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How To......Cardioid Sub Arrays

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kevinmcdonough View Drop Down
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    Posted: 17 April 2009 at 9:34pm
Hey

With all the talk of Rog’s Delta Array and the general idea of Cardioid sub arrays I thought it would be good to type up a quick tutorial on the basics of the theory of this technique and how to set it up in the real world, partly for all you good folks but partly for myself as well, as I’ve always found it a great test of your own knowledge if you can explain it to other people successfully.

As a quick introduction for people who don’t know what I’m talking about, the idea of a cardioid sub array is simply to set the subs up in a particular way so as to be able to control the direction of the bass output of your speakers (which is usually omni directional). You use the fact that when sound waves meet out of phase they cancel to create a null of energy behind the subs. You minimise the backwash of sound from the subwoofers and help to stop it travelling towards the stage, which makes your life easier when you have vinyl decks or open mics or anything else that is prone to feedback, and if done properly you can also harness this normally rear firing energy and use it our front.

Most of my knowledge comes from a couple of threads on the PSW forums (Pro Sound Web) which i’ll link at the end, and on there you can see nice MAPP diagrams and people who have actually set these up and taken real life measurements so it all definitely works.

Also note that as Rog reminds us in the other thread, this is all just theory, dealing with a “perfect” subwoofer and “perfect” conditions. In real life subwoofers aren’t perfect point sources and they have ports and group delay and lots of other nice real life issues so the calculations below should be used as a guide, and then when you actually set this all up you should play around with things a little to get the best settings for your particular set up.




OK, so the most common way to do create a Cardioid subwoofer array this is what’s known as an End Fire array (although to be honest I don’t know why, don’t really know what’s so End Fire about it LOL ).

There are a couple of basic variations on how to set it up, but the main idea is that you set up two rows of subwoofers, front and back, and you use a combination of time delay, physical distance and phase inversion to create a situation where behind the array the sound from the two rows meets destructively and cancels out, and in front on the audience side they meet in phase and combine.



Preparation

So the first step is to pick a frequency that will be the centre of your cancelation band. As we know every frequency has its own wavelength and as this trick relies on distance and delay is only properly effective across a band of frequencies, centred around whichever one you pick.  If your playing Dub, D&B, Reggae or anything else with big deep synths and lots of really low energy your gonna wanna move this down a bit, and if your playing more kicky stuff like House or Rock then you’ll wanna take that into account. Some report that you may get as much as an octave either side of the centre frequency although I don’t know if it’d effectively cover just as much as that.

So pick a frequency and work out its wavelength and also 1/2 and 1/4 of this, and also worth working out at this point what times these equate to for setting your delays later. 



Physical Set Up

So you have your frequency chosen, the next step is to set up the array. We need to create a path difference of half the wavelength of your chosen frequency, and to get our ideal conditions we will do this half with distance and half with signal delay. This means we have to set up our two rows of speakers so that there is a 1/4 wavelength physical spacing between the sound sources (drivers for front loaded or horn mouth for horns.)  This second row can also be facing forward if you like and have the space.

If your subs aren’t too deep and you can fit them in and still preserve the 1/4  wavelength spacing, you can spin the second row around and have them back to back which’ll save you a little bit of floor space.

For reflex subs I don’t think it’ll make much difference either way but for horns you will have to consider the fact that because if the nature of the horn they will already have some measure of directivity themselves. If you turn the second row around you may get away with using less in that row because the front row will be putting out less sound towards the back and the back row will be putting its full measure of sound backwards to cancel it. Some experimentation with your particular subs would help confirm this.

Note also however that for one of the two processing methods below we also have to reverse the phase of the rear speakers. If you set it up with both sets of speakers facing forwards you have the option of doing this with processing if you like, but if you reverse the back row to save space this effectively does a phase reversal for you so you are limited to just that method.

(edit: after thinking on this i suppose you could also add a processing phase reversal, flipping your backwards facing speakers back into phase again if you really wanted to use method 2. Might be worth trying to see how effective it is in practice.)


However, as long as the distance between the two sound sources is 1/4 wavelength then your good.



Processing and Delay

Now we come to setting the delays. We must add another 1/4 wavelength delay to one of our rows here, which’ll complete the 1/2 wavelength path difference and get our cancelation going, and again here we have two ways we can do this but in this case it WILL affect the sound you get.


Method 1:  Delay the REAR SPEAKERS by 1/4 wavelength for (theoretically) perfect cancelation.

