mirror of
https://gitlab.science.ru.nl/mthesis-edeboone/m.internship-documentation.git
synced 2024-11-12 18:43:30 +01:00
thesis: shuffling content
move airshower chapter into introduction, merge beacon introduction into beacon_disciplining chapter, move gnss to grand section
This commit is contained in:
parent
4a329d95df
commit
b528735993
6 changed files with 154 additions and 219 deletions
|
@ -1,27 +0,0 @@
|
|||
\documentclass[../thesis.tex]{subfiles}
|
||||
|
||||
\graphicspath{
|
||||
{.}
|
||||
{../../figures/}
|
||||
{../../../figures/}
|
||||
}
|
||||
|
||||
\begin{document}
|
||||
\chapter{Airshowers}
|
||||
\label{sec:airshowers}
|
||||
|
||||
\section{Cosmic Rays}
|
||||
|
||||
\section{Detectors}
|
||||
|
||||
Pierre Auger,
|
||||
GRAND
|
||||
|
||||
\subsection{Surface Detector}
|
||||
|
||||
\subsection{Radio Detector}
|
||||
|
||||
\section{Interferometry}
|
||||
Requires $\sigma_t \lesssim 1\ns$
|
||||
|
||||
\end{document}
|
|
@ -12,6 +12,127 @@
|
|||
The main method of synchronising multiple stations is by employing a GNSS.
|
||||
This system should deliver timing with an accuracy in the order of $50\ns$.
|
||||
|
||||
|
||||
|
||||
\section{Beacon}
|
||||
\label{sec:time:beacon}
|
||||
|
||||
The idea of a beacon is semi-analogous to an oscillator in electronic circuits.
|
||||
A periodic signal is sent out from a transmitter (the oscillator), and captured by an antenna (the chip the oscillator drives).
|
||||
|
||||
In a digital circuit, the oscillator often emits a discrete (square wave) signal (see Figure~\ref{fig:beacon:ttl}).
|
||||
A tick is then defined as the moment that the signal changes from high to low or vice versa.
|
||||
|
||||
In this scheme, synchronising requires latching on the change very precisely.
|
||||
As between the ticks, there is no time information in the signal.
|
||||
\\
|
||||
|
||||
\todo{Possibly Invert story from short->long to long->short}
|
||||
Instead of introducing more ticks in the same time, and thus a higher frequency of the oscillator, a smooth continous signal can also be used.
|
||||
This enables the opportunity to determine the phase of the signal by measuring the signal at some time interval.
|
||||
This time interval has an upper limit on its size depending on the properties of the signal, such as its frequency, but also on the length of the recording.
|
||||
|
||||
|
||||
In Figure~\ref{fig:beacon:sine}, both sampling~1~and~2 can reconstruct the sine wave from the measurements.
|
||||
Meanwhile, the square wave has some leeway on the precise timing.\todo{reword sentence}
|
||||
\\
|
||||
|
||||
\begin{figure}[h]
|
||||
\begin{subfigure}{0.45\textwidth}
|
||||
\includegraphics[width=\textwidth]{beacon/ttl_beacon.pdf}
|
||||
\caption{
|
||||
Discrete (square wave) clocks are commonly found in digital circuits.
|
||||
}
|
||||
\label{fig:beacon:ttl}
|
||||
\end{subfigure}
|
||||
\hfill
|
||||
\begin{subfigure}{0.45\textwidth}
|
||||
\includegraphics[width=\textwidth]{beacon/sine_beacon.pdf}
|
||||
\caption{
|
||||
A sine wave clock, as will be employed throughout this document.
|
||||
}
|
||||
\label{fig:beacon:sine}
|
||||
\end{subfigure}
|
||||
|
||||
\caption{
|
||||
Two different beacon signals with the same frequency.
|
||||
Both show two samplings with a small offset in time.
|
||||
Reconstructing the signal is easier to do for the sine wave with the same samplelength and number of samples.
|
||||
}
|
||||
\label{fig:beacon:ttl_sine_beacon}
|
||||
\todo{Add fourier spectra?}
|
||||
\end{figure}
|
||||
|
||||
%% Second timescale needed
|
||||
|
||||
Instead of driving the antenna, the beacon is meant to synchronise the clock of the antenna with the clock of the transmitter.
|
||||
With one oscillator, the antenna can work in phase with the transmitter, but the actual synchronization can be off by a multiple of periods.
|
||||
To be able to determine this offset, a second timescale needs to be introduced in the signal.
