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| d958e3f12e |
@@ -3,8 +3,11 @@ image: registry.gitlab.com/islandoftex/images/texlive:latest
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build:
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script:
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- cd Auswertung
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- pdflatex Vorlage_main.tex
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- pdflatex Vorlage_main.tex
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- mkdir build
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- mkdir build/figures
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- pdflatex -shell-escape Vorlage_main.tex
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- pdflatex -shell-escape Vorlage_main.tex
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- pdflatex -shell-escape Vorlage_main.tex
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after_script:
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- cat Auswertung/Vorlage_main.log
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artifacts:
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@@ -0,0 +1,2 @@
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$latex = 'latex -interaction=nonstopmode -shell-escape';
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$pdflatex = 'pdflatex -interaction=nonstopmode -shell-escape';
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@@ -1,36 +1,37 @@
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\subsection{Signalreflexion bei Leerlauf, Kurzschluss und Anpassung}
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Im Folgenden werden die Messungen der Signalreflexion bei Leerlauf, Kurzschluss und mit einem 50 \unit{\ohm} Widerstand grafisch dargestellt. Dazu wurden Messpunkte mit einem zweikanaligen Oszilloskop aufgenommen und im Anschluss grafisch dargestellt. Ein Funktionsgenerator liefert das gemessene Signal auf der Leitung.
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Im Folgenden werden die Messungen der Signalreflexion bei Leerlauf, Kurzschluss und mit einem $50~\unit{\ohm}$ Widerstand grafisch dargestellt. Dazu wurden Messpunkte mit einem zweikanaligen Oszilloskop aufgenommen und im Anschluss grafisch dargestellt. Ein Funktionsgenerator liefert das gemessene Signal auf der Leitung.
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\begin{figure}[H]
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\centering
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\makebox[\textwidth][c]{\includegraphics[width=1.2\textwidth]{../Messungen/Diagramme/2.1/Reflexion_bei_Leerlauf.png}}
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\makebox[\textwidth][c]{\input{plots/Leerlauf.tex}}
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\caption{Reflexion bei Leerlauf}
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\label{fig:abb1}
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\end{figure}
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Die Abbildung \ref{fig:abb1} zeigt eine Reflexion einer Signalwelle auf einer Leitung mit einem offenen Ende. Am Leitungsende addieren sich die laufende und reflektierte Welle. Aus diesem Grund weist die Amplitude am Ende einen größeren Ausschlag auf.
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Die Abbildung~\ref{fig:abb1} zeigt eine Reflexion einer Signalwelle auf einer Leitung mit einem offenen Ende. Am Leitungsende addieren sich die laufende und reflektierte Welle. Aus diesem Grund weist die Amplitude am Ende einen größeren Ausschlag auf.
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\begin{figure}[H]
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\centering
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\makebox[\textwidth][c]{\includegraphics[width=1.2\textwidth]{../Messungen/Diagramme/2.1/ReflexionbeiKurzschluss.png}}
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\makebox[\textwidth][c]{\input{plots/Kurzschluss.tex}}
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\caption{Reflexion bei Kurzschluss}
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\label{fig:abb2}
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\end{figure}
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Bei der Reflexion mit einem kurzgeschlossenen Ende der Leitung ergibt sich ein Phasensprung der reflektierten Welle um $\pi$. Aus diesem Grund findet eine Auslöschung \ref{fig:abb2} der sich überlagernden Wellen statt.
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Bei der Reflexion mit einem kurzgeschlossenen Ende der Leitung ergibt sich ein Phasensprung der reflektierten Welle um $\pi$. Aus diesem Grund findet eine Auslöschung~\ref{fig:abb2} der sich überlagernden Wellen statt.
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\begin{figure}[H]
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\centering
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\makebox[\textwidth][c]{\includegraphics[width=1.2\textwidth]{../Messungen/Diagramme/2.1/Reflexion_mit_Endwiderstand.png}}
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\makebox[\textwidth][c]{\input{plots/Endwiderstand.tex}}
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\caption{Reflexion mit Endwiderstand}
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\label{fig:abb3}
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\end{figure}
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Bei der Reflexion des Signals mit einem 50 \unit{\ohm} Widerstand wird die Welle am Ende der Leitung nicht reflektiert. Demzufolge entspricht der Endwiderstand von 50 \unit{\ohm} der Impedanz der Signalleitung.