This is the method that includes the phase reversal, so we must do that first and then add a delay time that matches up with our 1/4 wavelength, all to the back row of speakers. So In this case whats happening is the sound coming from the rear of the front row of speakers will take 1/4 of a wavelength to reach the back row. We match that with a quarter wavelength delay on the rear speakers so that they would effectively be in phase normally (just like we would delay a delay tower or whatever to match it up) but because we have also reversed the phase of the back speakers either by processing or physically turning them around, the delays now put them perfectly out of phase which makes them cancel out and you get theoretically perfect cancelation and hence no (or in real life much less) sound behind the array.

In front of the array, the sound from the rear speakers travels forward which takes 1/4 wavelength of time, and is also delayed in processing by 1/4 wavelength so it is half a wavelength behind overall and would be out of phase, but the phase reversal puts it back into phase and it combines to add its energy to the front and hence the audience. 

Note however that this changes the nature of the bass sound slightly, because although the waves are combining together in phase out front they are actually half a wavelength behind and then inverted back into phase again so they are not perfect mirror images of each other and there is a subtle but noticeable sound difference. This is reported by actual users as an ever so slight “rounding” off of the sound, a very slight loss in kick or attack, but only really noticeable to a trained ear who has the ability to A/B the two sounds, for the most part it is regarded as unnoticeable to the public.

However if you would like to make sure that you have perfect sound out front then you can use...



Method 2: Delay the FRONT SPEAKERS by 1/4 wavelength for (theoretically) perfect sound out front.

OK so in this case we have NO phase reversal. What happens is now the reverse of what happened in method one. The sound travelling from the rear row takes 1/4 wavelengths of time to reach the front row, and as we have now delayed this front row by a matching 1/4 wavelength they meet exactly in perfect phase and they combine and all our sound out front is  normal, just like delaying speakers or towers to match up. From the perspective of behind the speakers the sound from the front speakers is delayed 1/4 already in processing, and then takes another 1/4 wavelength to travel back to the back ones so when it finally gets there it is 1/2 a wavelength behind and is out of phase. Not that like in the front of method 1 although it is out of phase it is not a perfect mirror image but is half a cycle out, and so will cancel very well but not as good as in method 1.

So method 1 to have maximum cancelation sacrificing a shade of sound out front, and Method 2 to have the best sound out front but loose a little of the cancelation.


Ok think I have that all right although feel free to throw in any comments or tell me i'm all wrong  Tongue


the link that i mentioned to the PSW thread is....


http://srforums.prosoundweb.com/index.php/mv/msg/3954/0/0/0/


where they have lots of pretty pictures to look at and graphs to see Tongue



kev


Edited by kevinmcdonough - 18 April 2009 at 1:43pm
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Post Options Post Options   Thanks (0) Thanks(0)   Quote jamwa Quote  Post ReplyReply Direct Link To This Post Posted: 17 April 2009 at 10:06pm
or if you use DB you can just point a thrid of your subs 180 degrees the other way run these on seperate amps and switch the CSA mode on - simples!!!!
 
 
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Post Options Post Options   Thanks (0) Thanks(0)   Quote roborg Quote  Post ReplyReply Direct Link To This Post Posted: 17 April 2009 at 10:53pm
For sub-bass control i'm not convinced there is any advantage over just pointing all the subs forward & forming a wide horizontal array, in most circumstances.  IE try to induce as much diffraction directivity as possible & then the radiation pattern tends to be cardioid shaped anyway.
  For really local cancellation, to stop mic feedback for example, it's prolly a really good idea, but i think only if the antisound source is placed close to where the cancellation is needed (like near a drumstack)
  With front & back facing boxes next to each other there is the possibility of good bass & mid-bass cancellation (because it's fairly directional anyway), but sub-bass being omnidirectional will be cancelled in all directions.  Theres no such thing as a free lunch in this application i think, i wish i had time, space & lots of speakers to play with this!


Edited by roborg - 17 April 2009 at 10:54pm
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Post Options Post Options   Thanks (0) Thanks(0)   Quote kevinmcdonough Quote  Post ReplyReply Direct Link To This Post Posted: 18 April 2009 at 1:41pm
Originally posted by roborg roborg wrote:

For sub-bass control i'm not convinced there is any advantage over just pointing all the subs forward & forming a wide horizontal array, in most circumstances.  IE try to induce as much diffraction directivity as possible & then the radiation pattern tends to be cardioid shaped anyway.


While it is true that a large horizontal line of speakers will have significant directivity, it seems to create more of a figure of 8 pattern than a cardioid. You can see it in Rog's bass guide, page 2, where even just a row of 4 subs has a significant figure of 8 shape and there is still a lot of bass directed backwards onto the stage.