|
||||
\\
|
||||
|
||||
This slower timescale allows to count the ticks of the quicker signal.\todo{Extend paragraph}
|
||||
|
||||
\begin{figure}
|
||||
\begin{subfigure}{0.45\textwidth}
|
||||
% \includegraphics[width=0.5\textwidth]{beacon/sine_beacon_multiple_periods_off.pdf}
|
||||
\caption{
|
||||
Two syntonised beacons.
|
||||
The actual synchronization is off by a multiple of periods.
|
||||
}
|
||||
\label{fig:second_timescale:off}
|
||||
\end{subfigure}
|
||||
\hfill
|
||||
\begin{subfigure}{0.45\textwidth}
|
||||
% \includegraphics[width=0.5\textwidth]{beacon/sine_beacon_multiple_periods_off.pdf}
|
||||
\caption{
|
||||
Two syntonised beacons, the actual synchronization is off by a multiple of periods.
|
||||
}
|
||||
\label{fig:second_timescale:on}
|
||||
\end{subfigure}
|
||||
\caption{
|
||||
}
|
||||
\label{fig:second_timescale}
|
||||
\todo{Fill figure and caption}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}
|
||||
\includegraphics[width=0.5\textwidth]{beacon/auger/1512.02216.figure2.beacon_beat.png}
|
||||
\caption{
|
||||
From Ref~\cite{PierreAuger:2015aqe}
|
||||
The beacon signal that the \PAObs\ employs.
|
||||
}
|
||||
\label{fig:beacon:pa}
|
||||
\end{figure}
|
||||
|
||||
|
||||
|
||||
\subsection{Fourier Transform}
|
||||
\begin{equation}
|
||||
\label{eq:fourier}
|
||||
\hat{f}(\omega) = \frac{1}{2\pi} \int \dif{t}\, f(t)\, \exp(i \omega t)
|
||||
\end{equation}
|
||||
|
||||
|
||||
|
||||
\subsection{Beacons in Airshower timing}
|
||||
To setup a time synchronising system for airshower measurements, actually only the high frequency part of the beacon must be employed.
|
||||
The low frequency part, from which the number of oscillations of the high frequency part are counted, is supplied by the very airshower that is measured.
|
||||
|
||||
|
||||
\begin{equation}
|
||||
\label{eq:correlation_cont}
|
||||
\Corr(\tau; u,v) = \int_{-\infty}^{\infty} \dif t \, u(t)\, v^*(t-\tau)
|
||||
\end{equation}
|
||||
|
||||
\begin{equation}
|
||||
\label{eq:correlation_sample}
|
||||
\Corr(k; u,v) = \sum_n u[n] \, v^*[n-k]
|
||||
\end{equation}
|
||||
|
||||
|
||||
|
||||
\section{Beacon synchronisation}
|
||||
|
||||
As outlined in Section~\ref{sec:time:beacon}, a beacon can also be employed to synchronise the stations.
|
||||
This chapter outlines the steps required to setup a synchronisation between multiple antennae using one transmitter.
|
||||
|
||||
|
|
|
@ -25,7 +25,10 @@ Use GRAND DU to do the same, also to do characterisation of hardware.
|
|||
|
||||
per filterchain time delay from phase differences
|
||||
|
||||
\subsection{GNSS}
|
||||
\subsection{Global Navigation Satellite System}
|
||||
\label{sec:grand:gnss}
|
||||
$\sigma_t \sim 20 \ns$
|
||||
|
||||
|
||||
|
||||
\subsection{Local Oscillator}
|
||||
|
|
|
@ -11,4 +11,33 @@
|
|||
\label{sec:introduction}
|
||||
|
||||
|
||||
\section{Cosmic Rays}
|
||||
\label{sec:airshowers}
|
||||
|
||||
\subsection{Airshowers}
|
||||
\label{sec:airshowers}
|
||||
|
||||
\subsection{Detectors}
|
||||
\label{sec:detectors}
|
||||
Pierre Auger,
|
||||
GRAND
|
||||
|
||||
\subsection{Interferometry}
|
||||
\label{sec:interferometry}
|
||||
Requires $\sigma_t \lesssim 1\ns$
|
||||
|
||||
|
||||
\section{Time Synchronisation}
|
||||
\label{sec:timesynchro}
|
||||
Need reference system with better accuracy to constrain
|
||||
See Section~\ref{sec:grand:gnss}.
|
||||
|
||||
\begin{figure}
|
||||
\centering
|
||||
\includegraphics[width=\textwidth]{clocks/reference-clock.pdf}
|
||||
\caption{
|
||||
Using a reference clock to compare two other clocks.
