I am taking a distance learning "lab" class in EE, using Multisim to simulate circuits at home. Unfortunately, e-mail communications with the professor sometimes does, and sometimes does not, result in clear answers, so once again I'm going straight to the pros.
We are simulating a 741 OpAmp circuit as a low-pass filter. My question is, what is the correct formula for the cutoff frequency? If I understand correctly, the cutoff frequency is the frequency where the output falls to 1/sqrt(2) = .707 of the input voltage. The circuit is shown at:
The measured cut-off frequency is around 300 Hz (1884 radians). And, using the formula for Vout (which I do have), and plugging in various values for w_in, I eventually find the cutoff frequency to be almost exactly 310 Hz (1947 radians).
The lab manual for the circuit does not give the formula. The textbook has a similar-but-not-identical circuit, for which the formula for the cutoff frequency is (referring to the diagram) w_cutoff = 1 / (C2 * R4). However, this formula is not really for the circuit we are simulating, and in fact does not give the correct cut-off frequency.
Hunting on the Web, I found what seems to be an identical looking circuit, and the cutoff frequency is given by: w_cutoff = 1 /sqrt (R2 * R4 * C1 * C2)
Once again, however, this does not give the actual, measured value for the cutoff frequency. Working from the formula for the output voltage, I tried to find the formula for w_cutoff myself, but got lost in a blizzard of algebra. If someone could tell me the correct formula -- and better yet, steer me towards a derivation somewhere on the Web -- that would be much appreciated.
FYI, the formula I arrived at for the output voltage is: Vout = ( Vin / R2 ) / [ (R4/c1) * (1/R2 + 1/c2) + 1/c1 + 1/R2 ];
where cn = 1 / ( j * w * Cn )
(One other thing that would be useful -- if someone could take the formulas above, and show me how to use Matlab to get the symbolic result for w_cutoff. I got stumped on that one as well!)
Thanks in advance for all replies.
Steve O.
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