# Operational Amplifier#

Abstract:

An operational amplifier (short op-amp) is a DC-coupled high-gain electronic voltage amplifier with a differential input and a single-ended output.

All amplifier circuits have the feedback to the negative input!
An Op-Amp does not draw current from the input!

## Voltage Follower/Buffer#

$$\(V_{\mathrm{out}} = V_{\mathrm{in}}$$\) Provides current at the output without loading the input.

## Non-Inverting Amplifier#

$V_{\mathrm{out}} = \left(1 + \frac{R_2}{R_1} \right) V_{\mathrm{in}}$

with resistances $$R_1, R_2 \in \R$$ and the voltages $$V_{\mathrm{in}}, V_{\mathrm{out}} \in \R$$.

## Inverting Amplifier#

$V_{\mathrm{out}} = -\frac{R_2}{R_1} V_{\mathrm{in}}$

with resistances $$R_1, R_2 \in \R$$ and the voltages $$V_{\mathrm{in}}, V_{\mathrm{out}} \in \R$$.

## Differential Amplifier#

$V_{\mathrm{out}} = \frac{R_2}{R_1}\left(- V_1 + V_2 \frac{R_4}{R_4 + R_3}\right) + \frac{R_4}{R_4 + R_3} V_2$

with resistances $$R_1, R_2, R_3, R_4 \in \R$$ and the voltages $$V_{\mathrm{in}}, V_{\mathrm{out}} \in \R$$.

## Schmitt-Trigger#

Offset: $$V_{\mathrm{ref}} \frac{R_2}{R_1 + R_2}$$
$$V^{+} = (V_{in} - V_{out}) \frac{R_4}{R_3 + R_4}$$
Bias: $$\Delta V$$