I have rigged up a notch filter from here. See below: -

enter image description here

Its the first circuit. Now I am trying to calculate its transfer function. I have calculated two equations, but I need the third one:

  1. (Vin-V2)/(1/SC1) = V2/R3
  2. (Vin-V1)/R1 = (V1-Vo)/(R2+(1/SC2))

V1 and V2 are the potentials at the input of the op-Amp.

  • 1
    \$\begingroup\$ As long as the opamp works in its linear region you can set V1=V2 (because the open-loop gain is very large). \$\endgroup\$
    – LvW
    Jun 10 '16 at 7:20
  • \$\begingroup\$ I didn`t check your two equations - however, did you forget the R4 path? \$\endgroup\$
    – LvW
    Jun 10 '16 at 10:01
  • \$\begingroup\$ This filter doesn't work. So now I need to design a new filter. \$\endgroup\$ Jun 11 '16 at 10:05
  • \$\begingroup\$ Interesting circuit, without R4 and C2 this circuit look just like a ordinary all pass filter. \$\endgroup\$
    – G36
    Jun 12 '16 at 12:01

Assuming an ideal op-amp, you have \$v_1=v_2\$ (as pointed out in a comment by LvW). Also note that your second equation is wrong because there is a current into or out of the output of the op-amp, so you can't just add up the impedances of \$R_2\$ and \$C_2\$.

Introducing another unknown voltage \$v_x\$ at the output of the op-amp, you can write down three equations:

$$(v_i-v_1)sC_1-v_1/R_3=0\\ (v_i-v_1)/R_1+(v_x-v_1)/R_2=0\\ (v_i-v_o)/R_4-(v_o-v_x)sC_2=0$$

where \$v_i\$ and \$v_o\$ are the input and output voltages, respectively, and \$v_1\$ is the voltage at both inputs of the op-amp. These equations can be solved for the transfer function \$H(s)\$, i.e., for the ratio \$v_o/v_i\$. With \$C=C_1=C_2\$ and \$R=R_3=R_4\$ and \$R_1=R_2\$ you get


From the numerator of \$(1)\$ you immediately get for the notch frequency


Note that as long as you choose \$R_1=R_2\$, the actual value of these resistors doesn't show up in the transfer function.


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