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Multi-Way Conventional loudspeakers with crossovers

Formulae for calculating crossover magnitude and phase based on component values
Formulae for calculating crossover magnitude and phase based on component values
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Old 7th March 2008, 10:34 AM   #1
alexclaber is offline alexclaber  United Kingdom
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Default Formulae for calculating crossover magnitude and phase based on component values

I'm looking to build a spreadsheet into which I can enter speaker SPL and phase and then inductor and capacitor values for given crossover networks and get a summed output. To do this I need the formulae for the effects of inductors and capacitors on signals but I can't seem to find this basic stuff. Could anyone point me in the right direction?

Am just looking to do 2nd order 2-way crossovers initially but presumably once you know the sums then one can extrapolate from there.

Thanks!

Alex
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Old 7th March 2008, 09:45 PM   #2
Ron E is offline Ron E  United States
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Look for Jeff Bagby's Passive Crossover Designer. It does what you want without needing to know the formulas.

Someone could give you the formulas, but they would have to type it all out.... and then not know if you even know how to use them. In my mind, if you knew how to use them, you could derive them yourself.
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Old 8th March 2008, 09:29 AM   #3
alexclaber is offline alexclaber  United Kingdom
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Quote:
Originally posted by Ron E
Look for Jeff Bagby's Passive Crossover Designer. It does what you want without needing to know the formulas.

Someone could give you the formulas, but they would have to type it all out.... and then not know if you even know how to use them. In my mind, if you knew how to use them, you could derive them yourself.
Thanks, have downloaded that. I do have a fair understanding of how this stuff works, I guess my engineering degree is finally proving useful. If I knew how to use them completely then I probably could derive them, however I am learning the fine details of all this and thus would need more info before I could work back from first principles.

Alex
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Old 8th March 2008, 03:06 PM   #4
cabbagerat is offline cabbagerat  South Africa
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Default Re: Formulae for calculating crossover magnitude and phase based on component values

Quote:
Originally posted by alexclaber
I'm looking to build a spreadsheet into which I can enter speaker SPL and phase and then inductor and capacitor values for given crossover networks and get a summed output. To do this I need the formulae for the effects of inductors and capacitors on signals but I can't seem to find this basic stuff. Could anyone point me in the right direction?
Draw the schematic, replace the capacitors with a resistor with resistance 1/(j 2 pi f C) (j is sqrt(-1), f is frequency, and C is the original capacitance), and the inductors with (j 2 pi f L). Then, treat the crossover like a normal resistor network, and derive a symbolic (function of f) transfer function.

Plot the magnitude of that function versus f for the magnitude response, and the phase versus f for the phase response. This approach is accurate and easy - if you aren't afraid of complex numbers.
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Old 8th March 2008, 06:20 PM   #5
gootee is offline gootee  United States
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If you're going to draw a schematic, you might as well draw it in LTspice (free from linear.com) and have the entire magnitude and phase response plotted automatically.

You will probably want to remember to include the parasitic series resistances of inductors and capacitors.
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Old 19th March 2008, 07:35 PM   #6
alexclaber is offline alexclaber  United Kingdom
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Have been messing with LTspice and also working on an excel spreadsheet. Suffice to say that my brain is melting...

Whilst I get my head round all that I've designed a simple 2nd order Butterworth crossover @ 750Hz (as this bass cab will rarely be on-axis I felt the flatter power response was more important than on-axis response). Have used the actual impedance at that point, not nominal impedance for the component calculation.

Hopefully as the impedance stays +50%/-20% an octave either side of the crossover point, the filter response won't be too far from theoretical?

Alex
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Old 19th March 2008, 11:08 PM   #7
Svante is offline Svante  Sweden
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Here is how to do a 2nd order lowpass to get you started

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Old 20th March 2008, 08:17 AM   #8
alexclaber is offline alexclaber  United Kingdom
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Thanks!

Can I just clarify a couple of things on there?

U0/U1 is the transfer function.

R is the resistance of the inductor.

|U0/U1| is the magnitude of the transfer function.

To calculate how the woofer and midrange combine acoustically, I presume I also need the argument (phase) of the transfer function?

Alex
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Old 20th March 2008, 04:08 PM   #9
Svante is offline Svante  Sweden
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Quote:
Originally posted by alexclaber
Thanks!

Can I just clarify a couple of things on there?

U0/U1 is the transfer function.
Yes, it is the ratio between the output voltage u0 and the input voltage u1, as in the circuit diagram.

Quote:
Originally posted by alexclaber

R is the resistance of the inductor.
No, the inductor is ideal. R is the load resistance. Simplified, it can be seen as the loudspeaker, but mostly that is an oversimplification that gives rather large errors.

Quote:
Originally posted by alexclaber


|U0/U1| is the magnitude of the transfer function.
Yes.

Quote:
Originally posted by alexclaber


To calculate how the woofer and midrange combine acoustically, I presume I also need the argument (phase) of the transfer function?

Alex
The phase is present in the u0/u1 equation, there is a "j" in there which makes the expression a complex number. Complex numbers have a magnitude and a phase, and I derived the magitude from that, only.

However, it messes things up if you start to split the equation into magnitude and phase and try to add them afterwards. It is better to just add the two complex transfer functions.

Are you familiar with complex numbers and the jw-metod?
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Old 20th March 2008, 06:40 PM   #10
sreten is offline sreten  United Kingdom
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Hi,

Why are you doing this ? It may save time making a set of purely
theoretical calculations. The reality is real crossovers done properly
bear little resemble to any simplistic approach, which this is.

You can go on line to easily find the simplistic (and wrong) values.

http://www.mhsoft.nl/CrossoverNetwor...udspeakers.asp

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