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Matthias Jung
2026-08-02 14:14:35 +02:00
parent 5851d19ec6
commit 82d8eed306
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contents/drawings/1119.tex
+327
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% 2026, Prof. Dr. Matthias Jung (DL9MJ)
\begin{tikzpicture}
\begin{axis}[
width=\linewidth*\getDarcImageFactor,
height=0.75\linewidth*\getDarcImageFactor,
xmin=-8.8,
xmax=11.8,
ymin=-3.5,
ymax=10.8,
axis lines=none,
clip=false,
]
% --------------------------------------------------------------------------
% Koordinatenachsen
% --------------------------------------------------------------------------
\draw[-Triangle]
(axis cs:0,0) -- (axis cs:11.4,0);
\draw[-Triangle]
(axis cs:0,0) -- (axis cs:-8.5,0);
\draw[-Triangle]
(axis cs:0,0) -- (axis cs:0,10.5);
\draw[-Triangle]
(axis cs:0,0) -- (axis cs:0,-3.3);
% Achsenbeschriftungen
\node[anchor=west]
at (axis cs:11.45,-0.25)
{$U_{CE}$ in \si{\volt}};
\node[anchor=east]
at (axis cs:-8.55,-0.25)
{$I_B$ in \si{\micro\ampere}};
\node[anchor=south]
at (axis cs:0.25,10.5)
{$I_C$ in \si{\milli\ampere}};
\node[anchor=north]
at (axis cs:0.25,-3.3)
{$U_{BE}$ in \si{\volt}};
% --------------------------------------------------------------------------
% Skalen rechts: U_CE in Volt
% --------------------------------------------------------------------------
\pgfplotsinvokeforeach{2,4,6,8,10}{
\draw
(axis cs:#1,-0.10) -- (axis cs:#1,0.10);
\node[anchor=north]
at (axis cs:#1,-0.13)
{\small #1};
}
% --------------------------------------------------------------------------
% Skalen links: I_B in Mikroampere
% Eine Koordinateneinheit entspricht 10 µA.
% --------------------------------------------------------------------------
\def\DARCIbTick#1/#2\relax{
\draw
(axis cs:#1,-0.10) -- (axis cs:#1,0.10);
\node[anchor=north]
at (axis cs:#1,-0.13)
{\small #2};
}
\pgfplotsinvokeforeach{-2/20,-4/40,-6/60,-8/80}{
\expandafter\DARCIbTick#1\relax
}
% --------------------------------------------------------------------------
% Skalen oben: I_C in Milliampere
% --------------------------------------------------------------------------
\pgfplotsinvokeforeach{2,4,6,8,10}{
\draw
(axis cs:-0.10,#1) -- (axis cs:0.10,#1);
\node[anchor=east]
at (axis cs:-0.14,#1)
{\small #1};
}
% --------------------------------------------------------------------------
% Skalen unten: U_BE in Volt
% Die geometrische Skala ist für die gemeinsame Darstellung gestreckt.
% --------------------------------------------------------------------------
\def\DARCUbeTick#1/#2\relax{
\draw
(axis cs:-0.10,#1) -- (axis cs:0.10,#1);
\node[anchor=east]
at (axis cs:-0.14,#1)
{\small #2};
}
\pgfplotsinvokeforeach{-1/{0{,}6},-2/{0{,}7},-3/{0{,}8}}{
\expandafter\DARCUbeTick#1\relax
}
% --------------------------------------------------------------------------
% Stromsteuerkennlinie I_C = beta * I_B
%
% Bei beta = 100 gilt:
% 10 µA Basisstrom entsprechen ungefähr 1 mA Kollektorstrom.
% --------------------------------------------------------------------------
\addplot[
DARCblue,
very thick,
domain=0:8,
samples=2,
]
({-x},{x});
\node[
anchor=south east,
align=right,
]
at (axis cs:-6.4,8.2)
{Stromsteuerkennlinie\\$I_C \approx \beta I_B$};
% --------------------------------------------------------------------------
% Eingangskennlinie
%
% Vereinfachte Exponentialkennlinie der Basis-Emitter-Strecke.
