Unterschiede

Hier werden die Unterschiede zwischen zwei Versionen angezeigt.

--- circuit_design:rechnung_umkehrintegrator [2021/09/21 04:56]
127.0.0.1 Externe Bearbeitung
+++ circuit_design:rechnung_umkehrintegrator [2023/03/28 14:44] (aktuell)
mexleadmin
@@ Zeile 1: / Zeile 1: @@
-~~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~~
+~~REVEAL~~
 ---->
-|$U_A = f(U_E)$  |mit III.|
+| $\;$ \\ $\;$ |$U_{\rm O} = f(U_{\rm I})$  |
-|$\qquad\qquad\qquad\qquad\qquad\quad$|$\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad\qquad$|
+| $\;$ \\ $\;$ | with III.|
+| |$\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|
 <----
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-|$U_A=\color{blue}{-U_D}-U_C$  |mit II.  und I.|$ \color{blue}{U_D} = { 1 \over A_D } \cdot U_A \overset{A_D -> \infty}\longrightarrow 0$|
+| $\;$ \\ $\;$ |$U_{\rm O}=\color{blue}{-U_{\rm D}}-U_C$  |
-|$\qquad\qquad\qquad\qquad\qquad\quad$|$\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad\qquad$|
+| $\;$ \\ $\;$ |with II.  and I.:$ \color{blue}{U_{\rm D}} = { 1 \over A_D } \cdot U_{\rm O} \overset{A_D -> \infty}\longrightarrow 0$|
+| |$\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|
 <----
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-|$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))$|
+| $\;$ \\ $\;$ |$U_{\rm O}= \quad  0 \quad -\color{blue}{U_C}$|
-|$\qquad\qquad\qquad\qquad\qquad\quad$|$\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad\qquad$|
+| $\;$ \\ $\;$ |with V.: $\color{blue}{U_C}={ 1 \over C }\cdot(\int_{t_0}^{t_1} I_C \ {\rm d} t+ Q_0(t_0))$|
+| |$\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|
 <----
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-|$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$|
+| $\;$ \\ $\;$ |$U_{\rm O} = {-{ 1 \over C }\cdot}(\int_{t_0}^{t_1} \color{blue}{I_C} \ {\rm d} t+ Q_0(t_0)) $|
-|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|
+| $\;$ \\ $\;$ |with IV.: $\color{blue}{I_C}=I_R$|
+| |$\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|
 <----
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-|$U_A = \color{blue}{-{ 1 \over C }\cdot(}\int_{t_0}^{t_1} I_R \ dt+ Q_0(t_0)\color{blue}{)} $|Ausklammern|
+| $\;$ \\ $\;$ |$U_{\rm O} = \color{blue}{-{ 1 \over C }\cdot(}\int_{t_0}^{t_1} I_R \ {\rm d} t+ Q_0(t_0)\color{blue}{)} $|
-|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|
+| $\;$ \\ $\;$ |Factor out|
+| |$\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|
 <----
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-|$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}$|
+| $\;$ \\ $\;$ |$U_{\rm O} = -{ 1 \over C }\cdot\int_{t_0}^{t_1} I_R \ {\rm d} t - \color{blue}{ Q_0(t_0) \over C } $|
-|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|
+| $\;$ \\ $\;$ |integration constant: $\color{blue}{ Q_0(t_0) \over C }= U_C(t_0) = -U_{\rm O0}$|
+| |$\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|
 <----
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-|$U_A = -{ 1 \over C }\cdot\int_{t_0}^{t_1} \color{blue}{I_R} \ dt + U_{A0}$|mit VI. und II.|$\color{blue}{I_R}={ U_R \over R}={ U_E \over R} $|
+| $\;$ \\ $\;$ |$U_{\rm O} = -{ 1 \over C }\cdot\int_{t_0}^{t_1} \color{blue}{I_R} \ {\rm d} t + U_{\rm O0}$|
-|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|
+| $\;$ \\ $\;$ |with VI. and II.: $\color{blue}{I_R}={ U_R \over R}={ U_{\rm I} \over R} $|
+| |$\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|
 <----
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-|$U_A = -{ 1 \over C }\cdot\int_{t_0}^{t_1} \color{blue}{1 \over R} \cdot U_E \ dt + U_{A0}$|Konstante vorziehen|
+| $\;$ \\ $\;$ |$U_{\rm O} = -{ 1 \over C }\cdot\int_{t_0}^{t_1} \color{blue}{1 \over R} \cdot U_{\rm I} \ {\rm d} t + U_{\rm O0}$|
-|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|
+| $\;$ \\ $\;$ |move constant ahead|
+| |$\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|
 <----
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-|$U_A = -{ 1 \over {R\cdot C} }\cdot\int_{t_0}^{t_1} U_E \ dt + U_{A0}$| Zeitkonstante \\ $\tau = R \cdot C$ einfügen |
+| $\;$ \\ $\;$ |$U_{\rm O} = -{ 1 \over {R\cdot C} }\cdot\int_{t_0}^{t_1} U_{\rm I} \ {\rm d} t + U_{\rm O0}$|
-|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|
+| $\;$ \\ $\;$ | insert time constant  $\tau = R \cdot C$ |
+| |$\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|
 <----
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-|$U_A = -{ 1 \over {\tau} }\cdot\int_{t_0}^{t_1} U_E \ dt + U_{A0}$| | |
+| $\;$ \\ $\;$ |$U_{\rm O} = -{ 1 \over {\tau} }\cdot\int_{t_0}^{t_1} U_{\rm I} \ {\rm d} t + U_{\rm O0}$|
-|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|
+| $\;$ \\ $\;$ | |
+| |$\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|
 <----