One of the biggest challenges every new generation of sound engineers
appears to struggle with is learning how to phase align subwoofers to
mains. A quest which at one point in my early career felt like
impossible.
In this article, I will disclose the method which has
been working flawlessly for me in the past couple of years. It’s a
two-step process consisting of a relative and absolute part.
Most
of the time is spent on the relative part, which you have to do only
once. However, it’s time well invested because it turns the absolute
part on site into a five-minute job at most.
The relative part’s
sole purpose is to convince yourself that the entire sound system is
appropriately phase aligned when the loudspeaker grills are flush,
living in the same plane (coplanar). If the sound system doesn’t meet
that condition, the challenge will become to “pre-align” the
loudspeakers until it does.
Conduct the relative part in the near
field where signal-to-noise (SNR) and direct-to-reverberant (D/R)
ratios are favorable, providing high-coherent, actionable data. Data
that tells you which buttons to press to achieve a successful alignment.
Anyone
that has attempted to do phase alignment in the far field knows from
experience that room interaction will likely make the phase traces go FUBAR unless you happen to be outside.
Place
a measurement microphone on the floor (half space) equidistant to the
grills (figure 1) but not so close that the direct radiators start to
dominate over the ports (vents) or vice versa. Typically, anywhere from
one to two meter suffices. Aim for coherence values of ninety-five
percent or more in the frequency range of interest.
“Amplitude always wins but, when levels are matched, phase is the tiebreaker.”
Bob “6o6” McCarthy
Set level first
Solo
the main loudspeaker and use the delay finder to synchronize to its
arrival time. From now on, it’s absolutely mission critical that you don’t touch the delay finder ever again for the remainder of this procedure! Store the main loudspeaker’s trace.
Solo the subwoofer and set its level to match the main loudspeaker’s level (unity gain). We’ll discuss “Up to eleven” (This is Spinal Tap) later. Store the subwoofer’s trace.
Based
on these two traces, you first need to determine the frequency span
where phase alignment is mandatory until level offset (isolation) comes
to the rescue and time no longer matters.
Watch the video below to see these steps in action.
Notice the excellent coherence. This is all signal and little to no noise. Such is the near field’s power. Actionable data!
By
making clever use of the analyzer’s offset function, I was able to
easily identify the frequency span where both loudspeakers have shared
custody and level offsets are within 10 dB or less.
In this
four-thirds of an octave-wide interval, phase alignment is mandatory if
serious ripple is to be prevented. Below 54 Hz however, the subwoofer is
sole custodian once it dominates by 10 dB or more over the main
loudspeaker and time no longer matters. The same is true for the main
loudspeaker above 125 Hz.
For more information regarding
isolation, ripple and the other summation zones, please consult the
chapter “Summation” which you’ll find in all three editions of Bob
McCarthy’s book “Sound Systems: Design and Optimization“.
How to read phase
Now
that we’ve identified the frequency range of interest, we can start
looking at the phase traces. But, before we proceed let’s establish some
ground rules.
The three trends we saw in the video, which can occur anywhere in the audible spectrum, are:
- flat phase trace (no slope) = measurement and reference are in time
- “rising” positive slope = measurement is leading (early) with respect to reference
- “declining” negative slope = measurement is lagging (late) with respect to reference
figure 2More slope (secant or tangent line) in the same frequency span implies more time offset and vice versa (figure 2).
When in doubt, consider spending some time with the phase calculator to gain more insight.
First attempt
Let’s attempt at putting our understanding of reading phase traces into practice.
In
the video above, I cycled the phase axis to cosmetically relocate any
wraparounds in the phase traces from my field of view (frequency range
of interest).
With the wraparounds out of the way, I can determine the slopes’ steepness. When in doubt, you can resort to a tool like PixelStick to measure the angle of the secant or tangent lines.
Of
the two traces, in the frequency span of interest, the blue subwoofer
trace is steeper and therefor the later. It’s my understanding that time
travel is not possible yet (as far as I know), so our only option is to
make the main loudspeaker equally late as the subwoofer, by introducing
delay.
figure 3Adding
delay will increase the steepness (figure 2) of the main loudspeaker’s
green phase trace which will then “spiral down” and exit the phase plot
in the bottom only to wrap around and reappear at the graphs’s top
(figure 3) where it continuous its journey (check the phase calculator).