Our cardioid array on the other hand, even with just the same 4 subs set up in two rows of 2
you would get something much more like what is shown on Rog's guide page 14. Obviously reflections and real life would mean that it wasnt as perfect as is shown here, but would still be a significant, and often scary, improvement in the amount of bass traveling back onto the stage.

But yeah totally agree, i'd really love a big pile of subs in a field and plenty of time to play about with this all and really get my head around it properly, at the moment its all theory in my head and i've not had very many chances to actually put it into practice.


Originally posted by jamwa jamwa wrote:

or if you use DB you can just point a thrid of your subs 180 degrees the other way run these on seperate amps and switch the CSA mode on - simples!!!!



LOL, yeah DB sub users have it easy Tongue    LOL, well for other users, even though we dont have DB's fancy processing and i'm sure staggered delay times to extend the bandwidth, this technique will also work to an extent. If you have relitivly deep subs then reversing one of a stack of 3 is going to move their acoustic sources back a fair bit of physical distance anyway. It probably wont be the proper 1/4 wavalength back and so wouldn't be as effective as having a seperate second row of subs, but in cases where you are really pushed for space if you play with the processing and delay times to make it all match up and cancel properly i'm sure you may get some fairly acceptable results. In most cases anyway there is no real need to cancel ALL of the sub energy going back to the stage just reducing it by a significant amount would be a big help.


k


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Post Options Post Options   Thanks (0) Thanks(0)   Quote Peter Jan Quote  Post ReplyReply Direct Link To This Post Posted: 28 April 2009 at 11:16am
Originally posted by jamwa jamwa wrote:

or if you use DB you can just point a thrid of your subs 180 degrees the other way run these on seperate amps and switch the CSA mode on - simples!!!!


Well... I do have and use Q-Subs and S2 cabs. The CSA method does work to some extend, but you need more gear ( cabs and amps ) to end up with less SPL than straightforward non-CSA. I tried it several times in various venues from very small to rather big and from my experience it's a small benefit at best at the cost of more gear. The feeling creeps on me that it's a marketting ploy to sell more gear because they ( not only D&B ) convinced you bass splill at the rear is THE BIG problem. But is rear spill really that big a problem ? I admid it can be in some cases, but an environmental problem primarly in open air gigs. Every time I used it, musicians start complaining they need more bass in the monitors... LOL. In small venues CSA is just plain useless. More cabs and amps where you don't have the place for it in the first place and definately a visual problem with one or more cabs facing the public with it's rear... try to sell that to your client... good luck ! Bass spill is slithly less behind the cabs, but nobody talks about what gets thrown in the air or in the ceiling. You have 50% more gear making noise and some of it interacts with the first 100%, but not all of it. In bigger setups I always get better result from stacking and arraying multiple sub and low cabinets and play with fysical positions, (sometimes) frequency overlap and delays between cabs or arrays of cabs. My main goal is allways to get the most possible SPL to the audience and as little as possible EVERYWHERE else, not only at the rear. The dimension and situation of a venue usually dictates placement and I start from there.
For me, CSA is just one of more out-of-the-box solution that 'can' sometimes partly fix a problem or part of a problem. Fine for folks that don't have the knowledge or time to figure things out for themselves in various situations and setups, but I prefer the 'manual' way. Far better result with the same gear instead of limited benefit at the cost of more gear.


Edited by Peter Jan - 21 June 2009 at 2:20am
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Post Options Post Options   Thanks (0) Thanks(0)   Quote cnics Quote  Post ReplyReply Direct Link To This Post Posted: 03 May 2009 at 4:41pm
Having done extensive measurements on the style of Cardioid array mentioned here, and CSA, and various other types, they all work differently.  They don't all do the same thing.

The simple array spoken about above will potentially give you more output at the front and less at the back,  the CSA gives you significantly less at 180degrees (directly behind) but also less out front.


It's not JUST about 0 degrees and 180 degrees.  It's often about 90 270 304  201  and every other angle from the cabinet.

For me CSA just doesn't work right in alot of situations.  The cardioid array above can do. though you do need distance from the rear wall.



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Post Options Post Options   Thanks (0) Thanks(0)   Quote Phil B Quote  Post ReplyReply Direct Link To This Post Posted: 04 May 2009 at 10:08pm
This thread...

http://srforums.prosoundweb.com/index.php/t/44778/7154/

and back to Dave`s blog for his take on it...

http://ratsound.com/blognav.htm

Highly informative and some intriguing questions?

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Post Options Post Options   Thanks (0) Thanks(0)   Quote Phil B Quote  Post ReplyReply Direct Link To This Post Posted: 15 August 2009 at 8:16pm
Here`s a little piece I wrote today about fun with the world of Cardioid! Apologies to Kevin if I`m repeating some of his stuff!

