the coil wrapped around the magnet. Where the sound so far has been a matter of string displacement (such as in an acoustic guitar), the signal out of the pickup coil is dependent on the speed of the point on the string vibration where the pickup is located.

To put icing on the cake the various transformations in the process adds various amounts of distortion due to the un-linearity of the signal processing. We are now at the output of the pickup where this section on pickup should take us. Further signal processing in the path to the speakers will be describer elsewhere. Please see the Amplifier and Guitar Electronics pages.

An Example

Before we look at some actual measurements, we can as an example see how the harmonics develop during the process described above. First it would be interesting to see how the before mentioned string plucking and pickup positions make a difference. In order not to make it too cluttered, we will concentrate on a plucking position p=L/6 and two pickup positions P=L/4 (neck) and P=L/9 (bridge). The resulting spectra of harmonics represented by relative amplitudes can be seen in Fig. G.

The figure shows the first 10 harmonics, well, 1 being the fundamental. The red columns are the string displacement harmonics. Now, the other two graphs are for the two different locations of the pickup and they are first of all differentiated to be representative of what the pickup “sees”, the speed of the string at the location of the pickup, but they are not yet showing the output of the pickup coil. What you have is the “input” to the pickup before the signal processing in the pickup. For ease of viewing all harmonics amplitudes are shown positive, even though not all are. It is displaying the so called absolute values. Notice that what has been mentioned earlier, the 6^th harmonic is completely missing (plucking position) and the green (neck) is missing the 4^th harmonic and the blue (bridge position) is missing the 9^th harmonic, just as predicted. Finally, please notice how the distribution of harmonics vary between the neck and the bridge pickups. The neck position is richer in the lower harmonics and the bridge position is richer in higher harmonics, surprise, surprise! Here I might have to refresh your memory, the representation of the harmonic spectrum in Fig G is of great interest because the spectrum is the first to develop after the string is plucked, usually referred to as the “attack” part of the undisturbed string motion over time. As mentioned earlier, this will gradually gravitate towards only containing the fundamental frequency after the higher frequencies die out. Now getting to the produced output voltage from the coil in unloaded condition we need to escape from the one dimensional description and apply the pickup’s un-linear behavior as indicated in Fig D above, because the motion is two-dimensional as seen from the pickup. The example only using the y-direction is valid because that direction is contributing most od the output voltage.

Measurement results and discussion

As mentioned elsewhere, I have designed and built various kinds of equipment for testing magnets and pickups and even a pickup winder. As I mentioned, science requires not only theory but also solid proof that the theory is correct, so I had to do it to back up the theory as described above and I also discover a few new things.

As I indicated earlier, the graphs of magnetic field that was presented were without a string present, somewhat relevant but mainly to show the principle of string vibration sensing. Next step is to introduce a string to the magnetic field and see how it changes the picture and how the magnetic field measured at the magnet top surface behaves with string location and movement using my newly constructed test equipment. As mentioned, the B field at the top surface of the magnet or pole piece closest to the string is the best measure to be able to calculate the flux through the coil.

Here is how we will attack it:

1. Magnetic field measured at the pickup magnet’s top surface with string location
2. When string moves how does that change the field at the top surface
3. How does the string movement cause a voltage to be induces across the coil terminals
4. The actual voltage measured when a string is moving in a circular motion

Measuring the B field (flux density) without a string and varying the distance from the magnet to the measuring point is somewhat different from measuring the B flux density at the surface of the magnet with a string made out of ferrous material placed at a certain location with the respect to the top surface center point. Using what we could describe as a “Fender style” cylindrical AlNiCo 5 magnet we measured the B flux density in the two cases.

The fact that it is two different entities we are talking about, the horizontal axis is in the case of curve “Bz” it is B as a function of distance, z, from the magnet, where as in case of Bos, it is B measured at the top surface of the magnet and the axis indicating the string’s center distance from the top surface of the magnet. As you can see, we are beginning to hit home since the latter distance is what we normally refer to as “string height”, h, which we will be using a lot during the rest of this section.

The exercise that was conducted earlier where we used the “other” curves to illustrate the effect of string movement will now be put in perspective. We could go in and do the same to the string version of Fig 1, but we would also have to include horizontal motion even though it represents a much smaller portion of the string displacement than the vertical displacement, but why not jump right to it.  