However, I’m strongly opposed to arbitrarily playing around with delay and polarity, hoping for a “happy accident” (Bob Ross).
In
anticipation of the “spiraling” wraparound phenomenon, I chose an
arbitrary frequency, preferably somewhere in the crossover range, which I
used as starting point for a simple calculation.
I went for 100
Hz because it makes for easy math. But, any other frequency will work as
well, provided that that frequency and its immediate neighbors are
represented by high-coherent, actionable data.
Δt=ϕ360×1000f(1)
Using equation 1, knowing that I can rely on the data, I calculated that it will take 6,7 ms of delay to introduce a 240° phase offset for 100 Hz and 100 Hz alone!
This time offset succeeded at introducing an intersection between the green (main loudspeaker) phase trace and the blue (subwoofer) phase trace at 100 Hz.
However, being in phase should never ever be mistaken for being in time which is confirmed by the mismatch in slopes.
After introducing the delay, the green (main loudspeaker) phase trace is now steeper (and therefor later) than the blue (subwoofer) trace. Apparently, I introduced too much delay.
Partial success
I call this intermediate result “partial success”. We’ve managed to successfully phase align 100 Hz and I’m not willing to give that up!
Regrettably, a crossover is not a one-note event. In this instance it involves a four-thirds of an octave-wide exchange where all frequencies (including 100 Hz) must be phase aligned.
I somehow want to tilt my main loudspeaker’s green phase trace, like a seesaw, around my 100 Hz “pivot” frequency where I’m already successful.
The phase trace slopes informed me that I need to take out delay for the main loudspeaker. But, whatever value we subtract from our initial 6,7 ms delay should preserve my successful phase alignment at 100 Hz!
Second Attempt
figure 4Phase alignment can always be preserved for a single frequency as long as you add or subtract n cycles or (n+0,5) cycles (in combination with a polarity reversal) worth of time offset where n can also be zero, i.e., half a cycle (figure 4).
So, if I want to reduce the 6,7 ms delay while preserving the 100 Hz phase aligment, I could start by substracting 5 ms (half a cycle of 100 Hz) in combination with a polarity reversal.
Notice that by taking out 5 ms, I introduced a 180° degree phase offset at 100 Hz which was to be expected. But, using PixelStick, I determined that the slopes of both phase traces matched throughout the crossover range.
In fact, using PixelStick as a 180-degree-tall “benchmark”, there appeared to be 180° of offset for all frequencies (including 100 Hz) throughout the crossover range. So reversing the polarity will not only fix 100 Hz but also all other frequencies of interest.
Ultimately, which polarity you choose to reverse is your prerogative, as long as you apply it to one loudspeaker exclusively. In the real-world I would have gone for the subwoofer instead of the main loudspeaker.
In this instance, half a cycle in combination with a polarity reversal did the trick. In practice, it’s all about finding the correct number of n cycles or (n+0,5)
cycles (in combination with a polarity reversal) that results in matched slopes that overlap around a certain pivot-frequency that you are free to choose.
For more information on the importance of matching slopes please watch this video.
Corridor of 60°
Things
are looking very good and I want a metric to inform me if my solution
needs further refinement or not. Do my phase traces overlap and are
their slopes matched for the frequency range of interest? Have I
achieved the best possible fit?
figure 5When
you sum two sine waves (pure tones) of equal magnitude but with 55° of
phase offset you will still gain 5 dB summation (figure 5). Very easy to
remember “555”. It’s the penultimate result because 6 dB is as good as
it gets.
Sixty degrees is awfully close to fifty-five degrees, so
you could argue that any phase offset of 60° or less should suffice for
5 dB of summation or more, provided your levels are matched.
Notice
that this time I used PixelStick as a 60-degree-tall “benchmark” to
determine the frequency span where both phase traces “live” within sixty
degrees of each other. I can visualize this by drawing a 60-degree-wide
corridor that entrenches both phase traces.
