![[op-amp-basic-schematic-symbol.svg]]

The operational amplifier has a very high input impedance which makes it very good for amplifying low voltage signals.


Basically the OpAmp is a function like this:

$\displaystyle Y = A_v (X_1 - X_2)$

Where:
$$
\begin{flalign}
&Y = \text{Output Voltage}&\\\
&A_v = \text{Open Loop Gain}\\
&X_1 = \text{Input V1 (Non Inverting Input)}\\
&X_2 = \text{Input V2 (Inverting Input)}\\
\end{flalign}
$$

# Regions
Op Amps functions in different regions, just like diodes, and transistors.

![[op-amp-regions.png|400]]

**Linear Region**
This is how the Op-Amp normally functions.

**Saturation Region**
When the output of the op-amp would be higher than $+V_{CC}$ or lower than $-V_{CC}$ the output value is clamped to those values.

In real life OpAmps have $A_V$ values as high as $10^8$ or $10^9$  due to this even very small input voltages would quickly leave the linear region. That is why we need 

**Negative Feedback**
To use negative feedback we connect the output of the OpAmp to one of its inputs. This connection is modified by a *feedback factor* ($\beta$) which can be in the range $0 \le \beta \le 1$. 

Due to this feedback the new formula for the output $V_O$ is now:

$$
\begin{flalign}
&V_o = A_V * V_\Delta&\\\
\\
&V_- = \beta * V_o\\
&\text{Now we can say that }V_\Delta \text{is equal to:}\\
&V_\Delta = V_+ - \beta *V_o &| \textit{ Solve for }V_o \\
&V_o = \frac{V_+ - V_\Delta}{\beta}
\end{flalign}
$$



# Non-Inverting Amplifier

```circuitjs
$ 64 0.000005 1.0312258501325766 50 5 50 5e-11
a 192 240 304 240 9 15 -15 1000000 4.9999000019999595 5 100000
r 192 320 192 400 0 1000
r 304 320 192 320 0 1000
w 192 320 192 256 0
w 304 240 304 320 0
O 304 240 368 240 1 0
g 192 400 192 432 0 0
v 96 352 96 224 0 0 40 5 0 0 0.5
w 96 224 192 224 2
g 96 352 96 432 0 0
b 144 288 289 401 0
x 264 386 278 389 4 24 β
```


# Buffer (Voltage-Follow)

```circuitjs
$ 64 0.000005 1.0312258501325766 50 5 50 5e-11
a 192 240 304 240 9 15 -15 1000000 4.999950000499995 5 100000
w 192 320 192 256 0
w 304 240 304 320 0
O 304 240 368 240 1 0
v 96 304 96 224 0 0 40 5 0 0 0.5
w 96 224 192 224 2
g 96 304 96 352 0 0
w 192 320 304 320 0
```