Thesis: Filterchain: WuotD

documents/thesis/chapters/grand_characterisation.tex

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+% vim: fdm=marker fmr=<<<,>>>
 \documentclass[../thesis.tex]{subfiles}
 
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 \chapter{GRAND characterisation}
 \label{sec:gnss_accuracy}
 
+% systematic delays important to obtain the best synchronisation
+The beacon synchronisation strategy hinges on the ability to measure the beacon signal with sufficient timing accuracy.
+In the previous chapters, the overall performance of this strategy has been explored by using simulated waveforms.
+\\
+% ADC and filtering setup most important component.
+As mentioned in Chapter~\ref{sec:waveform}, the measured waveforms of a true detector will be influenced by characteristics of the antenna, the filter and the \gls{ADC}.
+Especially the filter and \gls{ADC} are important components to be characterised to compensate for possible systematic (relative) delays.
+This Chapter starts an investigation into these systematic delays within \gls{GRAND}'s \gls{DU} V2.0\cite{GRAND:DU2}.
+\\
+
+%\section{GRAND DU}% <<<
+\begin{figure}
+	\begin{subfigure}{0.47\textwidth}
+		\includegraphics[width=\textwidth]{grand/DU_board_encased}
+	\end{subfigure}
+	\hfill
+	\begin{subfigure}{0.47\textwidth}
+		\includegraphics[width=\textwidth]{grand/DU_board_nocase}
+	\end{subfigure}
+	\caption{
+		\gls{GRAND}'s \acrlong{DU} V2.0 inside (\textit{left}) and outside (\textit{right}) its protective encasing.
+	}
+	\label{fig:grand_du}
+\end{figure}
+
+% ADC
+The \gls{DU} (see Figure~\ref{fig:grand_du}), at the base of every single antenna, is the workhorse of \gls{GRAND}.\Todo{rephrase}
+Its protective encasing has three inputs to which the different polarisations of the antenna are connected.
+Inside, these inputs are connected to their respective filterchains, leaving a fourth filterchain as spare.
+Finally, the signals are digitised by a 4-channel \Todo{n-bit} \gls{ADC} sampling at $500\MHz$.
+\Todo{filterchain, ADC properties}
+\\
+% timestamp = GPS + local oscillator
+The waveforms are timestamped using a local oscillator ($\MHz$\Todo{oscillator}) and the 1\gls{PPS} of a Trimble ICM 360 \gls{GNSS} chip\Todo{ref?}.
+\Todo{more timing, oscillator}
+\\
+
+\hrule
+Test GRAND setup $\mapsto$ two channel filter delay measurement
+\\
+Outlook:
+\\
+\quad Local oscillator (multiple sine waveforms within one second),
+\\
+\quad GPS-measurement (pulse + sine per DU)
+
+
+% >>>
+\section{Filterchain Relative time delays}% <<<
+Both the \gls{ADC} and the filterchains introduce systematic delays.
+Since each channel corresponds to a polarisation, it is important that relative systematic delays between the channels can be accounted for.
+Otherwise, \Todo{rephrase p}
+\\
+
+Figure~\ref{fig:channel-delay-setup} illustrates a setup to measure the relative time delays of the filterchain and \gls{ADC}.
+Two \gls{DU}-channels receive the same signal from a signal generator where one of the channels takes an extra time delay due to extra cable length.
+A second measurement is taken after interchanging the cables.
+\\
+The difference between the time delay of the first and second measurements gives twice the relative time delay without needing to measure the time delays due to cable lengths.
+\\
+%One of the two channels takes an extra (relative) time delay by extending one of the cables.
+%It relies on sending the same signal to two \gls{DU} channels with an extra (relative) time delay for one of the channels.
+%After measuring the time delay this way, the channels are interchanged so the other channel receives the extra time delay, and a second time delay is measured.
+%This way, the time delay due to different cable lengths can be accounted for without needing to measure their lengths.
+%Since the difference between the time delay of the first and second measurements gives twice the relative time delay without this additional time delay.
+%\\
+
+
+% signal
+We used a \Todo{name} signal generator to emit a single sine wave at frequencies $30 -- 150 \MHz$.\Todo{check}
+With the tools explained in Chapter~\ref{sec:waveform}, the phase of the sine wave in each channel is measured using a \gls{DTFT}\eqref{eq:dtft}.
+The phase difference then gives a time delay between the channels.
+\\
+
+% trigger?
+
+% cable time delays
+In Figure~\ref{fig:split-cable-timings}, the difference between the measurements is approximately $10\ns$.
+With cables length of $3.17\metre$ and $2.01\metre$, this is in accordance with the estimated extra time delay of roughly $4\ns$.
+
+\begin{figure}% <<<<
+	\begin{subfigure}{0.47\textwidth}
+		\includegraphics[width=\textwidth]{grand/setup/channel-delay-setup.pdf}
+	\end{subfigure}
+	\begin{subfigure}{0.47\textwidth}
+		\includegraphics[width=\textwidth]{grand/channel-delay-setup-picture}
+	\end{subfigure}
+	\caption{
+		Relative time delay experiment by sending the same signal to two channels of the \gls{DU}.
+		The loop in the upper cable incurs a large relative time delay.
+		A second measurement then interchanges the \gls{DU} channels, moving this time delay to the other channel.
+	}
+	\label{fig:channel-delay-setup}
+\end{figure}% >>>>
+
+\begin{figure}
+	\includegraphics[width=\textwidth]{grand/split-cable/split-cable-delay-ch1ch2-50mhz-200mVpp.pdf}
+	\caption{}
+	\label{fig:split-cable-timings}
+\end{figure}
+
+\begin{figure}
+	\includegraphics[width=\textwidth]{grand/split-cable/split-cable-delays-ch1ch4.pdf}
+	\caption{
+		\protect \Todo{only sine}
+	}
+	\label{fig:split-cable-delays}
+\end{figure}
+
+% >>>
+\section{Outlook}% <<<
+
+\begin{figure}
+	\includgraphics[width=\textwidth]{grand/setup/grand-gps-setup.pdf}
+	\caption{}
+	\label{fig:gps-delay-setup}
+\end{figure}
+
+
+
+
+
+% >>>
+\chapter{Old GRAND} % <<<
+
 Trimble ICM 360
 
 Wanted to use WR, but did not work out.
@@ -34,4 +160,5 @@ $\sigma_t \sim 20 \ns$
 \subsection{Local Oscillator}
 Should be $f_\mathrm{osc} = 500 \MHz$
 
+% >>>
 \end{document}