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 Multi-Way Conventional loudspeakers with crossovers

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Svante
diyAudio Member

Join Date: Feb 2004
Location: Stockholm
Quote:
 Originally posted by azira However, putting a speaker into a box produces some kind of high-pass like response. I can't find the theory/math behind this.
Ahh... That is easy. Sound pressure is proportional to cone acceleration. In mechanical analogies the cone velocity is the equivalent to the current. So a mechanical series resonance circuit would be bandpass for the *velocity*. Differentiate this and you have the acceleration. Differentiation corresponsds to a tilt of +6dB/oct. So the bandpass will be a highpass. Voilá!

azira
diyAudio Member

Join Date: Dec 2003
Location: Near Seattle
Quote:
 Originally posted by sreten Sealed box is 2nd order high pass filter theory. sreten.
I see it now. Very interesting, I will need to digest this...

Thank you very much sreten, Svante, you are both very knowledgeable here.

I just did a sim...
Attached Images
 filter.jpg (42.1 KB, 444 views)

Ron E
diyAudio Member

Join Date: Jun 2002
Location: USA, MN
Quote:
 Originally posted by azira The math is not the problem. I'm a analog/digital electronics engineer. I've read some articles on modeling resonances as LRC circuits because they behave similarily so I was trying to use my circuit knowledge to better understand speaker behavior. I'm trying to understand how to go from fig 1 -> fig 2. In a standard resonance circuit, the transfer function (and therefore freq response) slopes off on either side at the same rate (dB/dec). However, putting a speaker into a box produces some kind of high-pass like response. I can't find the theory/math behind this.

Dynamic simulation is a major interest of mine. The theory developed in the books I cited (I own them, too) is the hardest data I know of, and that is what you said you were looking for. I gave you the Resources you need. I was not willing to waste time spouting equations or theories you might not understand. A true understanding of this will not be had from a forum discussion, although this might be a fair place to come if you had questions. You'll find someday there's nothing like going to the source when you want results.

If you want a web resource, check out the Benson style Thiele/Small model that is developed by Robert Bullock in a windows help file format....Google for it.
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azira
diyAudio Member

Join Date: Dec 2003
Location: Near Seattle
Quote:
 Originally posted by Ron E I was not willing to waste time spouting equations or theories you might not understand. A true understanding of this will not be had from a forum discussion, although this might be a fair place to come if you had questions.
Fair enough. On the other hand, I'm not willing to dump \$100 on the first book that someone on this same forum says is the definitive guide to this or that. Same coin.
I agree I won't find the definitive answer, but atleast I might get a start with a direction to start exploring.
Anyway, only way to raise the educational level at which this forum is discussed is to contribute at that level.

 20th February 2004, 04:47 AM #15 f4ier   diyAudio Member     Join Date: Sep 2001 Location: Sydney Both books mentioned by Ron are a must-have for anyone interested in loudspeaker theory. I have a copy of the Acoustics book, it helped a great deal when I was making the current versions of my speaker programs; particularly SubSim. There are so many texts form the Journal of the Audio Engineering Society. You may also be interested in the book "Introduction to Electroacoustics and Audio Amplifier Design" by W.M. Leach Jr. whose JAES contributions I found most informative. __________________ Crossover/Subwoofer Simulator
Svante
diyAudio Member

Join Date: Feb 2004
Location: Stockholm
Quote:
 Originally posted by azira I just did a sim...
Try to simulate the circuit below instead. All parameters are T/S parameters, RML is the mechanical radiation resistance:

RML=(Ss*w)^2 * rho0 /(2*pi*c)

Note that it is dependent on the frequency squared.

Simulate this and you should see the driver impedance as the impedance connected to the voltage generator, and if you can find the *power* dissipated in RML, you have the HP function!
Attached Images
 speakerimp.gif (3.5 KB, 291 views)

Pjotr
diyAudio Member

Join Date: Nov 2002
Location: Netherlands
Hi,

If it helps to understand a loudspeaker unit, long time ago I made an electromechanical model to simulate in Pspice. Basically it is a second order mass-spring system. The acoustical output is proportional to the acceleration.

For a closed box, the springiness of the air in the box acts in parallel to the springiness (compliance) of the speaker itself. For a BR the speaker is coupled to a Helmholz resonator formed by the springiness of the air in the box acting on the BR-port and the air-mass in the BR port.

Cheers
Attached Images
 basic_ls.gif (4.7 KB, 281 views)

Svante
diyAudio Member

Join Date: Feb 2004
Location: Stockholm
Nice simulation! This is the Physisists way of doing it.

The electrical engineer might do it like this, using electric-mechanic-acoustic analogies. To the left currents are flowing through the cables and voltages appear over the components, in thew middle velocities "flow" through the components and forces appear over them, to the left, volume flows flow through the components and pressures appear over the components.
The diagram is the equivalent of a loudspeaker. We feed it a voltage (us) and a current (is) in the electric domain, and out of it we get a volume flow (Qs) and a pressure ((Ps) in the acoustic domain.

T=Bl and the symbol below the T is a gyrator, Ss is the cone area and the symbol below is an ideal transformer.
Attached Images
 speakerdiagram.gif (3.1 KB, 255 views)

ashwin
diyAudio Member

Join Date: Apr 2003
Location: Bangalore
Quote:
 Originally posted by Svante Nice simulation! This is the Physisists way of doing it. The electrical engineer might do it like this, using electric-mechanic-acoustic analogies. To the left currents are flowing through the cables and voltages appear over the components, in thew middle velocities "flow" through the components and forces appear over them, to the left, volume flows flow through the components and pressures appear over the components. The diagram is the equivalent of a loudspeaker. We feed it a voltage (us) and a current (is) in the electric domain, and out of it we get a volume flow (Qs) and a pressure ((Ps) in the acoustic domain. T=Bl and the symbol below the T is a gyrator, Ss is the cone area and the symbol below is an ideal transformer.
Svante,
thanks for that info. Just out of curiosity, Qms would be the Q of the mechanical RLC circuit (Rms, Mms, Cms), right? Then what would Qes be? There is no capacitor on the electrical side (left of the gyrator). Or have I got it all wrong?

Thanks
- Ashwin

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