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 = i_C and v_o = - R_i = - Ri_C. But since i_C (t) = Cdv_in (t) /dt ,we get

v_o (t) = - RC dv_in (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).