Phase Alignment Between Subwoofers And Mid-High Cabinets
A scaled down approach that can be applied to much larger systems...

April 14, 2014, by Joan La Roda

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FFT-based field measurement systems have made it possible for us to do phase alignment at fixed installations as well as at live events, where every venue demands a different approach. This is particularly important since mid-high boxes are often flown and subwoofers remain on the ground, meaning that phase differences at the listener location can be very significant.

Given the interest in the subject, and the remarkable improvement it can bring to a system, it seems like a good idea to detail the measurement process step by step. Before doing that, however, let’s go over the concept of phase.

Polarity & Phase

Polarity only has two discreet values: positive and negative. Polarity does not change with frequency, and may be accidentally inverted when the speaker cables are connected the wrong way, or when a signal cable is repaired and pins 2 and 3 get inverted, or when one of the bands has its polarity changed on the signal processor by mistake. Other times polarity is purposely reversed, such as when a passive crossover filter is used.

Phase may have any value in degrees: values are continuous. To find out what the phase response is for a given speaker, we need to measure it.

Throughout this article we’ll see measurements performed using SATLive. Phase curves are shown on the bottom part of the image, while the magnitude frequency response will be at the top of the image.

Figure 1 shows a typical subwoofer phase response in blue, with polarity reversal in green. A 180-degree shift can be clearly observed at all frequencies.

Figure 1.

Running a phase measurement on our systems, and storing it for reference, can be useful for checking for correct polarity after maintenance. Since we are only looking for a comparison, any measurement position that can be repeated easily would suffice.

For instance, the microphone can be placed directly in front of the loudspeaker, in its center, very close to the grille. This provides an easily repeatable measurement position and a clean measurement with no contamination from the environment.

What Makes Phase Vary?

Answer A: Any variation on a system’s magnitude frequency response will have an effect on the phase response.

For instance, the phase curve changes when equalization is added. Figure 2 shows the result of adding a bell-type filter centered at 5.04 KHz, with a width of 0.42 Oct and +10 dB gain, to the high-frequency band on a processor. Phase rises just before the center frequency and falls just after it. (The green trace shows the effect of a bell-type filter on the phase response.)

Figure 2.

Since equalization affects the phase response, outputs should never be EQ’d once phase alignment has been done, especially around crossover frequencies. Otherwise we would modify the phase of the output being equalized, hence affecting the relationship between phase responses, which is what we are trying to adjust for when adding delays. EQ’ing the input (on the processor itself or on a graphic equalizer or the mixing desk) will not affect phase alignment, since it happens before the crossover.

Answer B: Adding delay to a band, or physically displacing it backwards (such as moving a subwoofer away from the measurement microphone) will have the same effect on the phase response.

Figure 3 shows the effect on the phase response of adding delay to the mid-high cabinet. The blue trace corresponds to the mid-highs before being delayed, while the green one shows the result of adding 0.0313 ms (∆τφ= 0.0313 ms). To the point: when adding delay to a band, the effect on the phase response is larger for higher frequencies, where the added delay represents a bigger percentage of the period compared to low frequencies.

Figure 3.

The phase increase (∆φº) can be calculated from the equation ∆φº = 360f * ∆τφ. It can be clearly seen that the change in phase varies with frequency and as a function of the amount of delay added.

Since the delay is added to the whole band, the phase increase will be larger the higher the frequency, i.e. the lower the period. Figure 3 shows that the phase difference between traces becomes larger as the frequency increases.

The same thing happens to subwoofers. The blue trace in Figure 4 shows the phase response for a double 18-inch subwoofer, while the green trace shows the effect of physically moving it back 1.7 meters (about 5.6 feet).

Figure 4.

The delay (physical in this case) increases the slope of the phase curve in the pass band. Again, the effect increases with frequency. To the point: moving a source behind its initial placement has the same effect as adding a delay. The blue trace corresponds to the initial position, while the green one shows the phase curve of a subwoofer that has been shifted 1.7 meters behind.

Answer C: If the type of crossover filter is changed, the phase will change too, since the different filter types, and their correspondingly different slopes, will have their own effect on phase.

Figure 5 shows the responses of a Linkwitz-Riley 24 dB/octave high-pass filter as well as a Bessel one with identical cut-off frequency. If the filter type is changed on a processor, the magnitude as well as the phase frequency response changes. The figure shows the effect of an L-R 24 dB/oct high-pass filter (blue trace) and a Bessel 24 dB/ocavet one, both with the same cut-off frequency (1,410 Hz).

Figure 5.

What Do We Mean By Phase Alignment?

