Explain about differentiator, Electrical Engineering

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Q. Explain about Differentiator?

Shown in Figure is a differentiator which is obtained by replacing R1 in the inverting amplifier of Figure by a capacitor C. Assuming ideal op-amp characteristics, one has i = iC and vo = - Ri = - RiC. But since iC (t) = Cdvin (t) /dt ,we get

vo (t) = - RC dvin (t) / dt

which corresponds to a differentiator with a gain of -RC. In practice, however, differentiators are normally avoided because of high-frequency noise (which is accentuated due to a transfer function that increases with frequency) and stability problems (which make them oscillate).

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