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_and_electronics_1:block06 [2025/09/29 00:40] – angelegt mexleadminelectrical_engineering_and_electronics_1:block06 [2026/01/10 13:39] (aktuell) – mexleadmin
Zeile 1: Zeile 1:
-====== Block 06 — Real sources and source equivalents ======+====== Block 06 — Real Sources and Source Equivalents ======
  
-===== Learning objectives =====+===== 6.0 Intro ===== 
 + 
 +==== 6.0.1 Learning Objectives ====
 <callout> <callout>
   * Model **real (linear) sources** with an internal resistance/conductance; read and draw their $U$–$I$ characteristics.   * Model **real (linear) sources** with an internal resistance/conductance; read and draw their $U$–$I$ characteristics.
Zeile 10: Zeile 12:
 </callout> </callout>
  
-===== 90-minute plan =====+==== 6.0.2 Preparation at Home ==== 
 + 
 +And again:  
 +  * Please read through the following chapter. 
 +  * Also here, there are some clips for more clarification under 'Embedded resources'. \\ I strongly recommend to watch there the introductional video of EEVblog 1397 (at least the first 10 minutes). 
 + 
 +For checking your understanding please do the following exercises: 
 +  * E1.2 
 +  * 3.3.1 
 + 
 +~~PAGEBREAK~~ ~~CLEARFIX~~ 
 +==== 6.0.3 90-minute Plan ====
   - Warm-up (8–10 min):     - Warm-up (8–10 min):  
     - Spot the difference: ideal vs. real source (show $U$–$I$ lines).       - Spot the difference: ideal vs. real source (show $U$–$I$ lines).  
Zeile 22: Zeile 35:
   - Wrap-up (5 min): Summary + pitfalls.   - Wrap-up (5 min): Summary + pitfalls.
  
-===== Conceptual overview =====+==== 6.0.4 Conceptual Overview ====
 <callout icon="fa fa-lightbulb-o" color="blue"> <callout icon="fa fa-lightbulb-o" color="blue">
   - A **real (linear) source** is an ideal source plus an **internal resistance** $R_{\rm i}$ (or conductance $G_{\rm i}$). Its output follows a **straight load line** between $U_{\rm OC}$ and $I_{\rm SC}$.    - A **real (linear) source** is an ideal source plus an **internal resistance** $R_{\rm i}$ (or conductance $G_{\rm i}$). Its output follows a **straight load line** between $U_{\rm OC}$ and $I_{\rm SC}$. 
Zeile 32: Zeile 45:
 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
  
-===== Core content =====+===== 6.1 Core Content =====
  
 It is known from everyday life that battery voltages drop under heavy loads. This can be seen, for example, when turning the ignition key in winter: The load from the starter motor is sometimes so large that the car lights or radio briefly cuts out.\\ It is known from everyday life that battery voltages drop under heavy loads. This can be seen, for example, when turning the ignition key in winter: The load from the starter motor is sometimes so large that the car lights or radio briefly cuts out.\\
Zeile 46: Zeile 59:
  
 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
-==== From ideal to linear sources: load line, $U_{\rm OC}$ and $I_{\rm SC}$ ====+==== 6.1.1 From ideal to linear Sources: $U_{\rm OC}$ and $I_{\rm SC}$ ====
  
 <panel type="info" title="Example / micro-exercise"> <panel type="info" title="Example / micro-exercise">
  
-Practical Example of a realistic Source: For the ideal voltage source, it was defined that it always supplies the same voltage independent of the load. In <imgref imageNo2 >, in contrast, an example of a "realistic" voltage source is shown as an active two-terminal network.+Practical example of a realistic source: For the ideal voltage source, it was defined that it always supplies the same voltage independent of the load. In <imgref imageNo2 >, in contrast, an example of a "realistic" voltage source is shown as an active two-terminal network.
  
