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Old 24th October 2004, 07:25 PM   #1
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Default Driver Simulation Models Question

I have been looking into the idea of taking into account the speaker/enclosure's natural responce when deciding on XO frequencies/type . For this I need to model the drivers as a bandpass filter in my circuit sim program.

I know that a driver in a closed box has a high pass function of a butterworth filter (if the Q is .707) but I'm not sure about the lowpass.

I'm guessing Bessel but not 100% sure.

Does anyone know???

Paul
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Old 24th October 2004, 07:55 PM   #2
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I am not sure if I have an answer to your question, but Richard Small or Neville Thiele might.

I sent Richie00boy Small's papers on Direct Radiator Loudspeakers and Loudspeakers in Closed Boxes, Part 1 and 2. Also Thiele's Loudspeakers in Vented Boxes Part 1 and Part 2.

He has graciously put both the individual pages and the whole articles as pdf on his website.

Although I have the articles, I am not engineer and to tell the truth, I do not know if the answer is there or not. But that is certainly the first place I would look, if I were you.

Here is Richie00boy's website with the available papers:
http://www.richie00boy.pwp.blueyonde...pers/index.htm
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Old 24th October 2004, 08:17 PM   #3
f4ier is offline f4ier  Australia
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Keep in mind that the higher you go in frequency the harder it is to model any speaker system. Speakers do not necessarily have a Butterworth HP transfer function, the low frequency roll-off depends on the driver's electromechanical parameters + the enclosure type. The low-pass transfer function is easy enough to calculate provided you're below the frequency at which cone break-up occurs... Of course you still have to consider Baffle Diffraction, which is a function of driver-on-baffle placement, enclosure size, shape, roughness and room placement (which in itself affects the entire system -- not just BD).

Driver units are imperfect thanks mainly to cone break-up, which is difficult to model without stepping into the domain of Finite Element Analysis. This is why crossovers are designed, simulated and built around measured frequency response data -- not calculated data.

HTH

Isaac
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Old 25th October 2004, 11:46 AM   #4
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The main issue for me is to see how the phase response for the XO + Driver interact. The mid range driver + sealed enclosure will have a -3db of 101hz. The Q of teh enclosure will be .707. This gives a 2nd order butterworth highpass function.

The bit I dont know is how to model the lowpass function of the driver. As said the driver response will be all over the place at such a high frequency but I hazard a guess that the phase response will be fairly regular and will follow that of a particular type of filter alignment.

The purpose of all this is to give a rough idea of what type of filter and what XO frequencies will intergrate with the drivers best. The Active XO is going to be Sallen Key types and reconfigurable for either 1,2, or 4th order and various aligment types, Butterworth, Bessel, LR etc. I just would like to run a few simulations first so I have some idea of how the different types of XO's interact with the drivers

Paul
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Old 25th October 2004, 01:00 PM   #5
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F4ier's Subwoofer Simulator models system phase response and impedance phase response both, as well frequency response.

I find the frequency response from Subwoofer simulator to be a bit trucated, since it models the SPL without cone breakup. But the system phase and impedance phase should be accurate.

Perhaps by looking at the lowpass responses, you can backtrack to what kind of lowpass filters they are acting like.
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Old 25th October 2004, 01:08 PM   #6
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Bullock and White's DOS BopxModel also models system phase and impedance phase.

I'm not certain, but I am reasonably sure Martin J King's MathCAD sheets-sheets capable of being used with MathCAD free software-model impedance phase and system phase as well.
www.quarter-wave.com

I hope these help.
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Old 25th October 2004, 05:07 PM   #7
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Thanks for that everybody. I will give those programs a try when I get home to my non mac environment.

TTFN

Paul
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Old 25th October 2004, 06:17 PM   #8
4real is offline 4real  Netherlands
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Also note that a bandpass system could end up have a veryhigh group delay!
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Old 25th October 2004, 09:04 PM   #9
Ron E is offline Ron E  United States
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The lowpass function would depend on the driver, In order to know what to plug into a simulation, you would need access to measurements.

If you want to guess, just use the same butterworth coefficients as for the highpass function. Either that or you can by trial and error come up with some function.

Bullock ans white have a crossover simulator that does what you are trying to do (without measurements) It is called "FlexSys", IIRC. All it asks is how much peaking and what order rolloff. It asks for a crossover and plots the result. It is a DOS program though, so not guaranteed to work with newer OS's, you might have to set compatibility parameters.....

Another DOS program that does what you want is SD-LMP.

You can measure speakers with a free windows tool called Speaker Workshop. You can design passive crossovers and see how they sum with a circuit simulator that is included.
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Old 25th October 2004, 10:57 PM   #10
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Thanks for the info but I am still confused by some things that were said.

As far as I can gather a driver in a sealed enclosure can be considered as a bandpass filter. The high pass will be a butterworth alignment if the Qt of the driver/enclosure system is .707. The low pass according to Richard Small's paper will also be a butterworth alignment. Although the SPL at high frequencies will not be a smooth line ( Just look at a woofers FR at high frequencies) the phase should that of a regular butterworth band pass filter.

I dont fully understand Richard Smalls paper (as mentioned in previous post) but the lowpass function is determined by Diaphragm displacement function which is

Xs= 1/ (s^2 Ts^2 + s Ts / Qt + 1)

Ts= 1/ws^2

ws= 2pi Fs

s= the complex frequency variable.

I just cant work this out. Can anyone give an idiots guide with a few examples???

I want to model this and at this stage not to think about the effects of the actual XO that will be connected to the speaker at this stage. Once I have a reasonable model I will then look at the XO effects.

Paul
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