Driver matching

Compression & excursion

Diaphragm travel needed for a given acoustic power, and the lowest safe crossover for a compression driver.

Sheet: 16 / 25
Units: Metric
Air: 20 °C

Fig. 1Diaphragm excursion, peak, one way

4.00 W (+6 dB)1.00 W acoustic0.250 W (−6 dB)drag on plot to read

Peak excursion $x_{pk}$: 0.0658mm
Lowest safe frequency $f_{min}$: 176Hz
Phase-plug entry area $S_t$: 4.42cm²
Diaphragm area $S_d$: 44.2cm²
Equivalent entry diameter: 23.7mm
Diaphragm velocity: 0.234m/s rms
Pressure on diaphragm: 153.7dB SPL

Fig. 2Diaphragm and throat, schematic

How it works

A compression driver squeezes the air from a large diaphragm through a small opening. That raises the load and the efficiency, but the diaphragm still has to move further as frequency falls. The ratio of diaphragm area $S_d$ to the area $S_t$ of the openings facing it is the compression ratio. Air that leaves the diaphragm with velocity $u_d$ must pass the smaller opening faster:

n = \frac{S_d}{S_t} \qquad u_t = n\,u_d

The diaphragm therefore sees the throat resistance multiplied by $n$ , which is how a light dome can be matched to the air. Typical high-frequency drivers use about 10 : 1.

From power to velocity

If the horn presents a resistive load $\rho c / S_t$ , the acoustic power $W_A$ fixes the rms particle velocity in the opening:

W_A = u_t^{2}\,\rho c\,S_t \quad\Longrightarrow\quad u_t = \sqrt{\frac{W_A}{\rho c\,S_t}}

From velocity to excursion

For sinusoidal motion the peak displacement is the peak velocity divided by the angular frequency:

x_{pk} = \frac{\sqrt{2}\,u_d}{2\pi f} = \frac{1}{2\pi f\,S_d}\sqrt{\frac{2\,W_A\,S_t}{\rho c}}

For constant power the excursion doubles for every octave downward. Setting $x_{pk} = x_{max}$ gives the lowest frequency at which the driver can deliver that power cleanly:

f_{min} = \frac{\sqrt{2}\,u_d}{2\pi\,x_{max}}

Reading the chart

Where the red line crosses the dashed limit is the lowest sensible crossover frequency for that output. Allow a margin; most designers keep an octave between $f_{min}$ and the crossover.
A higher compression ratio reduces excursion for the same power, but raises throat pressure and with it air distortion. See the throat distortion sheet.
Near the horn’s cut-off the load is no longer resistive and real excursion is larger than shown.

E. C. Wente & A. L. Thuras, “A High-Efficiency Receiver for a Horn-Type Loud Speaker of Large Power Capacity”,
Bell Syst. Tech. J. 7 (1928). C. A. Henricksen, “Ultimate Performance of Wide-Range High-Frequency Compression Drivers”, J. Audio Eng. Soc. 24 (1976).

Loading sheet…

How it works

n = \frac{S_d}{S_t} \qquad u_t = n\,u_d

The diaphragm therefore sees the throat resistance multiplied by $n$ , which is how a light dome can be matched to the air. Typical high-frequency drivers use about 10 : 1.

From power to velocity

If the horn presents a resistive load $\rho c / S_t$ , the acoustic power $W_A$ fixes the rms particle velocity in the opening:

W_A = u_t^{2}\,\rho c\,S_t \quad\Longrightarrow\quad u_t = \sqrt{\frac{W_A}{\rho c\,S_t}}

From velocity to excursion

For sinusoidal motion the peak displacement is the peak velocity divided by the angular frequency:

x_{pk} = \frac{\sqrt{2}\,u_d}{2\pi f} = \frac{1}{2\pi f\,S_d}\sqrt{\frac{2\,W_A\,S_t}{\rho c}}

For constant power the excursion doubles for every octave downward. Setting $x_{pk} = x_{max}$ gives the lowest frequency at which the driver can deliver that power cleanly:

f_{min} = \frac{\sqrt{2}\,u_d}{2\pi\,x_{max}}

Reading the chart

Where the red line crosses the dashed limit is the lowest sensible crossover frequency for that output. Allow a margin; most designers keep an octave between $f_{min}$ and the crossover.
A higher compression ratio reduces excursion for the same power, but raises throat pressure and with it air distortion. See the throat distortion sheet.
Near the horn’s cut-off the load is no longer resistive and real excursion is larger than shown.

Compression & excursion

Inputs

How it works

From power to velocity

From velocity to excursion

Reading the chart

Inputs

How it works

From power to velocity

From velocity to excursion

Reading the chart

§ How it works

From power to velocity

From velocity to excursion

Reading the chart

§ How it works

From power to velocity

From velocity to excursion

Reading the chart

How it works

How it works