It looked like it would be of some value if I would go into more detail with the issue of string height and hoe the placement and the oscillation of the string would alter the magnetic field (flux density) Bo measured at the top surface of the magnet. As explained elsewhere, this is the “best” we can do to get a measure for the change in flux density that affects the pickup coil induced voltage and therefore the output voltage of the pickup. The magnet used is a “Fender -style” cylindrical magnet as used in single coil pickups and for this test, the Bo flux was measured as the string was displaced vertically above the magnet. The results presented are extracted from the three magnet comparison that shows the (small) difference between Neodymium, AlNiCo 5 and AlNiCo 2 magnets, Fig 6 on the main Pickup Physics page. Instead of just showing one specific height, h, here we will concentrate on making the string height, h, the main parameter and study what the difference is between different h-values. In case it is not indicated, the string rotation radius, r, is 1 mm. In graphs, the string height, h, is in mm too.
In Fig 1, we show the curve for the AlNiCo 5 magnet, this magnet is the one that these examples are based on. The figure is general for the specific string height of 6 mm. The use, in principle, is the read the values from the graph, for example with a string circular movement of radius r = 1 mm. You can determine the deviation in Bo by measuring the difference between the blue curve and the red curve at h values 5 mm and 7 mm. Doing this, you get the total deviation and the POS and NEG values that will be different and this difference will indicate the amount of distortion in the waveform you get from the string movement to the output signal from the pickup. For this particular string height, we can use other values of r and if r is reduced, we can see that the curve becomes more “linear” which means that the output waveform becomes more sinusoidal (it is assumed that the string has a circular rotational movement). This is exactly what we can observe as the string is “ringing” out, the behavior that can also be seen if we look at the harmonics of the pickup output voltage with a spectrum analyzer, the higher harmonics disappear and the only one left is the fundamental note.
Let us expand this as suggested above, using r = 1 mm, we get the curves in Fig 2. for the POS and the NEG and from this, the total deviation, TOT. The green curve in Fig 2, TOT, represents the output voltage from the pickup, indirectly, of course. We have to assume that we are dealing with the same string and the same note played so that the time difference for a complete cycle is constant.
Now as a further indication, we can take a stab at calculating a “distortion factor”, DP%. This is a parameter that is entirely invented by myself, but it appears to be pretty useful in explaining how the string-pickup dynamics work in principle. Fig 3 is showing this distortion factor in %. This factor is defined as how symmetrical the POS and NEG values are around the Bo field for the string at rest at the string height.
In Fig 3, the value that determines the deviation is Boav, the average value of the POS and NEG as a ratio between Boav and Bo(h), in percent. This is what we described earlier, at low h-values the distortion is high and it tapers off with increasing string height, h.
I do not know if that was the motivation for SRV to set his pickups as low as possible, maybe it was the sound he was looking for, the “cleaner” sound. Speaking of SRV, I was there at the concert at Alpine Valley the night before he died. Oh boy, that is about 30 years ago! Still makes me sad…
Difference in Magnet Type
Let us take the same numbers from the first part and present them in a different way. There is a lot of information out there about about what we can do to increase the output of a pickup by changing to a “stronger” magnet and, of course, stay with the same number of turns of the pickup coil. It is wide spread, unfortunately, that varying the field strength of the magnet or even demagnetize it will have all sorts of effects on the sound. There is in fact a whole myth culture concerning this. We will address this in the following.
To create the curves shown in the previous section, the magnets were measured including the basic B, the magnetic flux, at the top surface of the magnet and increasing the string height, the distance from the top surface of the magnet. The result of this measurement is shown in Fig 4.
To be clear, the magnets in this measurement are, Neodymium, AlNiCo2 and AlNiCo5, the typically used magnets as we can see are much lower in flux density than the Neodymium magnet, by a factor of 4-5. So the conclusion is by many that you will get the same factor in higher output voltage, that is the myth anyway. The thing is, just because think it is so, does not make it so. Why not? Well, I have read many papers, university level papers, and most of these do not deal directly with the magnetic field so there is not much to discuss in that context, but one paper, and it is included in the References, has the output voltage proportional to the B field at the magnet surface. I have been itching to discuss this equation and use it to make sense of the output voltage, but I have been hesitating because of this exact thing we are discussing here, I simply felt uneasy about that equation because, we know that the output voltage, the induced voltage in the coil is proportional to the time derivative of B, dB/dt, which is how much B changes with time, not with B itself. I still owe you this discussion, but it will be some other time.
Now, as said we are interested id how much B is changing, not in absolute value. For this purpose we find the value of Bo without a string present, string height is infinite if you wish. We will now subtract this value from the B values in Fig 4 and we ger the relative values of B, called Bosr.
This is the curves we see in Fig 5. It is pretty clear why I did this, it is because we are interested in the difference in B, not the absolute value of B as in Fig 4. let us look at an example, take the change if we have a change in distance from 3 to 4 (in mm), the change in B is the same in the two cases, referring to Fig 4 and Fig 5. In the case of the Neo magnet, that difference is 62 Gauss in both cases. Well it is not easy to see in Fig 4, but the tables tell me that the difference is the same, I did after all take the measurements!
We typically do not set our string height to anything below 5 mm (let us use this as an example), in that case, the curves can be simplified to only include heights over 4 mm. This was done and Fig 6 is the result.
The result is that the curves show us that the difference between magnets when we are looking at realistic operating conditions is not that great, in fact you can see that Neodymium and AlNiCo 5 are identical over 6 mm in distance from the magnet and they are identical for all three magnets above 8 mm. End result, the benefit on output is not that great. I think you get the picture!