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Phase Alignment Between Subwoofers And Mid-High Cabinets
A scaled down approach that can be applied to much larger systems...
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We’ll use two 4-inch speakers to get some practice with the phase adjustment procedure.

For our 4-inch speaker to behave acoustically like our real, full-scale systems, we will need to scale the crossover frequencies up.

To do that we’ll multiply the real system cut-off frequencies by the ratio of the real system to our scaled down box, i.e., we will multiply the cut-off frequencies by 18”/4” = 4.5.

Therefore the cut-off frequencies for the scaled down measurements, which will be entered in the processor for the 4-inch system, will be as follows,

Cut-off frequencies for the scaled down subwoofer system will be:

HPF LR24 dB/Oct, 30 Hz x 4.5 = 135 Hz
LPF LR24 dB/Oct, 85 Hz x 4.5 = 382 Hz

The cut-off frequencies for the scaled down mid-high system will be:

HPF LR24 dB/Oct, 50 Hz x 4.5 = 225 Hz
LPF LR24 dB/Oct, 20 kHz

We’ll leave the low-pass filter for the mid-high box at 20 kHz. Otherwise we would be in the ultrasonic range.

For these measurements we used a DAS Arco 4 subwoofer, lying on its side. The box used as a mid-high, also a DAS Arco 4, is placed somewhat higher up, and some 15 cm (6 inches) behind the box being used as a subwoofer, as shown in Figure 7.

The microphone is placed on the ground, at 90 cm (3 feet) from the simulated subwoofer.

Figure 7.

In order to notice more easily the difference between aligning the phases or not aligning them, it is recommended to set the acoustic levels of the mid-high and the subwoofer the same in the band being shared, 225 Hz to 382 Hz in our exercise.

The procedure is as follows:

1) Enter 20 ms as the delay time for each of the outputs in the processor (This is an arbitrary value; a different delay time can be used).

2) Let’s first work just with the mid-high. We’ll use the “Delay Finder” utility to add the required delay to the channel with the reference signal, i.e., to synchronise the reference signal to the measured signal. (See the user’s manual for SATlive or your analysis software for more information).

Figure 8.

3) Measure the magnitude frequency response for the complete system before doing phase adjustments. At worst, we will see significant cancellation in the frequency range being shared by both enclosures. The measurement can be seen in Figure 8, which shows the magnitude frequency response curve we are trying to improve on. A cancellation can be seen around 400 Hz, and therefore within the frequency band being reproduced by both boxes.

4) Mute the subwoofer output, and un-mute the mid-high output in the processor.

5) Measure the mid-highs and save the curve. In our example, the curve in Figure 9 is obtained, showing magnitude and phase frequency response for the mid-highs.

Figure 9.

6) Mute the mid-highs and un-mute the subwoofer output.

7) Do not use the “Delay Finder” again! (i.e., do not synchronize the reference signal to the measured signal again).

Remember that we are comparing phase on both outputs, i.e., we are measuring the difference in time arrival between the two signals as a function of frequency. Therefore the synchronization delay for the reference signal should not be changed on the measurement software again. Keep in mind that we took the mid-high box as our timing reference because it is the signal from which the best impulse response can be obtained.

8) Measure the subwoofer and compare the phase curve with that of the mid-high box. The result can be seen in Figure 10, showing the difference in phase between the subwoofer and the top box for the frequency band being shared (160 Hz to 400 Hz). This explains the cancellation seen near 400 Hz, and the fact that the level in the rest of this shared band does not increase significantly.

Figure 10.

9) Add or subtract delay from the subwoofer output until the two phase curves overlap around the crossover frequency. Do not forget to save the curves.

The curve with the steepest slope of the two is the one with the most delay. Therefore, it seems clear in this case that we will have to subtract delay from the green curve, i.e., the subwoofer output.

We’ll be able to do this because we initially added a delay of 20 ms to the two outputs.

Remove some of the delay from the subwoofer output and the green curve will loose slope and shift upwards, and the two phase traces will overlap within a fairly wide band.

Figure 11.

The delay on the subwoofer output ended up at 18.666 ms. From 150 Hz to 400 Hz the two curves overlap, i.e., they are in phase within the entire band they share. Figure 11 shows top box and subwoofer responses with phase adjustment. It can be seen that phase overlaps in the shared frequency band, which means they will be summing perfectly in phase.

Therefore, if we compare two phase curves and we want to minimize the difference in phase between them, we need to remember the following: if a curve has a steeper slope than the other, it’s arriving late and we need to take away delay. If a curve has a gentler slope than the other, it’s arriving early and we need to add delay.

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