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\r
% *** MY PACKAGES ***\r
-\usepackage{hyperref}\r
+% \usepackage[bookmarks=false]{hyperref}\r
+\usepackage{nohyperref} % This makes hyperref commands do nothing\r
+ % without errors\r
\usepackage{color}\r
\r
\usepackage{changes}\r
period) and the epoch counter ($\sim10~us$ period) complete the time\r
measurement with a total range up to $\sim45$ minutes. All these time\r
measurements are written to a ring buffer as illustrated in\r
-\autoref{fig:tdc_arch}.\r
+Figure \ref{fig:tdc_arch}.\r
\r
\begin{figure}[!t]\r
\centering\r
\subsection{Fine Time Interpolator}\r
\r
For the fine time interpolator the TDL method is implemented\r
-(\autoref{fig:tdl}), as the architectures of the modern FPGAs are well suited\r
+(Figure \ref{fig:tdl}), as the architectures of the modern FPGAs are well suited\r
for this method. This method utilises the intrinsic delays of the delay\r
elements for time measurements. While the start signal propagates through the\r
delay elements along the delay line, the rising edge of the stop signal, which\r
\r
Using the Nutt method \cite{nutt} the total time information of a hit signal\r
and the time interval between two hit signals on different channels\r
-(\autoref{fig:hitTime}) is calculated as in \autoref{eq:tDiff}. Note\r
+(Figure \ref{fig:hitTime}) is calculated as in Equation \ref{eq:tDiff}. Note\r
that the fine time interpolator is a backward counter.\r
\r
\begin{equation}\r
sensitivity of the TDL can be increased by applying the Wave Union Launcher\r
(WUL) method. Using the two transition WUL the maximum bin width is decreased\r
to $35~ps$ from $45~ps$, whereas the average bin width is reduced to\r
-$\sim10~ps$ from $\sim20~ps$ (\autoref{fig:bin_wid}). The effect of the WUL on\r
-the time precision is shown in \autoref{sec:results}.\r
+$\sim10~ps$ from $\sim20~ps$ (Figure \ref{fig:bin_wid}). The effect of the WUL on\r
+the time precision is shown in Section \ref{sec:results}.\r
\r
\begin{figure*}[!t]\r
\centerline{\subfloat[Traditional TDL method.]{\includegraphics[width=2.5in]{bin_wid_sing}%\r
\r
In our work, a semi-asynchronous pulse stretcher is designed to extend the\r
length of the hit signals more than one clock period. The demonstration of the\r
-stretcher is shown in \autoref{fig:stretcher}. The short pulse from the\r
+stretcher is shown in Figure \ref{fig:stretcher}. The short pulse from the\r
detector is connected to the clock input of the D-flipflop and with the rising\r
edge of the hit signal the logic '1' at the 'D' input is passed to the 'Q'\r
output. After two stages of registers the signal is used to reset the\r
length of the stretcher can be made one clock cycle shorter by removing the\r
middle stage register. However, as this is not the bottle neck of the dead\r
time limitation in our design, we chose to have a longer pulse. The results of\r
-the stretcher concept are discussed in the \autoref{sec:results}: \r
+the stretcher concept are discussed in the Section \ref{sec:results}: \r
\r
\begin{figure}[!t]\r
\centering\r
The non-linearity across the fine time interval is induced by the non-uniform\r
intrinsic delays along the carry-chain, as explained above. The maximum\r
differential and integral non-linearities, that we measure are 2.7 and 9~LSB\r
-respectively (\autoref{fig:non_linearity}). In order to calculate the effect\r
+respectively (Figure \ref{fig:non_linearity}). In order to calculate the effect\r
of the non-linearity on the time precision a time interval is calculated with\r
a constant quantisation step of $11~ps$ (calculated by dividing the clock\r
period of $5~ns$ by the number of delay elements in the carry chain) and\r
A look-up table for the non-linearity correction using the calculated bin\r
widths is generated. This correction process is done offline. The effect of\r
the number \textit{$H_T$} of measurements on the time precision is discussed\r
-in \autoref{sec:results}.\r
+in Section \ref{sec:results}.\r
\r
\begin{figure*}[!t]\r
\centerline{\subfloat[DNL]{\includegraphics[width=2.5in]{dnl}%\r
coaxial cables. At least $300\thinspace000$ measurements were collected at\r
