Index LoudspeakersSealed Enclosure

Sealed Enclosure

System Q, resonance and roll-off of a driver in a closed box.

System Q0.701

Box resonance59Hz

−3 dB point59.6Hz

Response peak0.00dB

Volume for Q = 0.70724.4L

Bass response

In this box
Driver on an infinite baffle

Alignment

over-damped

tight to flat

warm

boomy

Q of 0.5 is critically damped, 0.58 is Bessel, 0.71 is maximally flat (Butterworth). Above about 1.0 the bass turns boomy.

Input

Free-air resonance

f_s

Total Q of the driver

Q_{ts}

Equivalent compliance volume

V_{as}

Net box volume

V_b

How it works

Air as a spring

The air trapped in a sealed box resists the cone's motion like a spring added to the driver's own suspension. A smaller box is a stiffer spring. The ratio of the two compliances sets everything:

\alpha = \frac{V_{as}}{V_b}

Both the resonance frequency and the Q rise by the same factor:

f_c = f_s\sqrt{1 + \alpha}

Q_{tc} = Q_{ts}\sqrt{1 + \alpha}

Response shape

The system is a second-order high-pass filter, rolling off at 12 dB per octave below resonance:

\left|H(f)\right| = \frac{(f/f_c)^2}{\sqrt{\left(1 - (f/f_c)^2\right)^2 + \dfrac{(f/f_c)^2}{Q_{tc}^{2}}}}

The −3 dB frequency follows from setting that to $1/\sqrt2$ :

f_3 = f_c\sqrt{\frac{a + \sqrt{a^2 + 4}}{2}},

a = \frac{1}{Q_{tc}^{2}} - 2

Choosing a volume

For the flattest response aim for $Q_{tc} = 0.707$ , which needs

V_b = \frac{V_{as}}{\left(0.707 / Q_{ts}\right)^2 - 1}

Loosely filling the box with damping material makes it behave as if it were 15 to 25% larger. Volumes here are net: subtract the space taken by the driver, bracing and any internal amplifier.

References

A. N. Thiele, “Loudspeakers in Vented Boxes,” Proc. IRE Australia, vol. 22, no. 8, pp. 487–508, 1961. Reprinted J. Audio Eng. Soc., vol. 19, nos. 5–6, 1971. AES, part 1· AES, part 2
R. H. Small, “Direct-Radiator Loudspeaker System Analysis,” J. Audio Eng. Soc., vol. 20, no. 5, pp. 383–395, 1972. AES