To that extent, I will use a piece of the equipment that I have designed and built for this purpose. This equipment will use a real guitar string and move this in a circular motion over the pickup at a specific distance which is the so called pickup height, h. The string will rotate around  this point, not unlike a regular string on a guitar. The circular motion is picked because it comes close to how a guitar string moves and, more importantly, a circular motion represents a pure note in the form of a sinusoidal curve without any distortion. Thereby we can see the difference between input, the pure sine function, and the output of the pickup, and thereby assess the amount of distortion the pickup transfer causes.

I should mention that the reference to “SIM 3” is the name of the PU tester used, it is with a Boomer E-string (.042) moving in a circle  with a radius of 2 mm. First thing you notice is that the variation in Bo is a very small percentage of the average field. Figure 2 represents 4 full rotations. Just to avoid confusion, I should mention that the Bo is the magnetic flux density measured at the center surface of the magnet.

Now, the change in field strength is not the issue when we want to find the induced voltage, it is how fast the change takes place, so we have to manipulate the measured curve as described above as “differentiation” in order to get a measure for the induced voltage in the coil. I have done that numerically and the result looks like this:

Showing the principle of induced voltage here is a bit crude because the B measurement is only based on 10 values per circle, but that was the best I could do at the time. I have, however, built equipment that can perform 40 measurements per cycle that will make for a much more accurate when I get a chance to make some measurements. The vertical axis numbers are arbitrary and do not represent the output voltage! The horizontal axis from Fig 2 to Fig 3 is converted from “ticks” to radians, just in case you should wonder.

Just to bring the message home we can add a representation of the string movement to the graph showing 4 cycles. Fig 4 shows a little more of what is presented in Fig 3 and the original string rotation has been added in form of the green curve. The important part of Fig 4 is that it takes us through the transformation from string vibration to the output voltage of the pickup, again do not pay attention to the numbers on the vertical axis, it is about the change in shape that takes place from string movement to pickup voltage and how it is distorted just because of the transformation process in the pickup.

Different Magnets

Next step is to measure some other types of magnets and compare them to each other. Fig 5 shows an example of this:

The comparison is easily done by using the relative values, otherwise it would be difficult. The relative values can be used because we are not interested in the absolute value for determining a potentially induced voltage. One way where this is not giving the whole picture is the fact that the basic Bo is very large in case of the neodymium magnet, which means that this type of magnet will require a larger distance from the string in order not to cause any distortion due to magnetic pull on the string, something the other two magnets only display at a smaller distance of the string from the magnet.

This is described in more detail on the sub-page “String Height and Magnet”.

Figure 6 below shows the same graphs as in Fig 5, but we have zoomed in on a string height of 4 mm and made the B field relative to this value of h. The purpose is to show that the advantage of a stronger magnet diminishes as string height, h, increases and that the height must be larger for neodymium magnets that AlNiCo magnets in order to avoid any ill effects. As demonstrated earlier, the excursion from string rest position has an influence on un-linearity of the signal, the smaller the amplitude the less distortion of the signal which means that as the string, left to itself, dies out the output will gravitate towards the fundamental of the note played. Even though Fig 6 is based on a string height of 4 mm we can use a combination of Fig 5 and Fig 6 to get an impression of the effects of picking a different string height. Practically speaking, going for a string height less than 4 mm is probably not advantageous for a couple of reasons, first of all, the distortion increases and secondly, we get too close to the magnet. In case we increase the string height, the signal created is more symmetrical and that will mean that less harmonics are created and the signal becomes more sinusoidal and much weaker (less and less amplitude).

This has so far concentrated on pickups with magnet pole pieces which are typically the ones found in single coil “Fender style” pickups. Nowadays, you see this type pickup with ceramic bar magnets and steel pole pieces and you might say that there is no difference, well, I say there is and we will get into that in detail under pickup electronics.

What has been shown so far is mostly based on static measurements of magnet and string behavior which is important indeed, but the next step is to get into dynamic behavior of the string and include the magnet in a complete pickup as it relates to magnetics but bounding on electronics without getting deep into that.

This actual pickup voltage output is a very similar in shape to the shape showed previously that was based on static measurement of fairly crude character. The curve in Fig 7 is measured with high time base resolution, the numbers on the x-axis are in 10 micro second increments where as the y-axis is in actual volts. The string causing this output voltage is moving in a perfect circle above the pole and therefore acting like a source creating a sinusoidal waveform. As it can be noticed, the output is not a sinusoid, hence showing how a pickup distorts the signal from the string movement to the output voltage. This signal consists of a series of frequencies. In this case the generating signal, the vibrating string, is a perfect sinusoidal which means the only frequency is the fundamental. The output signal has gone through the process as described above and now consists not only of the fundamental but has an additional number of frequencies, the harmonics. Remember, we are past the attack spectrum as shown earlier, we have now entered the part of steady state signal, commonly known as “sustain”.

