Loudspeaker Driver Displacement Decomposition

This valuable tutorial offers a unique overview on the possibilities of three-dimensional analysis of loudspeaker driver displacement, using Phase Decomposition and Axial-Symmetrical Decomposition techniques.

- René Christensen

When looking at a frequency response from a loudspeaker driver magnitude and phase of the pressure in a microphone point), a lot of information can be extracted regarding its behavior. The magnitude response is typically the primary focus, and a flat response here is the desired outcome, whereas the oftentimes ignored) phase response holds information about the temporal aspects of the loudspeaker and generally of the setup regarding number of drivers and how they combine to the full response. However, the sound pressure is simply a zero-dimensional signal, which does not necessarily tell us the whole story about the three-dimensional aspects of the surface vibration and how it generates the sound. To really dissect where, for example, dips and peaks in the pressure response come from some other tools can help, and two such tools are the Phase Decomposition and the Axial-Symmetrical Decomposition techniques, respectively.

The Phase Decomposition technique 1] as well as the Axial Symmetrical Decomposition 2] have been promoted by Klippel, where they are built into measurement systems and so can be applied to measurements only. I was involved in the development of an add-on package that could take in simulated surface cone, dust cap, surround) displacement data, and analyze it as it had been measured. But shortly thereafter I developed a simulation setup in COMSOL Multiphysics where the phase decomposition could be carried out directly based on simulation data, and this approach has been used in the analysis and synthesis work for several clients since then.

Phase Decomposition

The first technique relies on knowing the complex pressure in a microphone point and relating the complex displacement across the loudspeaker surface to the pressure, or more specifically to the phase of said pressure. Knowing these quantities, the following displacement components can be established: