Second-order filter terminology

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jp1390

Joined Aug 22, 2011
45
Hi, I just have a couple questions about some of the terminology for the frequencies present in these types of filters. I was taught that all four specific filter types, (LPF, HPF, BPF, and BSF), could be formulated from this general formula:

\(T(s) = \frac{A_{2}s^{2} + A_{1}s + A_{0}}{s^{2} + (\frac{w_{0}}{Q})s + w_{0}^{2}}\)

Where,

LPF:
\(A_{2} = A_{1} = 0\)
\(A_{0} \neq 0\)

HPF:
\(A_{1} = A_{0} = 0\)
\(A_{2} \neq 0\)

BPF:
\(A_{2} = A_{0} = 0\)
\(A_{1} \neq 0\)

BSF:
\(A_{1} = 0\)
\(numerator = A(s^{2} + w_{0}^{2})\)

I am having trouble understanding what the -3dB frequency of second-order LPF and HPF are, as they each have two pole frequencies. Setting the magnitude of the response to 0.707 more than one frequency.

My question is, since you can have different RC values for say a Sallen-Key LPF/HPF, how do you know which of the pole frequencies will be the -3dB frequency or is it neither and some value in between as you will receive two poles when you solve the quadratic equation?

Also, is w0 the relaxation oscillation frequency that is produces the maximum peak determined by Q right before (LPF) or after (HPF) the -3dB break (corner) frequency?

Thanks a lot!
JP
 
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