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Thesis: Filterchain: WuotD

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documents/thesis/chapters/grand_characterisation.tex
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@ -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}