Driver matching

Front chamber

Upper roll-off set by the air trapped between diaphragm and throat. A free acoustic crossover when sized deliberately.

Sheet: 15 / 25
Units: Metric
Air: 20 °C

Fig. 1Front-chamber low-pass, first order

Responsedrag on plot to read

Corner frequency $f_{HC}$: 1803Hz
Mean chamber depth: 23.4mm
1 dB point: 918Hz
Chamber volume $V_{FC}$: 2000cm³
Velocity-source corner: 901Hz
Compression ratio $S_d/S_t$: 2.59: 1

Fig. 2Front chamber, schematic

How it works

The air trapped between the diaphragm and the throat is a small spring across the horn’s input. Above a certain frequency it shunts the cone’s output and the response rolls off. The chamber of volume $V_{FC}$ is an acoustic compliance in parallel with the throat resistance $R_{AT}$ :

C_{AF} = \frac{V_{FC}}{\rho c^{2}} \qquad R_{AT} = \frac{\rho c}{S_t}

The compliance also sees the output resistance of the driver, $R_{AS}$ . The corner frequency is where the reactance of the compliance equals the two resistances in parallel:

f_{HC} = \frac{1}{2\pi\,C_{AF}\,(R_{AT}\parallel R_{AS})} = \frac{c\,S_t}{2\pi V_{FC}}\left(1 + \frac{R_{AT}}{R_{AS}}\right)

Two limiting cases

Matched driver. With the optimum throat, $R_{AS} = R_{AT}$ and the bracket equals 2, giving $f_{HC} = c\,S_t / \pi V_{FC}$ .
Velocity source. If the driver is much stiffer than the load, $R_{AS} \to \infty$ and the bracket equals 1.

Using it deliberately

In a bass horn the front chamber is often sized on purpose so that $f_{HC}$ falls at the top of the intended band. It then acts as a free acoustic crossover and filters distortion products. In a midrange or compression driver the aim is the opposite: keep the volume as small as the excursion allows, which is the job of the phase plug.

Limits

The lumped model holds while the chamber is small compared with the wavelength. Once its depth approaches a quarter wavelength, standing waves in the chamber cause sharp dips that this sheet does not show.

D. B. Keele, AES preprint 1250 (1977).
H. F. Olson, Acoustical Engineering (1957), §8.3.

Loading sheet…

How it works

C_{AF} = \frac{V_{FC}}{\rho c^{2}} \qquad R_{AT} = \frac{\rho c}{S_t}

The compliance also sees the output resistance of the driver, $R_{AS}$ . The corner frequency is where the reactance of the compliance equals the two resistances in parallel:

f_{HC} = \frac{1}{2\pi\,C_{AF}\,(R_{AT}\parallel R_{AS})} = \frac{c\,S_t}{2\pi V_{FC}}\left(1 + \frac{R_{AT}}{R_{AS}}\right)

Two limiting cases

Matched driver. With the optimum throat, $R_{AS} = R_{AT}$ and the bracket equals 2, giving $f_{HC} = c\,S_t / \pi V_{FC}$ .
Velocity source. If the driver is much stiffer than the load, $R_{AS} \to \infty$ and the bracket equals 1.

Using it deliberately

Limits

D. B. Keele, AES preprint 1250 (1977).
H. F. Olson, Acoustical Engineering (1957), §8.3.

Front chamber

Inputs

How it works

Two limiting cases

Using it deliberately

Limits

Inputs

How it works

Two limiting cases

Using it deliberately

Limits

§ How it works

Two limiting cases

Using it deliberately

Limits

§ How it works

Two limiting cases

Using it deliberately

Limits

How it works

How it works