   - This active two-terminal network generates a voltage of $1.5~\rm V$ and a current of $0~\rm A$ when the circuit is open.   - This active two-terminal network generates a voltage of $1.5~\rm V$ and a current of $0~\rm A$ when the circuit is open.
Zeile 57: Zeile 70:
  
 <WRAP> <imgcaption imageNo2 | Battery model with load resistor> </imgcaption> \\ {{url>https://www.falstad.com/circuit/circuitjs.html?running=false&ctz=CQAgjCAMB0l3AWAnC1b0DYrTAZlwBwYCsGA7AEwK7G6RIIUj7jTEjUjECmAtGGABQAdxD8wTOgjEZpUqCLECmVSEonNI0yIIDO6lQjXimYMljUQAZgEMANru6Les8OYNuLemdNU-PUOAgtg5OAE7+8i6+RoEwQqJqUa7yOokB0QFpgfLKmtqCAA6BZhb5QWo6uGRJpu6W7hCVggDm4Bq5HbhlOtAgAEI2AC5DAMoAlgC2JSAqIAA6xUyVYswzAErcuuO6QwD2YQCidpPzumBnFPNhm9u7B8enurhnkNcAant2QzYt3I9nF7nKDzV5sV6g87waEQ2G6IyQsDguFvMHEQQIMBqAhqCiQAjtSRaIKDEYTaZvXQwdiUrHQuAgqlnBHncFM9nUxR5ToqSgKUS4OpYPKlBRAA noborder}} <WRAP> <imgcaption imageNo2 | Battery model with load resistor> </imgcaption> \\ {{url>https://www.falstad.com/circuit/circuitjs.html?running=false&ctz=CQAgjCAMB0l3AWAnC1b0DYrTAZlwBwYCsGA7AEwK7G6RIIUj7jTEjUjECmAtGGABQAdxD8wTOgjEZpUqCLECmVSEonNI0yIIDO6lQjXimYMljUQAZgEMANru6Les8OYNuLemdNU-PUOAgtg5OAE7+8i6+RoEwQqJqUa7yOokB0QFpgfLKmtqCAA6BZhb5QWo6uGRJpu6W7hCVggDm4Bq5HbhlOtAgAEI2AC5DAMoAlgC2JSAqIAA6xUyVYswzAErcuuO6QwD2YQCidpPzumBnFPNhm9u7B8enurhnkNcAant2QzYt3I9nF7nKDzV5sV6g87waEQ2G6IyQsDguFvMHEQQIMBqAhqCiQAjtSRaIKDEYTaZvXQwdiUrHQuAgqlnBHncFM9nUxR5ToqSgKUS4OpYPKlBRAA noborder}}
- 
 </WRAP> </WRAP>
 </panel> </panel>
Zeile 93: Zeile 105:
 </WRAP> </WRAP>
  
-==== Linear Voltage Source ====+==== 6.1.2 Linear Voltage Source ====
  
 The linear voltage source consists of a series connection of an ideal voltage source with the source voltage $U_0$ (English: EMF for ElectroMotive Force) and the internal resistance $R_\rm i$. To determine the voltage outside the active two-terminal network, the system can be considered as a voltage divider. The following applies: The linear voltage source consists of a series connection of an ideal voltage source with the source voltage $U_0$ (English: EMF for ElectroMotive Force) and the internal resistance $R_\rm i$. To determine the voltage outside the active two-terminal network, the system can be considered as a voltage divider. The following applies:
Zeile 108: Zeile 120:
 Is this the structure of the linear source we are looking for? To verify this, we will now look at the second linear source. Is this the structure of the linear source we are looking for? To verify this, we will now look at the second linear source.
  
-==== Linear Current Source ====+==== 6.1.3 Linear Current Source ====
  
 The linear current source now consists of a __parallel circuit__  of an ideal current source with source current $I_0$ and internal resistance $R_{\rm i}$, or internal conductance $G_{\rm i} = {{1}\over{R_{\rm i}}}$. To determine the voltage outside the active two-terminal, the system can be considered as a current divider. Here, the following holds: The linear current source now consists of a __parallel circuit__  of an ideal current source with source current $I_0$ and internal resistance $R_{\rm i}$, or internal conductance $G_{\rm i} = {{1}\over{R_{\rm i}}}$. To determine the voltage outside the active two-terminal, the system can be considered as a current divider. Here, the following holds:
Zeile 123: Zeile 135:
 So it seems that the two linear sources describe the same thing. So it seems that the two linear sources describe the same thing.
  
-==== Duality of Linear Sources ====+==== 6.1.4 Duality of Linear Sources ====
  
 Through the previous calculations, we came to the interesting realization that both the linear voltage source and the linear current source provide the same result. It is true: For a linear source, both a linear voltage source and a linear current source can be specified as an equivalent circuit! As already in the case of the star-delta transformation, this not only provides two explanations for a black box. Also, here linear voltage sources can be transformed into linear current sources and vice versa. Through the previous calculations, we came to the interesting realization that both the linear voltage source and the linear current source provide the same result. It is true: For a linear source, both a linear voltage source and a linear current source can be specified as an equivalent circuit! As already in the case of the star-delta transformation, this not only provides two explanations for a black box. Also, here linear voltage sources can be transformed into linear current sources and vice versa.
Zeile 149: Zeile 161:
  
 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
-==== Operating Point of a real Voltage Source ====+==== 6.1.5 Operating Point of a real Voltage Source ====
  
 <imgref imageNo5 > shows the characteristics of the linear voltage source (left) and a resistive resistor (right). For this purpose, both are connected to a test system in the simulation: In the case of the source with a variable ohmic resistor, and in the case of the load with a variable source. The characteristic curves formed in this way were described in the previous chapter. <imgref imageNo5 > shows the characteristics of the linear voltage source (left) and a resistive resistor (right). For this purpose, both are connected to a test system in the simulation: In the case of the source with a variable ohmic resistor, and in the case of the load with a variable source. The characteristic curves formed in this way were described in the previous chapter.
Zeile 165: Zeile 177:
  
 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
-==== Conversion of any linear two-terminal Network ====+==== 6.1.6 Conversion of any linear two-terminal Network ====
  
 In <imgref imageNob7 >, it can be seen that the internal resistance of the linear current source measured by the ohmmeter (resistance meter) is exactly equal to that of the linear voltage source. In <imgref imageNob7 >, it can be seen that the internal resistance of the linear current source measured by the ohmmeter (resistance meter) is exactly equal to that of the linear voltage source.
Zeile 171: Zeile 183:
 <WRAP> <imgcaption imageNob7 | Resistance of linear sources> </imgcaption> \\ {{url>https://www.falstad.com/circuit/circuitjs.html?running=false&ctz=CQAgDOB0YzCsICMZICYaoOyYMxgByoBsAnCZkiAgCw5UCmAtIogFABuIJRIqcP3JJh4QI1CAlFQ4rAE5ceiYUMXKIyGKwDuC3vxV6RrVIh6pU1Q7wsH1265b6qz+sPaXOHt1gEsQOdCsA9TUoeHtggxx8Sw9wOX8YqKSncCRYCJT9SNS3HWjY5WoiQqN8rJ5ix1djUxAqqwa4uwBzL1TzR3x8NLc2htSB7t7WACMQIkQkOFiiOixUePHUcmme6hZeTEW3AA9eElicGjgexGj6pB6AGx8AO3oAQ1kAHQBnAGMAV1lZejuAC7vN4Aex+H3orH2JSQODMeFhJEuiBu9yerze7BB1wBjxa9GBYNkENYQA noborder}} </WRAP> <WRAP> <imgcaption imageNob7 | Resistance of linear sources> </imgcaption> \\ {{url>https://www.falstad.com/circuit/circuitjs.html?running=false&ctz=CQAgDOB0YzCsICMZICYaoOyYMxgByoBsAnCZkiAgCw5UCmAtIogFABuIJRIqcP3JJh4QI1CAlFQ4rAE5ceiYUMXKIyGKwDuC3vxV6RrVIh6pU1Q7wsH1265b6qz+sPaXOHt1gEsQOdCsA9TUoeHtggxx8Sw9wOX8YqKSncCRYCJT9SNS3HWjY5WoiQqN8rJ5ix1djUxAqqwa4uwBzL1TzR3x8NLc2htSB7t7WACMQIkQkOFiiOixUePHUcmme6hZeTEW3AA9eElicGjgexGj6pB6AGx8AO3oAQ1kAHQBnAGMAV1lZejuAC7vN4Aex+H3orH2JSQODMeFhJEuiBu9yerze7BB1wBjxa9GBYNkENYQA noborder}} </WRAP>
  