 A signal out of the pickup as the above has been recorded and afterwards, I have used the recorded values to calculate the fundamental and the harmonics to demonstrate how a specific signal out of the pickup looks and how it is made up of specific frequencies. This has been done digitally as explained earlier.

The result of the process is shown in Fig 8. The dark blue curve (Vpu3) is the actual signal out of the pickup (unfortunately, it is covered mostly by the light grey/green curve, Vsum), V1 is the fundamental, V2 to V6 are harmonics. Ignore “bn”, please, it is small and just a helper variable that is irrelevant here. The light grey/green is the sum of V1 to V6 and should be identical to the measured curve Vpu3. I had only included up to V6, normally I have 10, but, as you can see, the higher ones are quite small.

To make it easier to understand, the amplitudes of the harmonics have been plotted in Figure 9. We typically select the fundamental to be of positive amplitude and in order to add up correctly some harmonics are negative. That does not change the frequency content as can be seen in Fig 8.

In most cases, when you see a diagram like this showing harmonics, all amplitudes are shown as positive, which makes in easier, I don’t know. The sign indicated which direction they go at the start, positive or negative. Here they are shown with sign in order to match Fig 8, meaning that if the curve of the harmonic starts out from 0 going negative the amplitude is negative.

No frequencies are shown here, but the fundamental (1) is 82 Hz, like an open E string, since the string here is a .042 Boomer. This situation is when the string is oscillating freely after the “attack” part has turned into the “sustain” part.

Different pickups and their outputs

I have recorded a large number of output waveforms from a lot of different pickups and individual magnets to show how they react to my string vibration simulators. Since a lot of the outputs are done on the same simulator, they can easily be compared:

• Humbuckers, covered or uncovered
• Homemade humbuckers or single coil
• Dual rail humbuckers
• Pole piece and bar magnet pickups
• Single coil pickups, Fender or Fender-style
• Different magnet types, AlNiCo 2, AlNiCo 5, Neodymium, Ceramic
• I think that pretty much covers the different types measured, here is what I have looked into
• One pickup, string vibrating directly over each pole and in between poles
• Pickup with or without german silver cover
• Pickup with or without different degrees of copper tape shielding, both single coil and humbuckers
• Included some pickups of other than traditional design

The equipment used, some time referred to as SIM 3 will give me a string height of 5 mm and the string is vibrating (rotating) with a 2 mm amplitude, height is distance from pole piece to center of string when at rest, similar to a guitar. As mentioned earlier the string motion is designed to produce a sinusoidal shape in order for the measured outputs from the pickup will show how the signal is distorted in the process of converting motion to electrical signal.

I have also performed similar testing with a simulator named SIM 1, the difference here is that I can go to a string height as low as 3 mm, but I can also go higher for a good reason, it is not likely that you would use that low a string height, because the string can get really close to the magnet in the process. The rotation radius is 1.32 mm corresponding to a string vibration amplitude of the same dimension, 1.32 mm.

I have performed Fourier analysis, similar to what is shown in Fig 9, on some of the output signals to extract the different harmonics that add up to the total signal, I will show a few of the results.

This will be a sample of the most interesting ones because it would be entirely too much to show all of them here, I might consider that for a future project even though I keep adding new ones to the file. It appears to be the most interesting to concentrate on subjects that are on most people’s minds, such as:

• Pickup output sound spectrum (one already shown in Fig 8), but we will look at some more
• Output from each pickup pole individually, waveform shape
• What happens when the string is between pole pieces
• Same pickup coil with different magnets installed

Taking one single coil pickup through its paces

First, let us look at if we use the same string, vibrating with the same frequency and amplitude over different poles. We will mainly be concentrating on the pickup’s output voltage, meaning the coil voltage. The string height is 5 mm and the string amplitude over the poles is 2 mm, the string is still a .042 Boomer treated as an open E-string. This is the raw output voltage, the pickups are unloaded, meaning no volume pot or anything.

We will attempt to answer some burning questions, such as if the position of the pole will matter, in case the string is outside pole 1 or 6 (assuming a six string pickup), what happens between two poles.

