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25th September 2017, 04:10 PM  #1 
diyAudio Member
Join Date: Nov 2014

How to calculate SPL with filters in Excel
Hi there,
Maybe this is stupid question but I have never been good in math. I made xls spreadsheet where I can calculate SPL, excursion, impedance and power of driver in sealed boxes in function of frequency. I am struggled becouse I also would like to calculate transfer function of various filters in Excel and to plot its influence on SPL curves. Unfortunately I cannot find clear and easy to implement set of formulae to calculate it in function of frequency giving Q, f and n of the filters. Do you know good source of such formulae? Thanks! What I need to do (this is only an example): filter: Butterworth order: 2 corner freq: 10 Hz freq. raw SPL filtered SPL 10 Hz 60 dB 55 dB 11 Hz 62 dB 53 dB 12 Hz 64 dB 51 dB 13 Hz 66 dB 49 dB Thanks! 
26th September 2017, 12:44 AM  #2 
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Join Date: Jun 2002
Location: USA, MN

2nd order transfer functions
HP H(s)=s^2/(s^2+s*wo/Q+wo^2) LP H(s)=wo^2/(s^2+s*wo/Q+wo^2) wo=filter cutoff s=complex frequency Q is Q Butterworth Q is 0.707 Linkwitz Riley 0.5 Bessel 0.577
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26th September 2017, 12:29 PM  #3 
diyAudio Member
Join Date: Nov 2014

Thanks,
But still I quite don't know how to interpret "complex frequency" term. If I substitute 's' with sound frequency in cycles per second (Hz) I am still getting wrong results from this formulae. 
26th September 2017, 02:09 PM  #4 
diyAudio Member
Join Date: Oct 2008

This guy talks about doing complex number calculations in Excel:
Complex Numbers in Excel  EngineerExcel If you don't want to go through all that, you could use these formulas (see enclosed picture).
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26th September 2017, 02:35 PM  #5 
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Join Date: Jul 2004
Location: Scottish Borders

your results Raw vs Filtered show the SPL going down as frequency increases.
This seems to be a low pass filter. Surely your 10Hz filter should be a high pass.
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regards Andrew T. 
26th September 2017, 05:19 PM  #6  
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Join Date: Nov 2014

Quote:


26th September 2017, 06:07 PM  #7 
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Join Date: May 2008


26th September 2017, 06:11 PM  #8 
diyAudio Member
Join Date: Mar 2007
Location: Michigan

I became very skilled at Excel filter calculations when I wrote my "Active Crossover Designer" Excel tools. See my web page:
the Active Crossover Designer web page You need to be able to calculate the filer response using complex numbers. The complex number includes an amplitude and phase component. At the end you back out the scalar quantities magnitude and phase from the complex number and convert magnitude to SPL and phase to degrees. Excel has a set of built in complex number functions that are very complete, but a bit clumsy to work with. My ACD spreadsheets do not include any hidden sheets and all formulas can be looked at. You are welcome to use them as a resource on how to do filter calcs in Excel, and then create your own version or feel free to use ACD. 
26th September 2017, 09:07 PM  #9 
diyAudio Member
Join Date: Nov 2014

Great Thanks Charlie!
Your formulas and overal level of Excel operations inside are well beyond my level of understanding and imagination. I've got few inspirations from you for troubleshooting and handling of my simple formulas. I don't know how you've made logscaled x axis but there it is (I wasn't able to do it on my own) so I've borrowed your graph layout to my spreadsheet if you don't mind. To everyone. I am working on one tool which can help user to design his own magnetic circuit and voice coil inside of driver. It can approximate magnetic flux density inside the gap from given neo magnet ring (or slug) dimensions. User can enter gap dimensions and VC parameters like wire gauge, number of layers, conductor type and shape, VC height etc. Then every parameter can be calculated like BI, Re, geometric Xmax, Qes etc... Then, such a driver with spec'ed by the user cone and motor properities can be simulated in sealed box and compared with production driver's database. It is still much work to be done... Last edited by Windforce85; 26th September 2017 at 09:10 PM. 
26th September 2017, 09:08 PM  #10  
diyAudio Member
Join Date: Oct 2008

Quote:
For a single order lowpass filter and highpass filter, we have as you see in the attached picture, where f3 is the 3 dB corner frequency. Of course, if you're looking for a general approach, Charlie's way may be the one for you.
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