Unterschiede

Hier werden die Unterschiede zwischen zwei Versionen angezeigt.

--- elektronische_schaltungstechnik:rechnung_umkehrintegrator [2020/05/21 17:50]
tfischer angelegt
+++ elektronische_schaltungstechnik:rechnung_umkehrintegrator [2021/06/24 13:59] (aktuell)
tfischer
@@ Zeile 1: / Zeile 1: @@
-~~REVEAL theme=whide&fade=fade&controls=1&show_progress_bar=1&build_all_lists=1&show_image_borders=1&horizontal_slide_level=2&enlarge_vertical_slide_headers=0&show_slide_details=0&open_in_new_window=1&size=1324x168~~
+~~REVEAL theme=white&fade=fade&controls=1&show_progress_bar=1&build_all_lists=1&show_image_borders=1&horizontal_slide_level=2&enlarge_vertical_slide_headers=0&show_slide_details=0&open_in_new_window=1&size=624x158~~
+---->
+|$U_A = f(U_E)$  |mit III.|
+|$\qquad\qquad\qquad\qquad\qquad\quad$|$\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad\qquad$|
+<----
 ---->
-$I.\quad$ Betrachtung der Ströme
+|$U_A=\color{blue}{-U_D}-U_C$  |mit II.  und I.|$ \color{blue}{U_D} = { 1 \over A_D } \cdot U_A \overset{A_D -> \infty}\longrightarrow 0$|
+|$\qquad\qquad\qquad\qquad\qquad\quad$|$\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad\qquad$|
 <----
 ---->
-|aus (2+3)|$\color{blue}{I_p} = \color{blue}{I_m} = 0$  |$I_p$ und $I_m$ sind damit definiert|
+|$U_A= \quad  0 \quad -\color{blue}{U_C}$|mit V.|$\color{blue}{U_C}={ 1 \over C }\cdot(\int_{t_0}^{t_1} I_C \ dt+ Q_0(t_0))$|
-|$\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|
+|$\qquad\qquad\qquad\qquad\qquad\quad$|$\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad\qquad$|
 <----
 ---->
-|aus (3) und (5)|$\color{blue}{I_o} = I_m = 0$  |$I_o$ ist damit definiert|
+|$U_A = {-{ 1 \over C }\cdot}(\int_{t_0}^{t_1} \color{blue}{I_C} \ dt+ Q_0(t_0)) $|mit IV.|$\color{blue}{I_C}=I_R$|
-|$\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|
+|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|
 <----
 ---->
-$II.\quad$ Betrachtung der Spannungsverstärkung
+|$U_A = \color{blue}{-{ 1 \over C }\cdot(}\int_{t_0}^{t_1} I_R \ dt+ Q_0(t_0)\color{blue}{)} $|Ausklammern|
+|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|
 <----
----->>
+---->
-|aus (0)  |$\color{blue}{A_V}=\frac{U_A}{U_E}$  |  $\quad$|
+|$U_A = -{ 1 \over C }\cdot\int_{t_0}^{t_1} I_R \ dt - \color{blue}{ Q_0(t_0) \over C } $|Integrationskonstante \\ betrachten|$\color{blue}{ Q_0(t_0) \over C }= U_C(t_0) = -U_{A0}$|
-|$\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|
+|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|
-<<----
+<----
----->>
+---->
-| $\quad$  |$A_V=\frac{U_A}{\color{blue}{U_E}}$  |mit (4)|
+|$U_A = -{ 1 \over C }\cdot\int_{t_0}^{t_1} \color{blue}{I_R} \ dt + U_{A0}$|mit VI. und II.|$\color{blue}{I_R}={ U_R \over R}={ U_E \over R} $|
-|$\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|
+|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|
-<<----
+<----
----->>
+---->
-| $\quad$  |$A_V=\frac{U_A}{\color{blue}{U_A+U_D}}$  | $\quad$  |
+|$U_A = -{ 1 \over C }\cdot\int_{t_0}^{t_1} \color{blue}{1 \over R} \cdot U_E \ dt + U_{A0}$|Konstante vorziehen|
-|$\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|
+|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|
-<<----
+<----
----->>
+---->
-| $\quad$  |$A_V=\frac{\color{blue}{U_A}}{\color{blue}{U_A}+U_D}$  |mit (1) |
+|$U_A = -{ 1 \over {R\cdot C} }\cdot\int_{t_0}^{t_1} U_E \ dt + U_{A0}$| Zeitkonstante \\ $\tau = R \cdot C$ einfügen |
-|$\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|
+|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|
-<<----
+<----
----->>
-| $\quad$  |$A_V=\frac{\color{blue}{A_D\cdot U_D}}{\color{blue}{A_D\cdot U_D}+U_D}$  | $\quad$ |
-|$\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|
-<<----
----->>
+---->
-| $\quad$  |$A_V=\frac{A_D\cdot U_D}{A_D\cdot U_D + U_D}$  | $\quad$ |
+|$U_A = -{ 1 \over {\tau} }\cdot\int_{t_0}^{t_1} U_E \ dt + U_{A0}$| | |
-|$\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|
+|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|
-<<----
+<----
----->>
-| $\quad$  |$A_V=\color{blue}{\frac{A_D\cdot U_D}{A_D\cdot U_D + U_D}}$  |Erweitern mit $\frac{1}{A_D\cdot U_D}$ |
-|$\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|
-<<----
----->>
-| $\quad$  |$A_V=\color{blue}{\frac{A_D\cdot U_D\cdot\frac{1}{A_D\cdot U_D}}{(A_D\cdot U_D + U_D)\cdot \frac{1}{A_D\cdot U_D}}}$  | $\quad$ |
-|$\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|
-<<----
----->>
-| $\quad$  |$A_V=\color{blue}{\frac{1}{1 + \frac{1}{A_D}}}$  | $\quad$  |
-|$\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|
-<<----
----->>
-| $\quad$  |$A_V=\frac{1}{1 + \frac{1}{A_D}}$  | $\quad$  |
-|$\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|
-<<----
----->>
-| $\quad$  |$A_V=\frac{1}{1 + \color{blue}{\frac{1}{A_D}}}$  |mit $\frac{1}{A_D} \xrightarrow{A_D \rightarrow \infty} 0$  |
-|$\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|
-<<----
----->>
-| $\quad$  |$A_V=\frac{1}{1 + \color{blue}{0}}$  | $\quad$  |
-|$\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|
-<<----
----->>
-| $\quad$  |$A_V=\frac{1}{1}=1$  | $\quad$  |
-|$\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|
-<<----