diff --git a/Areas/electricity/active-components/op-amp.md b/Areas/electricity/active-components/op-amp.md index afb862c..dd7ecda 100644 --- a/Areas/electricity/active-components/op-amp.md +++ b/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 @@ -79,4 +99,55 @@ 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 -``` \ No newline at end of file +``` + +# 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 +``` + +$\displaystyle V_O = \frac{R2}{R1}(V_2-V_1)$ \ No newline at end of file diff --git a/Areas/electricity/formulas.md b/Areas/electricity/formulas.md index 5671568..65a9a6d 100644 --- a/Areas/electricity/formulas.md +++ b/Areas/electricity/formulas.md @@ -149,4 +149,5 @@ $Z = \sqrt{R^2 + (X_L - X_C)^2}$ $\displaystyle I_{EQ} = \frac{V_{BB}-{V_{BE}}}{\frac{R_B}{(\beta+1)}+R_E}$ -# Non-Inverting Amplifier Gain \ No newline at end of file +# Non-Inverting Amplifier Gain +