I confess that since I’ve begun designing passive crossovers, I’ve never use any other crossover slopes except the second-order. The reason is I don’t know how to deal with it without calculators. Lol
Thanks to Dickason’s cookbook, it provides a formula for calculating the Q-factor of the second-order filters. And I always utilize it. But that is limited for the second-order only.
Therefore, I wonder whether the other ordered crossovers; the 1st, 3rd, and 4th, have Q-factor?
And I’d like to ask everyone to share your designing procedure of any crossover orders besides the second-order filter.
For me, with second-order design, I use the standard resonance formula to find the corner frequency and, then, use the Q-factor formula, available in Dickason’s textbook, to find or adjust L/C values to achieve the desire Q.
Please share your procedures on other ordered crossovers to us.
Thanks to Dickason’s cookbook, it provides a formula for calculating the Q-factor of the second-order filters. And I always utilize it. But that is limited for the second-order only.
Therefore, I wonder whether the other ordered crossovers; the 1st, 3rd, and 4th, have Q-factor?
And I’d like to ask everyone to share your designing procedure of any crossover orders besides the second-order filter.
For me, with second-order design, I use the standard resonance formula to find the corner frequency and, then, use the Q-factor formula, available in Dickason’s textbook, to find or adjust L/C values to achieve the desire Q.
Please share your procedures on other ordered crossovers to us.
Any high-order transfer function can be decomposed into the product of 2nd-order sections (if even), or 2nd-order sections plus one 1st-order section (if odd). Each 2nd-order section will have its associated Q. Some people define the Q of the 1st-order section to be 1/sqrt(2) for mathematical convenience. The individual Q values are independent, though there are occasionally some relationships between them: for example, in a Butterworth filter the product of the Qs is 1/sqrt(2).
So, could it be concluded that the Q value of the 3rd-order filter could be simply calculated by the product of the 2nd-order’s Q and 1/sqrt(2)?
Attached is the formula of Q of the 2nd-order filters provided in Dickason’s cookbook.
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One must be careful about generalizing. It happens that a 3rd-order Butterworth filter consists of a 2nd-order filter with Q=1 plus a 1st-order filter, but the same cannot be said of higher-order filters.