Subwoofer Box Calculator

Enclosure design is a filter alignment problem. A driver in free air behaves as a second-order high-pass system defined by three Thiele-Small parameters: Fs, the free-air resonance in hertz; Qts, the total damping at that resonance; and Vas, the volume of air whose compliance equals that of the suspension. Sealing the driver in a box adds the trapped air as a second spring, raising resonance to Fc and total Q to Qtc. The expression Vb = Vas / ((Qtc/Qts)^2 - 1) is that relationship solved for volume. A Qtc of 0.707 gives a Butterworth maximally flat response with no peak; 0.5 is critically damped and demands a much larger box; 1.0 yields a compact box with a few dB of lift just above cutoff and audibly slower decay. Rules of thumb follow from Qts: below about 0.4 a driver suits a vented box, above 0.5 a sealed one, and between the two either works. A sealed box rolls off at 12 dB per octave, a vented one at 24 dB per octave below tuning, where cone excursion is also unloaded and the driver is vulnerable without a high-pass filter. Practical limits deserve respect. Vas and Qts drift with break-in and temperature, and published parameters commonly differ from measured ones by 10 to 20 percent. Driver, port and bracing displacement must be added back to net internal volume, typically 5 to 10 percent, and port air velocity above roughly 17 m/s produces audible chuffing.

The vented enclosure came first and was not initially well understood. Albert L. Thuras at Bell Laboratories filed the patent for the bass reflex cabinet in 1930, describing the port and cabinet air as a Helmholtz resonator that reinforces output near tuning. For the next three decades vented boxes were tuned largely by ear, because no published method connected a driver's measurable properties to the volume it required. The sealed alternative was popularised by Edgar Villchur, who applied acoustic suspension in the Acoustic Research AR-1 in the mid 1950s, using the enclosed air as the dominant restoring force so that a small cabinet could produce low, low-distortion bass. The design equations arrived by way of Australia. A. Neville Thiele, an engineer at the Australian Broadcasting Commission, published an analysis in the Proceedings of the IREE Australia in 1961 showing that a driver and vented box together form a fourth-order high-pass filter that can be aligned using standard filter tables. The work reached a wide audience only after the Journal of the Audio Engineering Society republished it in 1971. Richard H. Small then extended and systematised the approach in a series of JAES papers on closed-box, vented-box and passive-radiator systems in 1972 and 1973, defining the parameter set that manufacturers have printed on driver datasheets ever since.