Analog Electronics

Op-Amp Integrator

Thanks to the virtual ground at the inverting input, the input current is Vin/R and all of it flows into the feedback capacitor: the output is the negative of the input’s integral.

Feed in a square wave and the output becomes a triangle wave made of linear ramps — this is the triangle core of function generators. Feed in a sine and out comes a sine shifted 90° in phase (−cos).

An ideal integrator also integrates DC offset and drifts into saturation; in practice a large resistor (Rf) in parallel with C limits the low-frequency gain and keeps the circuit stable.

Formulas

Vout = −(1/RC)·∫Vin dt

Triangle peak ≈ Vin·T/(4RC)

DC gain limit = −Rf/R

⚡ Open this lesson in the simulator — free

Test Yourself

If a square wave is fed into an integrator, what is the output?

Answer: Triangle — The integral of a constant input is a linear ramp → triangle.

Why is Rf (in parallel with C) added?

Answer: To keep DC offset from driving the output into saturation — Rf limits the DC gain to −Rf/R; drift cannot accumulate.

← Relaxation Oscillator (Astable) Difference Amplifier and CMRR →