From 88050d5f04b13384c78281ba5cd707fcc78d8365 Mon Sep 17 00:00:00 2001 From: Eric Teunis de Boone Date: Tue, 14 Nov 2023 12:17:18 +0100 Subject: [PATCH] Thesis: GRAND: finalising --- .../chapters/grand_characterisation.tex | 145 +++++++++++------- 1 file changed, 86 insertions(+), 59 deletions(-) diff --git a/documents/thesis/chapters/grand_characterisation.tex b/documents/thesis/chapters/grand_characterisation.tex index f5ae783..611ba27 100644 --- a/documents/thesis/chapters/grand_characterisation.tex +++ b/documents/thesis/chapters/grand_characterisation.tex @@ -44,7 +44,8 @@ These inputs are connected to their respective filterchains, leaving a fourth fi 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. +In our setup, the channels are read out after one of two internal ``monitoring'' triggers fire. +%The ten-second trigger (TD) is linked to the \gls{1PPS} of the \gls{GNSS} chip. \\ % timestamp = GPS + local oscillator @@ -89,21 +90,13 @@ The sum of the ``forward'' and ``backward'' time delays gives twice the relative = (t_\mathrm{forward} + t_\mathrm{backward})/2 = ([\Delta t + t_\mathrm{cable}] + [\Delta t - t_\mathrm{cable}])/2 . -\end{equation} -\\ +\end{equation}\\ % setup: signal -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 $5\ns$. -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} +We used a signal generator to emit a single sine wave at frequencies from $50\MHz$ to $200\MHz$ at $200\;\mathrm{mVpp}$. +Note that we measured the phases to determine the time delays for each channel. +In Figure~\ref{fig:grand:signal} the time delay between the channels is clearly visible in the measured waveforms as well as in the phase spectrum. \\ -\Todo{only 50MHz} - \begin{figure}% <<< fig:grand:signal \begin{subfigure}{0.47\textwidth} \includegraphics[width=\textwidth]{grand/split-cable/waveform_eid1_ch1ch2.pdf} @@ -112,71 +105,105 @@ However, because it is symmetric for both setups, this does not affect the measu \hfill \begin{subfigure}{0.47\textwidth} \includegraphics[width=\textwidth]{grand/split-cable/waveform_eid1_ch1ch2_spectrum.pdf} - \label{fig:split-cable:waveform} + \label{fig:split-cable:waveform:spectra} \end{subfigure} \caption{ - Waveforms of the sine wave measured in the ``forward'' setup and their spectra near the testing frequency of $50\MHz$.. + Waveforms of the sine wave measured in the ``forward'' setup and their spectra around the testing frequency of $50\MHz$.. The sine wave was emitted at $200\;\mathrm{mVpp}$. } \label{fig:grand:signal} \end{figure}% >>> -\begin{figure}% <<< fig:grand:phaseshift - \centering - \includegraphics[width=0.47\textwidth]{grand/split-cable/sine-sweep/ch2ch4fig8-histogram.50.pdf} - \caption{ - Histogram of the measured phase shifts in Figure~\ref{fig:grand:phaseshift:measruement}. - } - \label{fig:grand:phaseshift} -\end{figure}% >>> +% Frequencies above 50mhz not true measurement +In our setup, the cable length difference was $3.17-2.01 = 1.06\metre$, resulting in an estimated cable time delay of roughly $5\ns$. +At a frequency of $50\MHz$, the difference between the forward and backward phase differences is thus expected to be approximately half a cycle. +Figures~\ref{fig:grand:phaseshift:measurements} and~\ref{fig:grand:phaseshift} show this is in accordance with the measured delays. +\\ \begin{figure}% <<< fig:grand:phaseshift:measurements \centering \begin{subfigure}{0.47\textwidth} - \includegraphics[width=0.47\textwidth]{grand/split-cable/sine-sweep/ch2ch4fig9-measurements.forward.50.pdf} + \includegraphics[width=\textwidth]{grand/split-cable/sine-sweep/ch2ch4fig9-measurements.forward.50.pdf} + \caption{} + \label{fig:grand:phaseshift:measurements:forward} \end{subfigure} \hfill \begin{subfigure}{0.47\textwidth} - \includegraphics[width=0.47\textwidth]{grand/split-cable/sine-sweep/ch2ch4fig9-measurements.backward.50.pdf} + \includegraphics[width=\textwidth]{grand/split-cable/sine-sweep/ch2ch4fig9-measurements.backward.50.pdf} + \caption{} + \label{fig:grand:phaseshift:measurements:backward} \end{subfigure} \caption{ - The measured phase shifts at $50\MHz$ converted to a time delay. + The measured phase differences between channels 2 and 4 at $50\MHz$ converted to a time delay for the \subref{fig:grand:phaseshift:measurements:forward}~forward and \subref{fig:grand:phaseshift:measurements:backward}~backward setups. + The dashed vertical lines indicate the mean time delay, the errorbar at the bottom indicates the standard deviation of the samples. + Crosses are TD-triggered events, circles are MD-triggered. + The measurements are time-ordered within their trigger type. } - \label{fig:grand:phaseshift} + \label{fig:grand:phaseshift:measurements} \end{figure} -%\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} +\begin{figure}% <<< fig:grand:phaseshift + \centering + \includegraphics[width=0.47\textwidth]{grand/split-cable/sine-sweep/ch2ch4fig8-histogram.50.pdf} + \caption{ + Histogram of the measured phase differences in Figure~\ref{fig:grand:phaseshift:measurements}. + The relative signal chain time delay for the portrayed means is $0.2\ns$. + } + \label{fig:grand:phaseshift} +\end{figure}% >>> +\cleardoublepage + +% Conclusion +Figure~\ref{fig:channel-delays} shows the measured total time delays and the resulting signal chain time delays between both channels 1 and 2, and channels 2 and 4. +Apart from two exceptional time delays upto $0.2\ns$, the signal chain time delays are in general below $0.05\ns$. +\\ +Note that the reported signal chain time delays must be taken to be indications due to systematic behaviours (see below). +\\ +Still, even when taking $0.2\ns$ as the upper limit of any relative signal chain time delay, the electric field at the antenna are reconstructable to a sufficient accuracy to use either the pulsed or sine beacon methods (see Figures~\ref{fig:pulse:snr_time_resolution} and~\ref{fig:sine:snr_time_resolution} for reference) to synchronise an array to enable radio interferometry. +\\ + +Note that at higher frequencies the phase differences are phase-wrapped due to contention of the used period and the cable time delay. +Because it is symmetric for both setups, this should not affect the measurement of the signal chain time delay at the considered frequencies. +Nevertheless, the result at these frequencies must be interpreted with some caution. +\\ + +% Discussion +The time delays for both TD- and MD-triggered events in Figure~\ref{fig:grand:phaseshift:measurements} show a systematic behaviour of increasing total time delays for the forward setup. +However, in the backward setup, this is not as noticable. +\\ +This skewing of the channel time delays in one of the setups is also found at other frequencies (see Figures~\ref{fig:grand:phaseshift:ch1ch2} and~\ref{fig:grand:phaseshift:ch2ch4}), raising questions on the stability of the setup. +Unfortunately, it is primarily visible in the larger datasets which correspond to measurements over larger timescales. +As the number of these large datasets is limited, further investigation with the current datasets is prohibited. +\\ +The skewing might also be an artifact of the short waveforms ($N\sim500\;\mathrm{samples}$) the data acquisition system was able to retrieve at the time of measurement. +Since the data acquisition system is now able to retrieve the maximum size waveforms, this systematic behaviour can be investigated in a further experiment. +\\ + +\begin{figure}% <<<< + \centering + \begin{subfigure}{0.48\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}{0.48\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 (\textit{upper}) and signal chain (\textit{lower}) time delays between \subref{fig:channel-delays:1,2} channels 1 and 2, and \subref{fig:channel-delays:2,4} 2 and 4. + The dark grey vertical lines in the upper panes indicate the maximum measurable time delays at each frequency. + Due to systematic effects in the measurements, the signal chain time delays depicted here must be taken as indicative of upper limits. + See text for discussion. + } + \label{fig:channel-delays} +\end{figure}% >>>> % >>> \end{document}