From cf173c30cb0e102d81c8d22f531b640c11c182e9 Mon Sep 17 00:00:00 2001 From: Roger Wolf <roger.wolf@kit.edu> Date: Mon, 28 Oct 2024 09:45:47 +0100 Subject: [PATCH] adding new files --- Schaltlogik/doc/Einfache-Gatter.md | 164 ++++++++++++++++++++ Schaltlogik/figures/Dioden-AND.odg | Bin 0 -> 14733 bytes Schaltlogik/figures/Dioden-AND.png | Bin 0 -> 12203 bytes Schaltlogik/figures/Dioden-OR.odg | Bin 0 -> 14061 bytes Schaltlogik/figures/Dioden-OR.png | Bin 0 -> 9607 bytes Schaltlogik/figures/NAND-mit-Transistor.odg | Bin 0 -> 20847 bytes Schaltlogik/figures/NAND-mit-Transistor.png | Bin 0 -> 20601 bytes Schaltlogik/figures/Symbol-AND.odg | Bin 0 -> 12037 bytes Schaltlogik/figures/Symbol-AND.png | Bin 0 -> 5576 bytes Schaltlogik/figures/Symbol-NAND.odg | Bin 0 -> 12257 bytes Schaltlogik/figures/Symbol-NAND.png | Bin 0 -> 6438 bytes Schaltlogik/figures/Symbol-NOT.odg | Bin 0 -> 11557 bytes Schaltlogik/figures/Symbol-NOT.png | Bin 0 -> 4267 bytes Schaltlogik/figures/Symbol-OR.odg | Bin 0 -> 12141 bytes Schaltlogik/figures/Symbol-OR.png | Bin 0 -> 5265 bytes Schaltlogik/figures/Symbole-Gatter.odg | Bin 0 -> 19968 bytes Schaltlogik/figures/Symbole-Gatter.png | Bin 0 -> 37616 bytes Schaltlogik/figures/Transistor-AND.odg | Bin 0 -> 17659 bytes Schaltlogik/figures/Transistor-AND.png | Bin 0 -> 17232 bytes Schaltlogik/figures/Transistor-NOT.odg | Bin 0 -> 16907 bytes Schaltlogik/figures/Transistor-NOT.png | Bin 0 -> 12595 bytes 21 files changed, 164 insertions(+) create mode 100644 Schaltlogik/doc/Einfache-Gatter.md create mode 100644 Schaltlogik/figures/Dioden-AND.odg create mode 100644 Schaltlogik/figures/Dioden-AND.png create mode 100644 Schaltlogik/figures/Dioden-OR.odg create mode 100644 Schaltlogik/figures/Dioden-OR.png create mode 100644 Schaltlogik/figures/NAND-mit-Transistor.odg create mode 100644 Schaltlogik/figures/NAND-mit-Transistor.png create mode 100644 Schaltlogik/figures/Symbol-AND.odg create mode 100644 Schaltlogik/figures/Symbol-AND.png create mode 100644 Schaltlogik/figures/Symbol-NAND.odg create mode 100644 Schaltlogik/figures/Symbol-NAND.png create mode 100644 Schaltlogik/figures/Symbol-NOT.odg create mode 100644 Schaltlogik/figures/Symbol-NOT.png create mode 100644 Schaltlogik/figures/Symbol-OR.odg create mode 100644 Schaltlogik/figures/Symbol-OR.png create mode 100644 Schaltlogik/figures/Symbole-Gatter.odg create mode 100644 Schaltlogik/figures/Symbole-Gatter.png create mode 100644 Schaltlogik/figures/Transistor-AND.odg create mode 100644 Schaltlogik/figures/Transistor-AND.png create mode 100644 Schaltlogik/figures/Transistor-NOT.odg create mode 100644 Schaltlogik/figures/Transistor-NOT.png diff --git a/Schaltlogik/doc/Einfache-Gatter.md b/Schaltlogik/doc/Einfache-Gatter.md new file mode 100644 index 0000000..6c82602 --- /dev/null +++ b/Schaltlogik/doc/Einfache-Gatter.md @@ -0,0 +1,164 @@ +# Hinweise für den Versuch Schaltlogik + +## OR-Gatter + +Logische Verknüpfungen (Gatter) werden z.B. durch **Wahrheitstafeln** definiert. Die Wahrheitstafel für das **OR-Gatter** ist +$$ +\begin{equation*} +\begin{array}{cc|c} + \mathrm{A} & \mathrm{B} & \mathrm{Y = A \lor B} \\ + \hline + 0 & 0 & 0 \\ + 0 & 1 & 1 \\ + 1 & 0 & 1 \\ + 1 & 1 & 1 \\ +\end{array} +\end{equation*} +$$ +Hierzu definieren wir A und B als Eingänge und Y als den Ausgang des Gatters und führen die folgenden Bezeichnungen ein: + +- 0/LOW: GND ($=0\ \mathrm{V}$) +- 1/HIGH: VCC ($=+5\ \mathrm{V}$). + +Die Zustände 0 und 1 werden durch die elektrischen