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Time & Phase Alignment

Going inside one of the principal concepts of system optimization.

The setting of delay times in signal processors is one of the principal techniques of system optimization.

In most cases the timing is set to “align” two (or more) signal sources so as to create the most transparent transition between them. The process of selecting that time value can be driven by time or phase, hence the relevant terms are “time alignment” and “phase alignment.”

These are related but different concepts and have specific applications. It’s important to know which form to use to get your answers for a given application.

Time alignment connotes a synchronicity of sources, e.g., they both arrive at 14 milliseconds (ms). Phase alignment connotes an agreement on the position in the phase cycle, e.g., they each arrive with a phase vector value of 90 degrees.

Time alignment is most applicable when the sources are matched and have the same operating frequency range, e.g., a full-range main loudspeaker and the same model used as a side fill. Phase alignment is called upon when sources cover different frequency ranges, e.g., mains and subs.

Both time and phase alignment together may be required when unmatched sources cover matched frequency ranges, e.g., Papa Bear mains, Mama Bear side fills and Baby Bear delays. These are the broad strokes. Now let’s dig deeper.

And They’re Off…

How can we explore a complex subject such as phase and time without resorting to “click-to-the-next-article math”? We will use both analogy and pictures of the real stuff in action.

The first analogy is a relay race. The first runners are aligned to a single starting point. The race begins with the starter pistol, the moment of time alignment between all sources. If the runners travel at the same speed, they are both phase aligned (their radial position on the track) and time aligned (the elapsed time puts them the same distance from the start). If one runner goes faster than another, then both phase and time fall out of alignment. If the difference reaches a complete lap, then the phase is aligned (again) but the time is not.

It’s a relay race, which means the first runner for each team must hand off the baton to the second. The critical element here is that the two runners on our team must be phase aligned to make the handoff. The second runner intersects the first at the designated radial meeting point (the phase) regardless of the time (one team may be ahead of another but the handoff occurs at the same place). Each handoff is a “crossover” of the baton to another member of the team.

Our 3-way sound system is like a relay race, with tweeter, midrange and subwoofer running the segments. They must be phase aligned at each crossover to keep from dropping the sound to the ground and blowing the race.

Terminology

Let’s go through a bit of phase terminology to standardize the discussion, specifically: phase shift, phase delay, phase offset and phase alignment. Phase shift is frequency-dependent delay quantified in degrees, phase delay is the same thing quantified in ms, and phase alignment is the process of phase matching at a particular frequency and location.

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The term “group delay” is used by some for phase delay but the distinction is not relevant here. Let’s illustrate by example: A filter attenuates the amplitude and causes the phase response to bend 90 degrees at 1 kHz: phase shift of 90 degrees or phase delay of 0.25 ms. The same would go for a loudspeaker that has low frequencies lagging behind the highs (as in 99.9 percent of loudspeakers). One loudspeaker has 90 degrees of phase shift at 1 kHz and the other does not: phase offset of 90 degrees or 1/4 wavelength (the difference).

Time offset terminology is easier because it is frequency independent. Time offset causes phase offset, however, which is frequency dependent. A time offset of 1 ms causes 3,600 degrees of phase offset at 10 kHz, 360 degrees at 1 kHz, and 36 degrees at 100 Hz.

Applications

The easiest way to visualize the need for time alignment is mismatched latency between devices in a common path. Latency is frequency independent, so the difference is a fixed time offset. The solution is time alignment by delaying the earlier signal.

The propagation time of a sound source through air is effectively “acoustic latency.” Two matched loudspeakers arriving from different acoustical path lengths have a latency offset that can be compensated by time alignment.

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).

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