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 0.0313ms (∆τφ= 0.0313ms).

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.

Figure 3: 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.

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

The delay (physical in this case) increases the slope of the phase curve in the pass band. Again, the effect increases with frequency.

Figure 4: 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 1.7m behind.

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 24dB/oct high-pass filter as well as a Bessel one with identical cut-off frequency.

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.

Figure 5: If the filter type is changed on a processor, the magnitude as well as the phase frequency response changes. The figure above shows the effect of an L-R 24dB/oct high-pass filter (blue trace) and a Bessel 24dB/oct one, both with the same cut-off frequency (1410 Hz).

To accomplish that goal we need to get the phase traces to overlap.

Sometimes we will reach complete overlap, whilst 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.

Stay tuned for the coming articles in this series, where we’re lay out several examples. Want to get a jump on the reading? Head on over to the DAS Audio Website where you can DAS Audio Engineering Department.

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