Thesis: Filterchain: tiny bit of feedback incorporated

documents/thesis/chapters/grand_characterisation.tex

@@ -8,7 +8,7 @@
 }
 
 \begin{document}
-\chapter{GRAND characterisation}
+\chapter{GRAND signal chain characterisation}
 \label{sec:gnss_accuracy}
 
 % systematic delays important to obtain the best synchronisation
@@ -37,7 +37,8 @@ This chapter starts an investigation into these systematic delays within \gls{GR
 %\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}
+At the base of every single antenna, a \gls{DU} is mounted.
+%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.
 These inputs are connected to their respective filterchains, leaving a fourth filterchain as spare.
 Each filterchain bandpasses the signal between $30\MHz$ and $200\MHz$.
@@ -47,9 +48,9 @@ In our setup, the channels are read out after using one of two internal ``monito
 \\
 
 % timestamp = GPS + local oscillator
-The \gls{DU} timestamps an event using a combination of the 1\gls{PPS} of a Trimble ICM 360 \gls{GNSS} chip\Todo{ref?} and counting the local oscillator running at $500\MHz$.
-At trigger time, the counter value is stored to obtain a timing accuracy of roughly $2\ns$.
-The counter is also used to correct for fluctuating intervals of the 1\gls{PPS} by storing and resetting it at each incoming 1\gls{PPS}.
+%The \gls{DU} timestamps an event using a combination of the 1\gls{PPS} of a Trimble ICM 360 \gls{GNSS} chip\Todo{ref?} and counting the local oscillator running at $500\MHz$.
+%At trigger time, the counter value is stored to obtain a timing accuracy of roughly $2\ns$.
+%The counter is also used to correct for fluctuating intervals of the 1\gls{PPS} by storing and resetting it at each incoming 1\gls{PPS}.
 
 
 \begin{figure}% <<<<
@@ -62,10 +63,9 @@ The counter is also used to correct for fluctuating intervals of the 1\gls{PPS}
 \end{figure}% >>>>
 
 % >>>
-\section{Filterchain Relative Time Delays}% <<<
+%\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.
-\Todo{expand}
 \\
 
 \begin{figure}[h]
@@ -80,20 +80,20 @@ Since each channel corresponds to a polarisation, it is important that relative
 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 $\Delta t_\mathrm{cable}$ due to extra cable length.
 In this ``forward'' setup, both channels are read out at the same time, and a time delay is derived from the channels' traces.
-Afterwards, the cables are interchanged and a second (``backwards'') time delay is measured.
+Afterwards, the cables are interchanged and a second (``backward'') time delay is measured.
 \\
 The sum of the ``forward'' and ``backward'' time delays gives twice the relative time delay $\Delta t$ without needing to measure the time delays due to the cable lengths $t_\mathrm{cable}$ separately since
 \begin{equation}\label{eq:forward_backward_cabling}
 	\phantom{.}
 	\Delta t
 	= (t_\mathrm{forward} + t_\mathrm{backward})/2
-	= ([\Delta t + \Delta t_\mathrm{cable}] + [\Delta t - t_\mathrm{cable}])/2
+	= ([\Delta t + t_\mathrm{cable}] + [\Delta t - t_\mathrm{cable}])/2
 	.
 \end{equation}
 \\
 
 % setup: signal
-We used a \Todo{name} signal generator to emit a single sine wave at frequencies $50$--$ 200 \MHz$ at $200\mathrm{\;mVpp}$.\Todo{check}
+We used a signal generator to emit a single sine wave at frequencies $50$--$ 200 \MHz$ at $200\mathrm{\;mVpp}$ (see Figure~\ref{fig:grand:signal}).
 Therefore, the time delays have been measured as phase differences.
 % Frequencies above 50mhz not true measurement
 In our setup, the cable length difference was approximately $3.17-2.01 = 1.06\metre$, resulting in an estimated cable time delay of roughly $5\ns$.
@@ -103,6 +103,21 @@ For higher frequencies, the phase differences can not distinguish more than one
 However, because it is symmetric for both setups, this does not affect the measurement of the filterchain time delay.\Todo{prove}
 \\
 
+\begin{figure}% <<< fig:grand:signal
+	\begin{subfigure}{0.47\textwidth}
+		\protect \Todo{2ch waveforms}
+	\end{subfigure}
+	\hfill
+	\begin{subfigure}{0.47\textwidth}
+		\protect \Todo{FFT}
+	\end{subfigure}
+	\caption{
+		Waveforms of the sine wave measured in the ``forward'' setup and the phase shift between the channels.
+		The sine wave was emitted at $50\MHz$ at $200\;\mathrm{mVpp}$.
+	}
+	\label{fig:grand:signal}
+\end{figure}% >>>
+
 \begin{figure}% <<<<
 	\centering
 	\begin{subfigure}{0.45\textwidth}