I have been reading the section about magnets and magnetics on the main Pickup Science page and the feeling that something is missing is growing. I think it is time to get in more detail about permanent magnets and blend that into how they are used in guitar pickups. It is going to be about magnetic fields and there will be a lot of illustrations to back up the various issues with different types of magnets and pickup constructions. Again, this is because of increased frustration with YouTube videos and because the high degree of misinformation in the presented.
Some fundamental observations
When we are applying magnets in connection with guitar pickups, there are a few things that we need to get straight first. A magnet, in this case a permanent magnet, has the function of providing a magnetic field, to narrow it down, we are interested in the magnetic flux density in the coil of wire that the magnet produces. Or more specific, since we are interested in the voltage induced in the coil, the change in time created and how the string movement is reflected into the created voltage that can be measured across the winding (the coil). Here we will only concentrate on the permanent magnet alone or a permanent magnet in combination with a ferromagnetic steel slug.
Let me start by raining on a lot of peoples parades by saying that “a magnet is a magnet” and the field and flux change with time has no frequency spectrum even close to be within the range of frequencies that is interesting in connection with guitar pickups. A certain pickup material does not pick up any frequencies more than others so there are no magnet type that “has” more treble than others or more mid-range and so on. The frequency spectrum is flat, completely flat, in the entire frequency range and way beyond. The reason for pickups “sounding” different maybe attributed to the amplifier, not to mention the listener’s imagination! Now we are at it, it is not the winding process nor the magnet wire. Just about all of this is explained in detail on other pages on this website. That said, let us get back to the subject…
The BH curve for permanent magnets
The fundamental way of characterizing a magnetic material is by its BH curve. This curve is different for different materials and magnets and it indicates how the magnet behaves under different circumstances, it also shows the typical parameters that you would also find in a table of magnets, for example. Fig 1 shows a BH curve with some of the key parameters indicated.
In this case, the BH curve is for a magnetized magnet, what is not shown is the curve indicating the magnetization of the magnet, this curve originates at (0,0) and stretches up to the point indicates as Bmax. This is the saturation point for the magnet, which means that even if the magnet, in this example an AlNiCo 5 magnet, is magnetized with a much stronger magnet, it will not exceed this value. Personally, I use bar NdFeB magnets (best known as Neodymium) to magnetize AlNiCo pole pieces, see picture later. The value of flux density Br, the residual flux density is the maximum flux density the material can assume after being removed from the magnetization process. This is the internal FD (flux density), typically in the center of the magnet. That said, the FD in the magnet will assume a value entirely determined by the way the magnetized magnet is placed and what surrounds the magnet. In Fig 2, the magnet is places in a circuit that consists of ferromagnetic steel without any type of air gap or other sources of leakage. If the material has a high permeability, the Bm, the internal FD, will be of a value close to Br. Please note that the curve is only of the second quadrant of what is shown in Fig 1, this is the “operative” part of the curve, the so called demagnetization curve, for better or for worse, it has nothing to do with demagnetization of the magnet in this context, please remember that, because that is not in the context of guitar pickups.
That case has very little relevance in connection with guitar pickup designs, so if we turn our attention to Fig 3, we see a situation that is familiar to the pickups that are based on single pole piece magnets.
Now in this case the internal Bm has dropped significantly from the much higher value, Br, the value of Bm is the point where the horizontal line crosses the B axis, drawn from the dotted “load line” intersects the BH curve. In this case, the magnet pole piece is all by itself, so to speak. The “air gap” is now the largest possible, basically from top of magnet all the way around to the bottom of the magnet. We are not done yet, there is a reason why Bm is not indicated on the figure, because this value is not at all fixed yet. The point indicated on the BH curve in Fig 3 that was briefly called “Bm”, the magnet flux density is far from fixed, it depends on many other factors that we will discuss next.
