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electrical_engineering_and_electronics_1:block07 [2025/09/29 01:27] – mexleadminelectrical_engineering_and_electronics_1:block07 [2025/10/28 00:07] (aktuell) – mexleadmin
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 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
 +===== Preparation at Home =====
  
 +And again: 
 +  * Please read through the following chapter.
 +  * Also here, there are some clips for more clarification under 'Embedded resources'. 
 +
 +For checking your understanding please do the following exercises:
 +  * 7.1
 +  * E3.3.3
 +
 +~~PAGEBREAK~~ ~~CLEARFIX~~
 ===== 90-minute plan ===== ===== 90-minute plan =====
   - Warm-up (8 min): recall passive/active sign convention; quick unit check for $P=U\cdot I$.   - Warm-up (8 min): recall passive/active sign convention; quick unit check for $P=U\cdot I$.
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 <callout icon="fa fa-lightbulb-o" color="blue"> <callout icon="fa fa-lightbulb-o" color="blue">
   - Real sources are modeled by an **ideal source** plus **internal resistance** $R_{\rm i}$; the terminal voltage **drops under load**.     - Real sources are modeled by an **ideal source** plus **internal resistance** $R_{\rm i}$; the terminal voltage **drops under load**.  
-  - **Efficiency** $\eta$ compares *delivered* to *drawn* power. In the simple DC source–load case, $\displaystyle \eta=\frac{R_{\rm L}}{R_{\rm L}+R_{\rm i}}$ (dimensionless). High-efficiency design wants $R_{\rm L}\gg R_{\rm i}$.+  - **Efficiency** $\eta$ compares **delivered** to **drawn** power. In the simple DC source–load case, $\displaystyle \eta=\frac{R_{\rm L}}{R_{\rm L}+R_{\rm i}}$ (dimensionless). High-efficiency design wants $R_{\rm L}\gg R_{\rm i}$.
   - **Utilization rate** $\varepsilon$ compares delivered power to the **maximum** available from the ideal source: $\displaystyle \varepsilon=\frac{R_{\rm L}R_{\rm i}}{(R_{\rm L}+R_{\rm i})^2}$. It peaks at $R_{\rm L}=R_{\rm i}$ with $\varepsilon_{\max}=25~\%$. This is the **maximum power transfer** condition.    - **Utilization rate** $\varepsilon$ compares delivered power to the **maximum** available from the ideal source: $\displaystyle \varepsilon=\frac{R_{\rm L}R_{\rm i}}{(R_{\rm L}+R_{\rm i})^2}$. It peaks at $R_{\rm L}=R_{\rm i}$ with $\varepsilon_{\max}=25~\%$. This is the **maximum power transfer** condition. 
   - Different goals → different $R_{\rm L}$:   - Different goals → different $R_{\rm L}$:
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 Application: Application:
-  - In __communications engineering__ the impedance matching of the source (the antenna) and the load (the signal-acquiring microcontroller) uses resistors, capacitors, and inductors.  There, we want to get the maximum power out of an antenna. For this purpose, the internal resistance of the source (e.g., a receiver) and the load (e.g., the downstream evaluation) are matched. An example can be seen in this {{electrical_engineering_1:anp084a_en_-_impedance_matching_for_near_field_com.pdf#page=4|application note for near field communication}}.+  - In __communications engineering__ the impedance matching of the source (the antenna) and the load (the signal-acquiring microcontroller) uses resistors, capacitors, and inductors.  There, we want to get the maximum power out of an antenna. For this purpose, the internal resistance of the source (e.g., a receiver) and the load (e.g., the downstream evaluation) are matched. An example can be seen in this {{anp084a_en_-_impedance_matching_for_near_field_commu.pdf#page=4|application note for near field communication}}.
   - Furthermore, also for __photovoltaic cells__ one wants to get the maximum power out. In this case, the concept is often called **{{https://en.wikipedia.org/wiki/Maximum_power_point_tracking|Maximum Power Point Tracking (MPPT)}}  **   - Furthermore, also for __photovoltaic cells__ one wants to get the maximum power out. In this case, the concept is often called **{{https://en.wikipedia.org/wiki/Maximum_power_point_tracking|Maximum Power Point Tracking (MPPT)}}  **
  
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 A source has $U_0=9.0~\rm V$, $R_{\rm i}=1.0~\Omega$. A source has $U_0=9.0~\rm V$, $R_{\rm i}=1.0~\Omega$.
   - (a) Choose $R_{\rm L}=9.0~\Omega$. Compute $I_{\rm L}$, $U_{\rm L}$, $P_{\rm L}$, $\eta$, $\varepsilon$.   - (a) Choose $R_{\rm L}=9.0~\Omega$. Compute $I_{\rm L}$, $U_{\rm L}$, $P_{\rm L}$, $\eta$, $\varepsilon$.
-  - (b) Choose $R_{\rm L}=1.0~\Omega$. Repeat. Which choice maximizes $P_{\rm L}$? Which yields higher $\eta$?  +  - (b) Choose $R_{\rm L}=1.0~\Omega$. Repeat. \\ \\ Which choice maximizes $P_{\rm L}$? Which yields higher $\eta$?  
 **Strategy:** use the boxed formulas in this block; for (b) note $R_{\rm L}=R_{\rm i} \Rightarrow \eta=50~\%$.  **Strategy:** use the boxed formulas in this block; for (b) note $R_{\rm L}=R_{\rm i} \Rightarrow \eta=50~\%$. 
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   - Compute $\eta_{\rm total}$.     - Compute $\eta_{\rm total}$.  
   - If the battery provides $5.0~\rm W$, what power reaches the sensor?   - If the battery provides $5.0~\rm W$, what power reaches the sensor?
-</WRAP></WRAP></panel> 
- 
-<panel type="info" title="Exercise 7.3 — Simplify by Thevenin/Norton (preparation for Block 08)"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%><WRAP> 
-Simplify the following circuits (//NT// for Norton, //TT// for Thevenin) to a single source plus $R_{\rm i}$, then compute $U_{\rm L}$ and $\eta$ for a given $R_{\rm L}$. 
-<imgcaption BildNr3_0 | Simplification by Norton / Thevenin theorem> </imgcaption> {{drawio>BildNr3_0.svg}} 
-</WRAP> 
-Tip: Short ideal voltage sources and open ideal current sources to determine the internal resistance. 
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