The corridor’s shape
is of no concern, it’s the corridor’s length or extend that I’m
interested in. I want the corridor to last for as many frequencies as
possible which in this instance is all the way up to 250 Hz. The
importance of this will become clear very soon!
The corridor is a
super tiebreaker, because you can spent countless of hours more on
optimizing this crossover, but what is the return on that
time-investment?
The phase traces already live within sixty
degrees of each other and the table is set for 5 dB summation or more
(provided your levels are matched) with a maximum of 6 dB. So tweaking
this, until you see blue in the face, will yield only one dB more efficiency! It’s good enough. There are bigger fish to catch.
I would not waste any more time on this.
“(Sound) system engineering is also knowing when to stop.”
Merlijn van Veen
Up to eleven
So,
what if I now want to increase the level of my subwoofers, which
appears to be the rule and not the exception, should I start from
scratch?
Clearly,
there’s no reason to measure anything again because cranking up the
level doesn’t change a loudspeaker’s phase response (provided it’s in
its linear mode of operation). So we might as well use an offset to fake
the effect of increasing the subwoofer level.
How loud can I go?
Until, the corridor of 60° stops! Once the phase traces no longer live
within sixty degrees of each other, subwoofer and main loudspeaker are
no longer phase aligned.
So, by the time the corridor comes to an
end, the main loudspeaker must have sole custody and dominate over the
subwoofer by 10 dB or more for the remainder of the audible spectrum.
In
this instance, that means that I can turn the subwoofer up to +25 dB at
most with respect to the main loudspeaker, while preserving 10 dB of
isolation for 250 Hz and up, if I don’t want to “push” myself out of
alignment.
Notice that this practice effectively shifts the
acoustic crossover up in frequency which is no problem as long as the
corridor lasts. That’s why making the corridor as long as is
realistically possible, is so important, because it determines the
“expiration date” (read maximum level) of your subwoofers in respect to
the mains.
Whether you should increase the subwoofer level or not, is a different topic. But, if you have the time be sure to read this article and watch this video.
My
sole concern is, if the subwoofer level is increased, which is likely
to happen, possibly even dynamically (aux-fed subwoofers), is alignment
preserved and how far can we push the envelope? The corridor of 60° will
be your friend.
Overlapping and unity crossovers
figure 6What
we’ve achieved so far, is known as an overlapping crossover, because
both loudspeakers are still running in their full-range “native” mode
where high- and low-pass filters haven’t been applied yet (figure 6).
Only
at unity gain, in the frequency span where both loudspeakers are
virtually equally loud because of the overlap, will you observe
summation of as much as 6 dB which leaves us with a residual bump, a
surplus, that’s not part of the sonic signature of either loudspeaker.
This can be easily remedied by applying the same, identical, parametric equalization (PEQ) in both
output channels of the loudspeaker management system. Making the
subwoofer a true low-frequency extension. The processor’s input side, in
my opinion, should always be reserved for voicing the system!
When
the subwoofers are turned up, this “EQ-patch” is no longer required
because the crossover shifts up in frequency and effectively becomes a
skewed unity crossover which we’ll discuss next.
figure 7In
a unity crossover the overlap has been removed, by applying additional
low- and high-pass filters on top of the previous alignment, and -6 dB
meets -6 dB at a frequency of our choosing (figure 7).
It’s
advised to choose a convenient crossover frequency close to the center
of the previous overlap (figure 5) where both loudspeakers operate at
near-identical levels. In this instance 80 Hz.
Again, there’s no reason to measure everything again and I could engage these filters blindly (which I did) provided you:
- Use the same constant-slope typology for both loudspeakers
i.e., Butterworth and Linkwitz-Riley - Use the same even filter orders for both loudspeakers
i.e., 2nd, 4th, 6th, 8th, etc. (certain orders might require polarity reversal) - Use the same corner frequency for both lousdpeakers
Sticking to these pointers will affect the phase response of both loudspeakers equally.
Consequentially, what was phase aligned before the introduction of the
filters should remain phase aligned after introducing the filters with
exception of the occasional polarity reversal depending on the filter
order.