Let us start with the basic equation, the relationship between magnetic flux, Φ, and the flux density, B:
Φ = B . A (1)
Where A is the area of the surface being penetrated by the flux. Also, in the previous figure we have a mapping of B and H, where H is indicating the magnetic field strength, the magnetic force or in a case like Fig 2 where we have a closed magnetic circuit, an equivalent to electric current, in the Fig 2 case H ~ 0. The relationship between B and H, as we can see from the graphs, is not linear and the function that relates the two is pretty complicated. One factor that is important to us is ratio L/D, where L is the length of the permanent magnet, and D is the diameter, assuming the magnet is cylindrical which is very common for pickup magnet pole pieces. If we return to Fig 3 and look at the curve and consider where Bm is on the B-axis, we come to the conclusion that the larger the ration L/D is, the higher up Bm will be on the B-axis. Now, what that means is that, for the same diameter, the longer the magnet is, the larger the magnet flux density, Bm. In other parts of this website we have used measurements of the flux density at the top surface of the magnet, we called it Bos and Bo, depending on a string being present or not.
The mission in the following is to explore the relationship between Bo and Bm and to see how these react if we add a string to the equation. The whole purpose of this is to determine how string movement or at least string location has an effect on Bm and how it rubs off on Bos, the only parameter we can measure, but the output voltage from the pickup depends entirely on how Bm and subsequently Bos reacts in time with the string movement as we have seen elsewhere. This exercise will be more directed at magnetics and magnetic field behavior. Just to make it clear, Bm is the interesting FD because that is what the pickup coil “sees”, Bos, however, is the quantity we can measure so we have to rely on a relationship between the two.
If we consider a magnetized AlNiCo pole piece as it sits in a pickup, the field around the magnet will look like can be seen in Fig 4. This is the ideal situation with no ferromagnetic material near the magnet.
I have to mention that the field lines should be smooth without any kinks, the wiggly lines are due to the limitations of the software I use for the simulation, but I believe you get the picture. What you need to know about the lines is that they never cross and there is no beginning or end, they are closed curves as can be clearly seen in Fig 4. Also, the distance between the lines is an indication of B in that particular spot, the closer the stronger the field.
As an example, we can look at the exact same magnet when surrounded entirely by a ferromagnetic material as shown in Fig 5. The magnet and the steel “keeper” form a closed circuit and since there are no gaps (air gaps), there is no leakage. In complete contrast to what is shown in Fig 4 which was almost entirely leakage.
What we see in Fig 5, has very little relevance when we are talking guitar pickups, but it is included here to illustrate how magnetic fields react and how a ferromagnetic material present can greatly affect the field. It would be nice to have a completely “organized” field in our pickups, but we have to deal with something like what is seen in Fig 4, a highly disorganized field with a coil of copper, a non-magnetic material, wrapped around the magnet to capture the changes in time of the B-field. Since copper will not disturb the field as seen in Fig 4, that is exactly what we are going to get with the coil included.
Now, as mentioned, it is the magnet alone as shown in Fig 4 that is of interest here. We can take a look at a “close-up” of the top of the magnet and add some arrows to show the field direction, Fig 6. This is showing the field without a string.
Let us see what happens to the field lines if we add a string, the string is not moving at this point, but the distance to the top of the magnet is the important part here because changing the distance, normally referred to a string height, h, the flux density B will change and that will cause an induced voltage in a coil as described elsewhere. Adding a string will change the field “picture” as shown in Fig 7. The string is now part of the magnetic circuit, by no means as heavily as in Fig 5, but the presence of a string has some effect on the B flux pattern inside the magnet as well as outside.
The most noticeable difference is right above the magnet’s top surface, in Fig 6, these field lines would just “swing around” in a natural way, in Fig 7 we can see that the field lines point straight upwards toward the string, and we can see how the string acts as a guide for the magnetic field, not unlike the extreme case in Fig 5. What we do not see on the string because of the magnified look are the lines going left and right in the string is that these will eventually return to the bottom end of the magnet.
