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1st July 2012, 06:09 PM  #1 
diyAudio Member
Join Date: Dec 2009

Error in one of R. H. Small's papers?
Not sure the best place to post this, thought subwoofers would be close because Small's papers are about lowfrequency response of woofers. I was hoping that someone could help me out. Acoustics and electrical engineering are not my background.
I found a problem that I can't get around in R. H. Small's "DirectRadiator Loudspeaker System Analysis" paper. Equation (9) has an "s" in the denominator that I think should not be there. I solved his circuit in Fig. 3 for Uo, and I get his expression but I have no s in my the solution. If there is an s there, he should have included it in the G(s) term. But then G(s) would not be the lowpass filter transfer function. Between equations (10) and (11) he writes, "Eqs. (5) and (9) may be combined with Eq. (7) to yield..." I think this should instead have stated "Eqs. (3) and (9) may be combined with Eq. (7) to yield..." Equation (5) seems to have nothing to do with equation (7), and I think he meant equation (3) instead of equation (5). When I try to obtain Equation (11) by combining (3) and (5) with (7), I obtain his expression for (7), except that I have an omega^2 (omega=frequency in radians/sec) in the numerator which he does not have. A look at equations (2), (3), (6), and (7) seems to show that there must be an omega^2 in his expression for efficiency in equation (7). I googled for errata for these papers, but could not find anything. 
1st July 2012, 06:55 PM  #2 
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Join Date: Jan 2011

post up the actual equations. I'm not an electrical engineer either, but I'm pretty good at algebraic manipulations.

1st July 2012, 07:52 PM  #3 
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Join Date: Dec 2009


2nd July 2012, 12:25 AM  #4 
diyAudio Member
Join Date: Jun 2002
Location: USA, MN

Equation 11 is correct, and so is equation 9.
equation 9 has an s in the denominator because it is a relation in volume velocity, if you multiply both sides by s, you get a relation in acceleration, and sound pressure is proportional to acceleration.
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3rd July 2012, 04:09 AM  #5 
diyAudio Member
Join Date: Dec 2009

Yes, equations 9 and 11 are correct. I found my mistake, I fouled up the algebra in solving for eq. 9. That s in the denominator of eq. 9 turns out to be the key to getting rid of the omega^2 which shows up when obtaining eq. 11.
Small's reference to eq. 5 when arriving at eq. 11 should definitely have been a reference to eq. 3 and not eq. 5. 
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