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electrical_engineering_and_electronics_1:block22 [2025/12/14 23:36] – mexleadminelectrical_engineering_and_electronics_1:block22 [2026/01/10 10:01] (current) – mexleadmin
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 ====== Block 22 — Negative-feedback Op-Amp Circuits ====== ====== Block 22 — Negative-feedback Op-Amp Circuits ======
  
-===== Learning objectives =====+===== 22.0 Intro ===== 
 + 
 +==== 22.0.1 Learning objectives ====
 <callout> <callout>
 After this 90-minute block, you can After this 90-minute block, you can
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 </callout> </callout>
  
-===== Preparation at Home =====+==== 22.0.2 Preparation at Home ====
  
 Well, again  Well, again 
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   * ...   * ...
  
-===== 90-minute plan =====+==== 22.0.3 90-minute plan ====
   - Warm-up (10 min):   - Warm-up (10 min):
     - Quick recall: ideal op-amp model and “golden rules” in negative feedback: \\ $I_{\rm p}\approx 0$, $I_{\rm m}\approx 0$, and (with feedback) $U_{\rm D}=U_{\rm p}-U_{\rm m}\rightarrow 0$.     - Quick recall: ideal op-amp model and “golden rules” in negative feedback: \\ $I_{\rm p}\approx 0$, $I_{\rm m}\approx 0$, and (with feedback) $U_{\rm D}=U_{\rm p}-U_{\rm m}\rightarrow 0$.
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     - Outlook: differential amplifier as subtraction / common-mode rejection; application circuits (PGA, instrumentation concepts).     - Outlook: differential amplifier as subtraction / common-mode rejection; application circuits (PGA, instrumentation concepts).
  
- +==== 22.0.4  Conceptual overview ====
-===== Conceptual overview =====+
 <callout icon="fa fa-lightbulb-o" color="blue"> <callout icon="fa fa-lightbulb-o" color="blue">
   * Negative feedback turns a very large (and imperfect) op-amp gain $A_{\rm D}$ into predictable closed-loop behavior: the circuit “chooses” $U_{\rm O}$ so that the differential input voltage $U_{\rm D}=U_{\rm p}-U_{\rm m}$ becomes (almost) zero.   * Negative feedback turns a very large (and imperfect) op-amp gain $A_{\rm D}$ into predictable closed-loop behavior: the circuit “chooses” $U_{\rm O}$ so that the differential input voltage $U_{\rm D}=U_{\rm p}-U_{\rm m}$ becomes (almost) zero.
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 </callout> </callout>
  
-===== Core content =====+===== 22.1 Core content =====
  
 <WRAP> <WRAP>
 <callout type="info" icon="true"> <callout type="info" icon="true">
-==== Introductory Example ====+==== 22.1.1 Introductory Example ====
  
 In various applications, currents must be measured. In an electric motor, for example, the torque is caused by the current flowing through the motor. A motor control and a simple overcurrent shutdown are based on the knowledge of the current. For further processing, a voltage must be generated from the current. The simplest current-to-voltage converter is the ohmic resistor. A sufficiently large voltage as required by a microcontroller, for example, cannot be achieved with this. So not only does the current have to be converted, but also the generated potential difference has to be amplified. In various applications, currents must be measured. In an electric motor, for example, the torque is caused by the current flowing through the motor. A motor control and a simple overcurrent shutdown are based on the knowledge of the current. For further processing, a voltage must be generated from the current. The simplest current-to-voltage converter is the ohmic resistor. A sufficiently large voltage as required by a microcontroller, for example, cannot be achieved with this. So not only does the current have to be converted, but also the generated potential difference has to be amplified.
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 </callout></WRAP> </callout></WRAP>
  
-==== Voltage follower ====+==== 22.1.2 Voltage follower ====
  
  
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  </WRAP> ~~PAGEBREAK~~ ~~CLEARFIX~~  </WRAP> ~~PAGEBREAK~~ ~~CLEARFIX~~
  
-==== Non-inverting amplifier ====+==== 22.1.3 Non-inverting amplifier ====
  
 So far, the entire output voltage has been negative-feedback. Now only a part of the voltage is to be fed back. \\ To do this, the output voltage can be reduced using a voltage divider $R_1+R_2$. The circuit for this can be seen in <imgref pic5>. So far, the entire output voltage has been negative-feedback. Now only a part of the voltage is to be fed back. \\ To do this, the output voltage can be reduced using a voltage divider $R_1+R_2$. The circuit for this can be seen in <imgref pic5>.
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 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
  
-==== Inverting Amplifier ====+==== 22.1.4 Inverting Amplifier ====
  
 The circuit of the inverting amplifier can be derived from that of the non-inverting amplifier (see <imgref pic8>). \\  The circuit of the inverting amplifier can be derived from that of the non-inverting amplifier (see <imgref pic8>). \\ 
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 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
-==== Inverting Summing Amplifier ====+==== 22.1.5 Inverting Summing Amplifier ====
  
 <WRAP><panel type="default">  <WRAP><panel type="default"> 
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 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
-==== Differential Amplifier / Subtractor ====+==== 22.1.6 Differential Amplifier / Subtractor ====
  