% Parameter u entspricht U_BE.
% --------------------------------------------------------------------------
\addplot[
DARCblue,
very thick,
domain=0.50:0.80,
samples=160,
variable=\u,
]
(
{-0.054*exp((\u-0.55)/0.05)},
{-10*(\u-0.50)}
);
\node[
anchor=north east,
]
at (axis cs:-6.0,-3.0)
{Eingangskennlinie};
% --------------------------------------------------------------------------
% Ausgangskennlinien
%
% Vereinfachtes Modell:
% I_C nähert sich für größere U_CE dem durch I_B festgelegten Wert an.
% --------------------------------------------------------------------------
\pgfplotsinvokeforeach{1,2,3,4,5,6,7,8}{
\addplot[
DARCblue,
thick,
domain=0:10,
samples=150,
]
{#1*(1-exp(-x/0.25))};
}
\node[
anchor=south west,
]
at (axis cs:4.5,9.5)
{Ausgangskennlinien};
% Beschriftung ausgewählter Basisströme
\def\DARCoutputLabel#1/#2\relax{
\node[
anchor=west,
font=\scriptsize,
fill=white,
inner sep=1pt,
]
at (axis cs:9.7,#1)
{$I_B=\qty{#2}{\micro\ampere}$};
}
\pgfplotsinvokeforeach{2/20,4/40,6/60,8/80}{
\expandafter\DARCoutputLabel#1\relax
}
% --------------------------------------------------------------------------
% Arbeitsgerade
%
% Beispiel:
% U_0 = 10 V
% R_C = 1 kOhm
%
% I_C = (U_0 - U_CE) / R_C
% Bei der gewählten Skalierung ergibt sich I_C[mA] = 10 - U_CE[V].
% --------------------------------------------------------------------------
\addplot[
black,
densely dashed,
very thick,
domain=0:10,
samples=2,
]
{10-x};
% --------------------------------------------------------------------------
% Arbeitspunkt Q
%
% U_CE = 5 V
% I_C = 5 mA
% I_B = 50 µA
% --------------------------------------------------------------------------
\addplot[
only marks,
mark=*,
mark size=2.3pt,
DARCgreen,
]
coordinates {
(5,5)
};
% --------------------------------------------------------------------------
% Hilfslinien zwischen den Kennlinien und dem Arbeitspunkt
% --------------------------------------------------------------------------
% Projektion von I_B auf die Stromsteuerkennlinie und zum Arbeitspunkt
\draw[
DARCgreen,
thick,
densely dashed,
]
(axis cs:-5,0)
-- (axis cs:-5,5)
-- (axis cs:5,5)
-- (axis cs:5,0);
% Zugehöriger Punkt auf der Eingangskennlinie:
% bei I_B ungefähr 50 µA ergibt sich U_BE ungefähr 0,78 V.
\draw[
DARCgreen,
thick,
densely dashed,
]
(axis cs:-5,0)
-- (axis cs:-5,-2.77)
-- (axis cs:0,-2.77);
\fill[DARCgreen]
(axis cs:-5,5)
circle[radius=1.5pt];
\fill[DARCgreen]
(axis cs:-5,-2.77)
circle[radius=1.5pt];
% --------------------------------------------------------------------------
% Beispielhafte Aussteuerung entlang der Arbeitsgeraden
% --------------------------------------------------------------------------
\node[
rotate=-45,
anchor=south,
fill=white,
inner sep=0pt,
outer sep=5pt,
font=\small,
]
at (axis cs:5.0,5.0)
{\textcolor{DARCgreen}{Arbeitspunkt}};
% --------------------------------------------------------------------------
% Signalübertragung durch das Kennlinienfeld
% --------------------------------------------------------------------------
% Scheitelwerte des Eingangssignals, über die drei Kennlinien bis zum
% Ausgangssignal projiziert.
