Unterschiede

Hier werden die Unterschiede zwischen zwei Versionen angezeigt.

Link zu dieser Vergleichsansicht

Beide Seiten der vorigen Revision Vorhergehende Überarbeitung
Nächste Überarbeitung 		Vorhergehende Überarbeitung
electrical_engineering_1:circuits_under_different_frequencies [2023/03/27 09:55]
mexleadmin 		electrical_engineering_1:circuits_under_different_frequencies [2023/09/19 23:37] (aktuell)
mexleadmin
Zeile 1: Zeile 1:
-====== 7. Networks at variable frequency ======+====== 7 Networks at variable frequency ======
  
 Further content can be found at this [[https://www.electronics-tutorials.ws/accircuits/series-circuit.html|Tutorial]] or that [[https://www.khanacademy.org/science/electrical-engineering/ee-circuit-analysis-topic/ee-natural-and-forced-response/a/ee-rlc-natural-response-intuition|Tutorial]] Further content can be found at this [[https://www.electronics-tutorials.ws/accircuits/series-circuit.html|Tutorial]] or that [[https://www.khanacademy.org/science/electrical-engineering/ee-circuit-analysis-topic/ee-natural-and-forced-response/a/ee-rlc-natural-response-intuition|Tutorial]]
Zeile 168: Zeile 168:
 \begin{align*}  \begin{align*} 
 \vphantom{\HUGE{I }} \\ \vphantom{\HUGE{I }} \\
-\underline{A}_{\rm norm} = \frac{x}{\sqrt{1 + x^2}}    \cdot {\rm e}^{{\rm e}\left(\frac{\pi}{2} - arctan x \right)} +\underline{A}_{\rm norm} = \frac{x}{\sqrt{1 + x^2}}    \cdot {\rm e}^{{\rm j}\left(\frac{\pi}{2} - arctan x \right)} 
                          = \frac{U_{\rm O}}{U_{\rm I}} \cdot {\rm e}^{{\rm j}\varphi}                           = \frac{U_{\rm O}}{U_{\rm I}} \cdot {\rm e}^{{\rm j}\varphi} 
 \end{align*} \end{align*}
Zeile 198: Zeile 198:
  
 \begin{align*}  \begin{align*} 
-R            &= \omega L \\ +R               &= \omega L \\ 
-\omega_{c}  &= \frac{R}{L} \\ +\omega _{\rm c} &= \frac{R}{L} \\ 
-2 \pi f_{c} &= \frac{R}{L} \quad \rightarrow \quad \boxed{f_{\rm c} = \frac{R}{2 \pi \cdot L}} \end{align*}+2 \pi f_{\rm c} &= \frac{R}{L} \quad \rightarrow \quad \boxed{f_{\rm c} = \frac{R}{2 \pi \cdot L}} \end{align*}
  
 ==== 7.2.2 RL Low Pass ==== ==== 7.2.2 RL Low Pass ====
Zeile 212: Zeile 212:
  
 \begin{align*}  \begin{align*} 
-\underline{A}_{\rm norm} = \frac {1}{\sqrt{1 + (\omega L / R)^2}}\cdot {\rm e}^{-{\rm j} \; arctan \frac{\omega L}{R} } +\underline{A}_{\rm norm} = \frac {1}{\sqrt{1 + (\omega L / R)^2}}\cdot {\rm e}^{-{\rm j} \; \arctan \frac{\omega L}{R} } 
 \end{align*} \end{align*}
  
Zeile 236: Zeile 236:
  
 \begin{align*}  \begin{align*} 
-\underline{A}_{\rm norm} = \frac {\omega RC}{\sqrt{1 + (\omega RC)^2}}\cdot {\rm e}^{\frac{\pi}{2}-{\rm j} \; arctan (\omega RC) } +\underline{A}_{\rm norm} = \frac {\omega RC}{\sqrt{1 + (\omega RC)^2}}\cdot {\rm e}^{\frac{\pi}{2}-{\rm j} \; \arctan (\omega RC) } 
 \end{align*} \end{align*}