Is Console Output Delay Precise Enough?
In sound system design, there are a few key areas in your space that you want to have at the same level and frequency response. Each speaker should be designed to cover it's own portion of the audience or room and you create a reference response at a position called ON-AXIS. This is halfway back to the end of the speakers coverage area and directly in line with the cabinet. With this reference you can tell if the high end drops off too much at the edge of coverage due to bad aiming or the wrong propagation angle (the wrong speaker being used). The other area that needs to match this ONAX reference measurement is any spacial crossover (XOVR). This is a point in space where two sources match in level across the frequency spectrum.
The XOVR area will not match the ONAX measurement with one speaker or the other on by itself. Sound will combine and sum to 6 dB more than either as long as the two sources are phase aligned throughout the range. If the speakers are exactly symmetrical and the gains are exactly the same and there are no reflections, this XOVR point can be found and you will see the 6 dB sum across the whole range with no additional processing. In practice it usually does not work out this perfectly. You might need to add delay to one of the sources to create the same time and position of phase arrival at that spot from both sources.
I'm referring to the XOVR of 2 or more full range boxes here, be it FF and mains, two mains, mains and delays etc. Our goal is to match the phase trace of one to the other. It is assumed we found our microphone position which represents the proper place for our XOVR but there is a slight mismatch of arrival times due to aim, placement, reflections, processing or issues with different models.
Some engineers will bring along a processor that has precise delay settings. Sometimes all you have is the output delay on the console you are using.
So how precise is precise in delay setting world? The very highest frequencies take minuscule amounts of delay to shift their phase response. 20 kHz will complete one cycle in just .05 ms! 16 kHz (which is our practical upper limit for this demonstration) will complete one cycle in .0625 ms.
The most accurate processors I've used will add delay as precise as .01 ms at a time. Lets talk about .01 ms for a bit. Each addition of .01 ms of delay will shift the phase by:
- .1 degree at 28 Hz
- 1 degree at 280 Hz
- 10 degrees at 2800 Hz
- 57.6 degrees at 16 kHz
- 72 degrees at 20 kHz
As you can see, even with such tiny amounts of delay it is still a fairly coarse adjustment up at 16 kHz. The next image is a measurement two sources spaced exactly the same distance from the microphone and are the same model. The phase is matched. If we were to measure with both of them on, we would see a 6 dB sum of level across the whole range.
Lets see what happens when we mis-align them by our lowest increment .01 ms.
In laboratory conditions (MAPP XT Prediction Software) the measured difference in phase is 53.2 degrees at 16 kHz.
At 1600 Hz the difference is around 6 degrees and at 160 Hz the difference is less that 1 degree.
Next lets look at trying to match the phase of two sources with slightly different arrival times because they are different distances from the microphone. This will be the most common condition you will come across.
The red trace is now the speaker that is farther from the microphone (Speaker A). The white trace is the closer one (Speaker B) as we can tell by the phase trace sloping upward. Between the two at around 1600 Hz, they are about 192 degrees out of phase meaning the closer speaker is ½ a wavelength closer at 1600 Hz.
At 16 kHz they are about 40 degrees out of phase.
In the field, the quickest way to delay the closer one properly would be to look at the impulse response arrival time. In MAPP once I measured the first/farther speaker, I set the Auto-Delay which stored the offset it detected and removed the wraps from the display. With that stored, now you really see the difference between them. The second/closer speaker also has an impulse response arrival time. When you take the difference and add that delay to the closer speaker it should neatly align the phase all throughout the frequency response. This works well with identical model speakers. The magic delay time for this example is given as .32 ms. Lets look at how this works.
We are in phase up to about 100 Hz, there the closer speaker begins to depart, finally fully out of phase at 1600 Hz. If we were to measure both speakers on with this phase relationship we would see a big cancel at 1600 Hz. The pink trace below is exactly that.
To find the correct delay time to fix only 1600 Hz we need a formula. The difference in phase at one frequency divided by 360 divided by the frequency (Delta Phase/360/Frequency). This answer is our delay time in seconds that will make the higher/steeper/earlier speaker's phase trace match the other, cancelling our cancellation. Here we get 154.6 degrees minus negative 26.3 degrees (or 154.6+26.3) divided by 360 divided by 1670 Hz equals .000300 seconds or .3 ms.
Above 1600 Hz, the traces start to depart from each other again. The .3 ms had just the right amount of effect at 1600 Hz, very little effect below 1600 Hz and a huge spin of the phase wheel above it. In fact, .3 ms meant 7488 degrees of shift at 16 kHz. This is a complete wrap around the phase wheel 20.8 times! You could calculate the exact phase shift it will have on your upper limit frequency target, it has to do with the number of periods and more importantly the fraction of a period of 16 kHz that goes into .3 ms. Previously we discovered that if there was no additional time delay, a change of .01 ms would shift 16 kHz by 57 degrees. Here is 16 kHz at .3 ms.
Here it is at .31 ms.
The total shift at 16 kHz was 59 degrees from the .3 ms delay time to the .31 ms delay time. We still need to go another 42 degrees.
This is as close as we can get with the increments of .01 ms available. It overshot the target by about 19 degrees but we will have the best summation with this setting.
Here we have some beautiful summation and this trace should match the ONAX measurement. This is acceptable in the field but we are working with our best case scenario. What if we didn't have as precise of a delay setting?
Some mixers have delay settings where the hundredth of a millisecond only dials to an even number. You can only add .02, .04, 06 etc. This would be OK for this example but if the natural phase relationship required a delay time that ended with .03 what would happen? We can flip the variables and pretend our mixer only will dial to odd hundredths of milliseconds.
Let us dial in .31 and .33 ms since it is our only option.
The purple is Speaker B with .33 ms and the white is Speaker B with .31. Our target was to match the red one. We have failed and while .31 is closer, the summation will suffer and will not be as close to our ONAX measurement as we would like.
Unfortunately it can get worse. There are plenty of mixers out there that will only dial delay in to a tenth of a millisecond. Now lets look at that disaster.
The purple is .4 ms and the white is .3 ms.
If we slide our precision scale from a hundredth to a tenth, we find that now tenths of a ms are making 1 degree phase changes at 28 Hz, 10 degree changes at 280 Hz and 100 degree changes at 2.8 kHz!
Very high frequencies are locally variant by physics and as you move around even the “shadow” of your head will change the response. The reason it is important to get your XOVR position to be the best it can be is that if the system was designed correctly, as you move in any direction away from the XOVR, you should either be entering isolation (dominance of one speaker) or your time arrivals from both should be the same. This keeps the variance to a minimum and you know the combing issues are not because of the speaker summation. Regardless there are phase issues well below 16 kHz when you are accurate to .1 ms.
Field work will be harder to read and the math results will take losses due to factors and will not be as perfect as the chalkboard or in Meyer Sound's Software Laboratory. One thing I have found is that most times I can achieve max summation throughout 90-95% of the frequency spectrum by using the delay on the mixers I am sent with. That being said, I will take a processor that can do .01 ms all day!
© 2019 Michael Reed