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Bei der Reflexion des Signals mit einem $50~\unit{\ohm}$ Widerstand wird die Welle am Ende der Leitung nicht reflektiert. Demzufolge entspricht der Endwiderstand von $50~\unit{\ohm}$ der Impedanz der Signalleitung.
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Im Folgenden wird die Ausbreitungsgeschwindigkeit der Signalwelle auf der Leitung berechnet.
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Die Ausbreitungsgeschwindigkeit ergibt sich aus der verstrichenen Zeit und der dabei zurückgelegten Strecke.
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Es werden somit die Amplituden \ref{fig:abb1} betrachtet, vom Scheitelwert $t_1$ bis zum Scheitelwert $t_2$ verstreicht eine Zeit von $\varDelta t = 50,04~\unit{\ns}$.
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Es werden somit die Amplituden~\ref{fig:abb1} betrachtet, vom Scheitelwert $t_1$ bis zum Scheitelwert $t_2$ verstreicht eine Zeit von $\varDelta t = 50,04~\unit{\ns}$.
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Bei der Zeit $t$ handelt es sich um die Laufzeit des Signals. Die Leitungslänge beträgt $s = 10~\unit{\meter}$.
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Die Berechnung der Ausbreitungsgeschwindigkeit der Signale auf der Leitung ergibt sich wie folgt:
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@@ -14,13 +14,9 @@ Betrachtet man die experimentelle Ermittlung des Reflexionsfaktors, so lässt si
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r_{Messung} = \frac{u_{2,max}(R)}{u_{2,max}(50 ~\unit{\ohm})}-1
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\end{equation}
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\vspace{\baselineskip} % Fügt einen zusätzlichen vertikalen Abstand ein
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Die Messwerte und Berechnungen sind in der folgenden Tabelle~\ref{table:1} aufgetragen.
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Die Messwerte und Berechnungen sind in der folgenden Tabelle \ref{table:1} aufgetragen.
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\vspace{0.5cm}
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\begin{center}
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\begin{minipage}{0.8\linewidth}
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\begin{table}[H]
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\centering
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\begin{tabular}{|c|c|c|c|c|c|}
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\hline
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@@ -41,9 +37,6 @@ Die Messwerte und Berechnungen sind in der folgenden Tabelle \ref{table:1} aufge
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\end{tabular}
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\captionof{table}{Theoretische und experimentelle Reflexionsfaktoren $r$}
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\label{table:1}
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\end{minipage}
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\end{center}
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\vspace{0.5cm}
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\end{table}
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Zuerkennen ist, dass die experimentell ermittelten Werte teilweise stark von den Theorie-Werten abweichen. Dies lässt sich schätzungsweise auf Messfehler und -ungenauigkeiten durch das genutzte Messgerät zurückführen.
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@@ -1,28 +1,30 @@
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\subsection{Ermittlung der Signalverfälschung bei unterschiedlichen Abschlusswiderständen}
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In diesem Abschnitt werden drei Diagramme dargestellt. Es behandelt die Signalverfälschung bei unterschiedlichen Abschlusswiderständen, in diesem Fall bei Leerlauf, Kurzschluss und mit einem $50$ \unit{\ohm} Widerstand.
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In diesem Abschnitt werden drei Diagramme dargestellt. Es behandelt die Signalverfälschung bei unterschiedlichen Abschlusswiderständen, in diesem Fall bei Leerlauf, Kurzschluss und mit einem $50~\unit{\ohm}$ Widerstand.
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\begin{figure}[H]
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\centering
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\makebox[\textwidth][c]{\includegraphics[width=1.2\textwidth]{../Messungen/Diagramme/2.3/Leerlauf.png}}
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\makebox[\textwidth][c]{\input{plots/1_3_Leerlauf.tex}}
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\caption{Signalverfälschung bei Leerlauf}
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\label{fig:abb4}
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\end{figure}
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Die Abbildung \ref{fig:abb4} zeigt das Verhalten bei Leerlauf. Rot gezeichnet kann das hinlaufende Signal betrachtet werden. Grün umrandet ist das rücklaufende Signal.
