End fired Sub array (only in English)   3 comments

I did a article on End fired sub array’s more than a year ago but only in Dutch so now the English version . The end fired sub array has the advantage of summation in front of the array and cancelation at the back of the array . It needs in a 4 element array 4 amps and 4 processor channels where you might need only 1 or 2 amps and 1 channel of processing in a conventional stack of subs .

If executed correctly the level of sub leakage in the back from 4 subs is the same as 1 single sub and reduces as the distance increases where with a conventional stacked array of 4 subs the level in the back is about 12dB more than with 1 single sub .

The screen shots in this article are made with the MAP on line program from Meyer sound the RBV2-9 phase calculator (by exporting the impulse response (I.R.) from virtual sim within map and importing the I.R. in to RBV2-9 the phase can be displayed) . After the simulations i also have the data from the Meyer sound SIM3 measurement system from a real live situation .

So here goes .

The end fired line consists of most of the time 2 3 or 4 subs (can be more but this is practical in a real world situation) . In this example i’m going for a 4 element array of 4 HP700 subs .End fired start

So if i were to put this array in to action without processing applied you would get a lot of cancellation @ the position of the front mic (audience area) due to the spacing between Sub 1-4 .

End fired no processing freq resp. plus overlay s1 s4 

The blue line represents all 4 subs without processing applied Cancelations between S2 – S4 and S3 – S4 can be clearly seen . The cancelation between S1 and S4 can’t be seen in front of the array due to the level difference between S1 and S4 (inverse square law) . All of this happens when a end fired line is put in to action without processing applied to it . A lot of comb filtering inside the coverage area . The screenshots below demonstrate what that means .

ef @171Hz s3 s4 

The bottom 2 pasted screen shots (in the above image) give the phase relationship between 2 subs 1mt apart if no processing is applied to them meaning S1 + S2 (no processing applied) S2 + S3 (no processing applied) & S3 + S4 (no processing applied) will cancel @ 171Hz in a end fired line @ the on axis position (front mic).

So all of this happens between 2 sub 1 meter apart but because I’m using 4 subs in this example i also need to take a look at what happens between 2 subs 2 meters apart and 2 subs 3 meters apart again with no processing applied yet . So first i take a look at 2 subs 2 meters apart with no processing applied to them in a end fired configuration .

End fired no processing @ 85Hz S2 S4 

The bottom 2 pasted screen shots (in the above image) give the phase relationship between 2 subs 2meters apart if no processing is applied to them meaning S1 + S3 (no processing applied) S2 + S4 (no processing applied) will cancel @85Hz & @ 250Hz in a end fired line @ the on axis position (front mic) .

End fired no processing @ 55 Hz S1 S4 

The bottom 2 pasted screen shots (in the above image) give the phase relationship between 2 subs 3 meters apart if no processing is applied to them meaning S1 + S4 (no processing applied) will cancel @58Hz & @ 171Hz in a end fired line @ the on axis position (front mic) .

Before i continue i need to make a small point . All the screenshots are simulations meaning you will never see a frequency nor phase response like the screenshots in a real world situation . First you get to deal with room acoustics and second the distance between in this case subs would cause level differences something that’s not visible within RBV2-9 . So why ?

First a screenshot with the impulse responses from S1 to S4 solo with the front mic onax @ 1 mt distance from the end fired array within RBV2-9 that were imported from virtual sim from MAP on Line .

                                                       RBV impulse response S1-S4 solo

Clearly visible is that there’s no level difference between al impulses . They al have their peak at 1 . In a real live measurement S4 will be closer to the mic and will have more level but this is a computer generated world of measurement . In order to get the impulse response of a single sub i have to mute all other subs and by doing that MAP puts the peak of the impulse at 1 automatically regardless of distance (or time) to the mic . If i were to put multiple subs in to action you would expect multiple impulses visible but because of the wavelength/period of the sub frequencies you will not clearly see the peaks as in the above screen shot but something like the following 1 .

impuls 4 subs no processing 

Sorry but i do not see 4 peaks (also in a real world measurement the peak of a impulse response measurement of a sub is hardly visible and requires a lot of averaging and zooming in on the peak) .