What we are after is a sum of the subwoofers and the mid-highs that result in maximum achievable sound pressure level, i.e., no cancellation (partial or total) in the crossover region. To accomplish that goal we need to get the phase traces to overlap. Sometimes we will reach complete overlap, while other times we will not, as we shall see in the examples, but there will normally be an improvement as compared to a system that has not been phase aligned.

A final magnitude frequency response measurement will always be required after delays have been applied, so improvements can be checked against the curve for the system without delays.

When complete overlapping is not reached with the use of delay alone, we can improve upon the results if our processor provides phase filters.

To simplify the understanding of this technique, however, our examples will only use delay.

Coherence Curve

The coherence curve that Fast Fourier Transform (FFT) based measurement systems provides indicates the probability that the measurement is reliable.

It’s very common to find a coherence curve (ranging from 0 to 1, or from 0 to 100 percent, depending on the measurement system) with low values in part of the spectrum. We should not trust the magnitude or phase frequency responses for those bands for which our measurement system shows low coherence.

There are two main reasons for poor coherence:

1) Reference signal is badly synchronized with the measured signal. We can test for this easily if we initiate a measurement without having first synchronized the measurement signal using the “Delay Finder” on SATLive or the equivalent function in other systems.

In this case it will be seen that coherence for the high frequencies is very low, as seen in Figure 6. SATLive’s coherence scale can be seen on the right-hand side, ranging from 0 to 1. This curve’s coherence trace has been stored and loaded with the Trace Manager utility, and is shown as a thinner blue trace.

2) Reflections. These will cause coherence in some frequency bands to be low. We should not trust measurements on those bands.

If we are interested in measuring a part of the spectrum that has poor coherence, we can change the microphone location.

Figure 6.

When it comes to adjusting phase, we should check the coherence in order to know which parts of the measurement are reliable and which ones are contaminated by reflections, reverberation, etc.

Example 1: “Scaled down measurements: the subwoofer and the mid-high box share a frequency band.”

Before trying to do these adjustments for the first time in a real-life situation, where one may not always have enough time and where conditions are far from ideal, scaled down measurements can be handy to get some practice with the procedure.

We’ll assume that you already know how to take transfer function measurements with the measurement system you are using, and that the equipment used is adequate. To synchronize the reference signal to the measurement signal, we need to measure the system’s impulse response, which is better obtained from the high frequency band, and therefore we’ll always use the mid-high units for synchronization.

There will be times when we’ll need to shift the subwoofers backward by adding delay, and times when we will need to move them “forward” with “negative delay.” Since such a thing doesn’t exist, we’ll add an initial time delay that is the same for all bands, so that we will be able to add or subtract delay from the subwoofers’ initial delay time. Once the system has been adjusted, we’ll get rid of excess delay, as will be seen in the examples.

Let’s now run a scaled down measurement of an 18-inch subwoofer and a mid-high unit.

Subwoofer cut-off frequencies for the real system will be:

HPF LR24 dB/Oct, 30 Hz

LPF LR24 dB/Oct, 85 Hz

Cut-off frequencies for the real mid-high unit will be:

HPF LR24 dB/Oct, 50 Hz

LPF LR24 dB/Oct, 20 kHz

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.

Keep in mind that, in our example, the subwoofer was physically forward with respect to the top box, so we could have mistakenly assumed it was the subwoofer that needed delaying.

Do not forget that filters have an effect on phase, and therefore we cannot predict if we need to add or remove delay until we see the measurements.

Let’s see what would have happened if we had increased the delay time to the subwoofer instead of reducing it.

In Figure 12 delay has been added to the subwoofer output until the most overlap was obtained.

The subwoofer delay ended up as 22.276 ms. Phase overlaps in the 250-300 region, which is very little.

In this specific case, delaying the subwoofer does not make the phase traces overlap for the entire band.

Below 250 Hz the blue phase trace is below the green one, whereas above 300 Hz the green curve is below the blue one; i.e., there’s phase difference between them.

Figure 12.

10) Measure the system frequency response and compare it to the initial measurement.

If phase has been correctly adjusted, subwoofers and mid-highs will sum in phase and this will be reflected on the magnitude frequency response.

Figure 13 compares the system combination without adjustment (red trace), with 22.2766 ms delay on the subwoofer (green trace) and with 18.666 ms (blue trace). In this particular case, the subwoofer and the mid-high box sum optimally when we take away delay from the subwoofer.

Figure 13.

It can be clearly seen that the best sum occurs for the 18.666 ms subwoofer delay.

11) Take the lowest delay value and subtract it from the subwoofer and mid-high so that at least one of the outputs has a delay time of 0 ms. At this time there’s a delay of 20 ms on the mid-high and 18.666 ms on the subwoofer.

