This is the last of the cardioid sub arrays I’ll explain . If there’s no room for a end fired or a reverse end fired sub array or the budget only allows 3 subs a side and there’s no room for a end fired line of 3 subs there’s 1 array you can try . The CSA (according to some developed by D&B) . I’m again using the MAP on Line program and the RBV2-9 phase calculator .

So the first thing i have to verify is level in front and in the back of the subs i use in the simulations . I do this by comparing levels at the front and back with the mic1 and mic2 position @ 1mt from the cabinet .

As it turns out the level in front of the sub is 3 dB higher than at the back of the cabinet @ 1mt. Also the frequency response @ the front is a little different from the response @ the back .

So a HP700 sub is not a true Omni-directional sub but we still treat as a Omni source because it comes close to being Omni directional . There’s probably a mathematical equation you can apply to this but i do not know it (now) i just except it and move on .

**The inverse square law still applies but only after you get the relative level at a location X . After that 2X becomes –6dB , 4X becomes –12dB , 8X becomes –18dB etc.**

**So if i apply the numbers again you get :**

**Mic front of sub @ 1 mt = 117dB . **

**So mic front of sub @ 5 mt = 117dB – 20log(5/1) = 117dB – 13,98dB = 103,02dB(little error in the screenshot)**

**Mic back of sub @ 1 mt = 114dB . **

**So mic back of sub @ 5 mt = 114dB – 20log(5/1) = 117dB – 13,98dB = 100,02dB(little error in the screenshot)**

So this is what a CSA stack looks like .

You have a stack of 3 subs where the bottom 1 and top 1 face the coverage area and the middle 1 is facing the back of the stack .

If i export the Impulse response data from Virtual Sim into RBV2-9 i need to take in account the level difference because all impulse response data is normalized to 1 . So in order to get the frequency response within RBV to about 0db(relative) I’ve lowered the level on S2 by –52db and on S1a to –55dB and S1b to –54,7dB . The level difference between S1a & S1b is just to show you there are 2 subs there .

As you can see S2 needs delay to be in phase with the orange trace . The orange trace from S1b lies on top of a red trace S1a indicating it’s in phase with S1a . The level difference i put on S1b shows up in the frequency response window .

The calculation for the delay value is as follows .

**@ 100Hz a phase difference of 120° between S2 & S1a/b exists . **

**100 Hz time period for a full cycle (360°) = 10 ms . 120° = 1/3 of a cycle so = 10ms/3 = 3,333ms .**

By applying 3,333 ms delay on S2 it’s in phase with S1a/b meaning you have addition @ the mic2 position . This is @ the stage side of the coverage area and i want to cancel the low-end so i need to flip polarity on S2 .

So by applying 3,333ms of delay and polarity reversal on S2 you reduce the level @ the mic2 position by about 6db (the black trace in the frequency window (top window) is the sum of S1a S1b & S2) .

The above screenshot shows all traces .

The bottom trace is the sum off all so S1a+S1b+S2(with 3,33ms delay & polarity reversal) =95,4dB @ 69Hz @ mic2 pos.

The 2nd trace is S1a or S1b solo @ 5mt = 100,7dB @ 69Hz

The 3rd trace is S2 solo @ 5mt = 104 db @ 69Hz

The 4rt trace is S1a + S1b = 106,7 dB @ 69Hz ( = S1a or b + 20log(2/1) so 100,7dB + 6dB = 106,7dB )

The 5ft trace is S1a + S1b + S2 3,33 ms delay . S1a & b are –3dB relative to S2 .

So the log calculation becomes S1a+ S1b+S2 3,33 ms delay =S2+20log((0,707(S1a)+0,707(S1b)+1(S2))/1)=104dB+20log(2,414) = 111,65dB(*) (*) = where the relative phase difference between all traces = 0°

So now i need to take a look what happens @ the mic1 position .

S1a and S1b both get to their normal level (for visibility I’ve given them a –52dB offset so that there amplitude gets to 0dB in the frequency window of RBV) . The level of S2 is 3dB less than S1a or S1b because it is facing the other way . So first S1a + S1b . Both are at the same distance from the mic1 position so this becomes a 20log(2/1) ratio meaning they will have a 6dB summation @ the mic1 position .

So if i add S2 into the sum of S1a & b __and do not take the phase differences in to account__ the max level of this set up is again a logarithmic sum .

The sum being 20log((S1a+S1b+S2(-3dB))/1) = 20log((1+1+0,707)/1) = 20log(2,707) = + 8,65dB .

The 8,65dB addition will only be reached where S2 is in phase with S1a & b . If you take a look at the above screenshot MAP predicts going from 104dB @ S1b solo to 110dB @ S1a + S1b (20log(2/1)=+6dB) to 112,5dB @ S1a + S1b + S2 .

In the above screenshot you can see the phase difference between S1a&b vs. S2 @ the mic1 position . From +/-63Hz to about 80Hz or 90Hz the phase difference between the 2 traces is +/-30° or less (i can’t be more specific because of the scaling of RBV) and in this area you’ll find maximum addition between S1a S1b & S2 wich also shows up in the next screenshot from RBV .

I’ve pasted the amplitude/frequency window so that you still see the separate phase response in the bottom screen (so it’s a edited screenshot as most of the screenshot @ my blog) .

**Overall this set-up will have addition over the sub frequency range up to 125Hz but how much addition depends on relative level and phase between sources .**

CSA @ 160 Hz ( @ this frequency it’s not working any more you think? it’s a nice image though ) .

* At the start of this article we found a level difference between the front and back of the sub of 3 dB . One of the main reasons is that the sound waves travel straight too the front mic and have to go around the cabinet to reach the back mic causing a difference in distance and thereby causing a level distance .

** I did build this set-up once or twice but due to lack of time at most jobs not all traces from SIM3 where saved during those jobs . If i have time to do a measurement and save the data properly I’ll post the results as soon as i have them(this also goes for the reversed end fired array) .

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Tim, could you tell me where I can buy or download the RBV phase calculator that you have used for this article? Many thanks & best regards, Ian

The RBV programm was made available to me during the meyersound seminars by magu . I have sent a pm to the guy who as far as i know wrote the programm . He might give a reaction trough here i do not know…….

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