| Electronics > Beginners |
| Notch active filter transfer function |
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| alex.martinez:
--- Quote from: MrAl on April 07, 2019, 07:34:03 am ---Hi, I got this for the transfer function: ((s^2*C1*C2*R1*R3-s*C2*R2)*R4+s*C1*R1*R3+R1)/((s^2*C1*C2*R1*R3+s*C2*R1)*R4+s*C1*R1*R3+R1) That might be the same but i did not check. I came up with bandwidth and Q but the expressions were a little too complicated. I'd have to try to simplify them a little. Also, the Q will depend on component selection accuracy and op amp open loop gain so an true expression would have to include some other things besides the component values, except in theory of course. If you ever worked with a passive notch filter you would see how critical component selection can be in order to get a deep notch. I have graphs of the notorious passive twin T notch filter around i'll look up if you are interested. --- End quote --- Yes, looks good (the natural frequency is included in the TF, so I guess it's correct). I always try to leave s^2 alone and then obtain the parameters from the "canonical" 2nd order response. Here is my solution to the TF which, I believe, is the same as yours and the one posted by kulky64. |
| kulky64:
How did you arrive from wo/Qp=1/(R3*C1)+1/(C2*R4) to Qp=wo^(-1)/(C2*R4+R3*C1) ? |
| MrAl:
--- Quote from: kulky64 on April 07, 2019, 01:05:52 pm ---How did you arrive from wo/Qp=1/(R3*C1)+1/(C2*R4) to Qp=wo^(-1)/(C2*R4+R3*C1) ? --- End quote --- Hi, That does not look correct. wo/Q is just the same as wo/(wo/BW) which equates to just BW. SO that means BW=1/(R3*C1)+1/(C2*R4) and there is no R1 or R2 in there. Anybody test that yet? |
| The Electrician:
--- Quote from: kulky64 on April 07, 2019, 01:05:52 pm ---How did you arrive from wo/Qp=1/(R3*C1)+1/(C2*R4) to Qp=wo^(-1)/(C2*R4+R3*C1) ? --- End quote --- I assume you're referring to the algebra mistake? Edit: In the second image in reply #10, the algebra leading from the expression wo/Qp = 1/(R3 C1) + 1/(C2 R4) to the expression Qp = (wo^-1)/(C2 R4 + R3 C1) would be incorrect if it weren't for the definition of wo as 1/sqrt(R3 R4 C1 C2). Considering only the apparent algebraic manipulation from the first expression to the second, the algebra appeared to be mistaken. Taking into account the definition of wo, all is well. Setting R3 and R4 to 10k ohms, and C1 and C2 to .01 uF, we get these numerical values for various expressions. The second expression for Q in the image below comes from reply #2, and appears to be incorrect. |
| MrAl:
--- Quote from: The Electrician on April 07, 2019, 06:34:53 pm --- --- Quote from: kulky64 on April 07, 2019, 01:05:52 pm ---How did you arrive from wo/Qp=1/(R3*C1)+1/(C2*R4) to Qp=wo^(-1)/(C2*R4+R3*C1) ? --- End quote --- I assume you're referring to the algebra mistake? --- End quote --- Hi, What that formula actually tested yet though? |
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