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electrical_engineering_and_electronics_2:block08 [2026/04/21 03:58] – created mexleadminelectrical_engineering_and_electronics_2:block08 [2026/04/21 04:01] (current) – mexleadmin
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 ===== Core content ===== ===== Core content =====
  
- +===== From Two-Terminal Network to Four-Terminal Network =====
- +
-====== 7 Networks at variable frequency ====== +
- +
-Further content can be found at this __ BROKEN-LINK:[[https://www.electronics-tutorials.ws/accircuits/series-circuit.html|Tutorial]] LINK-BROKEN __ 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]] +
- +
-==== Introduction ==== +
- +
-In the previous chapters, it was explained what the "influence of a sinusoidal current flow" of capacitors and inductors looks like. To describe this, the impedance was introduced. This can be understood as a complex resistance for sinusoidal excitation. +
- +
-It applies to the capacitor: +
- +
-\begin{align*}  +
-\underline{U}_C = \frac{1}{{\rm j}\omega \cdot C} \cdot \underline{I}_C \quad \rightarrow \quad  +
-\underline{Z}_C = \frac{1}{{\rm j}\omega \cdot C}  +
-\end{align*} +
- +
-and for the inductance +
- +
-\begin{align*}  +
-\underline{U}_L = {\rm j}\omega \cdot L \cdot \underline{I}_L \quad \rightarrow \quad  +
-\underline{Z}_L = {\rm j}\omega \cdot L  +
-\end{align*} +
- +
-Complex impedances can be dealt with in much the same way as ohmic resistances in Electrical Engineering 1 (see: [[:electrical_engineering_1:simple_circuits|simple DC Circuits]], [[electrical_engineering_1:non-ideal_sources_and_two_terminal_networks|linear Sources and two-terminal network]], [[:electrical_engineering_1:network_analysis|Analysis of DC Networks]]). In these transformations, the fraction $ j\omega \cdot$ is preserved. Circuits with impedances such as inductors and capacitors will show a frequency dependence accordingly. +
- +
-<callout> +
- +
-=== Targets === +
- +
-After this lesson, you should: +
- +
-  - know that … +
-  - know that … is formed. +
-  - be able to … can … +
- +
-</callout> +
- +
-===== 7.1 From Two-Terminal Network to Four-Terminal Network =====+
  
 <WRAP> <imgcaption imageNo01 | Two-Terminal Network to Four-Terminal Network> </imgcaption> \\ {{drawio>ZweipolundVierpol.svg}} \\ </WRAP> <WRAP> <imgcaption imageNo01 | Two-Terminal Network to Four-Terminal Network> </imgcaption> \\ {{drawio>ZweipolundVierpol.svg}} \\ </WRAP>
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 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
  
-===== 7.2 RL Series Circuit =====+===== RL Series Circuit =====
  
 <WRAP> <imgcaption imageNo02 | RL-series> </imgcaption> \\ {{drawio>RLReihenschaltung.svg}} \\ <WRAP> <WRAP> <imgcaption imageNo02 | RL-series> </imgcaption> \\ {{drawio>RLReihenschaltung.svg}} \\ <WRAP>
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 These three points are now to be gone through. These three points are now to be gone through.
  
-==== 7.2.1 RL High Pass ====+==== RL High Pass ====
  
 For the first step, we investigate the limit consideration: We look at what happens when the frequency $\omega$ runs to the definition range limits, i.e. $\omega \rightarrow 0$ and $\omega \rightarrow \infty$: For the first step, we investigate the limit consideration: We look at what happens when the frequency $\omega$ runs to the definition range limits, i.e. $\omega \rightarrow 0$ and $\omega \rightarrow \infty$:
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 2 \pi f_{\rm 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 ====+==== RL Low Pass ====
  
 <WRAP> <imgcaption imageNo04 | Circuit, pointer diagram, and amplitude and phase response of RL low-pass filter> </imgcaption> {{drawio>AmplitudenPhasengangRLTiefpass.svg}} </WRAP> <WRAP> <imgcaption imageNo04 | Circuit, pointer diagram, and amplitude and phase response of RL low-pass filter> </imgcaption> {{drawio>AmplitudenPhasengangRLTiefpass.svg}} </WRAP>
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 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
  
-===== 7.3 RC Series Circuit =====+===== RC Series Circuit =====
  
-==== 7.3.1 RC High Pass ====+==== RC High Pass ====
  
 <WRAP> <imgcaption imageNo05 | Circuit, pointer diagram, and amplitude and phase response of the RC high-pass filter> </imgcaption> {{drawio>AmplitudenPhasengangRCHochpass.svg}} </WRAP> <WRAP> <imgcaption imageNo05 | Circuit, pointer diagram, and amplitude and phase response of the RC high-pass filter> </imgcaption> {{drawio>AmplitudenPhasengangRCHochpass.svg}} </WRAP>
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 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
  
-==== 7.3.2 RC Low Pass ====+==== RC Low Pass ====
  
 <WRAP> <imgcaption imageNo06 | Circuit, pointer diagram, and amplitude and phase response of RC low-pass filter> </imgcaption> {{drawio>AmplitudenPhasengangRCTiefpass.svg}} </WRAP> <WRAP> <imgcaption imageNo06 | Circuit, pointer diagram, and amplitude and phase response of RC low-pass filter> </imgcaption> {{drawio>AmplitudenPhasengangRCTiefpass.svg}} </WRAP>
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 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
  
-===== 6.4 Applications of Inductors =====+===== Applications of Inductors =====
  
   * ferrite bead   * ferrite bead
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   * unwanted coupling and circuit design   * unwanted coupling and circuit design
  
-===== 6.5 Examples =====+===== Examples =====
  
 === Decoupling Capacitor on the Microcontroller === === Decoupling Capacitor on the Microcontroller ===