Op amp filter

1. Sep 16, 2007

engineer23

1. The problem statement, all variables and given/known data

We have a filtered amplifier (diagram is attached). We do not know Cf or Rf.
We know that:
1 volt input at 5 Hz = 9.25 volt output
1 volt input at 200 Hz = 6.77 volt output
1 volt input at 500 Hz = 3.66 volt output

2. Relevant equations

The transfer function for the first amplifier is H(w) = -Zf/Zi = -10000/2000=-5
The transfer function for the second amplifier is H(w) = -Zf/Zi, where Zi = 5000 and
Zf = Rf/(Rf j w Cf + 1).

3. The attempt at a solution
If we multiply the two transfer functions above, we obtain
H(w) = V0/Vi = Rf/(1000(Rf j w Cf + 1))

I multiplied the frequencies by 2*pi and made appropriate substitutions in the above equation to get the following three expressions:
9.25 = Rf/(1000(31.4159 Rf j Cf + 1))
6.77 = Rf/(1000(1256.64 Rf j Cf + 1))
3.66 = Rf/(1000(3141.59 Rf j Cf + 1))

Three equations for only two unknowns?

I get that Cf = -5.3E-8 i and Rf = 9395.

What am I doing wrong?

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2. Sep 17, 2007

antonantal

Since you are only given the magnitudes (and not the phases) of the input and output signals you must work with the absolute value of the transfer function.