In this example, I have selected PU 14 which is a single coil, “Fender Style”, pickup, Chinese made and it came with a ceramic magnet in the bottom and typical steel pole pieces. After the measurements were completed, the magnet and pole pieces were removed and AlNiCo magnets were put in place of the pole pieces and the pickup with the same coil but with A5 and subsequently A2 pole magnets were measured in the same way as the ceramic magnet in the original pickup.

An example of pickup output voltage is shown in Fig 10. As mentioned, this is a single coil pickup and it is susceptible to noise. My test equipment has some noise problems that I have not corrected at the point of recording these voltages. The wavy lines is a result of this noise and should be ignored. As we shall see later on, the wavy character of the humbuckers does not exist which goes to show how sensitive the single coil is, this particular pickup has not been shielded.

As the chart indicates, the measurements are taken over pole 3 and pole 4 and between the two poles (3/4). The output for the two poles are very similar and the placement between poles has a lower amplitude. But that is not the only thing, if you look closely, the red curve representing the “tweener” has also shifted in frequency content. If we think harmonics, we can see that the peak of this is shifted towards the center, meaning that it will contain more fundamental frequency that the pole examples. The result of this is that if the string is vibrating between poles it will be a more “clean” note. When I get a chance I will repeat this measurement with a humbucker to avoid the wavy noise.

Just to show a similar situation, Fig 11, is the above experiment repeated with AlNiCo 5 magnet pole pieces replacing the ceramic system. Notice that there is a difference in amplitude meaning the output is a higher voltage with ceramic system. Looking at the magnetics and the difference between the two, there is something that is not clear to me yet, but I am working on it. Intuitively, it appears correct that the ceramic has a higher output voltage.

In the two previous figures we have looked at pole 3 and 4, now, if we take a closer look at Fig 12, we see a recording of all 6 poles and no “tweeners”. Here we see that poles 2 – 5 are very similar, where as 1 and 2 are different in a couple of areas. First these two are not symmetrical as 2 – 5 are. Pole 1 represented by the dark blue line crosses 0 volts earlier that all the others, where the orange line representing pole 6 crosses later than all the others. And if you can “extract” 1 and 6 only, they display an odd symmetry with each other even though the curve for a single pole is far from symmetrical. It is almost if you rotated the curve for pole 1 around the center point, you would get the curve for pole 6! This symmetry is not a mystery, however, they are a opposite ends of the pickup and both are missing a third pole, where as the other poles have not only the pole itself, not a pole on either side, for example pole 3 has pole 2 and pole 4, where pole 1 only has pole 2 on one side. I hope that makes sense. Spend a little time looking close at the curves, it should give you a picture of how the pickup is functioning. The AlNiCo 2 curves are used as an example here, the situation with the previous ceramic and AlNiCo 5 examples is similar to this one. So it is not a matter of magnet type, it is a matter of placement and string location.

We will end discussion of PU 14 by showing Fig 13. The curves for the three magnet types show great similarity from a frequency content point of view. Output voltage amplitude is a different story, ceramic is obviously the highest, but the fact that A5 is the lowest will require some additional investigation. You would expect A5 to be higher than A2, one thing that comes to mind is that string height may come in to play here. I think a more dedicated experiment focusing on amplitude may be warranted. One thing we can learn without doing a Fourier analysis on the curves is that the AlNiCo curves are just about identical from a frequency content point of view, the magnetic curve appears to lean towards lower frequencies, so much for the high brittle sound of a magnetic pickup!

More Pickups – Humbuckers

Time for a look at humbuckers, in this section we will take a closer look at some the ones I have looked at and analyzed.

The curves in Fig 14 represent vastly different pickups, although the curves look quite similar. As I have mentioned elsewhere “a pickup is a pickup”, meaning that there is a difference between humbuckers and single coil pickups, but pickups of the same characteristic are very similar in frequency spectrum and therefore in shape of output voltage. They are, however, very different when it comes to output voltage, something that would be expected because of the difference in construction and material for the five pickups.

PU 1 is humbucker with all pole piece slugs with a ceramic magnet, what you would call a “cheap” pickup, if you look closer, the peaks occur closer to beginning and end of the cycle, this indicates that the output of this pickup has a slightly higher frequency content than the other pickups in Fig 14. This can be seen in Fig 15. Please beware, the colors are different in the two figures, go by legend.

