From 628864a3cf38080c699881a01f50dd00f9cc722f Mon Sep 17 00:00:00 2001
From: Roger Wolf <roger.wolf@kit.edu>
Date: Tue, 21 May 2024 17:02:55 +0200
Subject: [PATCH] intermediate commits, while growing the instructions

---
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diff --git "a/Operationsverstaerker/doc/Hinweise-Verst\303\244rker.md" "b/Operationsverstaerker/doc/Hinweise-Verst\303\244rker.md"
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+# Hinweise für den Versuch Operationsverstärker
+
+## Verstärker
+
+Ein [Verstärker](https://de.wikipedia.org/wiki/Verst%C3%A4rker_(Elektrotechnik)) ist ein in der Elektrotechnik verwendetes aktives elektronisches Bauelement, dass den zeitlichen Verlauf eines Eingangssignals mit erhöhter Leistung treu wiedergibt. dabei bedeutet das Attribute "aktiv", dass das Bauelement über eine eigene Spannungsversorgung verfügt. Eine wichtige Eigenschaft eines Verstärkers ist seine **Linearität**, d.h. ein um den Faktor $\alpha$ höheres Eingangssignal wird auch als ein um den Faktor $\alpha$ höheres Ausgangssignal wiedergegeben, sowie die **Bandbreite**, d.h. der Frequenzbereich, in dem er einsetzbar ist.
+
+## Röhrenverstärker
+
+Der grundsätzlich Aufbau eines Röhrenverstärkers ([Elektronenröhre](https://de.wikipedia.org/wiki/Elektronenr%C3%B6hre#Funktionsweise)) ist in **Abbildung 1** oben gezeigt:
+
+<img src="../figures/RoehreTransistor.png" width="1000" style="zoom:100%;"/>
+
+**Abbildung 1**: (Schematische Darstellung eines (oben) Röhrenverstärkers und (unten) npn-Transistors. Rechts unten sind die Schaltbilder eines npn- und pnp-Transistors gezeigt. Die Pfeilrichtungen im Schaltbild entsprechen den technischen Stromrichtungen)
+
+---
+
+Beim im Bild dargestellten Röhrenverstärker handelt es sich um einen Stromverstärker. An der Glühkathode (K) einer Vakuumröhre werden Elektronen freigesetzt und als freier Elektronenstrahl i.a. unter Hochspannung zur Anode (A) hin beschleunigt. An A ist der Elektronenstrahl als Strom $I_{A}$ messbar. Bereits sehr geringe Änderungen einer variablen, an der Gitterelektrode (G) anliegenden Steuerspannungen $U_{G}$ können durch diese Anordnungen als verstärktes Signal auf $I_{A}$ übertragen werden. Der Röhrenverstärker hat die Strom-Spannungs-Kennlinie einer Diode, die nur in einem begrenzten Bereich näherungsweise linear ist. Die Verstärkung hängt vom gewählten Arbeitspunkt in diesem Bereich ab und liegt i.a. in der Größenordnung von $\mathcal{O}(10-100)$. 
+
+## Transistor
+
+Ein [Transistor](https://de.wikipedia.org/wiki/Transistor) funktioniert nach dem gleichen Prinzip, wie der Röhrenverstärker. Der [Bipolartransistor](https://de.wikipedia.org/wiki/Bipolartransistor) (engl. *bipolar junction transistor*, BJT) besteht aus zwei gegeneinander geschalteten pn-[Halbleiterdioden](https://de.wikipedia.org/wiki/Diode). Je nach [Dotierung](https://de.wikipedia.org/wiki/Dotierung) unterscheidet man npn- von pnp-Transistoren. In **Abbildung 1** unten ist ein npn-Transistor gezeigt. Dabei ist die rechte Seite n- und die linke Seite stark n-dotiert; dazwischen befindet sich eine dünne p-dotierte Grenzschicht. Im Fall des pnp-Transistors sind die Dotierungen entsprechend vertauscht. Das elektrische Schaltbild für beide Transistorarten ist in **Abbildung 1** unten rechts gezeigt. 
