feat: start op amp notes

Areas/electricity/active-components/op-amp.md

@@ -64,11 +64,31 @@ 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
+x 240 345 252 348 4 12 Rf
+x 160 363 176 366 4 12 Rg
 ```
 
+What is the closed loop gain of this circuit?
+
+$$
+\begin{flalign}
+&V_- = V_+ = V_s&\\\
+&V_- \text{is the output of a voltage divider}\\
+\end{flalign}
+$$
+
+Because $V_-$ is equal to $V_+$ and 
+
+$V_- = V_s = V_o (\frac{R_g}{R_G+R_F})$
+t
+If we solve that equation for $\frac{V_O}{V_s}$ we get the following formula:
+
+$\displaystyle Gain =\frac{V_o}{V_s} = 1+\frac{R_F}{R_G}$
 
 # Buffer (Voltage-Follow)
 
+This circuit is usefull, because the output always replicates the voltage at the input. For example if you connect the output of a voltage divider you can drive a load wth $V_o$ and the impedance in the Load will not change the $V_o$
+
 ```circuitjs
 $ 64 0.000005 1.0312258501325766 50 5 50 5e-11
 a 192 240 304 240 9 15 -15 1000000 4.999950000499995 5 100000
@@ -80,3 +100,54 @@ w 96 224 192 224 2
 g 96 304 96 352 0 0
 w 192 320 304 320 0
 ```
+
+# Inverting Amplifier
+
+```circuitjs
+$ 64 0.000005 1.0312258501325766 50 5 50 5e-11
+v 48 304 48 192 0 0 40 5 0 0 0.5
+r 176 192 96 192 0 1000
+w 176 224 176 304 0
+g 176 304 176 352 0 0
+g 48 304 48 352 0 0
+r 176 112 336 112 0 1000
+w 336 112 336 208 0
+w 176 192 176 112 0
+w 336 208 416 208 0
+g 416 320 416 352 0 0
+p 416 208 416 320 1 0 0
+x 249 86 261 89 4 12 Rf
+x 129 166 141 169 4 12 Ri
+a 176 208 336 208 8 15 -15 1000000 0.00004999900001999959 0 100000
+w 96 192 48 192 2
+```
+
+$$
+\begin{flalign}
+&\frac{V_o}{V_S} = -\frac{R_F}{R_I}&\\\
+\end{flalign}
+$$
+# Difference Amplifier
+
+```circuitjs
+$ 64 0.000005 1.0312258501325766 50 5 50 5e-11
+R 144 192 96 192 0 0 40 5 0 0 0.5
+R 144 224 96 224 0 0 40 4 0 0 0.5
+r 144 192 224 192 0 1000
+r 144 224 224 224 0 1000
+a 224 208 352 208 8 15 -15 1000000 2.000009999800004 2 100000
+r 224 128 352 128 0 1000
+w 352 128 352 208 0
+w 224 192 224 128 0
+w 352 208 400 208 0
+p 400 208 400 320 1 0 0
+g 400 320 400 352 0 0
+r 224 224 224 320 0 1000
+g 224 320 224 352 0 0
+x 176 171 192 174 4 12 R1
+x 176 244 192 247 4 12 R1
+x 199 279 215 282 4 12 R2
+x 279 148 295 151 4 12 R2
+```
+
+$\displaystyle V_O = \frac{R2}{R1}(V_2-V_1)$

Areas/electricity/formulas.md

@@ -150,3 +150,4 @@ $\displaystyle I_{EQ} = \frac{V_{BB}-{V_{BE}}}{\frac{R_B}{(\beta+1)}+R_E}$
 
 
 # Non-Inverting Amplifier Gain
+