# what's the formula for 3rd order Butterworth ???

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#### bbaker6212

I need to make some calculations for a 3rd order high-pass butterworth using the formula, not online calculators. Anyone know what the formula is?

#### Jocko Homo

(s^2)/(s^2 + x*s + y) + (s/s+z)

That's the formula. What you also need are the coefficients.

Second-order section: f = 1.0, damping (the 'x' term......) = 1.0

First order section: f = 1.0

"Active Filter Cookbook", by Don Lancaster. Buy a copy.

Jocko

#### f4ier

Jocko, wouldn't you think that someone with knowledge of circuit analysis in the s-domain wouldn't be asking such a relatively simple question? bbaker6212, I hope these formulas help.

For HP section with nominal resistance, Rh:

C1 (uF) = 1000000/(3*pi*Fc*Rh)
L1 (mH) = 3000*Rh/(8*pi*Fc)
C2 (uF) = 1000000/(pi*Fc*Rh)

For LP section with nominal resistnace, Rl;

L2 (mH) = 3000*Rl/(4*pi*Fc)
C3 (uF) = 1000000/(1.5*pi*Fc*Rl)
L3 (mH) = 1000*Rl/(4*pi*Fc)

C1/L2, L1/C3 and C2/L3 form a "T" circuit with the other terminals of: C1/L2 pointing towards the amp, C2/L3 points towards the speaker(s) and L1/C3 towards the ground.

Isaac

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