2.1 KiB
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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.
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
$ 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)
$ 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