Since we had added 20 ms just as an arbitrary amount to be able to add or subtract from that as needed, once the adjustments have been made we no longer need that excess delay: subtract the lowest delay time from the two outputs so that one of them has 0 ms.

In our example the mid-high output will end up with 20 ms – 18.666 ms = 1.334 ms. The subwoofer output will have 18.666 ms – 18.666 ms = 0 ms.

Example 2: “Scaled down measurements: the subwoofer and the mid-high box crossed-over at the same frequency.”

Subwoofer crossover frequencies for the real system will be:

HPF LR24 dB/Oct, 30 Hz
LPF LR24 dB/Oct, 85 Hz

Crossover frequencies for the real mid-high unit will be:

HPF LR24 dB/Oct, 85 Hz
LPF LR24 dB/Oct, 20 kHz

Crossover frequencies for the scaled down subwoofer system will be:

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

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

HPF LR24 dB/Oct, 85 Hz x 4.5 = 382 Hz
LPF LR24 dB/Oct, 20 kHz

Place the boxes as for example 1 and follow the same procedure.

1)  Enter 20 ms as the delay time for each of the outputs in the processor (a different delay time can be used).

Figure 14.

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 synchronize the reference signal to the measured signal.

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. Figure 14 shows the magnitude frequency response that needs to be improved.

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

5) Measure the mid-highs and save the curve. In our example, the curve in Figure 15 is obtained, showing magnitude and phase response for the mid-high box.

Figure 15.

6) Mute the mid-highs and unmute the subwoofer output.

7) Do not use “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 chose the mid-high box as our timing reference because it is the signal from which the best impulse response can be obtained.

Figure 16.

8) Measure the subwoofer and compare the phase curve with that of the mid-high box. The result can be seen in Figure 16, where phase can be seen to be different at the crossover region, so it is clear that the sum between subwoofer and mid-high can be improved upon.

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. It is not very obvious in this example whether the subwoofer needs delay to be added or subtracted. Let’s try both and see which one works best.

Option A: Remove some of the delay from the subwoofer output. The green curve will shift upwards. Figure 17 shows mid-high and subwoofer responses once delay time on the latter has been adjusted such that the phase traces cross each other at the acoustical crossover frequency, which is 400 Hz in this case.

Figure 17.

The delay on the subwoofer output ended up at 18.270 ms. We have adjusted the delay time until the phase traces cross each other at the acoustical crossover frequency.

This way they sum perfectly in phase at that frequency. Above and below that frequency there is phase difference that needs to be evaluated when comparing the different sums for the boxes with the different delay times.

Option B: Add delay to the subwoofer output until phase values are the same at the acoustical crossover frequency. Phase matching is better above the crossover frequency than below it.

Figure 18 shows that when delaying the subwoofer, phase overlaps at the acoustical crossover frequency and above it, but not below it.

Figure 18.

Again, we will evaluate the result on the next step.

10) Measure the system magnitude frequency response again, and compare it to the initial measurement.

If phase has been adjusted correctly, the sum of the mid-high and the subwoofer will be better, and the magnitude frequency response will reflect this.

Figure 19 compares both boxes without delay (red trace), with 20.848 ms delay on the subwoofer (green trace) and with 18.270 ms (blue trace).

Figure 19.

It can be clearly seen that the green and blue traces significantly improve the magnitude frequency response. However, there is no significant difference between them.

11) Take the lowest delay value and subtract it from the subwoofer and mid-high so that at least one of the outputs has a delay time of 0 ms.

Let’s say we pick the blue curve. There’s a delay of 20 ms on the mid-high and 18.270 ms on the subwoofer.

Since we had added 20 ms just as an arbitrary amount to be able to add or subtract from that as needed, once the adjustments have been made we no longer need that excess delay: subtract the lowest delay time from the two outputs so that one of them has 0 ms.

In our example the mid-high output will end up with 20 ms – 18.270 ms = 1.73 ms. The subwoofer output will have 18.270 ms – 18.270 ms = 0 ms. If we wanted to run the same exercise with speakers of different size, we would just need to find the ratio between the subwoofer we mean to simulate, and the speaker to be used for the measurement.

Example 3: “Measurements on a real system.”

When measuring a real PA for live or installed use, only one of the arrays should be measured. Additionally, the microphone should be placed approximately halfway between the source and the maximum distance to be covered, assuming reasonable coherence is obtained at that location.

When we choose this center point for phase alignment we make sure that significant phase change will not occur at any other listening position within the audience area (unless we are really close to the array), be it closer or further away from the speakers.

