7. Wzmacniacze operacyjne

Wzmacniacz odwracający $$\left\{ \begin{matrix} U_{\text{we}} - R_{1}i - U_{\text{AB}} = 0\ \left( I \right) \\ U_{\text{AB}} - R_{2}i - U_{\text{wy}} = 0\ \left( \text{II} \right) \\ \end{matrix} \right.\ $$ UAB = 0 $$\left\{ \begin{matrix} i = \frac{U_{\text{we}}}{R_{1}}\ (I) \\ i = - \frac{U_{\text{wy}}}{R_{2}}\ (II) \\ \end{matrix} \right.\ $$ $$\boxed{U_{\text{wy}} = - \frac{R_{2}}{R_{1}}U_{\text{we}}}$$

Wzmacniacz nieodwracający $$\left\{ \begin{matrix} - R_{1}i - U_{\text{AB}} - U_{\text{we}} = 0\ (I) \\ U_{\text{we}} + U_{\text{AB}} - R_{2}i - U_{\text{wy}} = 0\ (II) \\ \end{matrix} \right.\ $$ UAB = 0 $$\left\{ \begin{matrix} i = - \frac{U_{\text{we}}}{R_{1}}\ (I) \\ i = \frac{U_{\text{we}} - U_{\text{wy}}}{R_{2}}\ \left( \text{II} \right) \\ \end{matrix} \right.\ $$ $$- \frac{U_{\text{we}}}{R_{1}} = \ \frac{\frac{U_{\text{we}} - U_{\text{wy}}}{R_{2}}}{R_{1} \cdot R_{2}}$$ −UweR2 = UweR1 − UwyR1 $$\boxed{U_{\text{wy}} = \frac{R_{1} + R_{2}}{R_{1}}U_{\text{we}}}$$

Całkujący $$\left\{ \begin{matrix} U_{\text{we}} - Ri - U_{\text{AB}} = 0\ \left( I \right) \\ U_{\text{AB}} - U_{c} - U_{\text{wy}} = 0\ \Rightarrow U_{c} = {- U}_{\text{wy}}\ \left( \text{II} \right) \\ \end{matrix} \right.\ $$ $$i = C\frac{dU_{c}}{\text{dt}}\ ,\ U_{\text{AB}} = 0$$ $$\left\{ \begin{matrix} i = \frac{U_{\text{we}}}{R}\ \left( I \right) \\ i = - C\frac{dU_{\text{wy}}}{\text{dt}}\text{\ \ }\left( \text{II} \right) \\ \end{matrix} \right.\ $$ $$\frac{U_{\text{we}}}{R} = - C\frac{dU_{\text{wy}}}{\text{dt}}$$ $$\boxed{U_{\text{wy}} = - \frac{1}{\text{RC}}\int_{}^{}{U_{\text{we}} + C_{1}}}$$

Różniczkujący $$\left\{ \begin{matrix} U_{\text{we}} - U_{c} - U_{\text{AB}} = 0\ \left( I \right) \\ U_{\text{AB}} - Ri - U_{\text{wy}} = 0\ \Rightarrow i = - \frac{U_{\text{wy}}}{R}\ \left( \text{II} \right) \\ \end{matrix} \right.\ $$ $$i = C\frac{dU_{c}}{\text{dt}}\ ,\ U_{\text{AB}} = 0$$ $$\left\{ \begin{matrix} i = C\frac{\text{dU}_{\text{we}}}{\text{dt}}\ \left( I \right) \\ i = - \frac{U_{\text{wy}}}{R}\text{\ \ }\left( \text{II} \right) \\ \end{matrix} \right.\ $$ $$C\frac{dU_{\text{we}}}{\text{dt}} = - \frac{U_{\text{wy}}}{R}$$ $$\boxed{U_{\text{wy}} = - RC\frac{dU_{\text{we}}}{\text{dt}}}$$