I am asked to simulate the following transfer function using operational amplifiers:

Transfer function

Obviously what it evokes is a second order filter, my question is what kind of filter should I use (Butterworth, Biquad, etc) and how should I calculate the components?


3 Answers 3


Rearrange the formula to this: -

H(s) = \$\dfrac{8336.6}{s^2 + s(189.26) + 8952.6}\$

And then note that is of the form: -

H(s) = \$\dfrac{N\cdot\omega_n^2}{s^2 + 2\zeta\omega_n s + \omega_n^2}\$

Numerically derive \$\zeta\$ (damping ratio), \$\omega_n\$ and N and try plugging the values into a sallen key type calculator like this one here: -

enter image description here

I plugged a couple of values in (red circles) that seemed appropriate and the TF (blue rectangle) roughly coincides with what you had in your question

  • \$\begingroup\$ I was wondering, how did you find the 15 Hz frequency? \$\endgroup\$
    – HCalderon
    Nov 5, 2015 at 11:37
  • \$\begingroup\$ @HCalderon \$\omega_n^2\$ = 8952.6 therefore \$\omega_n\$ = 94.618 radians per second = 15.06 Hz \$\endgroup\$
    – Andy aka
    Nov 5, 2015 at 11:46

All that you have to do is to add a derivators with gain based on the operational amplifiers.
Assuming that your transfer function is:

Y(s)/E(s)=d/(as^^2+bs+c), where Y is the output and E is the input
In the temporal presentation you have: Y(t)=(d/c)*E(t)-(b/c)*Y'(t)-(a/c)*Y''(t),
enter image description here

By using analog derivators and adders you can get the output signal y(t). Replace the blocs and the adders with OPA.


You don't need to copy a particular filter. Using analog computer design ideas you can outright build the filer you have. (some gain tweaking may be required) I was trying to find a good reference for you, this is all i could find. Take a look at chapter 3 elementary analog programming. http://www.analogmuseum.org/library/handbook_of_analog_computation.pdf


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