|
||||
}
|
||||
\label{fig:reference-clock}
|
||||
\end{figure}
|
||||
\end{document}
|
||||
|
|
|
@ -1,185 +0,0 @@
|
|||
\documentclass[../thesis.tex]{subfiles}
|
||||
|
||||
\graphicspath{
|
||||
{.}
|
||||
{../../figures/}
|
||||
{../../../figures/}
|
||||
}
|
||||
|
||||
\begin{document}
|
||||
\chapter{Time Synchronisation Mechanisms}
|
||||
\label{sec:time}
|
||||
Need reference system with better accuracy to constrain
|
||||
|
||||
|
||||
\begin{figure}
|
||||
\centering
|
||||
\includegraphics[width=\textwidth]{clocks/reference-clock.pdf}
|
||||
\caption{
|
||||
Using a reference clock to compare two other clocks.
|
||||
}
|
||||
\label{fig:reference-clock}
|
||||
\end{figure}
|
||||
|
||||
|
||||
\section{Global Navigation Satellite System}
|
||||
\label{sec:time:gnss}
|
||||
$\sigma_t \sim 20 \ns$
|
||||
|
||||
\section{White Rabbit Precision Time Protocol}
|
||||
\label{sec:time:gnss}
|
||||
\begin{figure}
|
||||
\centering
|
||||
\includegraphics[width=\textwidth]{white-rabbit/protocol/delaymodel.pdf}
|
||||
\caption{
|
||||
From \cite{WRPTP}.
|
||||
Delays between two White Rabbit nodes.
|
||||
}
|
||||
\label{fig:wr:delaymodel}
|
||||
\end{figure}
|
||||
\subsection{PTP}
|
||||
\begin{figure}
|
||||
\centering
|
||||
\includegraphics[width=\textwidth,height=0.5\textheight,keepaspectratio]{white-rabbit/protocol/ptpMSGs-color.pdf}
|
||||
\caption{
|
||||
From \cite{WRPTP}.
|
||||
Precision Time Protocol (PTP) messages
|
||||
}
|
||||
\end{figure}
|
||||
|
||||
\subsection{White Rabbit}
|
||||
SyncE
|
||||
\begin{figure}
|
||||
\centering
|
||||
\includegraphics[width=\textwidth,height=0.5\textheight,keepaspectratio]{white-rabbit/protocol/wrptpMSGs_1.pdf}
|
||||
\caption{
|
||||
From \cite{WRPTP}.
|
||||
White Rabbit extended PTP messages
|
||||
}
|
||||
\label{fig:wr:protocol}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}
|
||||
\centering
|
||||
\includegraphics[width=\textwidth,height=0.5\textheight,keepaspectratio]{clocks/wr-clocks.pdf}
|
||||
\caption{
|
||||
White Rabbit clocks
|
||||
}
|
||||
\label{fig:wr:clocks}
|
||||
\end{figure}
|
||||
|
||||
\section{Beacon}
|
||||
\label{sec:time:beacon}
|
||||
The idea of a beacon is semi-analogous to an oscillator in electronic circuits.
|
||||
A periodic signal is sent out from a transmitter (the oscillator), and captured by an antenna (the chip the oscillator drives).
|
||||
|
||||
In a digital circuit, the oscillator often emits a discrete (square wave) signal (see Figure~\ref{fig:beacon:ttl}).
|
||||
A tick is then defined as the moment that the signal changes from high to low or vice versa.
|
||||
|
||||
In this scheme, synchronising requires latching on the change very precisely.
|
||||
As between the ticks, there is no time information in the signal.
|
||||
\\
|
||||
|
||||
\todo{Possibly Invert story from short->long to long->short}
|
||||
Instead of introducing more ticks in the same time, and thus a higher frequency of the oscillator, a smooth continous signal can also be used.
|
||||
This enables the opportunity to determine the phase of the signal by measuring the signal at some time interval.
|
||||
This time interval has an upper limit on its size depending on the properties of the signal, such as its frequency, but also on the length of the recording.
|
||||
|
||||
|
||||
In Figure~\ref{fig:beacon:sine}, both sampling~1~and~2 can reconstruct the sine wave from the measurements.
|
||||
Meanwhile, the square wave has some leeway on the precise timing.\todo{reword sentence}
|
||||
\\
|
||||
|
||||
\begin{figure}[h]
|
||||
\begin{subfigure}{0.45\textwidth}
|
||||
\includegraphics[width=\textwidth]{beacon/ttl_beacon.pdf}
|
||||
\caption{
|
||||
Discrete (square wave) clocks are commonly found in digital circuits.
