Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revision Previous revision
Next revision		 Previous revision
electrical_engineering_and_electronics_1:block23 [2025/12/14 23:03] – mexleadminelectrical_engineering_and_electronics_1:block23 [2026/01/10 10:08] (current) – mexleadmin
Line 1: Line 1:
 ====== Block 23 — Comparator Circuits ====== ====== Block 23 — Comparator Circuits ======
  
-===== Learning objectives =====+===== 23.0 Intro ===== 
 + 
 +==== 23.0.1 Learning objectives ====
 <callout> <callout>
 After this 90-minute block, you will be able to After this 90-minute block, you will be able to
Line 17: Line 19:
 </callout> </callout>
  
-===== Preparation at Home =====+==== 23.0.2 Preparation at Home ====
  
 Well, again  Well, again 
Line 26: Line 28:
   * ...   * ...
  
-===== 90-minute plan =====+==== 23.0.3 90-minute plan ====
   - Warm-up (5–10 min):   - Warm-up (5–10 min):
     - Recall: op-amp with negative feedback vs. no feedback.     - Recall: op-amp with negative feedback vs. no feedback.
Line 46: Line 48:
     - Typical mistakes and outlook to further applications     - Typical mistakes and outlook to further applications
  
-===== Conceptual overview =====+==== 23.0.4 Conceptual overview ====
 <callout icon="fa fa-lightbulb-o" color="blue"> <callout icon="fa fa-lightbulb-o" color="blue">
   - A **comparator** is the “switching cousin” of the op-amp: it does not try to keep \(u_{\rm d}\approx 0\) with negative feedback. \\ Instead, it reports the **sign** of \(u_{\rm d}=u_{\rm p}-u_{\rm m}\) by saturating its output to one of two extreme levels.   - A **comparator** is the “switching cousin” of the op-amp: it does not try to keep \(u_{\rm d}\approx 0\) with negative feedback. \\ Instead, it reports the **sign** of \(u_{\rm d}=u_{\rm p}-u_{\rm m}\) by saturating its output to one of two extreme levels.
Line 61: Line 63:
 </callout> </callout>
  
-===== Core content =====+===== 23.1 Core content =====
  
-==== Comparator ====+==== 23.1.1 Comparator ====
  
 Up to now we focussed on operational amplifier, which is only usable in a closed-loop setup.  Up to now we focussed on operational amplifier, which is only usable in a closed-loop setup. 
Line 95: Line 97:
 </WRAP> </WRAP>
  
-==== Non-inverting Schmitt Trigger ====+==== 23.1.2 Non-inverting Schmitt Trigger ====
  
 Based on the comparator, we can try to setup a "op-amp like" circuitry.  Based on the comparator, we can try to setup a "op-amp like" circuitry. 
Line 104: Line 106:
  
  
-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  $R_{\rm O}\rightarrow \infty$).
  
Line 147: Line 149:
 {{drawio>electrical_engineering_and_electronics_1:HysteresisV01.svg}} {{drawio>electrical_engineering_and_electronics_1:HysteresisV01.svg}}
  
-==== Applications ====+===== 23.2 Applications =====
  
-=== Bang-Bang Control ===+==== 23.2.1 Bang-Bang Control ====
  
 In the shown simulation, **{{wp>Bang–bang_control}}** is realized with a comparator including hysteresis. and a simple first-order plant (RC network). In the shown simulation, **{{wp>Bang–bang_control}}** is realized with a comparator including hysteresis. and a simple first-order plant (RC network).
Line 176: Line 178:
 </WRAP> </WRAP>
 \\ \\ \\ \\
-=== De-Noise ===+==== 23.2.2 De-Noise ==== 
  
 Real analog signals are often corrupted by noise.\\ Real analog signals are often corrupted by noise.\\
Line 209: Line 211:
 </WRAP> </WRAP>
  
-===== Common pitfalls =====+===== 23.3 Common pitfalls =====
   * **Treating a comparator like a linear op-amp**: assuming the output follows a linear gain law \(u_{\rm O}=A_{\rm D}\,u_{\rm d}\). In reality, the output almost always saturates at \(U_{\rm sat,min}\) or \(U_{\rm sat,max}\).   * **Treating a comparator like a linear op-amp**: assuming the output follows a linear gain law \(u_{\rm O}=A_{\rm D}\,u_{\rm d}\). In reality, the output almost always saturates at \(U_{\rm sat,min}\) or \(U_{\rm sat,max}\).
   * **Using negative-feedback intuition**: expecting the circuit to automatically enforce \(u_{\rm d}=0\). Without negative feedback, \(u_{\rm d}=0\) is only the *switching boundary*, not an operating point.   * **Using negative-feedback intuition**: expecting the circuit to automatically enforce \(u_{\rm d}=0\). Without negative feedback, \(u_{\rm d}=0\) is only the *switching boundary*, not an operating point.
Line 225: Line 227:
  
  
-===== Exercises ===== 
  
-==== Conceptual checks ====+===== 23.4 Learning Questions =====
   - Explain in one or two sentences why a comparator is normally operated without negative feedback.   - Explain in one or two sentences why a comparator is normally operated without negative feedback.
   - What information about the input signal does the comparator output represent when \(u_{\rm O}\) is in saturation?   - What information about the input signal does the comparator output represent when \(u_{\rm O}\) is in saturation?
   - Why is \(u_{\rm d}=0\) a special point for a comparator, even though it is not a stable operating point?   - Why is \(u_{\rm d}=0\) a special point for a comparator, even though it is not a stable operating point?
  
-==== Exercises ====+===== 23.5 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%>