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Time & Phase Alignment

Going inside one of the principal concepts of system optimization.

By Bob McCarthy January 6, 2016

Phase alignment comes into play when devices have unmatched phase responses over frequency. This should be a minor issue in analog electrical signals unless they’re unmatched in terms of their upper and lower limits.

Differences in AC coupling filters at the bottom end and TIM filters at the top end can cause phase offsets around the extremes. One solution could be exotic phase alignment filters, but the simplest would be matching the amplitude responses first, which may reduce or eliminate the phase differences.

Time alignment is straightforward. We can use the impulse response of a modern analyzer and read the time offset directly. This is true any time the ranges of the devices being aligned are matched over the large majority of their ranges. They don’t have to be exact.

For example, a typical underbalcony loudspeaker has more very high frequency response and less low frequency range than the mains, yet time alignment should work fine because they have 6-plus octaves of overlap. Subwoofers ranging from 30 Hz up to 100 Hz can be merged with mains covering down to 60 Hz. There’s less than an octave of overlap, which means time alignment is a poor choice (phase alignment is used).

Moving Targets
Now let’s get to the tough reality about loudspeakers. They have lots of phase shift and phase delay. A good quality active loudspeaker can be engineered to keep the range from 500 Hz on up within ±60 degrees of phase shift (less than 1 ms of phase delay). By 100 Hz we can expect 5 ms of phase delay, rising rapidly below that.

This is important because in the LF range, the loudspeaker can’t be characterized as having a single arrival time. It has arrival times that span a very large range. For example, a 2-way system that reaches down to 70 Hz might have 10 to 15 ms of phase delay at the bottom (Figure 1).

Figure 1: Phase delay example for full-range loudspeaker.

A subwoofer covering from 30 Hz to 100 Hz typically shows more than 30 ms of phase delay between its upper and lower range, with a continuous range of values in between (Figure 2). We kid ourselves when we say the sub energy arrived at the mix position at 100 ms because it actually arrives spread over a 30 ms range around that.

Figure 2: Phase delay example for subwoofer.

How can we time align a thing that has 30 ms of slop factor over a course of two octaves? If you ever wonder why your analyzer has a hard time finding an impulse on subwoofers, think about the fact that the energy is spread over time – a lot of time. The ambiguous impulse response reading of the analyzer is the result of the temporal ambiguity of the system being measured, not the analysis method (even if you stretch out the measurement window and restrict the measured bandwidth).

The mains, by contrast, have widespread agreement about arrival time, with their upper six octaves all within 0.5 ms (at least the good ones do). This is why you see that beautiful impulse spike.

The causes of LF phase delay accumulation are a complex mix of electroacoustic behaviors and filters (maybe another article, another day), but the trend is observable on virtually any loudspeaker. Therefore our main array has phase shift (phase delay) that increases in the low end.

Matched models have matched phase delay, which means they have no phase offset (and hence no time offset). Such a matched pairing is inherently phase compatible. Any phase offset between them would have to be the result of time offset (such as a longer path) and would be remedied (if desired) by time alignment (Figure 3).

Figure 3: Examples of phase compatible and incompatible loudspeakers.

A different loudspeaker model may accumulate phase shift at a different rate over frequency, and therefore we will find phase offset begin to accrue between the pair. This is like the relay race where one team is faster than the other. If the amount of phase offset is small, we would classify the pairing as “phase compatible,” which means time alignment is still an applicable tool. If the offsets are large, then we will need to use both time alignment (to synchronize the compatible areas) and phase alignment (to reduce phase offset in the incompatible areas).

A marriage between 2-way and 3-way systems is a classic phase compatibility challenge. All-pass filters are the most typical tools for phase alignment of incompatible models.

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.

Figure 4: Phase delay train analogy.

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.


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About Bob

Bob McCarthy
Bob McCarthy

Director of System Optimization, Meyer Sound
 
Bob has been designing and tuning sound systems for over 30 years. The third edition of his book Sound Systems: Design and Optimization is available from Focal Press. He lives in NYC and is the director of system optimization for Meyer Sound.

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