-In the simulation, a measuring current $I_\Omega$ is used to determine the resistance value. ((This concept will also be used in an electrical engineering lab experiment on [[elektrotechnik_labor:1_widerstaende|resistor]]s in the 3rd semester.)) Let us have a look at the properties of the ohmmeter in the simulation by double-clicking on the ohmmeter. Here, a very large measuring current of $I_\Omega=1~\rm A$ is used. This could lead to high voltages or the destruction of components in real setups. \\+In the simulation, a measuring current $I_\Omega$ is used to determine the resistance value. ((This concept will also be used in an electrical engineering lab experiment on [[elektrotechnik_labor:1_widerstaende|resistor]]s in the 2nd semester.)) Let us have a look at the properties of the ohmmeter in the simulation by double-clicking on the ohmmeter. Here, a very large measuring current of $I_\Omega=1~\rm A$ is used. This could lead to high voltages or the destruction of components in real setups. \\
  \\  \\
 In order to understand why is this nevertheless chosen so high in the simulation, do the following: Set the measuring current for both linear sources to (more realistic) $1~\rm mA$. What do you notice? In order to understand why is this nevertheless chosen so high in the simulation, do the following: Set the measuring current for both linear sources to (more realistic) $1~\rm mA$. What do you notice?
Zeile 213: Zeile 225:
  
 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
-==== Simplified Determination of the internal Resistance ====+==== 6.1.7 Simplified Determination of the internal Resistance ====
  
 <callout icon="fa fa-exclamation" color="red" title="Note:"> <callout icon="fa fa-exclamation" color="red" title="Note:">
Zeile 235: Zeile 247:
 </panel> </panel>
  
-===== Exercises =====+===== 6.2 Common Pitfalls ===== 
 +  * **Wrong deactivation:** do **not** set an ideal voltage source to open or an ideal current source to short; the rules are: $U$-source→**short**, $I$-source→**open**. 
 +  * **Confusing goals:** **max power** ($R_{\rm L}=R_{\rm i}$, $\eta=50\%$) vs. **high efficiency** ($R_{\rm L}\gg R_{\rm i}$). Don’t equate them.  
 +  * **Ignoring ratings:** not every real source is short-circuit-proof—$I_{\rm SC}$ is a **model parameter**, not a recommended experiment.  
 +  * **Mixed conventions:** keep the **passive sign convention** for loads; use conventional current ($+$ to $-$). 
 + 
 +===== 6.3 Exercises =====
 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
 ==== Quick checks ==== ==== Quick checks ====
Zeile 247: Zeile 265:
 #@ResultEnd_HTML@# #@ResultEnd_HTML@#
 #@TaskEnd_HTML@# #@TaskEnd_HTML@#
 +
  