+
+Wie beim Röhrenverstärker befinden sich am Transistor drei Anschlüsse: der linke Anschluss (E) wird als Emitter bezeichnet, der rechte (C) als Kollektor und der mittlere (B) als Basis. Im Verstärkungsbereich, liegt eine jeweils an E negative und C positive Spannung von einigen (üblicherweise $\pm15\ \mathrm{V}$) an. Damit ist die EB-Diode in Durchlass- und die BC-Diode in Sperrrichtung geschaltet. Liegt an B keine Spannung an, ist der BJT *selbstsperrend*, d.h. mindestens eine Diode (im Fall des hier diskutierten npn-Transistors die BC-Diode) ist in Sperrrichtung geschaltet. Bereits geringe mit einem kleinen Basisstrom $I_{\mathrm{B}}$ verbundene Spannungen $U_{\mathrm{EB}}$ an B können allerdings zu einem erheblichen Fluss von Ladungsträgern zwischen E und C und damit zu einem hohen Kollektorstrom $I_{\mathrm{C}}$ führen. Dabei können, je nach Transistorart, sowohl Elektronen als auch [Defektelektronen](https://de.wikipedia.org/wiki/Defektelektron) zum Stromfluss beitragen. Eine Skizze zur Beschaltung eines npn-Transistors im Verstärkerbetrieb ist in **Abbildung 2** gezeigt:
+
+<img src="../figures/TransistorSchaltung.png" width="400" style="zoom:100%;"/>
+
+**Abbildung 2**: (Beschaltung eines npn-Transistors im Verstärkerbetrieb)
+
+---
+
+Legt man zwischen E und C eine Spannung $U_{\mathrm{EC}}>0$ an wird die EB-[Sperrschicht](https://de.wikipedia.org/wiki/Raumladungszone) verringert, die BC-Sperrschicht jedoch zur gleichen Zeit vergrößert. Zwischen E und C ließt nur ein geringer, zum [Sperrstrom](https://de.wikipedia.org/wiki/Sperrstrom) der BC-Diode betragsgleicher Strom $I_{\mathrm{C}}$. In der BC-Sperrschicht wirkt die [Diffusionsspannung](https://de.wikipedia.org/wiki/Diffusionsspannung) $U_{\mathrm{D}}$ ($U_{\mathrm{D}}\approx0.7\ \mathrm{V}$ für Silizium) der Diffusion von Elektronen und Defektelektronen entgegen. Legt man an den EB-Stromkreises eine Spannung $U_{\mathrm{EB}}>U_{\mathrm{D}}$, dann wird die EB-Diode leitend. Wie bei der einfachen pn-Halbleiterdiode basiert die Leitung auf zwei Effekten: 
+
+- Zum einen werden Defektelektronen aus B in E injiziert. Der dadurch entstehende Strom ist allerdings sehr gering und nimmt mit der [Diffusionslänge](https://de.wikipedia.org/w/index.php?title=Diffusionslänge&action=edit&redlink=1) der Defektelektronen ab. Die Defektelektronen rekombinieren daraufhin mit Elektronen in E. 
+- Zum anderen werden Elektronen aus E in B injiziert. 
+
+Da E höher als B dotiert ist, überwiegt der Elektronenstrom vom E nach B. Aufgrund der geringen Breite von B, die kleiner als die Diffusionslänge der Ladungsträger ist, rekombinieren nur wenige der Elektronen mit den Defektelektronen in B. Die meisten Elektronen (ca. 99 %) diffundieren durch B in die  BC-Sperrschicht, wo sie wegen des großen Potentialabfalls von $U_{\mathrm{BC}}>0$ weiter nach C [driften](https://de.wikipedia.org/wiki/Driftgeschwindigkeit). In Form von $I_{\mathrm{C}}$ fließen auf diese Weise Elektronen von E nach C, wobei $I_{\mathrm{C}}$ durch geringe Ströme $I_{\mathrm{B}}$ gesteuert werden kann. Das Verhältnis
+$$
+\begin{equation*}
+\beta=\frac{I_{\mathrm{C}}}{I_{\mathrm{B}}},
+\end{equation*}
+$$
+das man als statischer [Stromverstärkungsfaktor](https://de.wikipedia.org/wiki/Mathematische_Beschreibung_des_Bipolartransistors#Stromverst%C3%A4rkungsfaktor) bezeichnet, hängt vom Transistortyp und von $|I_{\mathrm{C}}|$ ab. Es kann Werte zwischen 4 und 1000 annehmen. 
