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4th May 2012, 05:18 PM  #1 
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Join Date: Mar 2008

Isobaric (Series vs Parallel)
Ok, so with an isobaric sub you are essentially 'creating' a new driver with slightly different T/S Parameters.
The Mechanical Resistance, Stiffness and Mass all double. Which is logical. Cms is 1 / Stiffness so that halves. The magnetic field strength effectively stays the same but the voice coil wire length doubles so the Bl doubles. Vas is a function of Cms and so the Vas halves which is why we can use enclosures of half the size. This all makes sense. What I'm struggling with is the fact that if you wire them in series then the Re doubles but if you wire them in Parallel then the Re halves. So there is a 4 times difference between series and parallel. Looking at the above equation. If we double Mms and Re and top of the division and double Bl^2 then the driver Q stays the same and so the response will stay the same. However if re is not doubled but halved then the Qes will be reduced by a factor of 4 which will in turn reduce Qts by a significant amount. Therefore the entire response of the system will be altered quite dramatically. This doesn't seem logical to me but i can't see what I'm missing?? So if we wire isobaric drivers in Series then the response will be unchanged but if we wire them in parallel it completely changes. Is this correct or have I missed something fundamental here? Last edited by schmeet; 4th May 2012 at 09:32 PM. 
5th May 2012, 04:44 AM  #2  
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Quote:
If you have a pair of speakers,an amp, a dB meter and test tones you can easily verify this fact for yourself. 

5th May 2012, 06:29 AM  #3 
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I think schmeet wants to understand the math behind it, not just verify it.
So do I
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5th May 2012, 06:57 AM  #4 
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Location: New Zealand

One related point on isobaric configuration: The drivers are better wired in parallel, because they aren't truly "isobaric". The compliance of the air between them means that they are loaded differently, will not move exactly in unison, so will reflect different impedances. The difference can be quite large if used in a resonant enclosure such as a ported enclosure or tapped horn.

5th May 2012, 07:17 AM  #5  
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Join Date: Jun 2007

Quote:
It is only for two drivers connected in series that Bl is doubled  Bl stays the same for two drivers connected in parallel. If it is assumed that Fs does not change (not strictly correct), then the value of Qes will remain constant. Single driver: Qes = Re / (2 * Pi * Fs * Cms * Bl ^ 2) Two series isobaric drivers: Qes = [2 * Re] / (2 * Pi * Fs * [Cms / 2] * [2 * Bl] ^ 2) = Re / (2 * Pi * Fs * Cms * Bl ^ 2) Two parallel isobaric drivers: Qes = [Re / 2] / (2 * Pi * Fs * [Cms / 2] * [Bl] ^ 2) = Re / (2 * Pi * Fs * Cms * Bl ^ 2) Kind regards, David
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5th May 2012, 07:54 AM  #6 
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Join Date: Mar 2008

Thanks David,
I know its not a perfect situation, but for the sake of modelling: Cms is Halved Mms is doubled Rms is doubled Bl is doubled in series Bl is the same in parallel Re is doubled in series Re is halved in parallel Lvc is doubled in series Lvc is halved in parallel I can then work out the other parameters from this and just model as a single driver.. 
5th May 2012, 08:02 AM  #7 
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Also, could you briefly explain why Bl stays the same when wired in parallel. I'd like to understand that...

5th May 2012, 08:55 AM  #8 
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Location: Gloucestershire, England, UK

Because the same current is flowing through the coil as would be for a single driver.
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5th May 2012, 09:24 AM  #9 
diyAudio Member
Join Date: Mar 2008

Hey richie00boy.
But Bl is B (Magnet strength in Teslas) multiplied by L (length of the voice coil wire). Current is not involved. Bl * Current gives you the force applied by the magnet. The magnet field strength of the magnet doesn't change and so I can only assume that the length of the wire is considered to be doubled in series and the same in parallel. Not completely sure why that would be though. 
5th May 2012, 11:43 AM  #10 
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Join Date: Mar 2008

Maybe i am allowed to use this picture for illustration:
B stays the same regardless whether wiring the two voice coils in series or parallel. Series wiring means doubling the length of the wire in the field but maintaining the same cross sectional area of the wire as in the single driver case. (Bl) doubles, because wire length (l) doubles. Rg doubles, because wire length (l) doubles. Parallel wiring instead means (effectively) doubling the cross sectional area of the wire in the field instead while maintaining the same length of the wire as in the single driver case. (Bl) stays the same, because B and l stay the same. Rg halves, because the cross sectional area of the wire doubles. __________________ However this illustration does not account for the wire to be wound as 2 separate coils and only holds for low frequencies. It does e.g. not explain why resulting voice coil inductance Lvc halves in the parallel case, which is because in fact we have 2 coils in parallel. Last edited by LineArray; 5th May 2012 at 11:56 AM. 
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