# Homework Help: Resonate Frequency of Bandpass Filter

1. May 2, 2012

### p75213

1. The problem statement, all variables and given/known data

See attached.

Can somebody explain how the resonant frequency w0=1/RC. I worked it out by setting imaginary Z(s)=0. The answer I get is j√2 which is obviously wrong. Is it wrong to calculate the resonant frequency in this manner in this case?

2. Relevant equations

3. The attempt at a solution

See Attached
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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2. May 2, 2012

### Staff: Mentor

For a bandpass function, as with any filter, we are interested in Vout/Vin. So they derived this transfer function as H(s) near the bottom of the solution. Are you able to examine that denominator and by relating it to the general second order system describe Ѡn and Q here? (Or the damping ratio, ζ zeta)?

As for your approach, I'm cautious about endorsing shortcuts. But I think it might be valid, thereby allowing you to determine Ѡn at least. But you haven't indicated how you changed Z(s) to something with imaginary terms, so that needs to be checked.

3. May 2, 2012

### p75213

Are you able to examine that denominator and by relating it to the general second order system describe Ѡn and Q here? (Or the damping ratio, ζ zeta)?

No. Are you aware of a good internet resource which explains it?

4. May 2, 2012

### Staff: Mentor

they state that the second-order filter denominator takes the form:

https://www.physicsforums.com/images/icons/icon2.gif [Broken] s² + (Ѡn/Q)s + Ѡ²n

where (Ѡn/Q) is the bandwidth, with Q being the "Q-factor" of the system.

It's well worth memorizing this expression, and what the co-efficients mean.

If you prefer the corresponding one from control theory, it's: s² + 2ζѠns + Ѡ²n
where zeta is the co-efficient of damping and you can see ζ=1/(2Q)

Last edited by a moderator: May 6, 2017
5. May 3, 2012

### p75213

Thanks for that. Makes things somewhat easier than how I was doing it.