So is there a bug in MAP on line ? No the levels of the subs can be seen in the frequency response screen of virtual sim . In the screenshot below i pasted the frequency response of S1 S2 & S3 on to the response of S4 . The mic is @ 1 mt distance from S4 so her you’ll see the highest level (118dB @ 69Hz) . S3 is @ twice the distance so you’ll see a level drop of 6dB due to the inverse square law (2 times the distance = –6dB so 118dB – 6dB = 112dB @ 69Hz) . S1 is @ 4 times the distance so again this means a level drop of –6dB (S4 is @ 118 S1 is @ 118db – 12dB = 106dB) . S2 is somewhere in the middle @ 108,5dB .

S1-4 fr mic @ 1  mt 

The reason for Map to put the peak @ 1 is visibility i presume . It’s easier to work with the program this way but you need to be aware of it when doing simulations with subs and comparing SOLO measurements of single cabinets in arrays . Second note : If the mic is @ 20 mt distance from the array the level differences become smaller because the ratio changes between individual subs regarding the distance to the mic .  

So now i am going to apply processing to this configuration (position of the mic is set @10mt again) . As demonstrated in the above screen shots i need to apply delay to S2 S3 & S4 in order to get the level of sub in front of the array and not to the side . By applying delay to S2 S3 & S4 the level in front of the array will rise with at least 12dB (why it’s 12dB will be explained and has to do with the 20log equation and is a matter of the ratio between 1 element vs 4 elements) .

By applying 2,8ms of delay on S2 it will align perfectly with S1 and gain 6dB ( 20log(2/1)=+6db .

Secondly i am going to take in account the level of sub 2 being higher because of the difference in distance . This means i am going to need the 20log power equation to calculate the dB difference vs distance difference . S1 (centre) = @ 7mt and S2 = @ 8mt . The front mic = @ 20mt.

If you put this in the log formula you get 20log(13/12) = 20log(1,083) = 0,7dB more level on S2 @ the front mic position (20mt – 7mt =13 & 20mt – 8mt = 12mt) . So for later use we need to remember the 1,083 number .

So first lets check if the level difference is visible within map . First S1 solo level @ 79Hz = 95dB @ the front mic .

S1 fr mic log 

Second S2 solo level @ 79Hz = 95,7dB @ the front mic .

S2 fr mic log 

So the level rises on S2 with 0,7dB as the calculation already predicted . If i put this in the RBV program you can see a small level difference on S2(red) and if you put the numbers in to the 20log formula you get :

20log((1+1,083)/1)= 20log(2,083)= + 6,37 dB so it’s a little more .

RBV S1 S2 log 0,7 db xtra 1,083

And in MAP the level of S1 + S2 plays out as calculated from :

S1 solo 95dB @ 79Hz to S1 + S2 = 95dB + 6,37dB = 101,37dB

S1 S2 log sum 

By applying 5,6ms of delay on S3 it will align perfectly with S1 & S2 and gain 9,54dB ( 20log(3/1)=+9,54db .

Secondly i am going to take in account the level of sub 2 & 3 being higher because of the difference in distance . This means i am going to need the 20log power equation again to first calculate the dB difference vs distance difference between S1 & S3 .

S1 (centre) = @ 7mt and S3 = @ 9mt . The front mic = @ 20mt. If you put this in the log formula you get 20log(13/11) = 20log(1,182) = 1,45 dB more level on S3 @ the front mic position (20mt – 7mt =13 & 20mt – 9mt = 11mt) .

So now i need the log formula again to calculate the SUM so log20((S1 + S2 + S3)/1) = log20((1+1,083+1,182)/1)) . At the end you will get 20log(3,265)=+10,28dB . If you put this in RBV2-9 it looks like the following screenshot .

RBV S1 S2 S3 log s3 1,45 db xtra 1,182 

And in map on line it also plays out to the calculated level . S1 + S2 + S3 = 105,3dB (the level on S1 was 95dB @79Hz and now it’s 95 dB + 10,28 dB = 105,28 dB) .

S1 2 3 log 105,3 dB 

So by applying 8,4ms of delay on S4 it will align perfectly with S1 S2 & S3 and gain 12dB ( 20log(4/1)=+12db .

Secondly i am going to take in account the level of sub 4 being higher because of the difference in distance . This means i am going to need the 20log power equation to calculate the dB difference vs distance difference again . S1 (centre) = @ 7mt and S4 = @ 10mt . The front mic = @ 20mt.

