I need help in designing a differentiator using an op-amp. I know that the equation for an op-amp differentiator circuit is Vo = RCdVin/dt, but I don't know how to calculate the component values to finish the design. All of the web resources that I have viewed so far shows the characteristic equation of the differentiator, but they don't give any guidance as to how to calculate the actual values. Can somebody help me with this please?
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2 Answers
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That formula is all you need...in theory.
In practice the circuit tends to be unstable due to the capacitance on the input interacting with the finite bandwidth of the op-amp. This is remedied by placing a resistor in series with the input capacitor:
This link gives an elementary explanation of why this works. It will also modify your differentiating characteristic somewhat, adding a pole at 1/(2*pi*R1*C1) So basically, it's an ideal differentiator at lower frequencies only. A more complete explanation of the stability issue can be found here.
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There isn't much more to it, note that it should be inverting, ie, Vo = -RCdVin/dt, RC is the gain you want for the system, so choose either R or C and calculate the other. For plain differentiation with unity gain solve 1=RC with R or C being any value of your choosing.
