Simplified Ltspice model of an electric guitar : magnet, vibrating string and pickup with core saturation.

Following is a Ltspice model of a vibrating ferromagnetic guitar string with a AlNiCo magnet and a coil pickup.

Model Download :

Dependencies :

TL072 Op-Amp model or any other Audio grade suitable op-amp

Explanation :

It assumes a single pickup with a copper wire wound around a Nickel Steel alloy core. Saturation is modeled.

In a realistic model, the magnetic excitation of the coil is as follows :

Because of the limitations of integration in Ltspice (time integral support, but not space integrals), the model of B) has been simplified – As if the magnet was vibrating like a string at a distance of the pickup, but taking into account geometry. A better model would be possible using “C++ black boxes” as it is possible now with QSpice, as the DLL engine is Turing complete which allows to render space integrals easily. The model of B) excited by A) is doable in QSpice and is explained in the paper (4). So B) has been simplified to a simple coupling parameter int the form of a factor “chi_wire” (or wire magnetic susceptibility).

Note that the code for such a model of B) has been explored as such, but not validated. It may be added here in a future release.

Finally the core Mechanical model is simplified and according to (1) :

It assumes a string displacement along the Z axis only, and bridge reaction is not modeled.

Bias magnetic field is modelled and as a notable contribution if the pickup core saturation is modelled.

Note that the coil is assumed to be wrapped around a single pole (as just one string is modeled), number of turns has been decreased to take into account the tighter magnetic coupling.

Pickup flux is the sum of self inductance times current + induced flux from time varying magnetic field. Since the preamp is very high impedance the current is negligible and only the EMF from the magnetic field has sensible contribution.

Finally a preamp has been added. (5)

References :

(1) Solving the Sound of a Guitar String
Jason Pelc
December 10, 2007
(Submitted as coursework for Physics 210, Stanford University, Fall 2007)

http://large.stanford.edu/courses/2007/ph210/pelc2/

(2) Magnetic Field of a Cylindrical Bar Magnet – Wolfram Demonstrations Project

https://demonstrations.wolfram.com/MagneticFieldOfACylindricalBarMagnet

(3) Analytical Functions of Magnetization Curves
for High Magnetic Permeability Materials

Mehran Mirzaei1 , and Pavel Ripka1
Faculty of Electrical Engineering, Czech Technical University, 16627 Prague, Czech Republic

https://ieeexplore.ieee.org/document/8356239

(4) Exact expression for the magnetic field of a finite cylinder with arbitrary
uniform magnetization
Alessio Caciagli 1, Roel J. Baars 1, Albert P. Philipse, Bonny W.M. Kuipers ⇑

(5) ELECTRIC GUITAR PREAMPLIFIER by EFI Bureau

https://www.electronicsforu.com/electronics-projects/electric-guitar-preamplifier