So far, we have concentrated on a single magnet. To expand a little bit we add a second magnet that in this case is a bit further away from the first magnet than in a normal pickup, but here it is to show the effect of adding a string to be placed above just one of the magnets. Fig 8 shows this situation, the string is unfortunately shown here as a diamond shape even though it is round (limitations of the software) and it is pointing out of the page so it only affects one magnet.
If you look at the B field lines above the magnets, it is noticeable that there is a difference in the way the lines “behave”, to the left with the string present (h = 5 mm), the lines are focused on the string and on the right, the lines are to some extent “disorganized”. When measuring the B field above the magnets, you will find that B is higher on the left than on the right because of the string and when the string moves, this field strength will change, and as we know that the change of B with time causes induction of a voltage in the surrounding coil, the faster the change the higher the voltage.
One very important thing to observe in Fig 8 is the B field lines between the two magnets. The distance is determining how deformed they get. In this case the magnets are oriented in the same direction as in a single coil pickup and as we can see, the distance between magnets has some influence on how the behave.
Slug and magnet
Some combination that has become popular is to build a pole piece by having a (thin) button magnet in under the steel pole piece as shown in Fig 9. As it can be observed, most of the magnetic flux shunts around back to the rear of the magnet, basically being wasted because not much reaches the top of the slug where the string is, or should be, as it turns out, the flux density at the top changes extremely little when a string is added. Measuring the B-field at the surface between magnet and slug and at the top surface, it turns out that only about 5% of the magnet’s field reaches the top, as can be seen in Fig 9. Conclusion is that the button magnet needs to be very strong to get any B flux at the string.
The direction of the B field is not shown, because the result is indifferent to the direction, so the magnet could be put on the slug either way and the end result would be the same. Please remember that if you do this to the 6 slugs in a pickup they need to be oriented exactly the same way in order not to totally oppose each other, because even if they are facing the same way, they will still influence each other’s field for a lesser performance. On the main page there are some results where I removed the ceramic magnet from a cheap single coil and put shorter slugs (like used in humbuckers) and 2 Neodymium button magnets of the same diameter which gave a decent output of the coil. Other measurements show, surprisingly enough, that the field at the top doubles.
Now, the reverse of the above would be to place a very short steel slug on top of a full length magnet, well, it can be done, but the effect of this is contradictive to what we seek, a strong enough field at the string and an arrangement that will give us a proper output voltage. The top slug will only weaken the top field due to leakage. We have to constantly remember where the coil is located, that is where the induction takes place so the B field must change the most there with string movement.
I am almost positive that the question is going to come up, “so what if we put the button magnet on top, that should give us a stronger field at the string, right?” No, not really! The string might see a higher B field, but the slug is where the coil is, it will not see anything different, just turn Fig 9 up side down.
Humbuckers
In case of humbuckers, the situation is quite a bit different, where the magnets in the single coil were magnet pole pieces were slightly opposing each other, in humbuckers the two sets are aiding each other, that is if we are referring to the two different rows. Same row, it is still the same as in the single row (coil) pickups. If we are using one bottom magnet and steel pole pieces or magnet pole pieces does not really make any difference. There are quite a few combinations that will give you a different reaction to string movement. For the most common, standard methods if you wish, there is not much difference in output as shown on the main page. Fig 10 shows a humbucker arrangement with a magnet in the bottom.
There is one kink that I added to this picture, there is a very small air gap between the left slug and the bottom magnet, you can see the B field lines “cutting” the corner there. When measuring the top surface B field, there is practically no difference between the two sides. This is good to know, because then we do not have to worry much about round slugs meeting a straight edge magnet and the resulting air gap. I should mention that the picture shows one set of poles, the left piece is pointing up and the right is pointing down, as you would expect. Also, it should be noted that the B field inside the magnet is much more organized, in other words a reduced case of Fig 5.
Now, we cannot mention a humbucker without showing a humbucker with rails instead of pole pieces. The solution using rails is in my opinion the only one that has all the plusses, none of the drawbacks as mentioned above and it also gives the most stable output, see Fig 11.
