Computer tools for the numerical simulation of electrodynamic loudspeakers, which are based on equivalent circuit representations, are well established [5,6,7,8]. An analysis based on electroacoustic analogues assumes that the electro-mechanical-acoustic quantities behave as single simple entities and do not show complex or wavelike properties. For example, a diaphragm is assumed to act like a superposition of simple, plane pistons [6], whereas the frequency dependence of the voice coil inductance, which is due to eddy currents in the pole structure and in the former, is ignored [8,9]. However, the main shortcoming of the equivalent circuit modeling scheme is that the circuit element parameters, like mechanical mass, compliance and damping resistance of the diaphragm, have to be determined empirically by measurements on a prototype or by some other numerical computations [6].
Finite-Element- and Boundary-Element-Methods, however, are based on the partial differential equations governing the magnetic, mechanical and acoustic field quantities and, therefore, consider the complex and wavelike properties. As input parameters these methods require only the precise geometry of the loudspeaker as well as material data of each part.
So far, neither FEM and BEM nor equivalent circuit representations have been effectively utilized in the development of electrodynamic loudspeakers and, therefore, most manufacturers still rely on experimental trial-and-error methods. While equivalent circuit representations suffer from the above mentioned drawbacks, the main reason for the lack of computer simulation tools based on FEM and BEM is the high complexity of such moving coil drivers, as shown in Figure 1. A cylindrical, small light voice coil is suspended freely in a strong radial magnetic field, generated by a permanent magnet. The magnet assembly, consisting of pole, back plate and top plate, helps to concentrate most of the magnetic flux within the magnet structure and, therefore, into the narrow radial gap. When the coil is loaded by an electric voltage, the interaction between the magnetic field of the permanent magnet and the current in the voice coil results in an axial Lorentz force. The voice coil is wound onto an aluminum former, which is attached to the rigid, light cone diaphragm in order to couple the forces more effectively to the air and, hence, to permit acoustic power to be radiated from the assembly. The dust cap which influences the acoustic radiation at high frequencies has mainly the task to prevent the penetration of dust to the magnet gap. The main function of the suspension and the surround is to allow free axial movement of the moving coil driver, while non axial movements are suppressed almost completely.
Since in the case of a loudspeaker the interaction with the ambient fluid must not be neglected, the electrodynamic loudspeaker represents a typical coupled magnetomechanical system immersed in an acoustic fluid. That is the reason, why for the detailed finite element modeling of these moving coil drivers the magnetic, the mechanical as well as the acoustic fields including their couplings have to be considered as one system, which cannot be separated.
Due to the complexity of this multi-field problem, the following points must be considered in a numerical simulation with a FEM- and BEM-software:
In the following, we, first, recall the theory of the coupled magnetomechanical transducer and describe the corresponding finite element scheme. This scheme has been implemented into the Finite-Element/Boundary-Element program CAPA [1], which is used here for the modeling of the dynamic behavior of electrodynamic loudspeakers. Next, comparisons between simulation results and according measured data are shown for verification purposes. Finally, we present the application of computer simulation studies in the optimization of electrodynamic loudspeaker design-parameters, especially the elimination of response dips at intermediate frequencies and an improvement in efficiency for higher frequencies.