 ==== Longer exercises ==== ==== Longer exercises ====
- 
-Quick checks 
-#@TaskTitle_HTML@##@Lvl_HTML@#~~#@ee1_taskctr#~~.1  Loaded divider as Thevenin   
-#@TaskText_HTML@# 
-A divider $R_1=3.3~\rm k\Omega$, $R_2=6.8~\rm k\Omega$ is fed from $U=10.0~\rm V$ and loaded by $R_{\rm L}=10.0~\rm k\Omega$. Replace the divider by its Thevenin equivalent, then compute $U_{\rm L}$ and the **loading error** relative to the ideal (no-load) divider output. 
- 
-#@ResultBegin_HTML~LongerExercise1~@# 
-$R_{\rm ie}=R_1\parallel R_2=\dfrac{(3.3)(6.8)}{3.3+6.8}~\rm k\Omega=2.22~\rm k\Omega$.   
-$U_{0\rm e}=\dfrac{R_2}{R_1+R_2}U=6.8/(3.3+6.8)\cdot 10.0~\rm V=6.80~\rm V$.   
-$U_{\rm L}=U_{0\rm e}\dfrac{R_{\rm L}}{R_{\rm L}+R_{\rm ie}}=6.80~{\rm V}\cdot \dfrac{10.0}{12.22}=5.56~{\rm V}$.   
-Ideal (no-load) output would be $6.80~\rm V$ ⇒ loading error $=1.24~\rm V$.   
-#@ResultEnd_HTML@# 
-#@TaskEnd_HTML@# 
  
 <panel type="info" title="Exercise 3.1.1 Convert current source to voltage source"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%> <panel type="info" title="Exercise 3.1.1 Convert current source to voltage source"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
Zeile 284: Zeile 290:
 </WRAP></WRAP></panel>  </WRAP></WRAP></panel> 
  
-<panel type="info" title="Exercise 3.2.1 Solving a circuit simplification I"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%> 
  
-{{youtube>xtOPwmUgPjc}}+<panel type="info" title="Exercise 3.3.1 Simplification by Norton / Thevenin theorem"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%> <WRAP>
  
-</WRAP></WRAP></panel>+Simplify the following circuits by the Norton theorem to a linear current source (circuits marked with NT) or by Thevenin theorem to a linear voltage source (marked with TT). 
  
-<panel type="info" title="Exercise 3.2.2 Solving a circuit simplification II"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>+<imgcaption BildNr3_0 | Simplification by Norton / Thevenin theorem> </imgcaption> {{drawio>BildNr3_0.svg}} </WRAP>
  
-{{youtube>UU_RJJ6ne4I}}+<button size="xs" type="link" collapse="Loesung_3_3_1_1_Lösungsweg">{{icon>eye}} Solution</button><collapse id="Loesung_3_3_1_1_Lösungsweg" collapsed="true">  
 +To substitute the circuit in $a)$ first we determine the inner resistance.  
 +Shutting down all sources leads to  
 +\begin{equation*}  
 +R_{\rm i}= 8~\Omega \end{equation*} 
  
-</WRAP></WRAP></panel>+Next, we figure out the current in the short circuit.  
 +In case of a short circuit, we have $2~V$ in a branch which in turn means there must be $−2~V$ on the resistor.  
 +The current through that branch is  
 +\begin{equation*} I_R=\frac{2~V}{8~\Omega} \end{equation*} 
  
-<panel type="info" title="Exercise 3.2.3 Solution sketch for a more difficult circuit simplification"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>+The current in question is the sum of both the other branches  
 +\begin{equation*} I_S= I_R + 1~A \end{equation*} 
  
-{{youtube>In3NF8f-mzg}}+To substitute the circuit in $b)$ first we determine the inner resistance.  
 +Shutting down all sources leads to  
 +\begin{equation*} R_{\rm i}= 4 ~\Omega \end{equation*} 
  
-</WRAP></WRAP></panel>+Next, we figure out the voltage at the open circuit.  
 +Thus we know the given current flows through the ideal current source as well as the resistor.  
 +The voltage drop on the resistor is  
 +\begin{equation*} R_{\rm i}= -4~\Omega \cdot 2~A \end{equation*} 
  