 <WRAP>{{url>https://www.falstad.com/circuit/circuitjs.html?ctz=CQAgjA7CAMB00LAThat6AcNYGYJJwDZCIMkAWQjHSCQkAVgCZHHpGBTAWjDACgAhiCYYsTJuRDkcLcZKxgGIHkrAJ17LoVgNy5BhggSM0Qk0IMlWnXsLkk0GaQxMI0VRuh8A7sNHgwWX8maCwvX2lZCSkZAJYvACc-BUCYll548HU+JOR01JEUzLUEHJAZdgqpBHKQmCzSgHM02vZI8qJ6xOTW8CQWKvYSrwB5FrkpJHoJ9i8AN3ARXpNe9nS8VlnsJD4AJVrennpB8BBCdiUtuAYfHqrC4XJZ26r7-0Hb9qqnyrrwvoGdUCWA+TxwUjA0yejD05WgknYGAA+kwkdAkU8kMi1Gj4OoJOQwE8zAwkWAyXwweBYRI1kY4QjqSi0Ri1KiQrjyeTUUSkThbnk4osijA9gcMspIUKhmcLvUcLAiYp+hYcAYkPhwdc+AtgUKVhK1uANpcurAdlSiZI9a50v16pBmejMciOXByeieRA+TqQCtXoCtiwIDRNmadgsDalYobhCAQ2Aw7NzXwAEbKchYFbicq6UXpzoGnNqhF8AAeUmtGHovGmBikwnYAEkAHYAFw4CS4AB1uy2AGadjgtgDGHG7AGdey2APYtydtgAW46nfYAMgBLFsccsZxMhGuSJixI-sAAmG-7-dgk+nAGUN40WwIADZ8IA noborder}} <WRAP>{{url>https://www.falstad.com/circuit/circuitjs.html?ctz=CQAgjA7CAMB00LAThat6AcNYGYJJwDZCIMkAWQjHSCQkAVgCZHHpGBTAWjDACgAhiCYYsTJuRDkcLcZKxgGIHkrAJ17LoVgNy5BhggSM0Qk0IMlWnXsLkk0GaQxMI0VRuh8A7sNHgwWX8maCwvX2lZCSkZAJYvACc-BUCYll548HU+JOR01JEUzLUEHJAZdgqpBHKQmCzSgHM02vZI8qJ6xOTW8CQWKvYSrwB5FrkpJHoJ9i8AN3ARXpNe9nS8VlnsJD4AJVrennpB8BBCdiUtuAYfHqrC4XJZ26r7-0Hb9qqnyrrwvoGdUCWA+TxwUjA0yejD05WgknYGAA+kwkdAkU8kMi1Gj4OoJOQwE8zAwkWAyXwweBYRI1kY4QjqSi0Ri1KiQrjyeTUUSkThbnk4osijA9gcMspIUKhmcLvUcLAiYp+hYcAYkPhwdc+AtgUKVhK1uANpcurAdlSiZI9a50v16pBmejMciOXByeieRA+TqQCtXoCtiwIDRNmadgsDalYobhCAQ2Aw7NzXwAEbKchYFbicq6UXpzoGnNqhF8AAeUmtGHovGmBikwnYAEkAHYAFw4CS4AB1uy2AGadjgtgDGHG7AGdey2APYtydtgAW46nfYAMgBLFsccsZxMhGuSJixI-sAAmG-7-dgk+nAGUN40WwIADZ8IA noborder}}
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 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
  
-==== Current-Voltage-Converter ====+==== 22.1.7 Current-Voltage-Converter ====
  
 <WRAP><panel type="default">  <WRAP><panel type="default"> 
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 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
-==== Voltage-to-Current Converter ====+==== 22.1.8 Voltage-to-Current Converter ====
  
 <WRAP><panel type="default">  <WRAP><panel type="default"> 
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 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
  
-==== Applications ==== +===== 22.2 Applications ===== 
-=== Programmable Gain Amplifier ===+=== 22.2.1 Programmable Gain Amplifier ===
  
 Often in applications an analog signal is too small to process (e.g. to digitalize it afterward). \\ Often in applications an analog signal is too small to process (e.g. to digitalize it afterward). \\
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 ~~PAGEBREAK~~ ~~CLEARFIX~~ ~~PAGEBREAK~~ ~~CLEARFIX~~
-===== Common pitfalls =====+===== 22.3 Common pitfalls =====
   * Mixing up open-loop and closed-loop gain:   * Mixing up open-loop and closed-loop gain:
       - open-loop: $U_{\rm O}=A_{\rm D}\,U_{\rm D}$,       - open-loop: $U_{\rm O}=A_{\rm D}\,U_{\rm D}$,
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       - finite supply rails limit $U_{\rm O}$ and can break the ideal assumptions.       - finite supply rails limit $U_{\rm O}$ and can break the ideal assumptions.
  
-===== Exercises =====+===== 22.4 Exercises =====
 ==== Worked examples ==== ==== Worked examples ====