Electronics Handbook/Circuits/Operational Amplifier Configurations

Linear Configurations

Type	Configuration	$\frac{V_o}{V_i}$
Inverting amplifier		$V_{\mathrm{o}\mathrm{u}\mathrm{t}}=-V_{\mathrm{i}\mathrm{n}}\left(\frac{R_f}{R_1}\right)$
Non-inverting amplifier		$V_{\mathrm{o}\mathrm{u}\mathrm{t}}=V_{\mathrm{i}\mathrm{n}}(1+\frac{R_2}{R_1})$
Voltage follower		$V_{\mathrm{o}\mathrm{u}\mathrm{t}}=V_{\mathrm{i}\mathrm{n}}$
Summing amplifier		$V_{\mathrm{o}\mathrm{u}\mathrm{t}}=-R_{\mathrm{f}}(\frac{V_1}{R_1}+\frac{V_2}{R_2}+\cdots +\frac{V_n}{R_n})$
Integrating amplifier		$V_{\mathrm{o}\mathrm{u}\mathrm{t}}=\underset{0}{\overset{t}{\int }}-\frac{V_{\mathrm{i}\mathrm{n}}}{RC}dt+V_{\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{a}\mathrm{l}}$
Differentiating amplifier		$V_{\mathrm{o}\mathrm{u}\mathrm{t}}=-RC\left(\frac{d{V}_{\mathrm{i}\mathrm{n}}}{dt}\right)$
Schmitt trigger		Hysteresis from $\frac{-R_1}{R_2}{V}_{sat}$ to $\frac{R_1}{R_2}{V}_{sat}$
Inductance gyrator		L = RLRC
Negative impedance converter		$R_{\mathrm{i}\mathrm{n}}=-R_3\frac{R_1}{R_2}$
Logarithmic configuration		$v_{\mathrm{o}\mathrm{u}\mathrm{t}}=-V_{\gamma }\ln \left(\frac{v_{\mathrm{i}\mathrm{n}}}{I_{\mathrm{S}}\cdot R}\right)$
Exponential configuration		$v_{\mathrm{o}\mathrm{u}\mathrm{t}}=-R{I}_{\mathrm{S}}{e}^{\frac{v_{\mathrm{i}\mathrm{n}}}{V_{\gamma }}}$

Further reading

• Electronics/Electronics Formulas/Op Amp Configurations
• Electronics/Electronics Op Amp Configurations
• Electronics/Op-Amps/Linear Configurations
• Electronics/Op-Amps/Non Linear Configurations
• Practical Electronics/Operating amplifiers
• "What is Schmitt trigger?"