# Operational Amplifier 

opamp non-inverting schmitt trigger

##### Definition

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