Potentiale an A, B und Y identifiziert. + +Das Schaltsymbol für das OR-Gatter ist in **Abbildung 1a** gezeigt: + +--- + +<img src="../figures/Symbole-Gatter.png" width="1000" style="zoom:100%;" /> + +**Abbildung 1**: (Schaltsymbole eines (a) OR-, (b) AND-, (c) NOT- und (d) NAND-Gatters) + +--- + +Die einfachste Realisierung erfolgt mit Hilfe von zwei Dioden, wie in **Abbildung 2** gezeigt: + +--- + +<img src="../figures/Dioden-OR.png" width="1000" style="zoom:100%;" /> + +**Abbildung 2**: (Realisierung eines OR-Gatters mit Hilfe von zwei Dioden) + +--- + +- Liegt **entweder A oder B auf 1/HIGH** ($=+5\ \mathrm{V}$), fließt Strom durch den Widerstand $R$ und die Diode $D_{\mathrm{A}}$ oder die Diode $D_{\mathrm{B}}$ wird in **Durchlassrichtung** betrieben. In Durchlassrichtung fällt an einer Silizium-Diode die Knickspannung ([Schwellenspannung](https://de.wikipedia.org/wiki/Schwellenspannung)) + + ```math + \begin{equation*} + U_{D}\approx-0.7\,\mathrm{V} + \end{equation*} + ``` + + ab (siehe [Hinweise zum Versuch Transistor und Operationsverstärker](https://gitlab.kit.edu/kit/etp-lehre/p1-praktikum/students/-/blob/main/Transistor_und_Operationsverstaerker/doc/Hinweise-Transistor.md)), der Großteil der Spannung fällt also über $R$ ab und Y liegt auf hohem Potential, d.h. auf 1/HIGH. + +- Liegen jedoch **weder A noch B auf 1/HIGH**, so fließt kein Strom. Da kein Strom fließt fällt auch keine Spannung über $R$ ab und Y liegt auf 0/LOW ($=0\ \mathrm{V}$). + +- Falls ein Eingang auf 1/HIGH und der andere auf 0/LOW liegt, ist immer eine der beiden Dioden in **Sperrichtung** geschaltet, so dass kein Strom zwischen A und B fließt. + +## AND-Gatter + + Die Wahrheitstafel für das **AND-Gatter** ist +$$ +\begin{equation*} +\begin{array}{cc|c} + \mathrm{A} & \mathrm{B} & \mathrm{Y = A \land B} \\ + \hline + 0 & 0 & 0 \\ + 0 & 1 & 0 \\ + 1 & 0 & 0 \\ + 1 & 1 & 1 \\ +\end{array} +\end{equation*} +$$ +Das Schaltsymbol für das AND-Gatter ist in **Abbildung 1b** gezeigt. + +### Dioden-AND-Gatter + +Die einfachste Realisierung eines AND-Gatters erfolgt mit Hilfe von zwei Dioden, wie in **Abbildung 3** gezeigt: + +--- + +<img src="../figures/Dioden-AND.png" width="1000" style="zoom:100%;" /> + +**Abbildung 3**: (Realisierung eines AND-Gatters mit Hilfe von zwei Dioden) + +--- + +- Liegt **entweder A oder B auf 0/LOW**, fließt Strom durch $R$ und die Diode $D_{\mathrm{A}}$ oder $D_{\mathrm{B}}$ wird in **Durchlassrichtung** betrieben, der Großteil der Spannung fällt also über $R$ ab und Y liegt auf niedrigem Potential, d.h. auf 0/LOW. +- Liegen jedoch **sowohl A als auch B auf 1/HIGH**, so fließt kein Strom. Alle Eingangspunkte der Schaltung liegen auf dem gleichen Potential von $+5\ \mathrm{V}$. Da kein Strom fließt fällt auch keine Spannung ab und Y liegt auf 1/HIGH. +- Falls ein Eingang auf 1/HIGH und der andere auf 0/LOW liegt, ist immer eine der beiden Dioden in **Sperrichtung** geschaltet, so dass kein Strom zwischen A und B fließt. + +Durch $U_{D}$ ist das Potential für 0/LOW an Y etwas höher als an den Eingängen von $D_{\mathrm{A}}$ und $D_{\mathrm{B}}$. Dadurch ist die Anzahl an Dioden-Gattern, die man hintereinander schalten kann begrenzt. Dieser Nachteil lässt sich durch die Verwendung von Transistoren umgehen. + +### Transistor-AND-Gatter + +Die Realisierung eines AND-Gatters mit Hilfe von zwei Transistoren ist in **Abbildung 4** gezeigt: + +--- + +<img src="../figures/Transistor-AND.png" width="400" style="zoom:100%;" /> + +**Abbildung 