Thesis: Filterchain: WuotD

documents/thesis/chapters/grand_characterisation.tex

@@ -18,114 +18,133 @@ In the previous chapters, the overall performance of this strategy has been expl
 % 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}.
+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}
+%\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}
+These inputs are connected to their respective filterchains, leaving a fourth filterchain as spare.
+Each filterchain bandpasses the signal between $30\MHz$ and $200\MHz$.
+Finally, the signals are digitised by a four channel 14-bit \gls{ADC} sampling at $500\MHz$.
+%The input voltage ranges from $-900\mV$ to $+900\mV$.
+In our setup, the channels are read out after using one of two internal ``monitoring'' triggers.
 \\
+
 % 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}
-\\
+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}.
 
-\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}
+	\centering
+		\includegraphics[width=0.5\textwidth]{grand/grand_DU_encased}
+		\caption{
+			\gls{GRAND}'s \acrlong{DU} V2.0 inside its protective encasing.
+		}
+		\label{fig:grand_du}
 \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}
+% >>>
+\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}
-	\includegraphics[width=\textwidth]{grand/split-cable/split-cable-delays-ch1ch4.pdf}
+\begin{figure}[h]
+	\centering
+	\includegraphics[width=0.4\textwidth]{grand/setup/channel-delay-setup.pdf}
 	\caption{
-		\protect \Todo{only sine}
+		Relative time delay experiment, a signal generator sends the same signal to two channels of the \gls{DU}.
+		The extra time delay incurred by the loop in the upper cable can be ignored by interchanging the cabling and doing a second measurement.
 	}
-	\label{fig:split-cable-delays}
+	\label{fig:channel-delay-setup}
 \end{figure}
+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.
+\\
+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
+	.
+\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}
+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 $5\ns$.
+Figure~\ref{fig:channel-delays} shows this is in accordance with the measured delays.
+At a frequency of $50\MHz$, the difference between the forward and backward phase differences is thus expected to be approximately half a cycle.
+For higher frequencies, the phase differences can not distinguish more than one period.\Todo{rephrase}
+However, because it is symmetric for both setups, this does not affect the measurement of the filterchain time delay.\Todo{prove}
+\\
+
+\begin{figure}% <<<<
+	\centering
+	\begin{subfigure}{0.45\textwidth}
+		\includegraphics[width=\textwidth]{grand/split-cable/sine-sweep/ch1ch2fig2-combi-time-delays.pdf}
+		\caption{
+			Channels 1,2
+		}
+		\label{fig:channel-delays:1,2}
+	\end{subfigure}
+	\hfill
+	\begin{subfigure}{0.45\textwidth}
+		\includegraphics[width=\textwidth]{grand/split-cable/sine-sweep/ch2ch4fig2-combi-time-delays.pdf}
+		\caption{
+			Channels 2,4
+		}
+		\label{fig:channel-delays:2,4}
+	\end{subfigure}
+	\caption{
+		Total and Filterchain Time Delays between \subref{fig:channel-delays:1,2} channels 1 and 2, and  \subref{fig:channel-delays:2,4} 2 and 4.
+		Dark grey vertical lines indicate the maximum measurable time delay per frequency.
+		\protect \Todo{
+			y-axes,
+			larger text
+		}
+	}
+	\label{fig:channel-delays}
+\end{figure}% >>>>
+
+Figure~\ref{fig:channel-delays} shows that in general the relative filterchain time delays are below $0.05\ns$, with exceptional time delays upto $0.2\ns$ between channels 2 and 4.
+\Todo{why}
+
+\Todo{discuss data}
 
 % >>>
 \section{Outlook}% <<<
+\Todo{write}
 
 \begin{figure}
-	\includgraphics[width=\textwidth]{grand/setup/grand-gps-setup.pdf}
-	\caption{}
+	\centering
+	\includegraphics[width=0.3\textwidth]{grand/setup/grand-gps-setup.pdf}
+	\caption{
+	}
 	\label{fig:gps-delay-setup}
 \end{figure}
 
@@ -133,32 +152,5 @@ With cables length of $3.17\metre$ and $2.01\metre$, this is in accordance with
 
 
 
-% >>>
-\chapter{Old GRAND} % <<<
-
-Trimble ICM 360
-
-Wanted to use WR, but did not work out.
-
-Use GRAND DU to do the same, also to do characterisation of hardware.
-
-\section{GRAND Digitizer Unit}
-
-
-\section{Characterisation}
-\subsection{Filterchain time delay}
-(split-cable experiment)
-
-per filterchain time delay from phase differences
-
-\subsection{Global Navigation Satellite System}
-\label{sec:grand:gnss}
-$\sigma_t \sim 20 \ns$
-
-
-
-\subsection{Local Oscillator}
-Should be $f_\mathrm{osc} = 500 \MHz$
-
 % >>>
 \end{document}