- #1
╔(σ_σ)╝
- 839
- 2
Homework Statement
I have a transfer function from a second order chebyshev filter and the general transfer function of a sallen-key circuit. I have some questions.
Homework Equations
I am using a 2nd order low-pass filter sallen key on page 8 of this pdf :http://focus.ti.com.cn/cn/lit/an/sloa024b/sloa024b.pdfMy R1 and R2 are the same and I have only one value of C1 and C2.
For the Sallen-key I know the tranfer function is
[tex] H \left( s \right) = \frac{k w^{2}}{ s^{2} + \frac{w}{Q}s + w^2} [/tex]
For a chebyshev filter I have a second order transfer function as follows [tex] H \left( s \right) = \frac{1}{ s^{2} + 0.1705s + 0.903} [/tex]
I know that [itex] K = 3 - \frac{1}{Q} [/itex]
K is my Gain.
[tex] k = 1+ \frac{R_{b}}{R_{a}}[/tex]
The Attempt at a Solution
My problem is that if I use the equation [itex] K = 3 - \frac{1}{Q} [/itex] I get a different value for K than if I use the equation [itex] k = \frac{1}{w^2} [/itex]
I got the equation [itex] k = \frac{1}{w^2} [/itex] from inspecting the transfor function of the Sallen-Key and noticing that [itex] kw^{2} = 1[/tex] for the chebyshev TF.
Apparently, the equation is not correct but I don't know why. I would like someone to shed more light on this.
Last edited: