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--- electrical_engineering_and_electronics_1:block21 [2025/12/13 21:32] – mexleadmin
+++ electrical_engineering_and_electronics_1:block21 [2026/01/10 10:05] (aktuell) – mexleadmin
@@ Zeile 1: / Zeile 1: @@
 ====== Block 21 — Op-Amp Basics ======
-===== Learning objectives =====
+===== 21.0 Intro =====
+==== 21.0.1 Learning objectives ====
 <callout>
 After this 90-minute block, you can
-  * ...
+  * explain what an operational amplifier (op-amp) is **as a black-box voltage amplifier** with two inputs (inverting / non-inverting) and one output.
+  * correctly label and use the voltages \(U_{\rm p}\), \(U_{\rm m}\) and the **differential voltage** \(U_{\rm D}\).
+  * state and apply the **basic equation** of the (idealized) op-amp.
+  * state and use the **golden rules** (ideal op-amp model)
+  * distinguish **open-loop gain** \(A_{\rm D}=U_{\rm O}/U_{\rm D}\) from **closed-loop / circuit voltage gain** \(A_{\rm V}=U_{\rm O}/U_{\rm I}\).
+  * explain what **feedback** is and clearly differentiate **negative feedback** (stabilizing) from **positive feedback** (reinforcing / potentially unstable).
+  * describe key **non-ideal** limitations of real op-amps at the qualitative level (finite gain, finite input resistance & bias currents, limited output swing and output current, nonzero output resistance).
+  * explain the difference between **bipolar** and **unipolar** op-amp power supply and what this implies for the possible output voltage range.
 </callout>
-===== Preparation at Home =====
+==== 21.0.2 Preparation at Home ====
 Well, again
@@ Zeile 16: / Zeile 25: @@
   * ...
-===== 90-minute plan =====
+==== 21.0.3 90-minute plan ====
-  - Warm-up (x min):
+  - Warm-up (10 min):
-    - ....
+    - Hook: audio amplifier clipping example (undistorted vs overdriven waveform/spectrum) → why “ideal amplification” is not automatic.
-  - Core concepts & derivations (x min):
+    - Recall: what does “amplify a voltage” mean? What would an ideal voltage amplifier look like (voltmeter at input, voltage source at output)?
-    - ...
+  - Core concepts & derivations (55–60 min):
-  - Practice (x min): ...
+    - Op-amp as a black box + symbols (10–15 min)
-  - Wrap-up (x min): Summary box; common pitfalls checklist.
+      - Triangle symbol(s), inverting/non-inverting inputs, output, supply rails.
+      - Differential voltage definition \(U_{\rm D}=U_{\rm p}-U_{\rm m}\).
+    - Ideal op-amp model (15 min)
+      - Basic equation \(U_{\rm O}=A_{\rm D}U_{\rm D}\).
+      - Golden rules; interpret each rule physically (input ≈ voltmeter, output ≈ ideal source).
+    - Real op-amp limits (10–15 min)
+      - Output saturation (rails / headroom), finite \(A_{\rm D}\), small input currents, limited output current.
+      - Unipolar vs bipolar supply: output range and operating point.
+    - Feedback concept (15 min)
+      - Meaning of feedback; block diagram vs circuit diagram.
+      - Sign convention: positive vs negative feedback.
+      - Big idea: with negative feedback and large \(A_{\rm D}\), the **closed-loop gain** becomes mostly set by the feedback network (introduce \(k\) and the result \(A_{\rm V}\approx 1/k\) as the motivating target; details can be finished in later blocks if needed).
+  - Practice (15–20 min):
+    - Quick symbol + sign drills: identify \(U_{\rm p}\), \(U_{\rm m}\), \(U_{\rm D}\), and predict the direction of \(U_{\rm O}\) change.
+    - “Golden rules” micro-exercises:
+      - Decide when you may set \(U_{\rm p}\approx U_{\rm m}\) and \(I_{\rm p}\approx I_{\rm m}\approx 0\).
+    - Feedback classification:
+      - Given a block diagram with \(kU_{\rm O}\) fed back, classify as positive/negative feedback and state the qualitative consequence (stabilize vs runaway/oscillate).
+  - Wrap-up (5 min):
+    - Summary box: basic equation, golden rules, open-loop vs closed-loop gain, feedback sign.
+    - Common pitfalls checklist (below).
-===== Conceptual overview =====
+==== 21.0.4 Conceptual overview ====
 <callout icon="fa fa-lightbulb-o" color="blue">
-  - ...
+  - Think of an op-amp as a **differential voltage sensor + powerful output stage**:
+      - it measures the difference \(U_{\rm D}=U_{\rm p}-U_{\rm m}\),
+      - then tries to produce \(U_{\rm O}=A_{\rm D}U_{\rm D}\).
+  - The “magic” of op-amp circuits comes from **negative feedback**:
+      - with large \(A_{\rm D}\), the circuit forces \(U_{\rm D}\) to be (almost) zero in normal operation,
+      - so you can treat \(U_{\rm p}\approx U_{\rm m}\) and \(I_{\rm p}\approx I_{\rm m}\approx 0\) as powerful design rules,
+      - and the **external feedback network** determines the closed-loop behavior (gain, impedance, linearity).
+  - Open-loop vs closed-loop is the key separation:
+      - **open-loop gain** \(A_{\rm D}\) is huge but poorly controlled,
+      - **closed-loop gain** \(A_{\rm V}\) is what we design to be stable, predictable, and useful.
+  - Reality check:
+      - real op-amps are limited by supply rails, maximum output current, finite speed, and nonzero input/output resistances.
+      - choosing unipolar vs bipolar supply changes what “zero” and “negative output” even mean in the circuit.
 </callout>
-===== Core content =====
+===== 21.1 Core content =====
 <WRAP>
@@ Zeile 35: / Zeile 79: @@
 <WRAP>
-==== Introductory example ====
+==== 21.1.1 Introductory example ====
 Acoustic amplifiers, such as those found in mobile phones, laptops, or hi-fi systems, often exhibit an unpleasant characteristic when heavily amplified: the previously undistorted signal is no longer passed on as usual, but [[https://en.wikipedia.org/wiki/Total_harmonic_distortion#Definitions_and_examples|clatters]]. It is distorted in such a way that it no longer sounds pleasant.
@@ Zeile 69: / Zeile 113: @@
-==== Circuit symbols and basic circuitry ====
+==== 21.1.2 Circuit symbols and basic circuitry ====
 This chapter deals with operational amplifiers. One application for these are the measurement of voltages, currents, and resistances. \\ These values must be determined very precisely in some applications, for example for accurate temperature measurement. In this case, amplification of the measurement signals is useful and necessary.
@@ Zeile 111: / Zeile 155: @@
 ~~PAGEBREAK~~ ~~CLEARFIX~~
-==== Basic Equation / Golden Rules ====
+==== 21.1.3 Basic Equation / Golden Rules ====
 The operational amplifier is a voltage amplifier. It simply measures on one side the voltage (like a voltmeter) and provides an amplified voltage on its output (like a voltage source). \\
@@ Zeile 175: / Zeile 219: @@
 \\ \\
-=== Power supply of the operational amplifier ===
+=== Voltage Supply of the Operational Amplifier ===
+The op-amp needs an additional voltage supply to be able to actively output more power. \\
+This two supplies are also called **rails**.
+In general, the rails are drawn on top and on below the triangular shape of the op-amp.