Weird World of Cardioid Subs





Firstly this isn`t some new thing to somehow gain a better sub sound. This is just ways to keep the sub sound you have in the right places. It was born out of one festival where the noise limits were frightening but only to the sides of the stage. There was a block of flats about 70m away from Stage left and a known "complainer"!. And it really only works if you have all the same type of sub with the same type of driver! And if you want to try it with scoops and " W" bins together...good luck & let me know how you get along!
So here`s how we worked out the mad set-up, first the maths! In dry air at 20 °C (68 °F), the speed of sound is 343 meters per second. The centre of our cardioid freq is at 60hz ( this is the freq we want to create the most rear or side rejection at) it can be any freq within the bandpass for that particular box.
There`s a few ways to get a rearward rejection,:
1)     Turn one box in an array around , flip the phase and apply a delay equal to the distance between forward and rear facing drivers, usually you can simply measure the width of the box if you have front loaded subs and apply that delay in mm ( or ms). For horn loaded subs you have to account for the horn path but again if you are using the same type of box ( hopefully!) in your array it`ll always be the distance between the front and back edges of the boxes.
2)     Space the boxes 1/4 wavelength apart (90 degrees apart). Now delay the front box another 1/4 wavelength (90 degrees). The output from the front box takes 1/4 wavelength to reach the rear box, and another 1/4 wavelength you added artificially, so cancellation ensues. The undelayed sound from the rear box takes 1/4 wavelength to get to the front box, so it sums in phase out front.

There are other configurations that use the same principles: a rearward delay to a tombstone etc etc. But we stuck to the two that others seemed to have the best results with

So to work out what 1/4 wavelength is to space the boxes …343/60/4 (Speed of Sound / centre frequency/ 4) = 1.429 m .
And to work out the delay time 1000/60/4 = 4.17 (Period (ms) = 1000 / Frequency)
Keep in mind the speed of sound changes with temperature so that 343m value will change and so the delays and spacings will change. This can be quite a lot over a 5 degree change in temp. I just go for what I think the temp will be during the event. Outdoors get a forecast …indoors have a guess at how hot & sweaty it`s gonna get!

What we did next was to try a few different configs to see what worked best. Excuse the crappy fone fotos…I need a new fone desperately! We only had 4 subs out as we didn`t want to piss the neighbours off too much with constant freq sweeps all day long at a reasonable level. So we laid out a circle and measured at 15 degree intervals around the arrays from front ( 0 degrees) to rear (180 degrees)and swept from 20hz to 200hz at each point. Highly dull and needs two people ( one to walk the mic around the yard and another to shout" ready" about a million times- never knew sound was so much fun!)

First is a straight stack of 3 subs with one inverted

Plot ......http://img22.imageshack.us/img22/8282/3xvsb218normal.jpg

The plot shows the standard box as a dotted line at different freqs and the colours correspond to the same freq with the hard line being the interted box measurements. The measurement is 180 degrees around the box so the front of the box is at 0 degrees at the right and the rear is to the left. Db is measured from the centre outwards...further out the louder it was! It`s quite tricky to read what`s going on as the traces all overlap etc etc but we were looking for an overall trend at all freqs. Notice the lump in standard ( dotted line) 30hz @ 30 degrees this is probably down to the ports on the NCA subs being on the outside and it picking up the phase changes at the measured distance 10m. Not a great amount of rear cancellation in fact quite a rag tag response.

In reality we were getting rear rejection but the nature of frontloaded boxes means that just by inverting one box we weren`t getting enough rejection at the rear ( or more especially the sides!)

Then a 2 x 2 Tombstone



Plot.....http://img22.imageshack.us/img22/4733/22vsb218.jpg

Ver similiar to a standard 3 high stack...? Sounded like we were getting a bit of rejection at 60 and 120 degrees but not much rear rejection.

Then 2 + 1 + 1 - Tombstone



Plot...http://img22.imageshack.us/img22/7830/211delayedvsb218.jpg

Starting to see a side rejection....

Finally 2 + 1 + 1 ( 1 inverted)



Plot...http://img9.imageshack.us/img9/4323/21reversed11vsb218plot.jpg

This is now a comination of Tombstoning and reversing a box.
Well that seems to work! We`ve not lost any forward gain and between 60 and 120 degrees we`ve got a good 7-10db gain reduction on all 3 measured freqs. Only problem is we are now getting processor hungry! We need 3 different delays on top of our standard set-up.