PU 3 is a “full size” rails pickup also with a ceramic magnet

PU 4 is a home made pickup, sort of. It came with ceramic magnet and steel slugs and screws. I replaced the screws and slugs with AlNiCo 5 magnets, one side N up the other side S up, just like a normal humbucker, this one is special because it is made up of magnets instead of the normal pole pieces with a bar magnet.

PU 6 is a humbucker of the “hot rails” type, it fits into a single coil space. The magnet is a ceramic and the rails are steel.

PU 10 is a “standard” pickup of the humbucker type with ceramic magnets. Brand name is Lace and the type is Death-bucker. You may be familiar with this type, it does not have a normal coil with thousands of turns and pole pieces, it has a a single winding with a magnet embedded as one side and a complementary and similar winding if similar style. they are coupled as a humbucker and acting as primary turn for a transformer, the secondary is stepping up the voltage to be comparable to a “normal” pickup. One output wire actually acts as a connection to a shield made up of the to primary loops. Very clever! For more information, please see the Lace website. This pickup type is also patented if you need that kind of information.

The waveforms were analyzed using my Fourier series method and if we use the absolute values the raw chart looks like in Fig 15. Please pay attention to the difference in color from Fig 14

It reflects the differences in output voltage level, so they may be hard to compare, so in order to make comparison easier, we can normalize the chart, in such a way that all fundamental components are 100% and the harmonics are related to the fundamental as shown in Fig 16.

When doing so, all pickups appear similar in frequency output, interesting part is that PU 1 stands out ever so slightly, it has not been modified in any way!

Now, it needs to be pointed out that these curves and graphs represent the stabilizes string vibration where its “input” is a sinusoidal motion as explained elsewhere. This can be compared to the “sustaining” part of a strings movement. At some point, we will take a look at the “attack” part of the plucked string, it will be much richer in harmonics, especially higher harmonics than shown here. We looked at that earlier using calculated values. In Fig 16, the higher harmonics are calculated, they are there, but so small that they will not show up on a linear scale chart like these. Remember what we see in the frequency charts above is how the pickup distorts the input signal. The input signal here is a string movement that simulates a sinusoidal waveform, a pure tone from the string’s point of view. That signal is transformed to a spectrum by the transfer function of the pickup as explained theoretically earlier.

I think that we proved a point, humbucking pickups are not different even if they are constructed quite differently. As we see from Fig 14, the curve representing PU 1 is slightly different than the rest giving it a little bit of an edge compared to the others. This is clearly shown in Fig 16 where the third harmonic is a bit higher than the rest. It is amazing what you can measure!

Other magnet types

I have made a pickup similar to PU 1, named PU 15, but with Neodymium magnets, the testing of these has not come very far and the results are a bit puzzling. Another approach was taking a single coil pickup and removing the ceramic magnet and replacing it with a number of neodymium discs and regular steel slugs. As it turns out, that works pretty well without being spectacular. You do not, however, get the “mega” output you would expect. There is a typo in the chart title, it should be “discs”, damn keyboard!

Same approach was tried with three discs in the bottom of each slug, the result was very slightly higher output voltage. One disc with original slugs was also tested, but the result was so poor that there is no need to show it.

On the other hand, if you look back at the comparison between magnets, Fig 6, it shows two very common magnets AlNiCo 2 and 5 and the Neodymium magnets and the difference is not that overwhelming, in fact at larger string distances (string heights) it gets smaller and smaller and because the B field is at least 4 times larger for the neodymium than the AlNiCo magnets, the distance would have to be larger for the Neo magnet than the others. This was touched on earlier, but before more detailed measurements were made.

I have some pickup specific magnet measurements to show once I have verified them, there were some irregular behavior in the recordings of the measurements that need to be investigated because they are possibly related to the test equipment. Like I said, this is science so you cannot publish anything before it has been verified to match theory. Isn’t this fun!

Follow up on the magnet issue

In order to investigate further, a new pickup was used, PU 22. This is a single coil pickup originally outfitted with slugs and a ceramic magnet in the bottom. The flux density B was measured at the top surface of the designated slug pole 3 and R, L and resonance frequency were measured and C calculated as in the example on the Electronics page, but this is concentrating on magnetics and the related pickup output voltage, but everything was measured to be complete. After the parameter measurements, the pickup was put in my string simulator to measure the output voltage. By the way, I have figured out how to get smoother curves, not the curvy ones that I complained about earlier!

