Driver matching

Driver to throat match

Keele’s Thiele/Small method: matched throat area, compression ratio, efficiency and the four band-edge corners.

Sheet: 13 / 25
Units: Metric
Air: 20 °C

Fig. 1Response into an ideal horn, 2.83 V at 1 m

SPLdrag on plot to read

The horn is taken as a pure resistance ρc/St at all frequencies, radiating into half space. Its own cut-off should sit at or below fLC.

Matched throat $S_t$: 366cm²
Compression ratio: 2.14: 1
Mid-band efficiency $\eta$: 48.9%
Low corner $f_{LC}$: 20.8Hz
Mass corner $f_{HM}$: 334Hz
Inductance corner $f_{HVC}$: 1492Hz
Cavity corner $f_{HC}$: 2052Hz
Total Q $Q_{ts}$: 0.240

Fig. 2What the parameters refer to

How it works

D. B. Keele showed in 1977 that the pass-band of a horn-loaded driver can be predicted from its Thiele/Small parameters alone, provided the horn behaves as a pure resistance above its cut-off. This sheet follows that model: it finds the throat area that matches the driver, then the four corner frequencies that bound the usable band.

Matching the throat

Seen from the cone, the motor and the horn each look like a mechanical resistance:

R_{ME} = \frac{(Bl)^{2}}{R_E}, \qquad R_{ML} = \rho c\,\frac{S_d^{2}}{S_t}

The driver delivers most power for a given voltage when the two are equal. Solving for the throat area, and rewriting in Thiele/Small terms:

S_t = \frac{\rho c\,S_d^{2}\,R_E}{(Bl)^{2}} = \frac{2\pi f_s\,Q_{es}\,V_{as}}{c}

A smaller throat (higher compression ratio) widens the band and lowers efficiency; a larger one does the opposite. Strong motors with low $Q_{es}$ call for small throats, which is why compression drivers have them.

The four corners

With the matched throat and negligible suspension loss, Keele's corner frequencies are

f_{LC} = \frac{Q_{ts}}{2}\,f_s, \qquad f_{HM} = \frac{2 f_s}{Q_{ts}}, \qquad f_{HVC} = \frac{R_E}{\pi L_E}, \qquad f_{HC} = \frac{2\,Q_{es}\,f_s\,V_{as}}{V_{fc}}

$f_{LC}$ : below it the suspension (and rear chamber) stiffness limits cone velocity.
$f_{HM}$ : above it the moving mass does. Note that $f_{LC}\,f_{HM} = f_s^{2}$ .
$f_{HVC}$ : voice-coil inductance starts to choke the current.
$f_{HC}$ : the air trapped between cone and throat shunts the horn.

For any other throat the calculator uses the exact expressions behind those shortcuts, with total mechanical resistance $R_{MT} = R_{MS} + R_{ME} + R_{ML}$ and the combined compliance $C_{MT}$ of suspension and rear chamber:

f_{LC},\,f_{HM} = \frac{\sqrt{R_{MT}^{2} + 4 M_{MS}/C_{MT}} \mp R_{MT}}{4\pi M_{MS}}

Efficiency

\eta = \frac{R_{ET}}{R_E + R_{ET}}\cdot\frac{R_{ML}}{R_{MS}+R_{ML}}, \qquad R_{ET} = \frac{(Bl)^{2}}{R_{MS}+R_{ML}}

At the matched throat this approaches 50 %, the theoretical limit for maximum power transfer. Real horns land well below it once mouth reflections, wall losses and the horn's own cut-off are included; use the system response sheet for that.

AfterD. B. Keele Jr., “Low-Frequency Horn Design Using Thiele/Small Driver Parameters”, AES preprint 1250, 1977.

Loading sheet…

How it works

Matching the throat

Seen from the cone, the motor and the horn each look like a mechanical resistance:

R_{ME} = \frac{(Bl)^{2}}{R_E}, \qquad R_{ML} = \rho c\,\frac{S_d^{2}}{S_t}

The driver delivers most power for a given voltage when the two are equal. Solving for the throat area, and rewriting in Thiele/Small terms:

S_t = \frac{\rho c\,S_d^{2}\,R_E}{(Bl)^{2}} = \frac{2\pi f_s\,Q_{es}\,V_{as}}{c}

The four corners

With the matched throat and negligible suspension loss, Keele's corner frequencies are

f_{LC} = \frac{Q_{ts}}{2}\,f_s, \qquad f_{HM} = \frac{2 f_s}{Q_{ts}}, \qquad f_{HVC} = \frac{R_E}{\pi L_E}, \qquad f_{HC} = \frac{2\,Q_{es}\,f_s\,V_{as}}{V_{fc}}

$f_{LC}$ : below it the suspension (and rear chamber) stiffness limits cone velocity.
$f_{HM}$ : above it the moving mass does. Note that $f_{LC}\,f_{HM} = f_s^{2}$ .
$f_{HVC}$ : voice-coil inductance starts to choke the current.
$f_{HC}$ : the air trapped between cone and throat shunts the horn.

f_{LC},\,f_{HM} = \frac{\sqrt{R_{MT}^{2} + 4 M_{MS}/C_{MT}} \mp R_{MT}}{4\pi M_{MS}}

Efficiency

\eta = \frac{R_{ET}}{R_E + R_{ET}}\cdot\frac{R_{ML}}{R_{MS}+R_{ML}}, \qquad R_{ET} = \frac{(Bl)^{2}}{R_{MS}+R_{ML}}

AfterD. B. Keele Jr., “Low-Frequency Horn Design Using Thiele/Small Driver Parameters”, AES preprint 1250, 1977.

Driver to throat match

Inputs

Driver

Horn coupling

How it works

Matching the throat

The four corners

Efficiency

Inputs

Driver

Horn coupling

How it works

Matching the throat

The four corners

Efficiency

Driver

Horn coupling

§ How it works

Matching the throat

The four corners

Efficiency

Driver

Horn coupling

§ How it works

Matching the throat

The four corners

Efficiency

How it works

How it works