So after deciding that a combination of both methods was for us Reay knocked up this little CAD for us to see how mad it looked before the gig!



The only difference on the day was to keep the two inverted boxes on the floor. I don`t like subs firing into each other directly and if it was with hornloaded boxes I would definitly try to keep the boxes from firing directly at each other. It sounded great out front no weirdness with the kick drum and with the two infill stacks covered right across the stage evenly. As you walked off to 40 degrees it started noticably tailing off. At 70 - 110 it was hard to tell if it was on! It didn`t reject at the rear the same as a standard one inverted box array but was still down on the usual standard 4 x 4 sub array.



I`ve picked all of this info up from the net. Mostly from PSW/ SPlans etc etc and am reading Dave Rat`s blog about his Vortex and Slotfire systems with great interest. It is a real world solution to getting sub in the right place ( as long as you have the room to start laying subs out!) . Rog`s article on bass arrays goes into this kind of arrangements in great detail and you can sim up different arrays with Mapp online. But I am always sceptical of how the actual array sounds. The fact you are introducing phase changes (delays) means that even though an array can sim up fantastically it could sound very strange! I have tried a few different set-ups on Carnival floats in an attempt to get more rearward sub ; some have worked, others haven`t. Not because the maths is wrong just the fact that it didn`t sound " right" !

Disclaimer...this is only a rough guide and wasn`t done to exacting standards ( there was a massive chiller unit next to us going on & off which probably was why the 30hz readings were all over the place!). It was a fun afternoon in the sun with some boxes and a few beers!


And maybe next time.....



But that`s another story....


.p.

Edited by Phil B - 15 August 2009 at 8:28pm
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Post Options Post Options   Thanks (0) Thanks(0)   Quote xlogic Quote  Post ReplyReply Direct Link To This Post Posted: 11 January 2012 at 2:26pm
Hi 

To contribute to this thread i'm performing some bass array/cardioid array experiments. Eventually I plan to do tests similar to what phil B has done but first i'm playing around at home.

The test:

Using 2 studio monitors I want to have a play around with an 80hz sine wave using delay and phase to see if I can hear cancellation and eventually measure it with a measurement mic or db meter.

Equipment available:

2 x Genelec 8030A speakers
1 x Motu ultralite soundcard
Logic pro 8

I tried with the 'test osc' on logic one on each of two separate channels playing an 80hz wave but as I am unsure as to whether both the oscillators are in sync ie in phase with each other I tried to bounce a sine waveform to an aif file and use the waveform instead. At the moment im having some troubles getting this sorted but i'm sure i'll work it out soon.

Also with the delay plugin im using the 'sample delay' as this is the only delay without extra gubbins that I don't need. Does anyone know how to get this to have the delay parameters in ms rather than samples or am I just going to have to change the delay in samples and do the conversion myself?

Getting close to just sacking off logic altogether and using a BSS LMS. If anyone has any tips on doing this with Logic that would be appreciated.
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Post Options Post Options   Thanks (0) Thanks(0)   Quote trots Quote  Post ReplyReply Direct Link To This Post Posted: 26 July 2013 at 5:30pm
Hi,

I'm running a small (500 cap) outdoor event on the weekend of 30th Aug - 1st Sept and am looking for someone with good experience of Cardioid arrays either to do a days paid work as a consultant to help setup up cardioid subs in 3 (very small 100 cap) tents or would be interested if anyone with cardioid experience was willing to do (fairly cheap) sound hire for one of the 3 tents in addition to helping with the setup of all tents. Obviously will have crew on hand - this is more an advisory / technical role due to noise restrictions from the council.

The event is 1 hr drive NW of London - please PM me if you have relevant experience and would be interested in helping out - or know of anyone who would.

Cheers!
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Post Options Post Options   Thanks (0) Thanks(0)   Quote Pasi Quote  Post ReplyReply Direct Link To This Post Posted: 26 July 2013 at 7:43pm
I can sort it out for you ;) Will PM.
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Post Options Post Options   Thanks (0) Thanks(0)   Quote Ohmen Audio Quote  Post ReplyReply Direct Link To This Post Posted: 10 August 2013 at 3:24pm
After reading this thread i have learned alot about the cardioid sub set ups but i am having great difficulty in figuring how i would apply this to my system in an effective manner considering i am running hogg scoops and 1850's. would i have to have a stack of just 1850's or hoggs or just a certain amount of each. say 1 hogg at the bottom led on its side with one 1850 on top facing forwards and and other 1850 facing backwards would this be applicable?? please excuse my lack of understanding if this seems to be a silly question but if someone could maybe build on this and lend a hand i would greatly appreciate it.
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