I always default to Linkwitz-Riley (also in these video
examples) which conveniently introduces 6 dB of attenuation at the
corner frequency, in contrast to Butterworth which introduces only 3 dB
of attenuation at the corner frequency, leaving you with a 3 dB bump for
loudspeakers that where equally loud at the crossover frequency prior
to introducing the filters.
That being said, there are superior
filters, involving complex slopes, e.g., Elliptic and Chebyshev filters,
which are of more interest but also beyond the scope of this article.
However, all the steps described in this procedure will make those work
for you as well!
In an appropriately phase aligned crossover at
unity gain, where -6 dB meets -6 dB at the crossover frequency, the
outcome will be 0 dB when both loudspeakers are turned on together.
Unlike the overlapping crossover, there’s no residual bump or surplus
which requires an additional PEQ-patch.
Which order to choose
From
what I am able to tell, the majority of the industry appears to have
settled for 4th order crossovers (regardless of the typology), with 24
dB per octave slopes, for reasons beyond the scope of this article.
In my book however, this constitutes 4th order acoustical crossovers which is the compound result of electronics in concert with the mechanical-acoustical properties of the loudspeakers themselves.
Therefor,
I would never pursuit a 4th order electrical crossover straight out of
the gate. When you apply these high- and low-pass filters to the
loudspeakers you’re trying to shave of one to two-thirds of on octave of
bandwidth at most.
However, the loudspeakers themselves come
with natural “native” frequency roll-offs which define their operational
range. In unity crossovers, you’re cutting awfully close to these
natural roll-offs and should be mindful of the compound effect of
electronics in concert with mechanical-acoustics.
Figure 7
contains red arrows indicating actual 4th order, 24 dB per octave
slopes. Notice that the 4th order electrical filters in concert with the
natural roll-offs, produce slopes which are too steep in the frequency
range of interest, for no good reason! That’s why I encourage restraint
with electronic filters and recommend to start with lower-order filters
first.
Typically, 2nd order, this close to the natural roll-offs,
works nicely while avoiding the unnecessary introduction of extra,
unjustified, phase shift, inherent to higher-order filters, to a part of
the frequency spectrum where most loudspeakers are already sluggish by
design!
In medicine, the principal precept is; first do no harm.
The same can be said for introducing phase shift. Less is more! Consult this article on group delay to understand why.
Up to twelve
Key
is to understand that our high- and low-pass filters haven’t affected
the corridor’s length or extend which still lasts till 250 Hz like
before, provided you stick to the pointers mentioned earlier!
The
low-pass filter assigned to the subwoofer, reduced its bandwidth which
effectively expedites the onset of main loudspeaker isolation. The
subwoofer level can now be increased by as much as +45 dB with respect
to the main loudspeaker (20 dB more than with the overlapping crossover)
before the corridor of 60° comes to an end and isolation becomes
mandatory. Eat your heart out!
Presets
What
we’ve basically been doing so far, is creating our own presets while
being equidistant, ergo equitemporal, to the flush, coplanar loudspeaker
grills. A process which colloquially can be thought of as
“pre-alignment”. And while doing so, we set the delay finder only once!
However, in today’s industry, most of the time, these steps have already been taken by the manufacturer provided you RTFM and use factory-recommended settings. Why wouldn’t they? It’s the sensible thing to do which keeps the phone from ringing.
If
tops and subs are supposed to be flown in a single “banana”, e.g., line
array (including ground-stacked), I sure hope the system is
appropriately phase aligned when the grills are flush, because that’s
how it has been deployed and the same could be said for pole-mounted
loudspeakers living on top of subwoofers.
However, never ever take this for granted and convince yourself first, in person, before proceeding with the absolute part!
In
the unlikely case that a manufacturer hasn’t made sure that these
conditions are met, you have to execute these steps yourself. However,
it’s set-and-forget. You only have to do it once.
If you make your own presets, you probably want take note of the following properties:
- subwoofer model
- main loudspeaker model
- overlapping or unity crossover (including crossover frequency)
- max LF with respect to the mains (determined by the corridor of 60°)
These properties should be easy to tell from the preset name you come up with.
