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electrical_engineering_1:network_analysis [2023/11/28 00:37] – mexleadminelectrical_engineering_1:network_analysis [2025/01/29 00:30] (aktuell) – mexleadmin
Zeile 406: Zeile 406:
 For conditioning, the input signal is to be fed via the series resistor $R_3$ to the center potential of a voltage divider $R_1 - R_2$ with $R_1$ to a supply voltage $U_{\rm s}$. For conditioning, the input signal is to be fed via the series resistor $R_3$ to the center potential of a voltage divider $R_1 - R_2$ with $R_1$ to a supply voltage $U_{\rm s}$.
  
-The following simulation shows roughly the situation (the resistor values are not correct).+The following simulation shows roughly the situation. Be aware that the resistor and voltage values are not correct!
  
-<WRAP>{{url>https://www.falstad.com/circuit/circuitjs.html?running=false&ctz=CQAgjCDMCmC0DsIBskB08CcGkA4AsYGADEQKxFIYjnUh6TVxhgBQATiLHjiAEy95kg-oKLgSJdkL4DpkIqOoSiUpMNlrwSMWN4SWAczkK5ekDpYAlaWG03ePHXTGlzboqlIsAbp0K8oE1h-PjwnCDC+Jx1PQz8MAPlBYISoMwsAd3iAgTEUnNkVDnyZZOxStzB9SFxpEQr6iwAjTl5SJHA8ZOZEgnMWAA9W0kSkRFgMCEgMRGFBJoBLAAcAewAbAEM2AB0AZwBlFYBXNgBjaD3t7YA7AApoVANUPY293ehr3ZW2AEpBkFShAYVSohA6cxAln+zF0REQYF4DF4VTooXA0IRfHgwLaWPBaN4-wwwlIoOYfCQAQhUKGwR4enGrmRYghkH+sBq4AwDBSXPxshp4Bwoymtigk1RsiO12W6y2bwW1wA1lc7g8nnsjgBhH5-SDwPLlepcemyCAWWlgHA8K3deAQK2zNGC4KULk8sCkYHlCH7FgrAHiQrODD0sRIVCKAKuFRAA noborder}} </WRAP>+<WRAP>{{url>https://www.falstad.com/circuit/circuitjs.html?ctz=CQAgjCBMCmC0AcUB08AMBmMA2SAWeAnLgKyRZi4jGpUi7pVxhgBQATiFpZHp5djRrVULAEp9wWGl3CREgukJALUSYiwBuIWGAKQQ6VJR16ouBRHOprUFcrUsA5tt37Dx1wcgqWAdxemeDQm+jyUIhwhULywBFjR4eDWIuhYiDJhCVmCLABG2pDE8RQeYG64ECIAHgWkBlgA7NoEEOgETdyUuQCWAA4A9gA2AIZsADoAzgDK-QCubADG0JNjYwB2ABTQSI5Ik8OTE9BrE-1sAJQsNQQE4AQMzMVxdGYgolfgYE3eTWCGUGAaJ1wB9HlB4BAyrc5JRgZAPgREGRfmBiFAGkDXu8amB4G5yAZsAYWi9eLM1n0hqNDt01gBrVabba7SazADC50u6AxzXimVg+CylWUHx08EQuI8DUh8A6WNF2FuugYOmID2ewKm7AkmRk7mUVGS2oyMUFmRo3msTgk+r13gN1W0-Fl4HVmN42PA3FQEEg3yMpMo6BY-U4kgN5kRtk4SESoRFQA noborder}} </WRAP>
  
 Questions: Questions:
Zeile 458: Zeile 458:
 \end{align*} \end{align*}
  
-The formula $(1)$ is the general formula to calculate the output voltage $U_{\rm O}$ for a changing input voltage $U_{\rm I}$, where the supply voltage $U_{\rm S}" is constant. \\+The formula $(1)$ is the general formula to calculate the output voltage $U_{\rm O}$ for a changing input voltage $U_{\rm I}$, where the supply voltage $U_{\rm S}$ is constant. \\
 </callout> </callout>
  
Zeile 536: Zeile 536:
 Based on the E24 series, the following values are next to the calculated ones: Based on the E24 series, the following values are next to the calculated ones:
 \begin{align*} \begin{align*}
-R_3 &= 43 {~\rm k\Omega}\\ +R_3^0 &= 43 {~\rm k\Omega}\\ 
-R_1 &= {{1}\over{3}}   (R_3 + 15 {~\rm k\Omega}) = 20 {~\rm k\Omega} \\ +R_1^0 &= {{1}\over{3}}   (R_3 + 15 {~\rm k\Omega}) = 20 {~\rm k\Omega} \\ 
-R_2 &= {{1}\over{5.09}}(R_3 + 15 {~\rm k\Omega}) = 12 {~\rm k\Omega} +R_2^0 &= {{1}\over{5.09}}(R_3 + 15 {~\rm k\Omega}) = 12 {~\rm k\Omega} 
 \end{align*} \end{align*}
  
 #@HiddenEnd_HTML~Result1,Result~@# #@HiddenEnd_HTML~Result1,Result~@#
  
-  * Find the relationship between $R_1$, $R_2$, and $R_3$ by investigating Kirchhoff's nodal rule for the node where $R_1$, $R_2$, and $R_3$ are interconnected.+2. Find the relationship between $R_1$, $R_2$, and $R_3$ by investigating Kirchhoff's nodal rule for the node where $R_1$, $R_2$, and $R_3$ are interconnected.
  
 #@HiddenBegin_HTML~Solution2,Solution~@# #@HiddenBegin_HTML~Solution2,Solution~@#
Zeile 579: Zeile 579:
 #@HiddenEnd_HTML~Solution2,Solution ~@# #@HiddenEnd_HTML~Solution2,Solution ~@#
  
-  * What is the input resistance $R_{\rm in}(R_1, R_2, R_3)$ of the circuit (viewed from the sensor)?+3. What is the input resistance $R_{\rm in}(R_1, R_2, R_3)$ of the circuit (viewed from the sensor)?
  
-#@HiddenBegin_HTML~~Solution3,~Solution~@#+#@HiddenBegin_HTML~Solution3,Solution~@#
  
 \begin{align*} \begin{align*}
Zeile 588: Zeile 588:
 \end{align*} \end{align*}
  
-#@HiddenEnd_HTML~~Solution3,~Solution~@#+#@HiddenEnd_HTML~Solution3,Solution~@#
  
-  * What is the minimum allowed input resistance ($R_{\rm in}(R_1, R_2, R_3)$) for the sensor to still deliver current?+4. What is the minimum allowed input resistance ($R_{\rm in, min}(R_1, R_2, R_3)$) for the sensor to still deliver current? 
 + 
 +#@HiddenBegin_HTML~Solution4,Solution~@# 
 + 
 +\begin{align*} 
 +R_{\rm in, min} &= {{U_{\rm sense}}\over{I_{\rm sense, max}}} \\ 
 +                &= \rm {{15 V}\over{1 mA}} \\ 
 +                &= 15 k\Omega \\ 
 +\end{align*} 
 + 
 +#@HiddenEnd_HTML~Solution4,Solution~@#
  
 #@TaskEnd_HTML@# #@TaskEnd_HTML@#