As earlier, I used the exact same coil but used different magnets and slug/magnets as well. For a complete comparison, these were measured in the pickup tester as well. The coil being the same, it was easier to get a uniform condition for the many combinations.

Now this information is similar to what is shown on the Electronics page for a different pickup, it is added here to identify the different modifications made to the pickup for use with the output voltage below. In this case we will add a table showing the magnetic measurements that go along with Table 1.

In Table 2, the different cases are identified a little differently from Table 1, but it should be possible to see the similarity between the two tables, from left to right we see the measured valued for the Case1, Case 4, Case 5, Case 6 and Case 7. If we look at the left column in Table 2, Amplitude refers to the curves in Fig. 18, Div B means the difference between maximum and minimum of the B field in 1 rotation of the string, The Ave B is the field at string rest point and Bo is the field measured with the pickup pole removed from the tester so there is no influence from the string.

Comparing the curves with the numbers in Table 2, using the Amplitude from the table we see that there is a few issues: The output voltage and the measured B flux density do not match what would be expected, one example is the A5 and the A2 numbers are far apart, but the curves (the output voltages) are almost identical! Also the Div B for the ceramic magnet case is almost the smallest, but the voltage waveform is the highest amplitude. Well, if we return to the numbers in Table 2, the Div B number is not really the most determining factor for the output voltage, but it is a good guide. One thing that needs to be investigated is the string height during measurement, even though all effort was put into having identical heights for all magnetic tests. Nothing can be learned from the complete rotation curves, they indicate that A5 should be higher than A2.

It looks like more research is most definitely needed and I can say it is already under way. Welcome to science!

Well, here is more. In order to get to some kind of resolution of the problem that I encountered in connection with what is shown in Fig 18, I started to perform some specific testing with just AlNiCo 2 and 5 magnets, called A2 and A5. Also, when you are mostly concerned with amplitude, much more than shape, you tend to focus on getting everything lined up for that. In the process, I discovered some shortcomings with my test setup that I should fix, not that I didn’t know about it, everything was just working to that point. Instead of repeating what I had already done using just PU22, I took a similar pickup and mounted it next to it. The two pickups were from the same set and measured the same after I removed the original ceramic magnet and slugs and put in A5 and A2 magnets, first I took the magnets as they were, they had been sitting around magnetized, the A2 magnets in a pickup magnet storage the A5 had been attached to a steel keeper, 3 x 3. The first results with the two pickups yielded some strange results so I decided to re-magnetize them as if they were new and without magnetization. Like I said, they had been sitting around and been in and out of pickups and other things. So the procedure was, magnetize the magnets and put them directly into pickups, I do this normally because magnets in a gang of 6 react differently than a single magnet, when I say react, I mean the measured B flux density measured on a top surface of the magnet.

OK, I might as well reveal how I magnetize pole piece magnets. These are all 18 mm of length and I take one at the time and attach it to a Neodymium bar magnet, B = 3200 Gauss after having a total of 6 magnets there I attach a second Neo bar to the other side at opposite polarity, of course. After some time, typically around an hour maybe, it is not critical I remove the pole pieces and put them into the bobbin. As you can see, I do not f around with moving them through a field from two Neo magnets mounted in a vice or something, I don’t know why I should! The magnets will end up with their specific B flux density anyway, and even if you mix A2 and A5 magnets in the same batch, they will end up with their specific magnetization regardless of Neo magnet strength. I just thought that you should know!

Back to the experiment, after some experimentation I came to a point where I had results that were comparable, shown in Fig 19.

In pickup measurements of the B flux density of the two pole pieces, the result was Ba5=872 G and Ba2=477 G. From the headline of Fig 19 we see that the two amplitudes of the output voltage waveforms are 117 mV for A5 and 64 mV for A2, which is just about identical in ration to the flux densities! It may be too good to be true, but it goes to show that as equation in Ref 3 indicates that the output voltage is proportional to B. I wanted to discuss this equation, but I was not sure it was correct with the B flux. Even though the equation is a very special case in normal life, it coincides with my experimental setup, even though it only covers the fundamental and the 2nd harmonic.

Just to be complete, I will show the pickup arrangement used here, see Fig. 20.

So what about the frequency spectrum? Well, I have been thinking about that and I have seen a different method to measure that, I mean different from the method used in the Resonance Frequency measurement discussed on the Electronics page, in a separate page.!