-<panel type="info" title="Exercise 3.2.4 Interesting circuit tasks"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%> +The voltage at the open circuit is  
- +\begin{equation*} U_{\rm S}= 2~V + 1~V + U_R \end{equation*}
-{{youtube>zTDgziJC-q8}}+
  
 +</collapse> <button size="xs" type="link" collapse="Loesung_3_3_1_2_Lösungsweg">{{icon>eye}} Final result</button><collapse id="Loesung_3_3_1_2_Lösungsweg" collapsed="true"> 
 +The values of the substitute resistor and the currents in the branches are 
 +\begin{equation*} 
 +\text{a)} \quad R=8~\Omega \qquad I=1.25~A \\
 +\text{b)} \quad R=4~\Omega \qquad U=-5~V 
 +\end{equation*} 
 +</collapse>
 </WRAP></WRAP></panel> </WRAP></WRAP></panel>
  
-<panel type="info" title="Exercise 3.1.1 Convert current source to voltage source"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%> 
  
-{{youtube>ZqohGL-40a4}} 
  
-</WRAP></WRAP></panel>+<panel type="info" title="Exercise 3.3.2 Simplification by Thevenin theorem"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%> <WRAP>
  
-<panel type="info" title="Exercise 3.1.2 Convert voltage source to current source"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>+The following simulation shows four cirucits.
  
-{{youtube>vVDNsztDmAk}}+1. Have a look on the both circuits 1a) with U_S(1a)=10 V and 1b) U_S(1b)=5 V. Start the simulation and change the load resistors for R_L(1a) and R_L(1b) with the sliders on the right. \\ What do you see on the values for the voltage and the current on both circuits, when you choose the same resistor values? Why? \\ \\ 
 +2. Simplify the circuit 2a) with U_S(2a)=10 V by the Thevenin theorem to a linear voltage source. \\ What would be the source voltage U_S(2b) of the equivalent voltage source? What would be the resistance R_i(2b) of the inner resistor?
  
-</WRAP></WRAP></panel>+<panel> 
 +<WRAP> <imgcaption imageNo2 | Circuits to be simplified> </imgcaption> \\ {{url>https://www.falstad.com/circuit/circuitjs.html?running=false&ctz=CQAgjCAMB0l3BWcMBMcUHYMGZIA4UA2ATmIxAUgpABZsKBTAWjDACgA3EJwm8YlN14g8VMbSphxY6AjYAnIX1G08I8VLgLV6nWAFRkWgO56DPPvsGQ2p4oV1Xd2NgHMl-QRZAoUfMdpOKk5OkvC2npE0aqFuINjYDk4JDr7+UBE00ZEpkTaKuSpZaipUlDZcucmJuuI0ZYYycgBG3PbxghhUKJQZdg5FJQGtuILYgjSEaj0BpjTtRdmlEQgGTsV52quCKtt5RjZzC2UGKi5HDth4fHtXfC6Kt9cUBvMOYSYvE+0bb3207TutGyQJsI0gYxqkzUCAQ-jYrSYgJqXQocIylShyMuzzqDWksm0uSBG1BIFIxHCc2yf1yfxs7jp2IoKDUsyi7TADnpgRxyioZM0DI8f28CFZjQiZ2eyWe53A3Pa3h5ii58RliveB203iBasF4S4yqVwjJVHqyEaUEJqtenIMBq0AA94ggINgsPFPVdzToAPxsF0sBI+PhI4g+ch8PzgACGAEpAz5hDGUMRplHQ+BmomXUR6OMI2nyAkJlmUDmk8H7mnuJp4uNaOWE0mwCh6GBsBGwMEaGW1QAlAD6ABkABRgFsu8WCMAWhAYbt0JuD0cTysu1hqLKzjBILL7hUgYfjlBTln0HcURaH1enjdeyyQCN9pJtlcOYcAS3Xua93M7WgJRoNVLE-IcfwrP9sHFWhCH3Vg4O3I8AFUhwAZTHKCk2wSZwFWCQkC5fsHDQzCwAfJgEA7QgICSYQwJAMiJ3PKjtwwCAIBoDA+EY5iz0TK4QAcAAxCBJAOOtjzXSdBJicgxMMTj4Ckk9fzYISPRARSJKFVS1wEjTpioHTwEklhpPvRMgA noborder}} 
 +</WRAP> 
 +</panel>
  
