Op-Amp Integrator Basics: how it works as better Low Pass Filter

This video compares the classic passive RC low-pass filter with the active inverting op-amp integrator (one input resistor and a feedback capacitor). We draw an approximate Bode diagram and show how negative feedback with an operational amplifier “boosts” the effective time constant, so the apparent RC increases roughly by the loop gain A. That means you can hit the same cutoff f_c with much smaller components: an op-amp can make a small C_f behave like a much larger capacitor (or a small R_in act like a larger resistor), at the cost of using an amplifier and loading it. For the passive RC low-pass we recall H(s) = 1/(1 + s R C) with corner f_c = 1/(2π R C). For the ideal inverting integrator we use V_out/V_in = −1/(R_in C_f s), the −20 dB/dec slope and −90° phase in its valid band, and explain real-world finite open-loop gain. We discuss the role of the virtual short at the inverting node, why a bleed resistor across C_f is often added to tame DC drift, how finite A_OL and the dominant pole limit the “RC multiplication,” and practical design checks (choose C_f, compute R_in = 1/(2π f_c C_f), . By the end you’ll understand when an op-amp integrator behaves like a low-pass filter, what you gain in size and flexibility, and the trade-offs in accuracy, stability, and op-amp loading.

0:00 Op-Amp Integrator as LPF
3:46 Classic (Passive) Low Pass Filter