Q. Explain basic working of Integrators?

Figure shows a noninverting integrator, which can be seen to be a negative impedance converter added with a resistor and a capacitor. Noting that v_o = 2v₁ and i₃ = v₁/R, the total capacitor current is

which shows that the circuit functions as an integrator.

Replacing R2 in the inverting amplifier of Figure by a capacitance C results in the somewhat simpler integrator circuit shown in Figure, known as an inverting integrator, or Miller integrator. With ideal op-amp techniques, i_C = i_in = v_in/R. The voltage across C is just vo, so that

which illustrates that the network behaves as an integrator with sign inversion.