reflections

doc/reflection/main.tex

@@ -16,7 +16,7 @@
 \newcommand{\eqline}{\noalign{\smallskip} \hline \noalign{\smallskip}}
 
 \title{
-    Reflection experiment\linebreak
+    Reflection Experiment\linebreak
     \large{EV6 - Hardware Implementation}
 }
 
@@ -51,7 +51,7 @@
     \subsection{Objective}
     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}
+    \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:
     \begin{itemize}[beginpenalty=10000]
         \item Rigol DG 2041A Function/Arbritrary Waveform Generator
@@ -137,7 +137,7 @@
         \caption{Pulse measurement, no cable}
         \label{fig:probe_only}
     \end{figure}
-    The resulting pulse is as expected and within tolerances. 
+    The resulting pulse is as described in section \ref{sec:Methodology}, and within tolerances.
 
     \subsection{Termination results}
         \subsubsection{Open termination}
@@ -165,7 +165,7 @@
         As expected, the matched termination results in no reflection at all.
 
 
-    \subsection{Cable length determination}
+    \subsection{Cable length determination} \label{sec:cable length determination}
     By measuring the difference in time between the original pulse and the reflection, we can calculate the length of the cable using the speed formula:
     \begin{align*}
         v &= \frac{s}{t}\\
@@ -194,7 +194,7 @@
 
     The actual length of the cable is 3 meters, so the result is somewhat off, there are several possible reasons for this:
     \begin{enumerate}
-        \item The speed of light in the cable and the male to male connectors is not exactly 66\% of the speed of light in a vacuum
+        \item The speed of light in the cable and the male to male connectors is not exactly 66\% of the speed of light in a vacuum. Each percent difference yields a difference of about 5 cm in this case.
         \item The cables are not exactly 1 meter long
         \item The length of the male to male connectors is not taken into account
     \end{enumerate}
@@ -205,11 +205,29 @@
         \caption{Result for unknown cable}
         \label{fig:unknown_cable}
     \end{figure}
-    In this example, we did not change the setting of the function generator, resulting in an initial pulse of rougly 3.5 volts instead of 2.5 volts. However, this does not affect the results of the measurement since we only look at the time difference between the original pulse and the reflection.
+    The cable with an unknown length is a 75 Ohm cable made by Belden. It has partnumber 9248 printed on the sheath of the cable. According to the datasheet of the cable, the propagation delay is 82 \%\footnote{Belden, "Part Number: 9248", 9248 datasheet, 2019}. 
     
-    Using the same method as before, we find that the cable is roughly 332482034 meters long.
+    Furthermore, the initial pulse shown in figure \ref{fig:unknown_cable} is 3.5 V instead of 2.5 V. This is because the cable is a 75 Ohm cable, and thus creats a different voltage division. However, this does not affect the results of the experiment, since the pulse does not change position with respect to time.
+
+    Using the same equations as in section \ref{sec:cable length determination}, the length of the cable can be calculated.
+
+    \begin{align*}
+        c &= 299792458 & [ms^{-1}]\\
+        v &= 0.82 \cdot c\\
+        &= 245829815,56 & [ms^{-1}]\\
+        t &= 223 & [ns]\\
+        &= 223 \cdot 10^{-9} & [s]\\
+        \frac{1}{2}t &= 116,5 \cdot 10^{-9} & [s] \\
+        s &= 245829815,56 \cdot (116,5 \cdot 10^{-9})\\
+        &= 27,4100243725 & [m]\\
+        \noalign{\smallskip} \hline \noalign{\smallskip}
+        s &\approx 27,4 & [m]
+    \end{align*}
 
     \section{Conclusion}
-    Reflection = bad, termination = good, depending on what you wish to achieve. 
+    Reflections can be used to measure distance in case of a faulty cable. However, an accurate propagation delay of the cable should be known. Otherwise, depending on the length of the cable, the measurement could be off by several meters to kilometers.
+
+    In conclusion, a reflection in a transmission line can be manipulated by its termination. A matched impedance will result in no reflections, whilst a mismatched reflection will cause reflections, either positive or negative. 
+    
 \end{multicols}
 \end{document}

scripts/reflection.py

@@ -6,7 +6,7 @@ import helper
 
 # load data
 data_reader = reader.Reader()
-data = data_reader.read_file(r".\data\T0001CH1.csv")
+data = data_reader.read_file(r".\data\T0004CH1.csv")
 
 # slice empty space, start and end time is in seconds
 data = helper.cut_time(data, -1e-7, 5e-7)
@@ -29,7 +29,7 @@ idx_diff = peaks[-1] - peaks[0]
 tim_diff = idx_diff*step
 print(f"Time between peaks: {tim_diff*1e9:.1f} ns")
 c = 299792458 
-k = 0.66
+k = 0.82
 c_coax = c * k
 print(f"Measured distance: {(tim_diff/2)*c_coax:.2f} m")