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electrical_engineering_and_electronics_1:block23 [2025/12/14 23:00] – mexleadminelectrical_engineering_and_electronics_1:block23 [2025/12/15 00:12] (aktuell) – mexleadmin
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-The **golden rules** ($R_{\rm I}=0$, $R_{\rm O}\rightarrow \infty$, $A_{\rm D}\rightarrow \infty$) also apply here. \\ \\+The **golden rules** ($R_{\rm I}\rightarrow \infty$, $R_{\rm O}=0$, $A_{\rm D}\rightarrow \infty$) also apply here. \\ \\
 Therefore, the currents through the resistors $R_1$ and $R_2$ are the same: $i_1 = i_2$ (given, that  $R_{\rm O}\rightarrow \infty$). Therefore, the currents through the resistors $R_1$ and $R_2$ are the same: $i_1 = i_2$ (given, that  $R_{\rm O}\rightarrow \infty$).
  
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 When such a signal is fed directly into a comparator, small noise amplitudes around the threshold can cause rapid switching of the output (chatter). When such a signal is fed directly into a comparator, small noise amplitudes around the threshold can cause rapid switching of the output (chatter).
  
-The Schmitt triggersolves this problem by its two distinct thresholds \(U_{\rm sh,u}\) and \(U_{\rm sh,l}\). \\ +The Schmitt trigger solves this problem by its two distinct thresholds \(U_{\rm sh,u}\) and \(U_{\rm sh,l}\). \\ 
 As long as the input signal remains between these two values, the output state does not change. As long as the input signal remains between these two values, the output state does not change.
  
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 ==== Exercises ==== ==== Exercises ====
- 
-===== Exercises ===== 
  
 <panel type="info" title="Task 23.1 Comparator Output States"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%> <panel type="info" title="Task 23.1 Comparator Output States"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
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 </WRAP></WRAP></panel> </WRAP></WRAP></panel>
 +
 +<panel type="info" title="Task 23.4 Thresholds from Resistor Ratio"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
 +
 +A Schmitt trigger uses resistors $R_1$ and $R_2$ for positive feedback. The output saturates at $\pm 8~{\rm V}$.
 +
 +  - Write expressions for $U_{\rm sh,u}$ and $U_{\rm sh,l}$.
 +  - Explain how the ratio $R_1/R_2$ influences the control band of the bang-bang controller.
 +
 +<button size="xs" type="link" collapse="Loesung_23_7_Tipps">{{icon>eye}} Tips for the solution</button><collapse id="Loesung_23_7_Tipps" collapsed="true">
 +  * Recall that the thresholds are proportional to the output saturation voltage.
 +</collapse>
 +
 +<button size="xs" type="link" collapse="Loesung_23_7_Result">{{icon>eye}} Result</button><collapse id="Loesung_23_7_Result" collapsed="true">
 +  * $U_{\rm sh,u}=+\dfrac{R_1}{R_2}\,8~{\rm V}$, $U_{\rm sh,l}=-\dfrac{R_1}{R_2}\,8~{\rm V}$.
 +  * A larger ratio $R_1/R_2$ widens the control band.
 +</collapse>
 +
 +</WRAP></WRAP></panel>
 +
 +
  
 ===== Embedded resources ===== ===== Embedded resources =====