Make sure the floor reflection does not create poor coherence at the crossover frequencies. This is a common occurrence when using a microphone stand.

In this example we are aligning phase between a DAS Aero 50 line array and some DAS LX218A subwoofers.

The level difference between the two will make the shared frequency range narrower or wider. In our example the two systems overlap in the 45 Hz to 125 Hz range.

The DAS LX218A subwoofer is a self-powered system incorporating signal processing (crossover and equalization), but we will use an external processor in order to add delay for alignment to the mid-highs.

A common mistake is to filter a self-powered system at the same crossover frequencies used in the equivalent passive system, this way the slope corresponding to the external processor adds to the slope provided by the integrated crossover.

So we end up, for instance, with a sort of 48 dB/oct filter instead of one that is 24 dB/oct. In our example, no filtering is used at the external processor. Only the filtering that is built into the subwoofer is used.

The DAS Aero 50 mid-high is a 3-way line array system. Each of its three bands has a factory specified delay time applied on an external processor.

The procedure is the same as for the previous examples:

1) Enter 20 ms as the delay time for each of the outputs in the processor (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 synchronize the reference signal to the measured signal.

Figure 20.

3) Measure the 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 top graph in Figure 20 shows the magnitude frequency response that we are trying to improve on. It is shown below that the low coherence above 100 Hz is due to the different arrival times for the mid -high and the subwoofer, with similar levels. The same effect would be seen with a single source and a reflection.

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

5) Measure the mid-highs and save the curve. In our example, the curve in Figure 21 is obtained, showing measurements for the mid-high box. In this case the system, normally complemented with subwoofers, uses a very low crossover frequency.

Figure 21.

6) Mute the mid-highs, and unmute the subwoofer output.

7) Do not use “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.

Figure 22.

Keep in mind that we chose 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 22, where phase can be seen to be significantly different between the subwoofers and mid-highs. The Aero 50 and LX218A sub overlap acoustically in the 45 Hz to 125 Hz region for the level ratio we selected.

9) Add or subtract delay from the subwoofer output until the two phase curves overlap around the crossover frequency, as seen on Figure 23. When lowering the delay time on the subwoofer output, the green trace shifts upwards (and reappears on the lower part of the scale) on the SATLive phase graph, decreasing its slope in the pass band. Do not forget to save the curves.

Figure 23.

In this example, the phase trace for the subwoofer shows a steeper slope at the pass-band than the mid-high system. It is evident that some delay will need to be removed from the subwoofer until the phase curves overlap as much as possible in the band that they share.

When reducing the delay time for the green curve on Figure 22 it will shift upwards, eventually disappearing and appearing again on the lower part of the graph.

We need to bear in mind that the phase graph only shows values between +180 degrees and -180 degrees. If a larger range were to be used, the traces would not zigzag as they do here.

10) Measure the system frequency response and compare it with the initial measurement.

If phase has been correctly adjusted, subwoofers and mid-highs will sum in phase, and this will be reflected on the m/divagnitude frequency response.

Figure 24 compares the system combination before (blue trace) and after (red trace) adjustment. Cancellation and poor coherence that were previously seen around 125 Hz have disappeared.

Figure 24.

As noted previously, low coherence was due to the fact that the same frequency band was arriving at different times, which is equivalent to a reflection of similar SPL.

Once the correct amount of delay is added, the shared band from the two systems arrives at the same time and coherence goes back to normal.

11) Take the lowest delay value and subtract it from the subwoofer and mid-high so that at least one of the outputs has a delay time of 0 ms.

The DAS Aero 50 mid-high is a 3-way line array system with external amplification. Resulting delay times are as follows:

DAS LX218A
Subwoofer: 14.458 ms

DAS Aero 50
Low: 20 ms
Mid: 25.9167 ms
High: 26.0104 ms

What we are really after is the time difference for the outputs to be phase aligned. Therefore, the lowest delay of all bands (14.458 ms in this case) needs to be subtracted from each of the bands.

Final delay times will thus be:

DAS LX218A
Subwoofer: 0 ms

DAS Aero 50
Low: 5.542 ms
Mid: 11.4587 ms
High: 11.5524 ms

Once the final delay times have been entered, it is good practice to run the measurement again to check that everything is correct. Before adjusting a real system for the first time, it makes sense to practice this procedure as often as possible and with whatever combination of gear we happen to lay our hands on, until we have mastered the technique.

Using scaled-down systems will allow us to become familiar with the procedures until we are confident to try larger systems.

 

Joan La Roda is a member of the DAS Audio Engineering Department.

 



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Phase Alignment Between Subwoofers And Mid-High Cabinets
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