Back loaded horn maths

[scraper]

Hi, I am trying to solve the equivalent circuit for a back loaded horn with a compression chamber in the back of the driver. I was able to get to the point of simplifying the circuit to this:



where
Pg = (Bl * eg) / Sd (Re + jLe*w) in newton per square meters [Pa]
U = unknown [m^3/s]
Raa = known
Zeq = resistance + imaginary part known
C1 = known
Z throat = known

Now, I need to find the "current" and "voltage" through the real part of the impedance of the throat to get the radiated pressure and the radiated volume velocity. How can I do that?

Thanks, Stéfane

[scraper]

Ok, maybe I should clarify what isn't clear to me right now. The problem is mostly knowing how to account for the imaginary part of the source voltage. I'm not so familiar with these equivalent circuits, I don't know what that complex part of the source represents.

Stef.

[rjbond3rd]

Hi scraper, this might be of some help: Horn Theory

[godfrey]

Hi Stéfane

Ouch, now you're making me think!

I'm not sure we're on the same page regarding the model. The picture below is how I see the mechanical circuit.

It's using mechanical units e.g. Source velocity is in M/S and source impedance is in N / (M/S).

Sorry, I just noticed it looks like you're using acoustical units e.g. pressure and volume velocity. That's an easy conversion anyway, based on Sd.

The important thing is that speakers are normally voltage driven, so when doing the transform to the mechanical circuit, we need to model the input as a velocity source, not a pressure source.

btw, Assuming you're OK with complex arithmetic, spreadsheets are wonderful for doing the number-crunching with this sort of thing.

Both MS-Office and OpenOffice support complex maths - but need to have "Engineering functions" (or whatever it's called) installed.

Cheers - Godfrey

[scraper]

thanks for the answer godfrey, I think that I have found my mistake. What program do you use for drawing electrical circuits? I used paint, but I'm sure there is some programs that could make it easier. I'm probably going to have some more questions in a near future!

It is possible to make a electrical circuit model driven by a pressure source. I use Beranek's Acoustics as a referance which uses pressure sources instead of working with the mecanical circuit.

stéfane

[godfrey]

I use MS Paint as well - just screen-print a couple of neat symbols from somewhere, then copy/paste and rearrange in Paint.

Originally Posted by scraper

It is possible to make a electrical circuit model driven by a pressure source.

Hmm... OK.
I suppose then you put the source impedance in series with the pressure source in the circuit.

Have to be careful calculating the source pressure, though...

[scraper]

Here is the detailed circuit that I get.




where:
j = sqrt(-1)
Source_pression = (Bl * eg) / (Sd (Re + j*Le))
R1 = ((Bl)^2)/(Sd^2 * Re)
C1 = (Sd^2 * Le)/(Bl)^2
Mas = Mmd/Sd^2
Ras = Rmd/Sd^2
Cas = Cmd * Sd^2
Maa = Mass in front of the driver
Raa = Acoustic resistance in front of the driver
Ca1 = Compliance of the chamber at the back of the driver
M_gorge = Mass of the air of the horn
R_gorge = acoustical resistance of the horn

I think that the circuit is correct. The only thing that I'm not sure about is if the mass M_gorge should be in serie or in parallel.

It is now possible to get the pressure drop at the front of the driver and at the horn using Matlab. Now, I want to find the sound pressure level at 1 m. In order to calculate it, I guess that i need to consider the directivity patterns. Is it possible to consider the driver and the mouth of the horn as pistons in an infinite baffle? if not, is there an analytical expresion for the directivity pattern of finite horns? Should I use the 20 x 10^-6 Pa as the reference pressure?

More questions are to come!

Stéfane

[godfrey]

I think Raa and Maa should be in parallel, not in series. To calculate the acoustic impedance at the throat is difficult. I think to model it as M_gorge and R_gorge is too simple. Perhaps you could find out how HornResp works.

It looks like I made a mistake in my diagram too.

Good luck - Godfrey

[Scottmoose]

Looks to me like you're trying to reinvent the wheel. Locanthi for e.g. had an AES paper on this back in '71: 'Application of electric circuit analogies to loudspeakers design problems.' It was what Augspurger modified to create his TL modelling approach ten years ago. There are also things such as Leach's SPICE model if you feel like some self-abuse.

[freddi]

weren't George's analog mobility models and following digital implementations based upon Bart Locanthi's work?
In Memorium

here's Karlson's circuits in 1952 for his coupled cavity speaker