82 lines
2.1 KiB
Markdown
82 lines
2.1 KiB
Markdown
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![[op-amp-basic-schematic-symbol.svg]]
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The operational amplifier has a very high input impedance which makes it very good for amplifying low voltage signals.
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Basically the OpAmp is a function like this:
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$\displaystyle Y = A_v (X_1 - X_2)$
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Where:
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$$
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\begin{flalign}
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&Y = \text{Output Voltage}&\\\
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&A_v = \text{Open Loop Gain}\\
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&X_1 = \text{Input V1 (Non Inverting Input)}\\
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&X_2 = \text{Input V2 (Inverting Input)}\\
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\end{flalign}
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$$
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# Regions
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Op Amps functions in different regions, just like diodes, and transistors.
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![[op-amp-regions.png|400]]
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**Linear Region**
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This is how the Op-Amp normally functions.
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**Saturation Region**
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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.
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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
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**Negative Feedback**
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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 $0 \le \beta \le 1$.
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Due to this feedback the new formula for the output $V_O$ is now:
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$$
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\begin{flalign}
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&V_o = A_V * V_\Delta&\\\
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\\
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&V_- = \beta * V_o\\
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&\text{Now we can say that }V_\Delta \text{is equal to:}\\
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&V_\Delta = V_+ - \beta *V_o &| \textit{ Solve for }V_o \\
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&V_o = \frac{V_+ - V_\Delta}{\beta}
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\end{flalign}
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$$
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# Non-Inverting Amplifier
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```circuitjs
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$ 64 0.000005 1.0312258501325766 50 5 50 5e-11
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a 192 240 304 240 9 15 -15 1000000 4.9999000019999595 5 100000
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r 192 320 192 400 0 1000
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r 304 320 192 320 0 1000
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w 192 320 192 256 0
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w 304 240 304 320 0
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O 304 240 368 240 1 0
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g 192 400 192 432 0 0
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v 96 352 96 224 0 0 40 5 0 0 0.5
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w 96 224 192 224 2
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g 96 352 96 432 0 0
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b 144 288 289 401 0
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x 264 386 278 389 4 24 β
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```
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# Buffer (Voltage-Follow)
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```circuitjs
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$ 64 0.000005 1.0312258501325766 50 5 50 5e-11
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a 192 240 304 240 9 15 -15 1000000 4.999950000499995 5 100000
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w 192 320 192 256 0
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w 304 240 304 320 0
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O 304 240 368 240 1 0
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v 96 304 96 224 0 0 40 5 0 0 0.5
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w 96 224 192 224 2
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g 96 304 96 352 0 0
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w 192 320 304 320 0
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```
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