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Die Abbildung~\ref{fig:abb4} zeigt das Verhalten bei Leerlauf. Rot gezeichnet kann das hinlaufende Signal betrachtet werden. Grün umrandet ist das rücklaufende Signal.
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\begin{figure}[H]
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\centering
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\makebox[\textwidth][c]{\includegraphics[width=1.2\textwidth]{../Messungen/Diagramme/2.3/Kurzschluss.png}}
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\makebox[\textwidth][c]{\input{plots/1_3_Kurzschluss.tex}}
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\caption{Signalverfälschung bei Kurzschluss}
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\label{fig:abb5}
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\end{figure}
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In Abbildung \ref{fig:abb5} wird das Verhalten bei Kurzschluss dargestellt. Es sind wieder das hin- und rücklaufende Signal markiert.
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In Abbildung~\ref{fig:abb5} wird das Verhalten bei Kurzschluss dargestellt. Es sind wieder das hin- und rücklaufende Signal markiert.
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\begin{figure}[H]
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\centering
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\makebox[\textwidth][c]{\includegraphics[width=1.2\textwidth]{../Messungen/Diagramme/2.3/50Ohm.png}}
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\caption{Signalverfälschung bei 50 \unit{\ohm}}
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\makebox[\textwidth][c]{\input{plots/1_3_Endwiderstand.tex}}
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\caption{Signalverfälschung bei 50~\unit{\ohm}}
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\label{fig:abb6}
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\end{figure}
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Die letzte Abbildung \ref{fig:abb6} zeigt das Verhalten bei einem optimal dimensionierten Endwiderstand, es findet keine Reflexion auf der Leitung statt.
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Die letzte Abbildung~\ref{fig:abb6} zeigt das Verhalten bei einem optimal dimensionierten Endwiderstand, es findet keine Reflexion auf der Leitung statt.
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@@ -1,27 +1,23 @@
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\subsection{Bestimmung der frequenzabhängigen Signaldämpfung}
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\vspace{0.5cm}
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In diesem Abschnitt wird die frequenzabhängige Signaldämpfung für die Frequenzen 500kHz, 1MHz und 2MHz bestimmt.
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Es werden die Signalspannungen am Leitungsanfang und am Leitungsende gemessen. \\
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Mithilfe der Formel \ref{eq:6} wird die Signaldämpfung errechnet.
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Mithilfe der Formel~\ref{eq:6} wird die Signaldämpfung errechnet.
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\begin{equation}
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\frac{a}{dB} = 20* lg(\frac{u_{1,max}(R)}{u_{1,max,reflektiert}}) = 20* lg(\frac{u(0m)}{u(20m)})
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\frac{a}{dB} = 20* \lg \left( \frac{u_{1,max}(R)}{u_{1,max,reflektiert}} \right) = 20* \lg\left(\frac{u(0m)}{u(20m)}\right)
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\label{eq:6}
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\end{equation}
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\vspace{.5cm}
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In der Tabelle \ref{table:2} werden alle Werte aufgelistet.
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\vspace{.5cm}
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In der Tabelle~\ref{table:2} werden alle Werte aufgelistet.
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\begin{center}
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\begin{minipage}{0.8\linewidth}
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\begin{table}[H]
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\centering
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\begin{tabular}{|c|c|c|c|}
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\hline
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\multirow{1}{*}{$f[\unit{\mega\Hz}]$}&
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\multirow{1}{*}{$u_{1max}\,[\unit{\volt}]$}&
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\multirow{1}{*}{$u_{1max,reflektiert}\,[\unit{\volt}]$}&
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\multirow{1}{*}{$u_{1max}\,[\unit{\volt}]$}&
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\multirow{1}{*}{$u_{1max,reflektiert}\,[\unit{\volt}]$}&
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\multirow{1}{*}{$\frac{a}{dB}$}\\
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\hline
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\num{0,5}&\num{2.605379} &\num{1.977879}&\num{2.3934237781}\\
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@@ -32,9 +28,6 @@ In der Tabelle \ref{table:2} werden alle Werte aufgelistet.
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\end{tabular}
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\captionof{table}{Theoretische und experimentelle Reflexionsfaktoren $r$}
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\label{table:2}
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\end{minipage}
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\end{center}
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\vspace{0.5cm}
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\end{table}
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Der Wert für die Signaldämpfung für die Frequenz entspricht nicht den theoretischen Erwartungen. Bei zunehmender Frequenz wird eine zunehmende Dämpfung erwartet. Der Dämpfungswert lässt sich auf mögliche Systemfehler zurückführen.