It should be noted that the field flux is in same direction as in Fig 10 and the little red mark on the left rail is for measuring the flux and flux change in the rail with string movement. Not shown, because it is a complicated operation with this software, will more like time consuming. Fig 11 should be to scale, Fig 10 was not quite to scale, but the principle is clear to see. Slugs could have been slightly longer.
Now, you would probably wonder why I did not include a humbucker with slugs in one row and screws in the other side. To be honest, I consider the screws in a humbucker the dumbest idea ever in connection with pickups. I guess if I get a chance I will set it up so you can see how dumb it is from a magnetic point of view, but it probably have some visual effect.
Well, here is the humbucker with one side being screws. I will treat the output voltage from each side in a different place, when I get to it. Also, I have not shown where the coil(s) that pick up the induced voltage is located, it will not show up on regular plot that are purely dealing with magnetics because they are copper, a non magnetic material, meaning they will have no influence on the magnetic “picture”. Fig 12 shows the magnetic picture with screws, the dimensions are to scale, or as close I can get it. The thing to notice is how different the fields are when comparing the two sides, this my have resulted in the two coils being wound differently in order to try to compensate for the difference in magnetic performance, so it is not because of in-accuracy it is for a good reason. The end result is not affected because the signals opposite and are added, the signals are but the noise on either side become different in amplitude so the advantage of a symmetrical pickup construction and its ability to cancel noise is reduced, contradiction the original intent. The fact that these are screws that can be adjusted seems to have little or no effect. I prefer pickups with slugs on both sides that are symmetrical and give you the maximum noise reduction.
As you can tell, the screw is a little longer at the end, this has minimum effect on the magnetic field. The screw is shown as having a flat top, but that will not alter the magnetic field. You may have wondered where the coil was in all the previous pictures, as it turns out the, the only way I can show the coils is by taking it from the model drawing that is the basis for the simulation, Fig 13.
What we see in Fig 13 should give an indication of how the pickup coils are arranged around either slug to the left or screw to the right. In Fig 13, the “mesh” that is the basis for the magnetic calculation using finite element analysis can be seen. That should make it clear why some of the magnetic field lines are so irregular.
Something interesting came up when I started a video on YouTube, it was a video about PAF pickups, and as most videos, this one was loaded with misinformation. That was not, however, what came up next, what appeared was videos about adjusting height of screws in a humbucker. We have already seen what screws in a pickup look like from a magnetic point of view, the screws do not exactly have a positive effect on the output of the pickup which is understandable if we take a look at Fig 12 and what we see is the field behavior is quite a bit different from what we see with a single coil pickup. The video was about adjusting the height of the screws to match the curvature of the strings (for reasons I can see any benefit of) and the adjustment amounted to 1/2 to 1 whole turn of the 4 screws in the middle of the row, claiming that this would give you a better sound than if the screws were all flush with the cover (without any proof, of course). So I had to run a simulation similar to Fig 12, and the result is what is presented in Fig 14. The screw was adjusted out by 1 mm, more than 1 turn!
If you compare the two figures, you see that the is NO difference. A measurement of flux density showed that this is confirmed. I do not know if the author of this video has changed his mind because it is a few years old, I doubt it, he is a pickup maker! Interestingly enough, the video was followed by another video about the screw side in pickups and why it was there at all because there were no screws in the original patent! The conclusion he drew was that the addition of screws was purely marketing originated and did not have a practical purpose. It was based on the P-90 that has a single line of screws, again to give the appearance of the user being able to adjust something? As I have mentioned, I am a fan of two rows of slugs in my pickups, unfortunately, they are few and far between thanks to marketing!
I will add more cases when ready, so far we have seen the most common. And I still have to figure out the relationship between Bo and Bm. It is evident that the relation is there because the testing I have done on actual pickups, measuring the B field on top of the pole piece and relating that to the actual measurement of the pickup output voltage.