Electric guitars use sensors based on magnetic induction to convert string vibration into electrical signals. This research explores a model of the induced voltage when the field of the permanent magnetic is assumed to be uniform. This approximation allows for the derivation of an analytical expression where the influence of different parameters, such as coil, magnet, and string are explicitly represented. The theoretical response of the pickup to a harmonic motion of the string at low frequencies is compared to experimental data obtained from a dedicated experimental bench. Some of the more interesting results are as follows: (1) the pickup is a velocity sensor and most sensitive to z polarization; (2) the furthest turns of the coil have little or no contribution to the output voltage; (3) for plain strings, the output level is proportional to the cross section of the string; (4) a wound string has the effect of decreasing the level of the fundamental and, thus, increasing the distortion; (5) the string materials appear to have no influence on the output voltage; (6) distortion depends mostly on the amplitude of the string displacement but weakly on the distance coil/string at rest.
https://www.aes.org/e-lib/browse.cfm?elib=19201
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