 For the voltage supply of the operational amplifier, a distinction is made between unipolar and bipolar:
@@ Zeile 192: / Zeile 240: @@
 ~~PAGEBREAK~~ ~~CLEARFIX~~
-==== Feedback ====
+==== 21.1.4 Feedback ====
 One of the fundamental principles of control engineering, digital technology, and electronics is **feedback**. \\
@@ Zeile 223: / Zeile 271: @@
 There is a big advantage of a real amplifier in negative feedback: \\ The voltage gain $A_\rm V$ of the whole system depends in this case only negligibly on the differential gain $A_\rm D$ (assuming $A_\rm D$ is very large). \\ \\
 In this case, the voltage gain is:
+$$A_{\rm V}=\frac {1}{k + \frac {1}{A_{\rm D}}} $$
 $$\boxed{ A_{\rm V}=\frac {1}{k} \quad \Bigg|_{A_{\rm D} \rightarrow \infty} }$$
 To avoid oscillation of the whole system, the amplifier must contain a delay element. \\
 This is present in the real amplifier in such a way that the output voltage $U_\rm O$ cannot change infinitely fast. [(Note2>That a voltage change can only take place in a finitely long time is also true for the input voltage. However, this cannot be influenced by the amplifier, but is externally specified.)].
@@ Zeile 260: / Zeile 312: @@
-===== Common pitfalls =====
+===== 21.3 Common pitfalls =====
-  * ...
+  * **Mixing up the inputs:** confusing the inverting input $U_{\rm m}$ (minus) with the non-inverting input $U_{\rm p}$ (plus). A wrong sign flips the whole behavior.
+  * **Wrong differential voltage:** forgetting that $U_{\rm D}$ = $U_{\rm p}$ - $U_{\rm m}$.
+  * **Using the golden rules outside their valid context:**
+      - $U_{\rm p} \approx $U_{\rm m}$ is only justified when the op-amp is in **linear operation** with **negative feedback** and not saturated.
+      - $I_{\rm p} \approx $I_{\rm m} \approx 0$  is an idealization; real input bias currents may matter in high-impedance circuits.
+  * **Assuming unlimited output voltage:** the output is limited by the **supply rails** (and headroom). Once saturated, linear equations break.
+  * **Confusing open-loop and closed-loop gain:** $A_{\rm D}$ (open-loop) is huge and device-dependent; $A_{\rm V}$ (closed-loop) is what the feedback network sets.
+  * **Ignoring supply type:** unipolar supply does **not** allow negative output voltages (without a mid-supply reference). Many textbook sketches silently assume bipolar rails.
+  * **Assuming unlimited output current:** real op-amps have output current limits; too-small load resistance causes clipping/distortion.
+  * **Treating block diagrams like circuit diagrams:** block diagrams show cause–effect; Kirchhoff’s laws do not automatically apply inside blocks.
+  * **Misclassifying feedback sign:** feeding output to the inverting input is typically **negative feedback**, while to the non-inverting input is typically **positive feedback** (depending on the network).
-===== Learning Questions =====
+===== 21.4 Learning Questions =====
   * Explain the difference between the unipolar and bipolar power supply of an opamp.
@@ Zeile 272: / Zeile 335: @@
   * What is the basic equation of the opamp?
-===== Exercises =====
+===== 21.5 Exercises =====
 <panel type="info" title="Exercise 1.3.2 Calculations for negative feedback">
@@ Zeile 296: / Zeile 359: @@
 </WRAP></WRAP></panel>
+<panel type="info" title="Exercise 21.1 Op-amp basics: symbols and signs">
+  * Given an operational amplifier symbol, label the following quantities:
+      - non-inverting input voltage $U_{\rm p}$,
+      - inverting input voltage $U_{\rm m}$,
+      - output voltage $U_{\rm O}$,
+      - (if present) the supply voltages $U_{\rm sp}$ and $U_{\rm sm}$.
+  * For each case below, state whether the output voltage $U_{\rm O}$ initially moves **upwards** or **downwards** (assume linear operation):
+      - $U_{\rm p}$ increases slightly over $U_{\rm m}$.
+      - $U_{\rm m}$ increases slightly over $U_{\rm p}$.
+      - $U_{\rm p} = U_{\rm m}$.
+  * Compute the differential voltage: $U_{\rm D}$ for $U_{\rm p} = 2.1\,\rm V$ and $U_{\rm m} = 2.0\,\rm V$.
+  * Using a differential gain of $A_{\rm D} = 200{'}000$, compute the **ideal** output voltage $U_{\rm O}$.
