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electrical_engineering_and_electronics_1:block06 [2025/10/24 19:45] – mexleadminelectrical_engineering_and_electronics_1:block06 [2026/01/10 13:39] (aktuell) – mexleadmin
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-====== 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.
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 </callout> </callout>
  
-===== Preparation at Home =====+==== 6.0.2 Preparation at Home ====
  
 And again:  And again: 
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 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
-===== 90-minute plan =====+==== 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).  
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   - 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 $I_{\rm SC}$. 
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 ~~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.\\
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 ~~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.
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 </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:
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 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:
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 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.
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 ~~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.
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 ~~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.
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 ~~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:">
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 </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 ====
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 The following simulation shows four cirucits. The following simulation shows four cirucits.
  
-1. Have a look on the both circuits 1a) with U_S(1a)=10 V and 1b) U_S(1b)=5 V. 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 volage and the current, when you choose the same resistor values? Why? \\ \\+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? 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?
  
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-{{page>task_3.1.3_with_calculation&nofooter}} +{{page>electrical_engineering_and_electronics:task_3.1.3_with_calculation&nofooter}} 
- +{{page>electrical_engineering_and_electronics:task_6tqttque1e2nf2c7_with_calculation&nofooter}} 
-~~PAGEBREAK~~ ~~CLEARFIX~~ +{{page>electrical_engineering_and_electronics:task_lefxcuaxiu8ewcr9_with_calculation&nofooter}}
-===== 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 $-$).+