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
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
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.blueyonder.co.uk/papers/index.htm
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.blueyonder.co.uk/papers/index.htm
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
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
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
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
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.
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.
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.
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.
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.
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.
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
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
If you understand transfer functions:
2.O. Highpass H(s) = s^2/(s^2+s/Q+1)
2.O. Lowpass H(s) = 1/(s^2+s/Q+1)
substitute s=j*wn into the first and take the magnitude and realise that wn = w/ ws = F/Fs and you get:
2.O. Highpass H(s) = Fn^2/sqrt((1-Fn^2)^2+(Fn/Q)^2)
2.O. Lowpass H(s) = 1/sqrt((1-Fn^2)^2+(Fn/Q)^2)
Magnitude in dB = 20 * log10( H(s) )
Good Luck.
2.O. Highpass H(s) = s^2/(s^2+s/Q+1)
2.O. Lowpass H(s) = 1/(s^2+s/Q+1)
substitute s=j*wn into the first and take the magnitude and realise that wn = w/ ws = F/Fs and you get:
2.O. Highpass H(s) = Fn^2/sqrt((1-Fn^2)^2+(Fn/Q)^2)
2.O. Lowpass H(s) = 1/sqrt((1-Fn^2)^2+(Fn/Q)^2)
Magnitude in dB = 20 * log10( H(s) )
Good Luck.
Paul,
I recommend that you read "Acoustics" by Leo Beranek if you really want to understand Thiele and Small's papers. In this excellent textbook the equivalent circuit elements are derived for basic acoustic, mechanical, and electrical modeling of systems as well as the complete acoustic and electrical circuits for closed and ported boxes. I found this book gave me a great foundation so that reading Thiele and Small was much easier and clearer. I could focus on what was being said rather then trying to struggle through all of the background equivalent circuit models and basic acoustics, that the reader is assume to already know, in the Thiele and Small JAES papers.
I recommend that you read "Acoustics" by Leo Beranek if you really want to understand Thiele and Small's papers. In this excellent textbook the equivalent circuit elements are derived for basic acoustic, mechanical, and electrical modeling of systems as well as the complete acoustic and electrical circuits for closed and ported boxes. I found this book gave me a great foundation so that reading Thiele and Small was much easier and clearer. I could focus on what was being said rather then trying to struggle through all of the background equivalent circuit models and basic acoustics, that the reader is assume to already know, in the Thiele and Small JAES papers.
primalsea said:
Any normal speaker in any type of enclosure (including no enclosure) can be considered a bandpass filter.
In a perfect, theoretical world, the phase is a function of the amplitude (frequency) response, so if the amplitude response is not smooth, the phase response will not be smooth either. Maybe if you applied a lot of smoothing, it would like some defined filter shape, but only if the frequency response looked like some defined filter shape when smoothed. In the real world, cone breakup is not necessarily minimum phase which means the phase may go off and do its own thing. In other words, simulating all this is only useful as a theoretical exercise. It will only correlate to getting good sound of real drivers by luck or if you use very flat, extended range drivers to cover very small frequency ranges. If you want to design a real crossover, measure your speakers' magnitude and impedance response in the box they will be in and use that information and a xover simulator to design your speaker.
John
I was only educated to slightly above intermediate level maths at secondary school level. So I dont fully understand transfer functions. I really need someone to show me what buttons to press on the calcuator before I grasp whats going on and start doing things for myself. Yes, its that bad!
Thanks again for the info and the software is still very useful. However, I assumed that the lowpass would be minimum phase and so easy to model. As this is not the case its a good job my planned crossover will be easy to change from various orders & alignments. This means I can just experiment and see (hear) what happens.
Paul
Thanks again for the info and the software is still very useful. However, I assumed that the lowpass would be minimum phase and so easy to model. As this is not the case its a good job my planned crossover will be easy to change from various orders & alignments. This means I can just experiment and see (hear) what happens.
Paul
Thinking about it could someone help.
in alot of calculations it has the term s. I gather for sinewaves s=jw. I know that w=2*pi*f but what is j. I have read it is an imaginary number but I dont understand what Im supposed to do with it.
Can someone show me an example, say a transfer function and also transpose some numbers in to the formula as an example.
I really need some one to show me what buttons to press on my calculator especially for jw. what is jw!!
Paul
in alot of calculations it has the term s. I gather for sinewaves s=jw. I know that w=2*pi*f but what is j. I have read it is an imaginary number but I dont understand what Im supposed to do with it.
Can someone show me an example, say a transfer function and also transpose some numbers in to the formula as an example.
I really need some one to show me what buttons to press on my calculator especially for jw. what is jw!!
Paul
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