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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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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.


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