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85
doc/crosstalk/main.tex
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@ -65,15 +65,19 @@
Since the experiment setup includes a series 180 $\Omega$ resistor, the characteristic impedance would be the sum of the impedance of the resistor and the impedance of the function generator. This would make the characteristic impedance 230 $\Omega$. The setup did include a terminator of 230 $\Omega$, but it seemed to be somewhat sketchy, being hand made, and we were not sure if it was part of the setup at all. We decided to use both the 50 $\Omega$ and 230 $\Omega$ terminators to be sure and to see if there was any difference in the results.
The experiment called for the students to determine the ideal frequency at which to measure the crosstalk. We setup the function generator to sweep the signal between 1 kHz to 40 MHz, the maximum frequency of the function generator, and observed the crosstalk on the near and using the oscilloscope. We determined the frequency at which the crosstalk was the highest, which was around 20 MHz.
\subsection{Equipment}
The following equipment will be used during the experiment:
\begin{itemize}[beginpenalty=10000] % This is to prevent the list from breaking across columns, but it doesn't do shit
The following equipment and settings will be used during the experiment:
\begin{itemize}[beginpenalty=10000]
\item Rigol DG 2041A Function/Arbritrary Waveform Generator
\begin{itemize}
\item Setup according to the method described in the lab manual:
\item Setup according to the method described in the lab manual and the determined frequency:
\begin{itemize}
\item Sinusoidal waveform
\item Frequency 20 MHz % I'm fairly certain we had to determine this at some point but we just tried some shit till it worked wheeeeee
\item Amplitude of 5 $V_{pp}$
\item Offset of 0 $V$
\item Frequency 20 MHz
\item Output impedance 50 $\Omega$
\end{itemize}
\end{itemize}
@ -112,8 +116,23 @@
The results expected for the different types of crosstalk are described in the following sections.\\
% CITATION NEEDED
\textbf{Capasive crosstalk}\\
Capacitive crosstalk is caused by the electric field of the signal conductor inducing a voltage on the interfered conductor. The crosstalk should be higher on the near side of the interfered conductor than on the far side. When the signal conductor is terminated, the voltage on the signal conductor is practically zero, making the capacitive crosstalk minimal. When the signal conductor is not terminated, the crosstalk should be at its maximum.\\ % Something smart about phase shfting here
\textbf{Capacitive crosstalk}\\
The formula for capacitive crosstalk is given by:
\begin{equation}
\begin{aligned}
U &= Z_0 \frac{j \omega C_{1,2} \cdot U_g}{2} \\
2U &= Z_0 \cdot j\omega C_{1,2} \cdot U_g \\
\frac{2U}{C_{1,2}} &= Z_0 \cdot j\omega \cdot U_g \\
C_{1,2} &= \frac{2U}{Z_0 \cdot j\omega \cdot U_g}
\end{aligned}
\end{equation}
Capacitive crosstalk is caused by the electric field of the signal conductor inducing a voltage on the interfered conductor.
When the signal conductor is terminated, the voltage on the signal conductor is practically zero, making the capacitive crosstalk minimal.
When the signal conductor is not terminated, the crosstalk should be at its maximum.\\
% Something smart about phase shfting here
\textbf{Inductive crosstalk}\\
Inductive crosstalk is caused by the magnetic field of the signal conductor inducing a voltage on the interfered conductor. The crosstalk should be higher on the far side of the interfered conductor than on the near side. When the signal conductor is terminated, the crosstalk should be at its maximum. When the signal conductor is not terminated, the crosstalk should be minimal.\\
@ -121,7 +140,61 @@
When the signal conductor is terminated with a characteristic terminator, the resulting will be a combination of the capacitive and inductive crosstalk since the voltage is not shorted and there is some current flowing through the signal conductor; Causing both the electric and magnetic field to induce a voltage on the interfered conductor.
\section{Results}
This section will show the measurement results of the experiment. The results will be presented in the form of graphs which include peak-to-peak voltage, frequency and phase shift within the legend. In the next section, the results will be analyzed and compared to the expected results.
\subsection{Measurements}
\subsubsection{Open termination}
\begin{figure}[H]
\includegraphics[width=\linewidth]{./img/Graph - Capacative - Near end.png}
\caption{Open termination near end}
\label{fig:graph_cap_near}
\end{figure}
\begin{figure}[H]
\includegraphics[width=\linewidth]{./img/Graph - Capacative - Far end.png}
\caption{Open termination far end}
\label{fig:graph_cap_far}
\end{figure}
\subsubsection{Short termination}
\begin{figure}[H]
\includegraphics[width=\linewidth]{./img/Graph - Inductive - Near end.png}
\caption{Short termination near end}
\label{fig:graph_ind_near}
\end{figure}
\begin{figure}[H]
\includegraphics[width=\linewidth]{./img/Graph - Inductive - Far end.png}
\caption{Short termination far end}
\label{fig:graph_ind_far}
\end{figure}
\subsubsection{Characteristic termination}
\textbf{50 Ohm terminator}
\begin{figure}[H]
\includegraphics[width=\linewidth]{./img/Graph - 50 Ohm - Near end.png}
\caption{50 Ohm termination near end}
\label{fig:graph_char_50_near}
\end{figure}
\begin{figure}[H]
\includegraphics[width=\linewidth]{./img/Graph - 50 Ohm - Far end.png}
\caption{50 Ohm termination far end}
\label{fig:graph_char_50_far}
\end{figure}
\textbf{230 Ohm terminator}
\begin{figure}[H]
\includegraphics[width=\linewidth]{./img/Graph - 230 Ohm - Near end.png}
\caption{230 Ohm termination near end}
\label{fig:graph_char_230_near}
\end{figure}
\begin{figure}[H]
\includegraphics[width=\linewidth]{./img/Graph - 230 Ohm - Far end.png}
\caption{230 Ohm termination far end}
\label{fig:graph_char_230_far}
\end{figure}
\subsection{Analysis}
\section{Conclusion}
\end{multicols}
\end{document}

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doc/reflection/main.tex
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@ -52,7 +52,7 @@
The purpose of the experiment is to learn the importance of proper termination of transmission lines. The results should include the effects of various different termination methods and the estimated length of an un-terminated transmission line of unknown length.
\section{Methodology}\label{sec:Methodology}
The experiment requires a pulse to be generated on the line and a way to measure any reflections, the equipment used is as follows:
The experiment requires a pulse to be generated on the line and a way to measure any reflections, the equipment and settings used are as follows:
\begin{itemize}[beginpenalty=10000]
\item Rigol DG 2041A Function/Arbritrary Waveform Generator
\begin{itemize}