So far, I have used my string movement simulators to create the pickup output voltages that can be seen in almost all graphs on this website. The simulators, as I have designed them, will give a signal that is based on a vibrating string, not the initial attack but the more steady state behavior of the string, more like the “sustain” part of the vibrating string which is sufficient to show guitar pickup characteristics, especially the resulting pickup distortion. It does, however, become more and more difficult to simulate the lighter strings at high frequencies. It is not hard to get higher frequencies, but the material used get too noisy to get good results, and it does not really add any useful information to the story. We are, however, interested how the pickups behave at higher frequencies, the frequency spectrum, if you wish.

So, I wound myself a small coil using some 28 AWG magnet wire, same type as used for winding pickups, just heavier. The coil was wound on a (don’t laugh!) bobbin normally used for sowing machines, a total of 76 turns. The hole in the spool was about the size of a pickup slug, so one was added for better directing the small field generated by the coil. The coil also connects better to a pickup and it is easier to center over a pole piece and it stays in place. The coil in series with a 100 Ohm resistor was connected to a function generator, such that you get a current generator for the coil, when supplied from a voltage source. The coil inductance was 96uH and .7 Ohm, so impedance wise much smaller than the 100 Ohm.

I have seen others perform testing like this online, but they usually have developed circuits to ease the testing. That makes sense if you are testing a large volume of pickups, but I am not doing that yet. So I did it the “hard” way. For each frequency, I recorded the actual waveform with a scope. The waveforms of the coil currents and the pickup output voltages, basically so I could make corrections for one thing or another if the data indicated a need. Some examples, the output waveforms had quite a bit of noise superimposed more the lower the frequency, so some correction was needed as well, the coil current would vary ever so slightly so a correction was necessary. The goal was to find the frequency characteristic of the pickup and to show that it is flat (as shown on the Electronics page), only difference being that here the pickup is magnetically excited as opposed to electrically excited. Result would be the same, with the magnetic excitement, I measured up to above the resonance frequency. Having done all this, I fully understand why some people people have designed electronic equipment to do this because it is a lot of work to start with just the raw results, but it was educational!

Well, here is my result for PU 22 with AlNiCo 5 magnets:

The curve shows what would be expected, a flat line. I mentioned the noise on the output voltage that needed correction, you can see a slight wobble at lower frequencies. I am hoping to debunk all this “mid-scoop” nonsense that people can “hear”. As I have said before, pickups do not display a “mid-scoop”! I know, before you bring it up, it is correct that amplifiers can display mid-scoop, that is if they are equipped with an EQ section! Not in pickups, they are “straight as an arrow”.

Before I get any concerned readers, it is probably in its place to show the entire frequency spectrum as I recorded it and crunched the data for, it stretches all the way to 15 kHz and include the resonance point.

Now, you might say that the frequency spectrum is a bit unusual as presented here. It is, the other frequency graphs on the Electronics page have all been shown with a logarithmic horizontal axis that gives a nice sharp resonance peak where as in this case it is shown with a linear axis giving the hump a wider look, so to speak. It was not considered in this case to do the logarithmic scale because the low end of the spectrum that is the one that matters is shown in detail in Fig 21. Also, this is a recording of the “raw” pickup, meaning that the pickup in unloaded, there are no volume pot or other circuitry that loads the pickup, so the upper end of the spectrum will look different as shown on the Electronic page.

And, of course, I had to show you a picture of the exciter coil. It is a little out of focus for reasons I cannot explain, but I think it shows the essence. Fig 23.

It looks like a method to measure the influence of the magnet type needs to be devised, I was hoping to come up with a method to show that a magnet is a magnet and that any frequency characteristics the material may display will occur at frequencies way above the range we are interested in. My search in literature has not turned up any mention of any frequency dependence on the flux change contributed to the magnet, influencing the pickup output voltage, the induced EMF. The entire frequency dependence is in the inductance and other parameters as can be seen in the equivalence diagram as discussed on the Electronics page.

A Humbucker Magnet Test

So far, a lot of the stuff presented have been centered around single coil pickups. I think I will turn my attention to some of the testing already done on humbuckers and get into it in more detail such as changing slugs and magnets, e.g. replacing screws with slugs and changing from ceramic magnets to AlNiCo or even Neodymium, sounds like a lot of fun, doesn’t it? I am also improving my test equipment to be able to expand my testing capability. I have made a humbucker based on Neo magnets, I think it may come in handy as far as getting a step further in the magnet discussion.