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Time & Phase Alignment

Going inside one of the principal concepts of system optimization.

Making Connections

Now on to our second analogy: freight trains. When did the train cross Main Street? The first car crossed at 12:00 but the last one did not cross until 12:05. Our loudspeakers cross the mix position like that.

First the highs, and then later, the lows. Let’s give each octave it’s own car and see how it works (Figure 4). If we had a loudspeaker with 4 ms of phase delay per octave, we would see evenly sized cars that are a total of 36 ms long.

Now let’s move this closer to audio reality. The first six cars (16 kHz to 500 Hz) are so small they only occupy 0.5 ms of track, but after that the cars get bigger and bigger until they stretch all the way to 36 ms (like the previous one).That would be a terrible loudspeaker, but stick with me here. We could have another train running next to it on a parallel track. Each car would line up to its counterpart, i.e., the trains have lots of phase delay but zero phase offset. They are time aligned.

Figure 4: Phase delay train analogy.

If we run this train next to the first one, they will match at the first and last cars – but the middle cars don’t match. The front and rear cars are time aligned but the middle section is full of phase offset. The systems are not “phase compatible.”

How do we connect a main train to a subwoofer train? This is a series connection (unlike the time alignment on the parallel track). Connect the rear of the main train to the front of the subwoofer train. The cars are phase aligned at the coupler between the two sections.

The Process

We can time align a full-range loudspeaker to a full-range loudspeaker or a subwoofer to a subwoofer since each pairing covers the same range. It’s when we want to marry mains to subs that time alignment goes out the window in favor of phase alignment.

The same principal applies for a crossover between an HF driver and a LF driver in a 2-way box, but in the modern world, this is handled by the manufacturers, right?

So how do you do it? That’s the easy part. Time alignment is a 3-step process. Use the impulse response because it will give readings directly in the applicable unit: time. Observe the impulse response of A (solo), and then B (solo), and delay whoever got there first.

Then take a look at the frequency responses and verify that maximum addition has occurred. A little trick here is to observe the highest frequency range bump the delay up or down by the smallest allowable increment (e.g., 0.01 ms) and see what gives the best addition.

Phase alignment follows the same steps, but we are going to use the phase response instead of the impulse. Look at A solo, then B solo, and add delay to the early one until the phase responses match (Figure 5). Polarity inversion can be considered in cases where this allows for a smaller amount of delay to be used.

Figure 5: Phase alignment example for main and subwoofer.

There are many ways to approach the alignment of sources that mix together. All of them affect phase and time. It’s very helpful to know which of the alignment paths is most suitable to your particular application.For example, a 100 Hz crossover might be phase aligned by 7 ms of delay on the subs or 2 ms and a polarity reversal. The later approach minimizes the overall time spread over the spectrum. Another approach to minimize overall time stretching could be all-pass filters in the affected area.

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Bob offers special thanks to Merlijn Van Veen for his help with this article.

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