+  * Explain briefly why this output voltage cannot be realized in practice when the op-amp is powered from supply rails of $\pm 5\,\rm V$.
+</panel>
+<panel type="info" title="Exercise 21.2 Differential vs single-ended thinking">
+An op-amp has $A_{\rm D}=150{'}000$ and is powered from $\pm 12\,\rm V$.
+  - Compute $U_{\rm O}$ for $U_{\rm p}=1.002\,\rm V$ and $U_{\rm m}=1.000\,\rm V$ (ideal equation).
+  - Decide whether the result is physically possible.
+  - Explain why even very small differences between $U_{\rm p}$ and $U_{\rm m}$ are sufficient to drive the output into saturation in open-loop operation.
+</panel>
+<panel type="info" title="Exercise 21.3 Unipolar supply and output biasing">
+An op-amp operates from a unipolar supply $0\,\rm V$ to $9\,\rm V$.
+  - What output voltage corresponds to “zero differential input” in a typical unipolar configuration?
+  - Why is this value often chosen close to $U_{\rm S}/2$?
+  -  Describe one practical consequence if the output is biased too close to one supply rail.
+</panel>
+<panel type="info" title="Exercise 21.4 Unipolar supply and virtual ground intuition">
+An op-amp uses a unipolar supply $0\,\rm V \dots 10\,\rm V$. \\
+If you want to amplify a small sinus signal centered around $0\,\rm V$, why is it a problem to connect it directly to an input?
+</panel>
+<panel type="info" title="Exercise 21.5 Classify feedback (fast diagnosis)">
+  * For each statement, mark **true/false** and correct the false ones:
+      -  Feeding back a fraction of the output to the inverting input always creates negative feedback.
+      -  With negative feedback and large $A_{\rm D}$, the op-amp tends to keep $U_{\rm D}$ close to 0.
+      -  Positive feedback generally stabilizes the operating point and improves linearity.
+      -  If the output is saturated at a rail, $U_{\rm p} \approx U_{\rm m}$ must still be true.
+  * For each configuration below, classify the feedback as positive or negative (assume resistive feedback networks):
+      -  Output fed through a divider to $U_{\rm m}$, $U_{\rm p}$ driven by the input source.
+      -  Output fed through a divider to $U_{\rm p}$, $U_{\rm m}$ driven by the input source.
+</panel>
+<panel type="info" title="Exercise 21.6 Saturation and clipping reasoning">
+An op-amp is powered from $\pm 5\,\rm V$ (bipolar). The output swing is limited to about $\pm 4\,\rm V$.
+  - If $U_{\rm D}=+50\,\mu\rm V$ and $A_{\rm D}=200{,}000$, compute the ideal $U_{\rm O}$. Is saturation expected?
+  - Repeat for $U_{\rm D}=+10\,\rm mV$.
+  - Explain in one sentence why clipping produces distortion in audio signals.
+</panel>
+<panel type="info" title="Exercise 21.7 Input bias currents (qualitative + estimate)">
+A sensor with source resistance $R_{\rm S}=1\,\rm M\Omega$ drives the non-inverting input. \\
+The real op-amp dows not only show an internal resistance, but also a small current source on the input pins. \\
+This input bias current is in this exercise $I_{\rm B}=200\,\rm nA$.
+   - Estimate the voltage error at the input caused by $I_{\rm B}$ flowing through $R_{\rm S}$.
+   - Explain when such an error matters and when it is negligible.
+</panel>
+<panel type="info" title="Exercise 21.8 Output current limit and load selection">
+A real op-amp can supply at most $I_{\rm O,max}=20\,\rm mA$. \\
+It is intended to drive a load resistor $R_{\rm L}$ from an output voltage of $U_{\rm O}=3\,\rm V$.
+  - What is the minimum $R_{\rm L}$ to avoid exceeding the output current limit?
+  - If $R_{\rm L}$ is smaller than this value, what happens to the output waveform for a sine input?
+Bonus: If the op-amp can also sink $20\,\rm mA$, does that change your answer to (a)?
+</panel>