4**: (Realisierung eines AND-Gatters mit Hilfe von zwei Transistoren) + +--- + +- Hier wird der Transistor nicht als Verstärker, sondern als Schalter verwendet: Liegt an der Basis keine Spannung an ($U_{\mathrm{B}}=0$) befindet sich der Transistor im **Sperrbetrieb**, für den Widerstand zwischen Kollektor und Emitter gilt $r_{\mathrm{C}}\gg 0$ und es fließt kein Strom. Da es zu keinem Stromfluss kommt liegt Y auf dem gleichen Potential wie GND und damit auf 0/LOW. +- Für $U_{\mathrm{B}}+U_{D}>0$ gilt $r_{\mathrm{C}}\approx 0$ und der Transistor befindet sich im **Sättigungsbetrieb**. Durch die Reihenschaltung von zwei Transistoren kommt es zum Stromfluss über $R_{E}$ nur dann, wenn sowohl A als auch B auf 1/HIGH liegen. Durch $r_{\mathrm{C}}\approx0$ fällt in diesem Fall die gesamte Spannung über $R_{E}$ ab und C liegt auf 1/HIGH. + +Die Vorwiderstände $R_{V}$ dienen zur Stabilisierung des Transistors (siehe Diskussion des Transistors für den Versuch [Transistor und Operationsverstärker](https://gitlab.kit.edu/kit/etp-lehre/p1-praktikum/students/-/blob/main/Transistor_und_Operationsverstaerker/doc/Hinweise-Emitterschaltung.md)). + +## NOT-Gatter + +Die Wahrheitstafel für das **NOT-Gatter** ist +$$ +\begin{equation*} +\begin{array}{c|c} + \mathrm{A} & \mathrm{Y = \overline{A}} \\ + \hline + 0 & 1 \\ + 1 & 0 \\ +\end{array} +\end{equation*} +$$ +Das entsprechende Schaltsymbol ist in **Abbildung 1c** gezeigt. Am einfachsten lässt sich das NOT-Gatter mit Hilfe eines Transistors realisieren, wie in **Abbildung 5** gezeigt: + +--- + +<img src="../figures/Transistor-NOT.png" width="500" style="zoom:100%;" /> + +**Abbildung 5**: (Realisierung eines NOT-Gatters mit Hilfe eines Transistors) + +--- + +- Liegt A auf 1/HIGH befindet sich der Transistor im **Sättigungsbetrieb**, es gilt $r_{\mathrm{C}}\approx0$ und Y liegt auf 0/LOW. +- Liegt A auf 0/LOW befindet sich der Transistor im **Sperrbetrieb**, es gilt $r_{\mathrm{C}}\gg0$, es fließt kein Strom und Y liegt auf 1/HIGH. + +## NAND-Gatter + +Kombiniert man ein AND- mit einem NOT-Gatter erhält man ein **NAND-Gatter**. Die entsprechende Wahrheitstafel für das NAND-Gatter ist +$$ +\begin{equation*} +\begin{array}{cc|c} + \mathrm{A} & \mathrm{B} & \mathrm{Y = \overline{A \land B}} \\ + \hline + 0 & 0 & 1 \\ + 0 & 1 & 1 \\ + 1 & 0 & 1 \\ + 1 & 1 & 0 \\ +\end{array} +\end{equation*} +$$ +Das Schaltsymbol ist in **Abbildung 1d** gezeigt. Die Realisierung erfolgt, z.B. wie in **Abbildung 5** gezeigt: + +--- + +<img src="../figures/NAND-mit-Transistor.png" width="600" style="zoom:100%;" /> + +**Abbildung 6**: (Realisierung eines NAND-Gatters mit Hilfe von zwei Dioden und einem Transistor) + +--- + +# Navigation + +[Main](https://gitlab.kit.edu/kit/etp-lehre/p1-praktikum/students/-/tree/main/Schaltlogik) diff --git a/Schaltlogik/figures/Dioden-AND.odg b/Schaltlogik/figures/Dioden-AND.odg new file mode 100644 index 0000000000000000000000000000000000000000..b7cfdecd29cc85e6387a6c86f8d45f54d228768e GIT binary patch literal 14733 zcmb`u1ymi|vM$^UcX!ty!QGtz!7V^=cXubadmy+4cXzh{!7X@z;O-8OoO}1(=bX3q z`R_l*s~&5t>K^@lJ*!vs>{T_Z6r{l+FaQ7s0E#R%HL}1N`rZNn@cZ+62(UJ{Hg<Bi zGuF4Wvobf-cQUuNVRW%EVzAYBG<RgMwKKLcvNd$JHnwqMFm=$kGcz}IRQMOdSC0P? zoL5cM*2cu#)Y;)5RE{i+uTW<LeFw(BN8$Yi%Ffo#+3q*=Ki~-d3g=*J>R{~X_@A%% zS4e$BLt`uB*J0cKr?LK(g-*7%R{!~We`Vosl%2kfvDJUD@UL)=PWn#H{~z}K)hJD@ zZ1tUt|C4RRe{ny}t@TZf9T`Q;oviik9RGW$FfcIx@TJ%D|3~0nHAg3RD`Q6nH*2dE 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