How to derive the crossover frequency given component values

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vinnybhaskar

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Joined 2006
#1
Ok so I want this backwards. All passive crossover calculators I have come across till now provide you the capacitor and inductor values to be used for a given crossover frequency. What is the formula to derive the crossover frequency given the component value? I'm looking for formulas for 1st, 2nd and 3rd order Butterworth filters.

Secondly, I hope the formula accounts for both the capacitance and inductance (rather than being calculated using individual formulas), so that when XO frequency and let's say the capacitance value is given, we can derive the inductance.

Vinny
 
#3
ppfred said:
Vinnie try a little math.

if a=b*c then b=c/a. Get it?

Your home work:
if x = ((y+c)/2 + (z*b))/c
find the value of b.

Not that hard. Tedious but not hard.
Click to expand...

Well, I know there's math involved and how a=b*c then b=c/a works. However, I cannot get to the math till I know the formula (equation) involved.

So, if you read my post, I asked for the formula, which unfortunately is not shown by any of the XO calculators out there that I came across.
 
#5
#7
Lojzek said:
I don't know how this math of yours works 🙂.

If 6=2*3, then 2=3/6 or b=1/b

I'm very sorry for I don't have the formulae you are looking for.
I'll try to do something about it.
Click to expand...

Lojzek, you got me there! I never validated the correctness of the equation by ppfred. I just copied pasted what he wrote. It was nothing but trolling. I never asked for coaching in elementary math. All I asked was for the correct formulas used for calculations in the Butterworth filter.
 
#8
vinnybhaskar said:
Ok so I want this backwards. All passive crossover calculators I have come across till now provide you the capacitor and inductor values to be used for a given crossover frequency. What is the formula to derive the crossover frequency given the component value? I'm looking for formulas for 1st, 2nd and 3rd order Butterworth filters.

Secondly, I hope the formula accounts for both the capacitance and inductance (rather than being calculated using individual formulas), so that when XO frequency and let's say the capacitance value is given, we can derive the inductance.

Vinny
Click to expand...

since you don't really know the filter alignment you can calculate the 2 corner frequencies. their spacing might give you idea.

best answer plug crossover values into a spice model and simulate with a load E.g. speakers Le and Re. now look where they cross over while adjusting for driver sensitivities.
 
#10
With a second order filter, half the story is in the frequency of resonance between the capacitor and inductor. The rest is in the damping, or load, and the acoustic response of the speaker. No straight answers here.

LC - fresonance:

1/(sqr(LC)*6.3)
 
#11
vinnybhaskar said:
All I asked was for the correct formulas used for
calculations in the Butterworth filter.
Click to expand...

BW1:

Rtw=1/(2*pi*Fc*C)

Rw=2*pi*Fc*L

BW2:

Rtw=1/(2*sgrt(2)*pi*Fc*C1)

Rw=1/(2*sqrt(2)*pi*Fc*C2)

Rtw=sqrt(2)*pi*Fc*L1

Rw=sqrt(2)*pi*Fc*L2

BW3:

Rtw=1/(3*pi*Fc*C1)

Rtw=1/(pi*Fc*C2)

Rw=2/(3*pi*Fc*C3)

Rtw=(8*pi*Fc*L1)/3

Rw=(4*pi*Fc*L2)/3

Rw=4*pi*Fc*L3

Rtw= tweeter's rated impedance (ohms)
Rw= woofer's rated impedance (ohms)
Fc=crossover frequency(Hz)
L= inductance (H)
C= capacitance (F)
 
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