The absolute part
When
main loudspeakers and subwoofers are deployed in actual venues, they
don’t necessarily end up in the same location or in any other way that
ensures that the audience members remain equidistant and therefor
equitemporal to their grills. This is when “shit hits the fans”
(plural).
Most of the time, we can fix this for one point in
space only (it’s a geometrical problem) and it’s one of few instances
(depending on the circumstances) where I’m likely to choose the
front-of-house position (FOH) and put all means at the king’s disposal
(monarchy). Provided, the FOH position is sensibly located, anywhere
from fifty to one hundred percent venue-depth.
I do this for the
sole purpose of preventing that the FOH-engineer ends up, unforeseen,
despite our best efforts, in a null for a particular frequency
throughout the crossover region which he or she is likely going to try
to fix with EQ. However, a level-band-aid is not gonna remedy a time
problem. It will not improve the situation at FOH and make things worse
for all other audience members!
figure 8figure 9In
the scenario shown in figures 8 and 9, the FOH-engineer is no longer
equidistant to the grills, the very condition that needs to be met in
order for the presets to work.
The subwoofer grills are
physically closer and therefor leading. This can be addressed by giving
the subwoofers a “virtual push” by means of delay. The amount of delay
can be determined in two ways.
The optical way (figure 8)
requires you the measure, preferably using a laser range finder, the
difference in trajectories and convert that physical offset into time.
The acoustical way (figure 9) makes use of a so-called proxy
loudspeaker.
Delay finders struggle with subwoofers because
subwoofers reproduce only a fraction of the audible spectrum leaving too
little data for the delay finder to lock onto.
Read this article to gain more insight as to why.
The
proxy loudspeaker’s sole purpose is to add the frequencies which are
missing from the subwoofer, allowing the delay finder to detect arrival
time again.
For this to work, it’s mission critical that you use the same make and loudspeaker model with the same preset as the main loudspeaker!
This
loudspeaker will sit flush, on top of the subwoofers, with its grill
living in the same plane as those of the subwoofers. The very condition
which makes the preset work. There, it will act as “ambassador” for the
subwoofers underneath.
Under these circumstances, we can
synchronize the delay finder to the main loudspeaker in which case the
proxy loudspeaker will be leading because its grill is physically
closer. The impulse response will inform you by how much.
Consequentially,
if the proxy loudspeaker is leading, then so are the subwoofers living
underneath the proxy loudspeaker. To make the main and proxy
loudspeakers arrive in time would require us to delay the proxy
loudspeaker and inherently the subwoofers which are represented by the
proxy loudspeaker.
Either approach for determining the time
offset (optical or acoustical) takes little to no time which I hope
you’re able to appreciate. Whatever time offset is found, is then added
to whichever grill is physically closer (in this case the subwoofer) on top of whatever it took to make the preset work in the first place!
Once
the proxy loudspeaker has served its purpose, you can strike it,
reattach it to the bottom of the array (in case of a line array) or keep
it as fill loudspeaker to add fresh and intelligible, mid- and
high-frequencies to the subwoofers.
Conclusion
The
relative/absolute method’s success relies entirely on your time spent
in the near field. However, only if you’ve convinced yourself, in
person, that the system is appropriately phase aligned when the grills
are flush, will the absolute part work.
In exchange, the absolute
part will take very little time on site and comfortably get you in the
“ballpark”. Afterwards, if you have time and energy left over, you can
consider verifying acoustically if the phase aligned crossover has
survived.
However, allow me to remind you that the loudspeaker’s
phase response, within its intended coverage, typically doesn’t change
over distance, unless you actually did something to the loudspeaker that
invokes actual phase shift, i.e., applying filters of some sort which
you should be able to rule out!
Room interaction however, will
make it appear like the loudspeaker’s phase response is changing over
distance because the room makes the traces go FUBAR. Don’t judge a book
by its cover.
However, if you paid your dues in the near field,
you should have near-anechoic traces (I think of them as Polaroids) that
inform you how the appropriately aligned crossover is supposed to look
which you can then use to identify your far field success once the room
enters your measurements.
