= Non-inverting operational amplifier
{title2=$K=1+R_f/R_g$}
A <non-inverting operational amplifier> applies the signal to its non-inverting input and returns part of the output to its inverting input through <negative feedback>. Connect <resistor> $R_f$ from the output to the inverting input, and <resistor> $R_g$ from that input to a reference <circuit node> at <electric potential> $V_{\rm ref}$.
In stable, unsaturated ideal operation, the inputs draw no <electric current> and their <electric potentials> are equal. Writing the signal as $V_{\rm in}$, <Kirchhoff's current law> at the inverting input gives
$$
\frac{V_{\rm in}-V_{\rm out}}{R_f}+\frac{V_{\rm in}-V_{\rm ref}}{R_g}=0,
$$
so
$$
V_{\rm out}=\left(1+\frac{R_f}{R_g}\right)V_{\rm in}-\frac{R_f}{R_g}V_{\rm ref}.
$$
For a grounded reference <circuit node>, the <voltage gain> is $1+R_f/R_g$. For example, $R_f=20\,\mathrm{k\Omega}$ and $R_g=10\,\mathrm{k\Omega}$ give gain three. The equal-input-potential approximation requires sufficiently large <loop gain>; <amplifier saturation> or unstable feedback invalidates it.<Operational-amplifier negative feedback by Analog Devices>[Sections 3.2–3.2.3, ideal input-error suppression, non-inverting gain and loop-gain limitations]{ref}
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