Electronics Handbook/Circuits/Operational Amplifier Configurations

Linear Configurations

Type	Configuration	${\frac {V_{o}}{V_{i}}}$
Inverting amplifier		$V_{\mathrm {out} }=-V_{\mathrm {in} }\left({R_{f} \over R_{1}}\right)$
Non-inverting amplifier		$V_{\mathrm {out} }=V_{\mathrm {in} }\left(1+{R_{2} \over R_{1}}\right)$
Voltage follower		$V_{\mathrm {out} }=V_{\mathrm {in} }\!\$
Summing amplifier		$V_{\mathrm {out} }=-R_{\mathrm {f} }\left({V_{1} \over R_{1}}+{V_{2} \over R_{2}}+\cdots +{V_{n} \over R_{n}}\right)$
Integrating amplifier		$V_{\mathrm {out} }=\int _{0}^{t}-{V_{\mathrm {in} } \over RC}\,dt+V_{\mathrm {initial} }$
Differentiating amplifier		$V_{\mathrm {out} }=-RC\left({dV_{\mathrm {in} } \over dt}\right)$
Schmitt trigger		Hysteresis from ${\frac {-R_{1}}{R_{2}}}V_{sat}$ to ${\frac {R_{1}}{R_{2}}}V_{sat}$
Inductance gyrator		L = R_LRC
Negative impedance converter		$R_{\mathrm {in} }=-R_{3}{\frac {R_{1}}{R_{2}}}$
Logarithmic configuration		$v_{\mathrm {out} }=-V_{\gamma }\ln \left({\frac {v_{\mathrm {in} }}{I_{\mathrm {S} }\cdot R}}\right)$
Exponential configuration		$v_{\mathrm {out} }=-RI_{\mathrm {S} }e^{v_{\mathrm {in} } \over V_{\gamma }}$