diff --git a/documents/thesis/chapters/grand_characterisation.tex b/documents/thesis/chapters/grand_characterisation.tex index 2d77497..7e9f678 100644 --- a/documents/thesis/chapters/grand_characterisation.tex +++ b/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} diff --git a/figures/grand/split-cable/sine-sweep/ch1ch2fig2-combi-time-delays.pdf b/figures/grand/split-cable/sine-sweep/ch1ch2fig2-combi-time-delays.pdf new file mode 100644 index 0000000..05460f6 Binary files /dev/null and b/figures/grand/split-cable/sine-sweep/ch1ch2fig2-combi-time-delays.pdf differ diff --git a/figures/grand/split-cable/sine-sweep/ch1ch2fig2-combi-time-delays.png b/figures/grand/split-cable/sine-sweep/ch1ch2fig2-combi-time-delays.png new file mode 100644 index 0000000..49322da Binary files /dev/null and b/figures/grand/split-cable/sine-sweep/ch1ch2fig2-combi-time-delays.png differ diff --git a/figures/grand/split-cable/sine-sweep/ch2ch4fig2-combi-time-delays.pdf b/figures/grand/split-cable/sine-sweep/ch2ch4fig2-combi-time-delays.pdf new file mode 100644 index 0000000..9f1e5be Binary files /dev/null and b/figures/grand/split-cable/sine-sweep/ch2ch4fig2-combi-time-delays.pdf differ diff --git a/figures/grand/split-cable/sine-sweep/ch2ch4fig2-combi-time-delays.png b/figures/grand/split-cable/sine-sweep/ch2ch4fig2-combi-time-delays.png new file mode 100644 index 0000000..0c87b99 Binary files /dev/null and b/figures/grand/split-cable/sine-sweep/ch2ch4fig2-combi-time-delays.png differ