If you put this in the log formula you get 20log(13/10) = 20log(1,300) = 2,28dB more level on S4 @ the front mic position (20mt – 7mt =13 & 20mt – 10mt = 10mt) . So for later use we need to remember the 1,300 number .

Again i’m using the log formula to calculate the SUM so :

log20((S1 + S2 + S3 + S4)/1) = log20((1+1,083+1,182+1,300)/1) . At the end you will get 20log(4,565)=+13,19dB . If you put this in RBV2-9 it looks like the following screenshot .

RBV S1 S2 S3 S4 log s3 2,28 db xtra 1,300 

And in map on line it also plays out to the calculated level . S1 + S2 + S3 + S4 = 108,2dB (S1 was 95 dB and now it’s 95 dB + 13,19 dB = 108,19 dB) .

S1 2 3 4 log 108,2 dB map

So if you look at the MAP on Line predictions at frequencies you find at any graphic eq. you get the following .

End Fired line 4 subs (processed) @ 40Hz

End fired 1mt spacing 40 hz 

End Fired line 4 subs (processed) @ 50Hz

End fired 1mt spacing 50 hz 

End Fired line 4 subs (processed) @ 63Hz

End fired 1mt spacing 63 hz 

End Fired line 4 subs (processed) @ 80Hz

End fired 1mt spacing 80 hz As you can see in front of the array no cancels with delay added to Sub 2 Sub 3 & Sub 4 and it’s 13,2 dB louder in front . Also pretty important : the blue colour at the back mic indicates that there’s cancelation going on at the back mic’s location .

To summarize the calculations i did for the front mic position they were :

S1 (@ 7 mt centre) measured @ the front mic position (20 mt) = 95dB

S2 (@ 8 mt centre) measured @ the front mic position (20mt)  = 95,7dB

S3 (@ 9 mt centre) measured @ the front mic position (20mt)  = 96,45dB 

S4 (@ 8 mt centre) measured @ the front mic position (20mt)  = 97,8dB

S1 + S2 = 20log((1+1,083)/1)= 20log(2,083)= + 6,37 dB = 101,37dB (@ the front mic position) .

S1 + S2 + S3 = 20log((1+1,083+1,182)/1)) = 20log(3,265)=+10,28dB (@ the front mic position) .

S1 + S2 + S3 + S4 = 20log((1+1,083+1,182+1,300)/1) = 20log(4,565)=+13,19dB (@ the front mic position) .

If i apply the same principle to the back mic position you get the following calculations .

S1 measures 98dB @ the back mic position . The distance S1 to the back mic is 6mt .

The distance S2 to the back mic is 7mt so 20log(6/7) = 20log(0,857)=-1,34dB . S2(back mic) 98 -1,34 = 96,66dB .

The distance S3 to the back mic is 8mt so 20log(6/8) = 20log(0,750)=-2,50dB . S3(back mic) 98 –2,50 = 95,50dB .

The distance S4 to the back mic is 9mt so 20log(6/8) = 20log(0,667)=-3,52dB . S4(back mic) 98 –3,52 = 94,48dB .

So first i verify if these levels match with MAP on Line .S1 bm level check

S1 measures 98dB @ the back mic position .

S2 bm level check 

The distance S2 to the back mic is 7mt so 20log(6/7) = 20log(0,857)=-1,34dB . S2(back mic) 98 -1,34 = 96,66dB .

S3 bm level check 

The distance S3 to the back mic is 8mt so 20log(6/8) = 20log(0,750)=-2,50dB . S3(back mic) 98 –2,50 = 95,50dB .

S4 bm level check 

The distance S4 to the back mic is 9mt so 20log(6/8) = 20log(0,667)=-3,52dB . S4(back mic) 98 –3,52 = 94,48dB .

All calculated levels check out within MAP so now lets load all impulse responses from S1 to S4 from Virtual sim  in to RBV with delays and all level differences .

RBV s1 bm solo 

In order to get the level of the sub around 0dB within RBV i did a offset in level of –50 db in all screenshots made from RBV . So the level of S2 becomes –50 dB + –1,34 dB = –51,34 dB .

