The usual procedure for direct-radiator low-frequency loudspeaker system design leads to the calculation of the driver's fundamental electromechanical parameters by an intermediate specification of the Thiele-Small parameters. A reformulation of the synthesis procedure to eliminate the intermediate Thiele-Small calculation leads to a set of equations that yield the driver's electromechanical parameters directly from the system specifications. These equations reveal some moderately surprising relationships when the different system types (closed box, fourth-order vented box, and sixth-order vented box) are compared. For example, for a specified low-frequency cutoff f(3), midband efficiency, and driver size the fourth-order vented-box driver is found to be roughly three times more expensive (judged on the amount of magnet energy required) than the closed-box driver. Conversely for a given f(3), enclosure volume V(B), maximum diaphragm excursion X(max), and acoustic power output P(AR) the fourth-order vented-box driver is some five times cheaper than the closed-box driver. It is also found that for direct-radiator systems in general, specified f(3), V(B), X(max), and P(AR) lead to the total moving mass M(MS) depending inversely on the sixth power of the cutoff frequency, that is, a one-third-octave reduction in f(3) results in a fourfold increase in mass. Furthermore, the same conditions reveal that the sixth-order vented-box driver moving mass is some 42 times lighter than that of the closed-box driver, providing the same midband acoustic output and f(3). If cone area and efficiency are held constant, the direct-radiator system driver actually gets less expensive as the low-frequency limit is extended.
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