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Clarifications on Time Coherence

Posted by RoyJ (M) on March 9, 2012 at 17:30:32

In Reply to: What Ever Happened To Phase Coherent Time Aligned Speakers posted by AudioSoul on February 19, 2012 at 17:01:54:

Hello to all,

Time coherence is best described as all frequencies getting to your ear at the same moment as each was supposed to/as recorded. There are no unwanted delays across the spectrum. The 'group delay' is constant, for the group of frequencies that we call 'audible'.

For this, a two-way's woofer and tweeter must move at the same moment on all frequencies they share, and also continue on with that same timing individually as far as possible, down into the lowest bass and into the highest highs. Every tone, high or low arrives in the same temporal order as it was recorded. On a `scope, we are preserving the shape of the waveform.

Time delays in speakers are imposed by four things:
- the speaker's crossover-circuit design
- by non-pistonic drivers
- by the low-frequency tuning of any raw driver, woofer or tweeter
- by the locations of the drivers relative to one's ear.

One indication of time-coherence (but not the sole one) can be seen in a speaker's specifications:
Each driver on its own, with its particular crossover circuit, has a frequency response at the listening position with an acoustic rolloff of six dB per octave (= a first-order slope) above (below) its crossover frequency.

More rapid rates of acoustic rolloff, such as 12, 18 or 24 dB/oct, inject time-delays that are also different at each frequency. These varying delays thus cannot be compensated for by just moving a tweeter back nor via standard DSP calculations.

Another indication of time coherence is found when examining the impulse or step-responses of woofer and tweeter separately. At the listening position, the signal's very first step-upwards on the `scope, from either woofer or tweeter, must BEGIN at Time = 0.

Note-- here we need not be concerned with 'when' each driver's final peak occurs on a `scope, if each is operating as a perfect or nearly-perfect piston. For in such drivers, those max peaks will happen when they are 'supposed to', if each driver's output started upwards from zero at the same moment (again, at your ear). When combined, they will then also produce a single-shot square wave at best, or a right-triangle response at worst, depending how far down the scale you measure-- in other words, how wide the step/pulse across the face of the 1scope. Furthermore, each driver's 'peak' loudness on a step/pulse input must be the same, when it finally does occur, whether it's from the woofer's slower rise time to full loudness or a tweeter's faster one.

Which are all devilishly hard to measure accurately, because of:
- the interference of floor reflections arriving late at the microphone (which we don't 'hear' in the same way on music)
- the phase shift above 2kHz in all affordable measurement microphones
- the fact we need to examine the very bottom of the signal, where our S/N ratio is the poorest, to see exactly where each driver's signal first left the horizontal graticule of the `scope.
- cabinet-surface reflections, which do not show up clearly on a `scope or MLSSA file.
- the step/pulse signal must sound VERY LOUD to show up on a `scope, which threatens driver excursions and power handlings. This is an SPL/energy vs width-of-pulse issue, not about a sufficient S/N ratio.

Speakers can have complicated first-order crossover circuits and produce time-coherent output. These circuits are complex in order to 'fix' drivers that do not have perfect pistons and for each driver's mechanical low-frequency cabinet tuning (woofer or tweeter).

Other notes:
One can have phase coherence without time coherence (but not the other way around). All this means is, at each crossover point, two drivers are separated by 1/2 of the wave period (of the crossover frequency) or 1 full wave period, instead of Zero (which is another indicator for time-coherence).

One-way speakers have mechanical phase shifts, both high and low.
Speakers with only a capacitor to the tweeter/nothing on the woofer, have varying mechanical time-delays both high and low.
Panel speakers can have varying time-delays both high and low, for several reasons.

I hope this helps!

Best regards,
Roy Johnson
Designer
Green Mountain Audio

Edits: 03/09/12

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