|
||||
}
|
||||
\label{fig:beacon:ttl}
|
||||
\end{subfigure}
|
||||
\hfill
|
||||
\begin{subfigure}{0.45\textwidth}
|
||||
\includegraphics[width=\textwidth]{beacon/sine_beacon.pdf}
|
||||
\caption{
|
||||
A sine wave clock, as will be employed throughout this document.
|
||||
}
|
||||
\label{fig:beacon:sine}
|
||||
\end{subfigure}
|
||||
|
||||
\caption{
|
||||
Two different beacon signals with the same frequency.
|
||||
Both show two samplings with a small offset in time.
|
||||
Reconstructing the signal is easier to do for the sine wave with the same samplelength and number of samples.
|
||||
}
|
||||
\label{fig:beacon:ttl_sine_beacon}
|
||||
\todo{Add fourier spectra?}
|
||||
\end{figure}
|
||||
|
||||
%% Second timescale needed
|
||||
|
||||
Instead of driving the antenna, the beacon is meant to synchronise the clock of the antenna with the clock of the transmitter.
|
||||
With one oscillator, the antenna can work in phase with the transmitter, but the actual synchronization can be off by a multiple of periods.
|
||||
To be able to determine this offset, a second timescale needs to be introduced in the signal.
|
||||
\\
|
||||
|
||||
This slower timescale allows to count the ticks of the quicker signal.\todo{Extend paragraph}
|
||||
|
||||
\begin{figure}
|
||||
\begin{subfigure}{0.45\textwidth}
|
||||
% \includegraphics[width=0.5\textwidth]{beacon/sine_beacon_multiple_periods_off.pdf}
|
||||
\caption{
|
||||
Two syntonised beacons.
|
||||
The actual synchronization is off by a multiple of periods.
|
||||
}
|
||||
\label{fig:second_timescale:off}
|
||||
\end{subfigure}
|
||||
\hfill
|
||||
\begin{subfigure}{0.45\textwidth}
|
||||
% \includegraphics[width=0.5\textwidth]{beacon/sine_beacon_multiple_periods_off.pdf}
|
||||
\caption{
|
||||
Two syntonised beacons, the actual synchronization is off by a multiple of periods.
|
||||
}
|
||||
\label{fig:second_timescale:on}
|
||||
\end{subfigure}
|
||||
\caption{
|
||||
}
|
||||
\label{fig:second_timescale}
|
||||
\todo{Fill figure and caption}
|
||||
\end{figure}
|
||||
|
||||
\begin{figure}
|
||||
\includegraphics[width=0.5\textwidth]{beacon/auger/1512.02216.figure2.beacon_beat.png}
|
||||
\caption{
|
||||
From Ref~\cite{PierreAuger:2015aqe}
|
||||
The beacon signal that the \PAObs\ employs.
|
||||
}
|
||||
\label{fig:beacon:pa}
|
||||
\end{figure}
|
||||
|
||||
|
||||
|
||||
\subsection{Fourier Transform}
|
||||
\begin{equation}
|
||||
\label{eq:fourier}
|
||||
\hat{f}(\omega) = \frac{1}{2\pi} \int \dif{t}\, f(t)\, \exp(i \omega t)
|
||||
\end{equation}
|
||||
|
||||
|
||||
|
||||
\subsection{Beacons in Airshower timing}
|
||||
To setup a time synchronising system for airshower measurements, actually only the high frequency part of the beacon must be employed.
|
||||
The low frequency part, from which the number of oscillations of the high frequency part are counted, is supplied by the very airshower that is measured.
|
||||
|
||||
|
||||
\begin{equation}
|
||||
\label{eq:correlation_cont}
|
||||
\Corr(\tau; u,v) = \int_{-\infty}^{\infty} \dif t \, u(t)\, v^*(t-\tau)
|
||||
\end{equation}
|
||||
|
||||
\begin{equation}
|
||||
\label{eq:correlation_sample}
|
||||
\Corr(k; u,v) = \sum_n u[n] \, v^*[n-k]
|
||||
\end{equation}
|
||||
|
||||
\end{document}
|
|
@ -31,12 +31,6 @@
|
|||
%% Introduction
|
||||
\subfile{chapters/introduction.tex}
|
||||
|
||||
%% Airshowers
|
||||
\subfile{chapters/airshowers.tex}
|
||||
|
||||
%% Timing
|
||||
\subfile{chapters/timing.tex}
|
||||
|
||||
%% Disciplining by Beacon (Simulation)
|
||||
\subfile{chapters/beacon_discipline.tex}
|
||||
|
||||
|
|
Loading…
Reference in a new issue