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--- electrical_engineering_and_electronics_1:block21 [2025/12/13 21:31] – mexleadmin
+++ electrical_engineering_and_electronics_1:block21 [2025/12/14 22:26] (aktuell) – mexleadmin
@@ Zeile 4: / Zeile 4: @@
 <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>
@@ Zeile 17: / Zeile 24: @@
 ===== 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 =====
 <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>
@@ Zeile 175: / Zeile 217: @@
 \\ \\
-=== 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 223: / Zeile 269: @@
 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 261: / Zeile 311: @@
 ===== 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).
-===== Exercises =====
-==== Learning Questions ====
+===== Learning Questions =====
   * Explain the difference between the unipolar and bipolar power supply of an opamp.
@@ Zeile 273: / Zeile 333: @@
   * What is the basic equation of the opamp?
+===== Exercises =====
 <panel type="info" title="Exercise 1.3.2 Calculations for negative feedback">
@@ Zeile 296: / Zeile 357: @@
 </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>