-{{page>task_3.1.3_with_calculation&nofooter}}+</WRAP></WRAP></WRAP> 
 +</panel>
  
-~~PAGEBREAK~~ ~~CLEARFIX~~ + 
-===== Common pitfalls ===== +{{page>electrical_engineering_and_electronics:task_3.1.3_with_calculation&nofooter}} 
-  * **Wrong deactivation:** do **not** set an ideal voltage source to open or an ideal current source to short; the rules are: $U$-source→**short**, $I$-source→**open**. +{{page>electrical_engineering_and_electronics:task_6tqttque1e2nf2c7_with_calculation&nofooter}} 
-  * **Confusing goals:** **max power** ($R_{\rm L}=R_{\rm i}$, $\eta=50\%$) vs. **high efficiency** ($R_{\rm L}\gg R_{\rm i}$). Don’t equate them.  +{{page>electrical_engineering_and_electronics:task_lefxcuaxiu8ewcr9_with_calculation&nofooter}}
-  * **Ignoring ratings:** not every real source is short-circuit-proof—$I_{\rm SC}$ is a **model parameter**, not a recommended experiment.  +
-  * **Mixed conventions:** keep the **passive sign convention** for loads; use conventional current ($+$ to $-$).+
  
  
Zeile 333: Zeile 358:
 ===== Embedded resources ===== ===== Embedded resources =====
  
-<WRAP> DC Voltage & Current Source Theory +<WRAP column half> 
 +DC Voltage & Current Source Theory
 {{youtube>AQK7RyecVW0}} {{youtube>AQK7RyecVW0}}
- 
 </WRAP> </WRAP>
- 
- 
  
 <WRAP column half> <WRAP column half>
Zeile 345: Zeile 367:
 {{youtube>w4N9CBc_nkA}} {{youtube>w4N9CBc_nkA}}
 </WRAP> </WRAP>
 +
 <WRAP column half> <WRAP column half>
 A more complex superposition example   A more complex superposition example  
Zeile 355: Zeile 378:
   * A **linear (real) source** is fully determined by $(U_{\rm OC},I_{\rm SC})$ or equivalently $(U_0,R_{\rm i})$ / $(I_0,G_{\rm i})$; both forms are **equivalent**.    * A **linear (real) source** is fully determined by $(U_{\rm OC},I_{\rm SC})$ or equivalently $(U_0,R_{\rm i})$ / $(I_0,G_{\rm i})$; both forms are **equivalent**. 
   * **Thevenin ↔ Norton**: $U_{\rm OC}=I_{\rm SC}R_{\rm i}$, $G_{\rm i}=1/R_{\rm i}$; deactivation rules let you find $R_{\rm i}$ quickly.    * **Thevenin ↔ Norton**: $U_{\rm OC}=I_{\rm SC}R_{\rm i}$, $G_{\rm i}=1/R_{\rm i}$; deactivation rules let you find $R_{\rm i}$ quickly. 
-  * **Efficiency vs. maximum power**: choose $R_{\rm L}\gg R_{\rm i}$ for high $\eta$, or $R_{\rm L}=R_{\rm i}$ for max $P_{\rm L}$. 
   * **Two-terminal reductions** (e.g., loaded divider) simplify analysis of larger networks.    * **Two-terminal reductions** (e.g., loaded divider) simplify analysis of larger networks.