Level, filters & alignment

Time alignment

Convert the set-back of a horn driver into delay, samples and phase at crossover, and see the comb filter it causes.

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

Fig. 1Acoustic centres, side view (not to scale)

Delay $\tau$: 0.437ms
DSP delay: 21.0samples at 48 kHz
Phase at crossover $\varphi$: 126°
Path offset $\Delta d/\lambda$: 0.350λ
Sum at crossover: -6.84dB
First null: 1144Hz

Fig. 2Two equal sources, one late, relative to perfect alignment

Summed leveldrag on plot to read

Only the region around the crossover matters in practice, since that is where both drivers are at similar level.

How it works

The diaphragm of a horn driver sits at the back of the horn, often 15 to 60 cm behind the baffle, while the woofer's acoustic centre is near its cone. Sound from the horn therefore arrives late. Around the crossover frequency, where both drivers contribute, that lateness becomes a phase error and the two outputs no longer add as the filter designer intended.

From distance to delay

\tau = \frac{\Delta d}{c}, \qquad \varphi = 360^{\circ}\,f_x\,\tau = 360^{\circ}\,\frac{\Delta d}{\lambda_x}

Every 34 cm of offset is one millisecond. In a digital crossover, multiply by the sample rate to get the setting: $N = \tau f_{sr}$ samples. The delay goes on the driver that is physically nearer the listener, normally the woofer.

What misalignment does

Two equal signals, one delayed by $\tau$ , sum to

\left|1 + e^{-j2\pi f\tau}\right| = 2\,\left|\cos(\pi f \tau)\right|

which is the comb filter in Fig. 2. The first null falls at $f = 1/(2\tau)$ , where the offset is half a wavelength. An offset of a quarter wavelength at crossover (90°) already costs 3 dB on axis and tilts the main lobe towards the later driver.

Ways to fix it

Delay the woofer electronically by $\tau$ . This is the cleanest fix and leaves the cabinet alone.
Move the horn forward, or the woofer back, until the acoustic centres line up. Classic stepped-baffle designs do this.
With a passive crossover, choose slopes and polarity so that the filter phase absorbs the offset at $f_x$ . This works at one frequency and on one axis.

The acoustic centre of a horn is not exactly at the diaphragm and moves a little with frequency. Treat the figure here as a starting value, then trim the delay by measurement: with one driver's polarity reversed, adjust for the deepest null at the crossover frequency.

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How it works

From distance to delay

\tau = \frac{\Delta d}{c}, \qquad \varphi = 360^{\circ}\,f_x\,\tau = 360^{\circ}\,\frac{\Delta d}{\lambda_x}

What misalignment does

Two equal signals, one delayed by $\tau$ , sum to

\left|1 + e^{-j2\pi f\tau}\right| = 2\,\left|\cos(\pi f \tau)\right|

Ways to fix it

Delay the woofer electronically by $\tau$ . This is the cleanest fix and leaves the cabinet alone.
Move the horn forward, or the woofer back, until the acoustic centres line up. Classic stepped-baffle designs do this.
With a passive crossover, choose slopes and polarity so that the filter phase absorbs the offset at $f_x$ . This works at one frequency and on one axis.

Time alignment

Inputs

How it works

From distance to delay

What misalignment does

Ways to fix it

Inputs

How it works

From distance to delay

What misalignment does

Ways to fix it

§ How it works

From distance to delay

What misalignment does

Ways to fix it

§ How it works

From distance to delay

What misalignment does

Ways to fix it

How it works

How it works