In the Blog posts SUBJES 01 and SUBJES 02 the only tools I used next to a 24dB per octave Linkwitz-Riley low-pass filter on each processor output were delay and polarity reverse.
The use of delay & polarity reverse works and if you’re time-table is limited a good option for doing cardioid sub array set-ups.
The following is an explanation on a way of doing these kind of arrays using next to delay and polarity reversal some other tricks that can work.
First I have to kind of explain the difference between Delay and a “mystery” companion of delay: Group Delay (phase delay or phase distortion are also terms I see online every now and then).
Setting up Smaart:
Since Smaart V8 is a “Multi everything” analyzer (multiple inputs / transfers / windows / what ever) I configured 2 groups with the same 1 transfer measurement where 1 shows a “standard” view of the Phase trace while the other is set to Phase as Group Delay. After that I moved the groups to there separate windows via right click on a Tab>Move to window.
(Use hotkeys Alt+T > set Phase as Group Delay)
The processor I Used for this post is a Lake LM26.
Here’s the first screen shot: Smaart synchronized at processor Latency (0.6ms in this case). No processing applied doesn’t mean the output is completely phase flat. There are high & low pass filters at the high-end & low end to prevent the processor from sending out signals below and above certain boundaries.
Processor output +1ms delay.
Group delay rises to +1ms at all frequencies. Phase also shows a 1ms of delay signature (from 1K to the left a 360º of phase shift). If I use the group delay formula (∆/360º)/∆F) you’ll end up with (360º/360)/(1000Hz-31Hz) which ends up as 1/969=0.00103=1.03ms.
Processor output +2ms delay.
Group delay rises to +2ms at all frequencies. Phase also shows a 2ms of delay signature (from 500 to the left a 360º of phase shift).
If I use the group delay formula (∆phase/360º)/∆F) you’ll end up with (360º/360º)/(500Hz-25Hz) which ends up as 1/475=0.00210=2.1ms. From 1kHz to 500Hz the value would be spot on ∆/360º)/∆F=(360º/360º)/500=0.002=2ms
If i synchronize Smaart on the processor output +2ms via the delay finder it will give you a time of 2.6ms. After synchronizing the phase trace goes flat and Group Delay shows 0ms.
Reducing the delay by 1ms after synchronizing Smaart on the processor output with 2ms of delay applied group delay shows a -1ms on all frequencies. This means the measured signal is ahead in time compared to the synchronization point of Smaart and thus phase goes up (negative delay 😉 ).
Reducing the delay by 2ms after synchronizing Smaart on the processor output with 2ms of delay applied group delay shows a -2ms on all frequencies. This means the measured signal is ahead in time by 2ms compared to the synchronization point of Smaart and thus phase goes up under a even steeper angle. (the same calculations apply here as before only ∆phase will be a negative number.
Everything above can be seen in the following screen capture (you might lower your volume: enoying pink stuff coming up).
So delay changes the timing on all frequencies by the same amount. Now let’s take a look at what happens if a Low-pass filter is implemented.
If I implement a Linkwitz-Riley 2nd order Low-pass filter phase goes down under “a angle” which means delay. But it’s not showing the signature of “all frequencies by the same amount” seen in the previous examples. This is what happens if x-over filters are implemented (non FIR).
Linkwitz-Riley 2nd order Low Pass filter @100Hz
Linkwitz-Riley 4rd order Low Pass filter @100Hz
Linkwitz-Riley 6th order Low Pass filter @100Hz
Linkwitz-Riley 8th order Low Pass filter @100Hz
A summery of the 4 screen shots above:
All can be viewed in the screen capture below.
Here’s some specific behavior characteristics for Linkwitz-Riley filters:
Linkwitz-Riley 2nd order > 90º of phase shift at the x-over frequency 180º over the full pass-band. At the X-over frequency level drops -6dB
Linkwitz-Riley 4rd order > 180º of phase shift at the x-over frequency 360º over the full pass-band. At the X-over frequency level drops -6dB
Linkwitz-Riley 6th order > 270º of phase shift at the x-over frequency 540º over the full pass-band. At the X-over frequency level drops -6dB
Linkwitz-Riley 8th order > 360º of phase shift at the x-over frequency 720º over the full pass-band. At the X-over frequency level drops -6dB
Before going to actual speakers here’s another thought: why not instead of using the same Low-Pass filter on all sub-woofers use a higher order filter on the Sub that is taking care of the reduction at the back of an array? This would be the Sub woofer that will be delayed and polarity inverted measured at the back of the array.
This can be done in the Reversed End Fired/Gradient and CSA/Front Back (Front) set-ups. For a End Fired Set-up delay and/or All-pass filters work well. Maybe there’s also another way but I have not experimented with it (YET 🙂 ).
