Loudspeaker enclosures
The front and rear surfaces of a diaphragm produce pressure with opposite polarity. If both reach the listener with similar amplitude and opposite phases, they cancel.
An enclosure controls the rear radiation by isolating it or by using it constructively.
Comparison
| Type | Main advantage | Main challenge |
|---|---|---|
| Sealed | Simple, predictable low-frequency behavior | Needs more excursion and power for deep bass |
| Bass-reflex | Greater output near tuning | Rapid roll-off and poor control below tuning |
| Passive radiator | Port-like behavior without a long air duct | Added cost, mass and excursion limits |
| Open baffle | Dipole radiation and no enclosed-air pressure | Large baffle, EQ and large excursion requirements |
| Transmission line | Uses a long, damped acoustic path | Size and design complexity |
| Horn loaded | High efficiency and directivity control | Physical size and construction complexity |
Sealed enclosures
A sealed enclosure isolates the rear radiation and adds the stiffness of the enclosed air to the driver’s suspension.
Making the box smaller:
- Increases air stiffness
- Raises system resonance \(F_C\)
- Raises system quality factor \(Q_{TC}\)
In a simplified loss-free model:
Solving for box volume:
These equations assume a simple small-signal model. Driver tolerances, leakage, damping material, cabinet losses, and amplifier resistance change the result.
Common sealed alignments
- \(Q_{TC}=0.50\) : Critically damped, gradual roll-off
- \(Q_{TC}\approx0.58\) : Bessel-type response
- \(Q_{TC}\approx0.71\) : Maximally flat Butterworth amplitude response
- \(Q_{TC} > 0.71\) : Increasing response peak at resonance
Excessive \(Q_{TC}\) can produce boomy, poorly controlled bass.
Bass-reflex enclosures
A bass-reflex enclosure adds a port. The air in the port acts as an acoustic mass, while the air in the enclosure acts as a spring. Together they form a tuned resonant system.
Near the tuning frequency \(F_B\):
- Port output is high
- Cone excursion is reduced
- Port and driver output are in phase and can combine constructively
Below tuning:
- Port and driver output become increasingly out of phase
- Acoustic output falls rapidly
- The driver loses much of the port’s protective loading
- Excursion can increase sharply
For this reason, high-output vented systems often use a high-pass filter below tuning.
A port must have enough cross-sectional area to keep air velocity under control. Flares can reduce turbulence. Very small ports may produce audible chuffing.
Passive-radiator systems
A passive radiator replaces the port’s moving air mass with an unpowered diaphragm carrying added mass.
It can be useful when the required port would be too long or too narrow. The passive radiator must have enough displacement capability and should not reach its suspension limits.
Open-baffle systems
An open baffle does not enclose the rear of the driver. The front and rear waves form a dipole radiation pattern.
At low frequencies, the path around the baffle becomes short relative to the wavelength, increasing cancellation. Deep bass therefore requires a large baffle, substantial diaphragm area, equalization, excursion, or some combination of these.
Open-baffle systems also interact with rooms differently from conventional monopole speakers.
Transmission-line systems
A transmission line connects the rear of the driver to a long acoustic path, usually filled or lined with absorbent material.
The path is often related to a quarter wavelength near the desired low-frequency region. Tapering and damping are used to control higher resonances.
Transmission lines can work well, but simplified “quarter-wave” rules are only a starting point.
Horn-loaded systems
A horn gradually transforms the high acoustic impedance at a small throat into a lower impedance at a larger mouth.
Benefits can include:
- Greater efficiency
- Higher output
- Lower diaphragm excursion for a given acoustic level
- Controlled directivity
Low-frequency horns become physically large because their dimensions are related to wavelength.