+
+## Operationsverstärker
+
+Ein Operationsverstärker (OPV) ist eine integrierte Schaltung bestehend aus mehreren Transistoren und i.a. einem externen Rückkopplungsnetzwerk. Die [Darlington-Schaltung](https://de.wikipedia.org/wiki/Darlington-Schaltung), als eines der einfachsten Netzwerke zur Verstärkung (ohne Rückkopplung), ist in **Abbildung 3** dargestellt: 
+
+<img src="../figures/DarlingtonSchaltung.png" width="400" style="zoom:100%;"/>
+
+**Abbildung 3**: (Darlington-Schaltung aus npn-Transistoren)
+
+---
+
+Dabei steuert der Ausgang des ersten (als [Emitterfolger](https://de.wikipedia.org/wiki/Transistorgrundschaltungen#Emitterfolger)) den Eingang des zweiten Transistors. Die Verstärkungsfaktoren beider Transistoren können in diesem Fall in etwa multipliziert werden: 
+$$
+\begin{equation*}
+\beta \approx \beta_{1}\cdot\beta_{2}.
+\end{equation*}
+$$
+Ohne äußere Beschaltung wäre $U_{\mathrm{EC}}$ abhängig von $U_{\mathrm{EB}}$ entweder maximal oder Null. Durch äußere Beschaltung verhindert man dieses Verhalten, wobei man den maximal erreichbaren Verstärkungsfaktor der Schaltung durch Gegenkopplung kontrolliert reduziert. Der (Strom-) Spannungsverstärkungsfaktor $v_{I}$ ($v_{U}$) der resultierenden Schaltung hängt dann nicht mehr vom oftmals ohnehin nicht sonderlich serienstabilen Verstärkungsfaktor $\beta$ des OPV sondern nur noch von der äußeren Beschaltung ab. Die Schaltsymbolik für einen OPV ist in **Abbildung 4** gezeigt: 
+
+<img src="../figures/OPVSymbolik.png" width="400" style="zoom:100%;"/>
+
+**Abbildung 4**: (Schaltsymbol eines Operationsverstärkers und Nomenklatur der anliegenden Ströme und Spannungen)
+
+---
+
+Der OPV besitzt i.a. mindestens fünf Pole, einen ($\ominus$) invertierenden und einen ($\oplus$) nicht-invertierenden Eingang, einen Ausgang und zwei (i.a. im Schaltbild nicht gezeigte) Anschlüsse zur externen Spannungsversorgung. I.a. ist der $\oplus$-Eingang als hochohmiger Spannungseingang ausgeführt; der $\ominus$-Eingang ist je nach OPV-Typ ebenfalls ein hochohmiger Spannungseingang oder ein niederohmiger Stromeingang. Entsprechend ist der Ausgang des OPV entweder als hochohmiger Stromausgang oder niederohmiger Spannungsausgang ausgelegt. 
+
+Der Stromfluss in den $\oplus$-Eingang wird im Folgenden mit $I_{P}$ bezeichnet, der Stromfluss in den $\ominus$-Eingang mit $I_{N}$, $U_{D}$ bezeichnet die Differenzspannung zwischen $\ominus$- und $\oplus$-Eingang und $I_{a}$ und $U_{a}$ bezeichnen Strom und Spannung des Ausgangs. Bei Gegenkopplung steigt $U_{a}$ nur so lange an, bis $U_{D}$ über das Rückkopplungsnetzwerk auf Null abfällt.
+
+# Navigation
+
+[Main](https://gitlab.kit.edu/kit/etp-lehre/p2-praktikum/students/-/tree/main/Operationsverstarker)
diff --git a/Operationsverstaerker/figures/DarlingtonSchaltung.odg b/Operationsverstaerker/figures/DarlingtonSchaltung.odg
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-- 
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