Effect of pole aperture using LTSpice

[aquin43]

I have put together a little Spice simulation of a pickup pole piece in which the aperture is divided up into thirteen parts arranged symmetrically with six different values so that various aperture shapes can be tried.

The idea is that the wave in the string propagates across the pole and the output from each part arrives at a different time related to the wave velocity and the distance between the sampling points.

All of the necessary variables are set by .param statements:
f0 = the fundamental frequency
scale = the scale length

pole_wide = the width of the pole

Inches or millimetres both work if used consistently.

The pole is represented as a series of delay lines with their outputs weighted and summed into a behavioural source. A cascade of equal delays would be nominally the same, but the Spice transient calculation comes out cleaner with this arrangement.

Sending a narrow pulse down the system gives a plot of the variation of sensitivity across the pole in arbitrary units.

Sending a sine wave through it gives a frequency response plot.

The string is the bottom E on a Gibson scale length and the effective pole is 0.25 inches wide. The sensitivity pattern is a guess.

This response would be multiplied by the effects of the pickup position and the plucking position.

Arthur

[antigua]

I'm impressed that you're able to model something spacial and physical with an electronics model. I don't undertstand how the T transmission like components work (but I haven't had time to find out, either). One thing I dont understand right off the bat though is where you say that the sensitivity is a guess, does that mean you need empirical data to set the sensitivity? I've done such a test once before, but I'm willing to try it again. It takes an hour or two to set up and conduct, though. 

Someone on another forum was just talking about wide Jazzmaster coils, and just as a quick and dirty test, I plugged a loose JM pickup into an amp, held it over the strings, and compared it to an SSL-1 I also have sitting here, and it seems that the Jazzmaster pickup, with it's shorter magnets and wider coil, does have a wider aperture that is also less intense at the pole tops. In other words, as the JM pickup approaches the strings, it becomes audible as the strings approaches the of the the rim of the coil, and it reaches peak loudness once it's at the edge of the pole piece. The Strat pickup also becomes audible as the string approaches the coil, but the Strat pickup achieves a louder overall sound as the string finally reaches the edge of the coil. I can think of two reasons for that 1) the Strat pickup pole pieces as stronger because they are longer, 2) the coil is amassed around the pole piece. I'd be interested in any sort of modeling that can relate the effect of coil and pole piece geometry. 

It seems to me though, that if a pickup picks up more voltage from farther away, and less voltage up close, as appears to be the case with a Jazzmaster pickup, it will cause a greater sum of cancellations than a pickup that has a more narrow intensity. 

[aquin43]

The T element is a lossless transmission line. It produces a pure delay with a voltage gain of unity, a delay as specified and a phase shift that is proportional to frequency. The concept being used here is that the signal on the string is a wave that travels down the string so an impulse on the string will cross the pole at a given rate. Therefore the response of the pole at any point can be modelled in terms of the delay to that point times the gain at that point. This should be a continuous function but is being sampled at 13 points. It is intended as a device to explore the effects of different pole widths and sensitivity contours. I don't know what the window width is or what the sensitivity contour is, so I just made up something that seemed plausible.

The problem with trying to estimate the width of the pole window by moving the pickup is that the pole both magnetises and senses the string. Moving the pickup changes the magnetisation pattern as well as moving the sensor.

Arthur

[antigua]

May 11, 2020 16:03:24 GMT -5 aquin43 said:

The T element is a lossless transmission line. It produces a pure delay with a voltage gain of unity, a delay as specified and a phase shift that is proportional to frequency. The concept being used here is that the signal on the string is a wave that travels down the string so an impulse on the string will cross the pole at a given rate. Therefore the response of the pole at any point can be modelled in terms of the delay to that point times the gain at that point. This should be a continuous function but is being sampled at 13 points. It is intended as a device to explore the effects of different pole widths and sensitivity contours. I don't know what the window width is or what the sensitivity contour is, so I just made up something that seemed plausible.

The problem with trying to estimate the width of the pole window by moving the pickup is that the pole both magnetises and senses the string. Moving the pickup changes the magnetisation pattern as well as moving the sensor.

Arthur

Thanks for that explanation. When I tested the effects of magnetic string pull with a spectral analysis, which is one of the earlier tests I had done here, I noticed that the string pull affected the harmonics that the pickup was also most sensitive too. For example, if I raised and lowered the bridge pickup which the neck pickup was producing the signal, the change in harmonic amplitudes was a lot smaller than when the neck pickup itself was raised and lowered, and vice versa. In other words, what a pickup is most sensitive to picking up, it is also most prone to change due to magnetic string pull. Even though all of the pickup's heights independently cause asymmetrical string damping, one pickup doesn't notice what the other pickups are doing to the string, so much so.

I'll do some practical aperture amplitude testing soon. The hard part is just setting up the constant string vibration, I have rig just for the purpose.