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|
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|
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@@ -1,4 +0,0 @@
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Temperatur, Geschwindigkeit, Höhe, Länge, Breite
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5,5,2,5,2
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2,3,5,6,7
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1,4,3,2,1
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@@ -1,3 +0,0 @@
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\section{1. Einleitung}
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\vspace{1cm}
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In dem Versuch V5
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@@ -1,3 +0,0 @@
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\begin{document}
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\end{document}
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@@ -5,7 +5,10 @@
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\sisetup{locale=DE, separate-uncertainty=true}
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\sisetup{round-mode = places, round-precision = 2} % Zum Formatieren des \num Befehls (Runden auf die 2 Dezimalstelle)
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\usepackage{graphicx} % Für Bilder
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% Für Bilder
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\usepackage{graphicx}
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\graphicspath{ {./Bilder/Diagramme/} }
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\usepackage{float} % Exaktes Plazieren von Figures
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\usepackage{caption} % Für Bildbeschriftung
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\usepackage{titling} % Für Titel
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@@ -25,9 +28,25 @@
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\usepackage[left=20mm, right=20mm, top=30mm, bottom=30mm]{geometry}
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\usepackage{fancyhdr}
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% Spacing zwischen Text und Tabellen / Figures setzen
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% \setlength{\intextsep}{0pt}
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% Zum Formatieren der Paragraphen
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\usepackage{parskip}
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% Für Graphen erstellt mit Python tikzplotlib
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\usepackage{pgfplots}
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\DeclareUnicodeCharacter{2212}{−}
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\usepgfplotslibrary{groupplots,dateplot}
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\usetikzlibrary{patterns,shapes.arrows}
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\pgfplotsset{compat=newest, width=\textwidth, height=0.55\textwidth} % Größe anpassen
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\pgfplotsset{/pgf/number format/1000 sep=} % Tausendertrennzeichen entfernen
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% PFG Plots einmal erstellen und wiederverwenden, reduziert die Kompilierzeit
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\usepgfplotslibrary{external}
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\tikzsetexternalprefix{build/figures/}
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\tikzexternalize
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\newdateformat{mydate}{\THEDAY.\ \monthname[\THEMONTH], \THEYEAR} % Datum im gewünschten Format
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\captionsetup[figure]{font={scriptsize, it}}
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@@ -0,0 +1,256 @@
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% This file was created with tikzplotlib v0.10.1.
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\begin{tikzpicture}
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\definecolor{darkgray176}{RGB}{176,176,176}
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\definecolor{darkorange25512714}{RGB}{255,127,14}
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\definecolor{steelblue31119180}{RGB}{31,119,180}
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\begin{axis}[
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tick align=outside,
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tick pos=left,
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title={\textbf{Relfexion mit Endwiderstand}},
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x grid style={darkgray176},
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xlabel={Zeit $t~[\unit{\ns}]$},
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xmajorgrids,
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xmin=0, xmax=220,
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xtick style={color=black},
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y grid style={darkgray176},
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ylabel={Spannung $U~[\unit{\V}]$},
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ymajorgrids,
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ymin=-1.53729, ymax=1.22349,
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ytick style={color=black}
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]
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\legend{Anfang, Ende}
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\addplot [thick, steelblue31119180, mark=*, mark size=1, mark options={solid}]
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table {%
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-1.0675562620163 -1.16079998016357
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0.934111833572388 -1.19219994544983
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2.93577980995178 -1.16079998016357
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4.93744802474976 -1.09800004959106
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6.93911600112915 -1.09800004959106
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14.9457883834839 -1.09800004959106
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20.9507923126221 -1.06669998168945
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22.9524612426758 -1.06669998168945
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24.9541282653809 -1.0353000164032
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74.9958267211914 0.533299922943115
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76.9974975585938 0.972500085830688
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78.9991683959961 1.09800004959106
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81.0008316040039 0.972500085830688
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||||
83.0025024414062 0.627500057220459
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85.0041732788086 0.15690004825592
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101.017517089844 -0.941200017929077
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