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elektronische_schaltungstechnik:rechnung_betragundphase_umkehrintegrator [2020/05/21 19:28] – tfischerelektronische_schaltungstechnik:rechnung_betragundphase_umkehrintegrator [2021/06/17 04:06] (aktuell) – tfischer
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 |$U_A = { 1 \over {R\cdot C} }\cdot {\hat{U}_E \over \omega} \cdot \color{blue}{[ cos(\omega \cdot t) ]_{t_0}^{t_1}} + U_{A0}$  |Grenzwerte einsetzen|$t_0=0$, $t_1=t$| |$U_A = { 1 \over {R\cdot C} }\cdot {\hat{U}_E \over \omega} \cdot \color{blue}{[ cos(\omega \cdot t) ]_{t_0}^{t_1}} + U_{A0}$  |Grenzwerte einsetzen|$t_0=0$, $t_1=t$|
-|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|+|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|
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 |$U_A = {{{\hat{U}_E } \over {\omega \cdot R\cdot C} } \cdot (} cos(\omega \cdot t) - \color{blue}{cos(0)} ) + U_{A0}$  | |$\color{blue}{cos(0)}=1$| |$U_A = {{{\hat{U}_E } \over {\omega \cdot R\cdot C} } \cdot (} cos(\omega \cdot t) - \color{blue}{cos(0)} ) + U_{A0}$  | |$\color{blue}{cos(0)}=1$|
-|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|+|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|
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 |$U_A = \color{blue}{{{ \hat{U}_E } \over {\omega \cdot R\cdot C} } \cdot (} cos(\omega \cdot t) - 1 \color{blue}{)} + U_{A0}$  |Ausmultiplizieren| | |$U_A = \color{blue}{{{ \hat{U}_E } \over {\omega \cdot R\cdot C} } \cdot (} cos(\omega \cdot t) - 1 \color{blue}{)} + U_{A0}$  |Ausmultiplizieren| |
-|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|+|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|
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-|$U_A = { {\hat{U}_E } \over {\omega \cdot R\cdot C} } \cdot cos(\omega \cdot t) \color{blue}{-{ {\hat{U}_E } \over {\omega \cdot R\cdot C}} + U_{A0}}$  |Betrachtung der nicht-Kosinus-Terme| | +|$U_A = { {\hat{U}_E } \over {\omega \cdot R\cdot C} } \cdot cos(\omega \cdot t) \color{blue}{-{ {\hat{U}_E } \over {\omega \cdot R\cdot C}} + U_{A0}}$  |Betrachtung der \\ nicht-Kosinus-Terme| | 
-|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|+|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|
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-|$U_A = { {\hat{U}_E } \over {\omega \cdot R\cdot C} } \cdot cos(\omega \cdot t) \color{blue}{-{ {\hat{U}_E } \over {\omega \cdot R\cdot C}} + U_{A0}}$  |Dieser Teil ist zeitlich unabhängig. Da wir von rein sinusförmigen Größen ausgehen, muss die für die anfängliche Spannung des Kondensators gelten: $U_{C0} = U_{A0}={{\hat{U}_E} \over {\omega \cdot R\cdot C}}$|| +|$U_A = { {\hat{U}_E } \over {\omega \cdot R\cdot C} } \cdot cos(\omega \cdot t) \color{blue}{-{ {\hat{U}_E } \over {\omega \cdot R\cdot C}} + U_{A0}}$  |Dieser Teil ist zeitlich unabhängig. Da wir von rein sinusförmigen Größen ausgehen, \\ muss die für die anfängliche Spannung des Kondensators gelten: $U_{C0} = U_{A0}={{\hat{U}_E} \over {\omega \cdot R\cdot C}}$|| 
-|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|+|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|
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 |$U_A = { {\hat{U}_E } \over {\omega \cdot R\cdot C} } \cdot cos(\omega \cdot t)$| |  |$U_A = { {\hat{U}_E } \over {\omega \cdot R\cdot C} } \cdot cos(\omega \cdot t)$| | 
-|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|+|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad\qquad$|$\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad$|
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