Multiphysics modeling is a perfect fit for simulating loudspeakers. What happens if I tweak the shape of my speaker horn? How will the driving force be affected if I use a different material in the pole piece? At what frequency does my insulating lining kick in? To some degree, all these questions can be addressed by models of select parts of the loudspeaker and its surroundings. Yet, multiphysics modeling of the entire system from the voice coil mechanism to the sound level experienced by the listener is surprisingly feasible and also quite easy to do.
The most important electromagnetic properties of a loudspeaker driver can be characterized by two parameters: the BL factor and the blocked coil impedance. The BL factor depends on the static magnetic field in the gap through which the voice coil moves. The blocked coil impedance is measured when the coil is held still. An example model in the Acoustics Module shows how to extract the BL factor using a static magnetic analysis and how to extract the blocked coil impedance with the help of an AC analysis. Taking advantage of the rotational symmetry of the driver, this model is set up in a 2D axisymmetric geometry. But, if you want to study the effects of the enclosure and the room surrounding the speaker, rather than just the driver, you need to move to 3D.
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Figure 1: The loudspeaker as it stands positioned near the corner of a room. Only half the geometry is modeled. |
Figure 1 shows the loudspeaker geometry. The enclosure has the driver mounted in a basket and a bass reflex vent to boost low frequencies. The loudspeaker has been placed near the corner of a room. The open side of the room is enclosed by a perfectly matched layer (PML), a subdomain that simulates the absorption of outgoing waves without any reflections.
You can now use the BL factor and blocked impedance from the 2D model to solve an equation of motion to find the acceleration on the cone, which would correspond to a given driving voltage. Other contributions to this equation of motion are the damping and restoration of the suspension force and the total acoustic pressure force, which you obtain by integrating the pressure load on the cone.
Solving the 3D model gives you the acoustic pressure distribution inside and outside the loudspeaker’s enclosure for a set driving voltages and a range of frequencies (Figure 2). It is now possible, for instance, to evaluate the acoustic impedance or plot the sound level at one or several listening positions anywhere in the room. Here you can locate resonances and evaluate the overall performance of the system. By making changes to the geometry and varying the operating parameters, you can study different effects, such as increasing the compliance of the suspension, attaching a dust cap to the cone, plugging the vent, or changing the position of the speaker in the room.
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Figure 2: The sound pressure level inside the loudspeaker and room at a frequency of 1500 Hz. |