RBV s1 s2 bm solo 

S1 + S2 cancel @ about 60 Hz with about 15 dB @ the position of the back mic . There’s a other cancel higher up @ about 180/200 Hz .

RBV s1 s3 bm solo 

The level of S3 becomes –50 dB + –2,50 dB = –52,50 dB .

S1 + S3 cancel @ about 80 Hz with about 12 dB @ the position of the back mic . There’s a other cancel higher up @ about 140/160 Hz . Due to the level difference between S1 & S3 the cancels are not as deep as between S1 & S2 .

There’s 1 other thing happening @ the 60 Hz area : addition . At that area S3 is @ about 540° and S1 is @ about 180° meaning S3 is a full cycle behind S1 and causes addition in that range . The same thing happens near 125 Hz where S3 is at 800° . Because of the level difference between S1 and S3 due to the difference in distance the addition is not +6 dB but about +4 dB . In the end S1 & S2 have a cancel also at 63 Hz of about –15 dB and in the next screenshot S1 + S4 also cancel at the same area so the addition of S1 + S3 is not a problem @ 60 Hz . However the addition @ 125Hz is a problem because it’s also happening between S1 & S2 and as you can see also between S1 & S4 in the next screenshot .

RBV s1 s4 bm solo

The level of S4 becomes –50 dB + –3,52 dB = –53,52 dB . Again you see some cancels but not real deep ones because of the difference in level due to the distance of S4 to S1 . Also S4 is causing addition again @ 125 Hz because it’s       @ 1260° and S1 is @ 180° . So S4 is in phase again @ 125Hz with S1 but is a few cycles (3 1/2 to be exact) behind S1 .

RBV s1 to s4 bm sum only

So if you put a end fired sub array in to action you have to use low pass filters on all subs because if you go higher than about a 90 or 100 Hz you get addition instead of cancellation @ the back of the array .

In the last 2 screenshots i pasted the predictions of Map on Line on to the screenshots of RBV . With a little imagination you can clearly see they are similar .

S1 to 4 Sum RBV 

Frequency calculation by RBV with the graph from virtual sim pasted on top of it .

S1 to 4 impulse response RBV 

And the same idea with the impulse response .

And now it’s time to welcome you all to the real world . The following screenshots come from the SIM3 set-up & data viewer which comes with the purchase of the SIM3 measurement system . It allows you to prepare measurements in advance of a measurement job and to view data from past measurements . I’m not going to do all the calculations again (because i do not feel like doing them again (i really hate mathematics)  and secondly i do not remember the distance between the mic and the subs) .

So here are all 4 subs . You can clearly see the level differences between them .

SIM 3 all 4 subs

S1 vs S2 both in solo mode . Not to much level difference between them (0,4 dB)

SIM 3 S1 & S2 nop

Clearly visible that the blue trace (S2) needs delay because the angle of the phase trace is less steep .

SIM 3 S1 & S2 p   zoom 

S2 with delay on it . S2 is now phase aligned with S1 .

SIM 3 S1 & S3 nop  

S1 vs S3 both in solo mode . Clearly visible that the green trace (S3) needs delay because the angle of the phase trace is less steep .

SIM 3 S1 & S3 p   zoom

S3 with delay on it . S3 is now phase aligned with S1 .  

SIM 3 S1 & S4 nop

S1 vs S4 both in solo mode . Clearly visible that the red trace (S4) needs delay because the angle of the phase trace is less steep . Also the level difference is more visible in the red trace .

SIM 3 S1 & S4 p   zoom

S4 with delay on it . S4 is now phase aligned with S1 .

SIM 3 S1 solo vs all subs 

S1 solo vs S1 + S2 + S3 + S4 . Summation is about 15 dB .

Now the phase response between subs at the back mic with processing applied to subs 2 3 & 4 (only delay) .

S1 vs S2 proc. back mic

S1 vs S2(blue) . Due to the phase differences there will be cancels at various frequencies .

S1 vs S3 proc. back mic

S1 vs S3(green) . Due to the phase differences there will be cancels at various frequencies .

S1 vs S4 proc. back mic

S1 vs S4(red) . Due to the phase differences there will be cancels at various frequencies .

S1 vs S1-4 back mic

And the final screenshot : S1 solo vs S1 + S2 + S3 + S4 (red) . As you can see the level does not rise @ the red trace @ the back mic position .

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