The theory of maximally flat loudspeaker systems

A convenient mathematical formulation is given for the absolute low-frequency response of an electrodynamic direct radiator loudspeaker mounted in a vented or unvented enclosure. The combined effects of speaker
Q
(ratio of reactance to resistance), enclosure size, and enclosure tuning are shown to control the convergence of the response curve towards its asymptotic value. Mathematical criteria are presented graphically, which enable the designer to find enclosure characteristics that give a frequency response curve flat through fourth order in reciprocal frequency, for a given loudspeaker
Q
. In addition, it is shown that for
Q = 0.383
the system can be made flat through sixth order by choosing the correct enclosure size and vent tuning. This "triple point" design represents the flattest possible response for direct radiator systems.