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Expected results

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Arne van Iterson 2024-04-12 13:39:44 +02:00
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doc/crosstalk/main.tex
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\usepackage{lipsum}
\usepackage{hyperref}
\usepackage{listings}
\usepackage{gensymb}
\title{
Crosstalk experiment\linebreak
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\section{Expected results}
The results expected for the different types of crosstalk are described in the following sections.\\
% CITATION NEEDED
\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
Capacitive crosstalk is caused by the electric field of the signal conductor inducing a voltage on the interfered conductor. This electric field is generated by the presence of a voltage on the signal conductor. Therefore, when the signal conductor is terminated by a short terminator, 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. Capacitive crosstalk does not have a phase shift. \\
\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.\\
Inductive crosstalk is caused by the magnetic field of the signal conductor inducing a voltage on the interfered conductor. The magnetic field is generated by the current flowing through the signal conductor. When the signal conductor is terminated, the crosstalk should be at its maximum since the current is as high as it can be. When the signal conductor is not terminated, the crosstalk should be minimal. The magnetic field generates a current in the interfered conductor that is opposite to the signal conductor, creating a 180$\degree$ phase shift\\
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.
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 completely, creating a resistor divider, 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.
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 analysed and compared to the expected results.
\subsection{Measurements}
\subsubsection{Open termination}
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\end{figure}
\subsection{Analysis}
\subsubsection{Characteristic termination}
From the measurements, it becomes clear that the correct characteristic termination is, in fact, 230 $\Omega$. The 50 $\Omega$ terminator does dampen the crosstalk on the far end of the conductor (Figure \ref*{fig:graph_char_50_far}), while the 230 $\Omega$ terminator effectively eliminates it (Figure \ref*{fig:graph_char_230_far}).
\section{Conclusion}