I am trying to figure out the transfer function for this bandpass filter (images below). I am sorry for badly drawn circuit. The operational amplifier is an ideal op amp.

I'd like to know if I correctly analyzed the circuit. I don't think so because when I try to simplify the transfer function into bandpass filter transfer function, something seems to be off.

enter image description here

enter image description here


1 Answer 1


By nodal analysis, using \$\large\Sigma\$(currents away from node) = 0:

Let \$\small V\$ be the voltage at the \$\small R_1,\: R_2,\: C_3,\: C_4\$ node, then:


And, at the summing junction node:


Eliminating \$\small V\$:


  • \$\begingroup\$ Thanks Chu for the answer. On your nodal analysis, You used +V/R2. Is it because R2 is directly branched by the ground? (the current runs from low voltage to high voltage) \$\endgroup\$
    – user167987
    Commented Nov 25, 2017 at 14:45
  • \$\begingroup\$ ALWAYS use the rule: sum of currents AWAY from each node =0. This helps to avoid errors due to getting the signs wrong. In each numerator term, the node voltage under consideration will appear first, once again minimising sources of error. \$\endgroup\$
    – Chu
    Commented Nov 25, 2017 at 18:22
  • \$\begingroup\$ You have an $R_3$ in your answer but there's no $R_3$ in the schematic \$\endgroup\$
    – Andrew
    Commented Aug 20, 2019 at 4:08
  • 1
    \$\begingroup\$ @Andrew Typo ... \$Z_3\$. Thanks \$\endgroup\$
    – Chu
    Commented Aug 22, 2019 at 21:54
  • \$\begingroup\$ user167987...after inserting Z3=1/sC3 and Z4=1/sC4 into the equation you should rewrite/simplify the formula with the goal to have the form: sT1/(1+sT2+s²T²). with T=R*C. This is the classical bandpass form for identifying bandwidth and midfrequency. \$\endgroup\$
    – LvW
    Commented Aug 23, 2019 at 9:37

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