\draw[gray,densely dashed]
(axis cs:0.75,-2.59)
-- (axis cs:-3.5,-2.59)
-- (axis cs:-3.5,3.5)
-- (axis cs:6.5,3.5)
-- (axis cs:6.5,-1.55);
\draw[gray,densely dashed]
(axis cs:0.75,-2.90)
-- (axis cs:-6.5,-2.90)
-- (axis cs:-6.5,6.5)
-- (axis cs:3.5,6.5)
-- (axis cs:3.5,-1.55);
% Eingangssignal u_BE(t): horizontal, da U_BE senkrecht aufgetragen ist.
\addplot[
DARCred,
thick,
domain=0.75:2.75,
samples=100,
variable=\t,
]
({\t},{-2.745 + 0.155*sin(720*(\t-0.75)/2.0)});
% Ausgangssignal u_CE(t): quer zur waagerechten U_CE-Achse. Die größere
% Auslenkung zeigt die Verstärkung, das Minuszeichen die Phasenumkehr.
\addplot[
DARCred,
very thick,
domain=-1.55:-0.35,
samples=100,
variable=\t,
]
({5.0 - 1.5*sin(360*(\t+1.55)/1.20)},{\t});
\end{axis}
\end{tikzpicture}
contents/drawings/1119.txt
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@@ -0,0 +1 @@
TODO
contents/sections/kollektorschaltung.md
+10
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@@ -28,8 +28,18 @@ Die Abbildung [ref:a_collector_circuit] zeigt eine einfache Kollektorschaltung m
[picture:140:a_collector_circuit:Kollektorschaltung mit Spannungsversorgung, Emitterwiderstand und Koppelkondensatoren]
</margin>
---
Für den Betrieb als linearer Strom-Verstärker benötigt der Transistor in der Kollektorschaltung einen definierten Arbeitspunkt (BIAS), der normalerweise durch einen Spannungsteiler an der Basis festgelegt wird.
Abbildung [ref:a_kennlinie] zeigt die Kennlinie eines NPN-Transistors mit dem durch den Spannungsteiler eingestellten Arbeitspunkt. Die Basisvorspannung wird so gewählt, dass auf dem linearen Teil der Eingangskennlinie gearbeitet wird. Dies impliziert auch, dass immer ein gewisser Ruhestrom fließt, auch wenn kein Eingangssignal anliegt. Das werden wir im Kapitel der Verstärkerklassen noch genauer betrachten.
Wird ein Eingangssignal, z.B. eine sinusförmige Wechselspannung, wie in dem Bild gezeigt angelegt, so wird dieses Signal durch die Eingangskennlinie verstärkt. Man beachte hier die Beschriftung der Achsen, aus Mikroampere werden Milliampere. Die resultierende Spannung am Ausgang kann auch aus dieser Kennlinie abgelesen werden
<margin>
[picture:1119:a_kennlinie:Kennlinie eines NPN-Transistors mit Arbeitspunkt und Signalüberlagerung]
</margin>
Der Emitterwiderstand wandelt den Strom, der durch die Kollektor-Emitter-Strecke fließt, in einen Spannungsabfall um, der am Emitter abgegriffen wird. Der Emitterstrom des Transistors fließt (gemeinsam mit dem normalerweise vernachlässigbaren Basis-Strom-Anteil) über den Emitter durch den Emitterwiderstand gegen Masse. Der Strom durch den Emitterwiderstand verursacht durch den entstehenden Spannungsabfall an diesem eine Erhöhung des Emitterpotenzials (Emitterspannung) und wirkt somit als Gegenkopplung für die Basis-Spannung. Hierdurch wird der Arbeitspunkt des Transistors zusätzlich stabilisiert, weil thermisch bedingte Änderungen des Kollektorstroms hierdurch ausgeregelt werden.
Die Ein- und Auskopplung der Signale an Basis und Emitter erfolgt über sog. Koppelkondensatoren. Diese haben die Aufgabe, Gleichspannungsanteile von der Verstärkerstufe, die zu einer Veränderung des Arbeitspunktes führen würden, fernzuhalten.