In the following screen capture I’ve simulated the measurement at processor level. If i work with the Meyer Sound 900LFC’s (the ones I happen to own) I most of the time end up with +/- 3ms of delay so that’s the number i’ll use here. If you think you can Copy/paste the values in the screen caps in to your processor of choice without measuring the Sum of both outputs the outcome could surprise you…..the same goes for doing the measurement on real speakers. Please verify everything via measurements.
If you want to know why here’s a nice post from Bennet Prescott on processors: SoundForumsNetwork A tale of 2 processors
For the screen capture the Lake LM26 has 2 outputs connected to a small mixer. The mixer output is patched back to Smaart to measure the solo outputs and sum of both.
If I measure a Front Back sub array my mic position is at the back of the array which will mean the sub aimed at the front will show more delay then the sub aimed to the back. If i synchronize smaart on the sub aimed to the front the sub aimed to the rear will show a phase trace going up under a different angle compared to the reference sub and can be phase aligned by adding delay to that sub.
So at processor level I have to synchronize smaart on a Full range signal with 3ms of delay added to processor output 1. After synchronizing Smaart I’ll implement a 4rd Order Linkwitz-Riley Low-pass filter (the same filter i use on the subs in the final screen capture.
The 2nd processor output will start at 0ms delay no processing and after that i’ll implement Bessel Low Pass filters @100Hz starting from 1st order up to 7th order. The group delay increases as does the filter order increases and when i get to the 7th order Bessel Low Pass phase matches with the Linkwitz-Riley 4rd order Low Pass +3ms of delay.
Here are the important screen shots from the measurements.
Smaart Synchronized at processor output 1 +3ms of delay. After that a LR4LP @100Hz is implemented on processor output 1.
Processor output 1: LR4LP 100Hz +3ms Processor output 2 no processing.
Processor output 1: LR4LP 100Hz +3ms Processor output 2 Bessel 1st @100Hz and Processor output 2 Bessel 1st @100Hz Polarity reversed.
Processor output 1: LR4LP 100Hz +3ms Processor output 2 Bessel 2nd @100Hz
Processor output 1: LR4LP 100Hz +3ms Processor output 2 Bessel 3rd @100Hz and Processor output 2 Bessel 3rd @100Hz Polarity reversed.
Processor output 1: LR4LP 100Hz +3ms Processor output 2 Bessel 4rd @100Hz
Processor output 1: LR4LP 100Hz +3ms Processor output 2 Bessel 5th @100Hz and Processor output 2 Bessel 5th @100Hz Polarity reversed.
Processor output 1: LR4LP 100Hz +3ms Processor output 2 Bessel 6th @100Hz
Processor output 1: LR4LP 100Hz +3ms Processor output 2 Bessel 7th @100Hz and Processor output 2 Bessel 7th @100Hz Polarity reversed.
SPEAKERS FINALY 😉
If you look at the screen cap from the processor outputs the Bessels filters have a different magnitude respons in the upper range of the lows. Specially the 7th order low-pass has less level in the upper range.
With real live Subs the upper range of a sub is already slightly directional so the sub aimed to the front shows less level there at the back mic position. Both 6th order and 7th order Bessel can work. The 7th order Bessel Low pass @106Hz is the one I would choose. The filters combination (4rd order LR LP @100Hz vs a 7th order Bessel @106Hz) on this particular set up works really well (2 x 900LFC in a Front Back configuration). You do not have to reverse polarity on the sub aimed to the back since the filter is 180º out of phase compared to the sub aimed to the front with the Linkwitz Riley 4rd order low pass implemented via processor output 1.
Here’s the TRF files from smaart taken during the screen capture.
Now let’s see if there is a ” DARK SIDE ” like there is with a Gradient/Reversed End Fired.
The following screen capture shows the respons at the front mic position to see if there is a “problem” like the gradient (dip in the x-over area and after the dip a area where level rises again).
At the front mic both phase traces do not differ more then about 120º so no reduction between them in the working range of the array….. (from 31Hz down it might become a problem with different subs running to lower frequencies since there phase passes the 120º which would mean reduction if levels are matched).
After the sub array was done I moved on to the top. The Subs are reducing levels at the back so that’s “kind of a good thing” and don’t show problems out front. But can they be aligned properly with a top without to much challenges.
First i did a AllPass alignment. The Top (a Meyer Sound UPQ1P) only needed a AP2 filter below the working range of the top. I can sort of “push the phase response up” by doing this and got a pretty good result (+6dB addition in the x-over area).
The x-over area would be around 100Hz. Higher then the spec sheet (somewhere around 60-80Hz) but in my opinion doing a CSA or Front Back sub array in this case doesn’t make sense if the top is reaching down low enough to again cause problems with the SPL managers ;-).
The advantage of doing the AllPass alignment instead of delay: it doesn’t change time higher up the frequency scale so if there are delay’s already time aligned to this “main system” you do not have to re-align them.
The other way to do the x-over alignment would be using delay like in the next screen capture.
Both delay and AllPass filters do the job but give a different phase response in the low end……
That’s it for now
Below you find 2 screen captures with all of the above screen captures.
Enjoy 😉
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