From b52873599309d88f515680ef03cb17850ca2fad5 Mon Sep 17 00:00:00 2001 From: Eric Teunis de Boone Date: Mon, 5 Sep 2022 18:01:53 +0200 Subject: [PATCH] thesis: shuffling content move airshower chapter into introduction, merge beacon introduction into beacon_disciplining chapter, move gnss to grand section --- documents/thesis/chapters/airshowers.tex | 27 --- .../thesis/chapters/beacon_discipline.tex | 121 ++++++++++++ .../chapters/grand_characterisation.tex | 5 +- documents/thesis/chapters/introduction.tex | 29 +++ documents/thesis/chapters/timing.tex | 185 ------------------ documents/thesis/thesis.tex | 6 - 6 files changed, 154 insertions(+), 219 deletions(-) delete mode 100644 documents/thesis/chapters/airshowers.tex delete mode 100644 documents/thesis/chapters/timing.tex diff --git a/documents/thesis/chapters/airshowers.tex b/documents/thesis/chapters/airshowers.tex deleted file mode 100644 index 1e385e4..0000000 --- a/documents/thesis/chapters/airshowers.tex +++ /dev/null @@ -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} diff --git a/documents/thesis/chapters/beacon_discipline.tex b/documents/thesis/chapters/beacon_discipline.tex index 8d03d2a..92689b1 100644 --- a/documents/thesis/chapters/beacon_discipline.tex +++ b/documents/thesis/chapters/beacon_discipline.tex @@ -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. diff --git a/documents/thesis/chapters/grand_characterisation.tex b/documents/thesis/chapters/grand_characterisation.tex index abf55b5..3c23c23 100644 --- a/documents/thesis/chapters/grand_characterisation.tex +++ b/documents/thesis/chapters/grand_characterisation.tex @@ -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} diff --git a/documents/thesis/chapters/introduction.tex b/documents/thesis/chapters/introduction.tex index 386102c..78c83d1 100644 --- a/documents/thesis/chapters/introduction.tex +++ b/documents/thesis/chapters/introduction.tex @@ -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} diff --git a/documents/thesis/chapters/timing.tex b/documents/thesis/chapters/timing.tex deleted file mode 100644 index 86b4504..0000000 --- a/documents/thesis/chapters/timing.tex +++ /dev/null @@ -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} diff --git a/documents/thesis/thesis.tex b/documents/thesis/thesis.tex index 6fe6a77..a40646e 100644 --- a/documents/thesis/thesis.tex +++ b/documents/thesis/thesis.tex @@ -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}