= Op amp integrator
{wiki}
An <op amp integrator> places a <resistor> $R$ between the input source and the inverting input of an <operational amplifier>, and a feedback <capacitor> $C$ between that input and the output, with the non-inverting input grounded. For an <ideal operational amplifier>, <Kirchhoff's current law> gives $v_{\mathrm{in}}/R=-C\,dv_o/dt$, hence
$$
v_o(t)=v_o(t_0)-\frac1{RC}\int_{t_0}^t v_{\mathrm{in}}(u)\,du,\qquad H(s)=-\frac1{sRC}.
$$
The initial capacitor charge supplies the integration constant. A parallel feedback <resistor> $R_f$ replaces the transfer by $H(s)=-(R_f/R)/(1+sR_fC)$: the direct-current gain becomes finite while integration is recovered when $|sR_fC|\gg1$. This limits offset-driven saturation. https://wiki.analog.com/university/courses/electronics/text/chapter-2[Analog Devices, Chapter 2, integrator and parallel feedback resistance]{ref}
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