stable environmental conditions for the offline calibration stage. The time\r
interval between the rising edges of the signals was calculated as explained\r
-in \autoref{eq:tDiff} for a set of data and entered into a histogram. The\r
+in Equation \ref{eq:tDiff} for a set of data and entered into a histogram. The\r
time precision was measured by calculating the root mean square (RMS) of the\r
peak without applying any curve fittings.\r
\r
The precision measurements were repeated for the designs with and without the\r
-WUL and the results are given in \autoref{fig:precision}. The time\r
+WUL and the results are given in Figure \ref{fig:precision}. The time\r
precision of the TDC is improved by a factor of $1.45\cong\sqrt{2}$, as we\r
divide the UWBs by performing two measurements in one channel.\r
\r
cable length of one of the hit signals by a certain amount. In other words, one\r
of the hit signals is shifted by a known amount of time relative to the other\r
one. Sets of measurements for $3~cm$, $6~cm$ and $9~cm$ were done and the results are\r
-shown in \autoref{fig:mean} with the original length.\r
+shown in Figure \ref{fig:mean} with the original length.\r
\r
For each $\sim3~cm$ incrementation in the cable length the mean is shifted by\r
$\sim150~ps$, which corresponds to the $\sim0.2~m/ns$ electrical signal speed\r
pulse were measured on two channels. The difference between these two channels\r
was recorded in a histogram after calibration.\r
\r
-In \autoref{fig:shortpulse} it can be seen, that the mean of the peak is at\r
+In Figure \ref{fig:shortpulse} it can be seen, that the mean of the peak is at\r
$519~ps$, which gives the width of the pulse. Also the measured error is not\r
considerably deteriorated ($12~ps$).\r
\r
The effect of the number of hits used for calibration is also\r
investigated. The same set of data collected at constant temperature was\r
analysed with different calibration tables generated with a different number of\r
-hits from the same data set. As it can be seen in the \autoref{fig:rms_vs_hit}\r
+hits from the same data set. As it can be seen in the Figure \ref{fig:rms_vs_hit}\r
with the increasing number of hits used, the fine time histogram starts to fill\r
out and the time precision decreases rapidly. The calculated precision starts\r
to saturate after $10\thinspace000$ samples and using more than\r
therefore, the required time to charge/discharge the output load increases. The\r
increasing delay of each delay element changes the bin widths. Moreover, the\r
calibration table generated at a certain temperature is no longer valid for\r
-other temperatures. \autoref{fig:rms_vs_temp} shows the change in the time\r
+other temperatures. Figure \ref{fig:rms_vs_temp} shows the change in the time\r
precision with the increasing temperature. As long as the calibration table is\r
updated for the temperature value, the time precision stays stable. Otherwise,\r
after a couple of degree $^\circ$C, the time precision starts to get worse.\r
analysed. Moreover, a 264 channel TDC platform - TRB3 - based on the FPGA TDC\r
design is elaborated.\r
% At last the terminology for the statistical approach based TDCs is\r
-% argued in \autoref{sec:pre_vs_res}, ``\textit{Precision vs Resolution}''.\r
+% argued in Section \ref{sec:pre_vs_res}, ``\textit{Precision vs Resolution}''.\r
\r
\r
\r
C. Ugur et al., ``Field programmable gate array based data digitisation with commercial elements'',\r
\href{http://dx.doi.org/10.1088/1748-0221/8/01/C01035}{\emph{Journal of Instrumentation} {\bf 8} C01035, (2013)}\r
\r
-\bibitem{precision}\r
-Organisation for Economic Co-operation and Development,\r
-\href{http://stats.oecd.org/glossary/detail.asp?ID=3791}{\emph{Glossaray of statistical terms}}\r
+% \bibitem{precision}\r
+% Organisation for Economic Co-operation and Development,\r
+% \href{http://stats.oecd.org/glossary/detail.asp?ID=3791}{\emph{Glossaray of statistical terms}}\r
\r
-\bibitem{resolution}\r
-Atmel, ``Guidelines to Keep ADC Resolution within Specification'',\r
-\href{http://stats.oecd.org/glossary/detail.asp?ID=3791}{\emph{8051\r
- Microcontrollers Application Note}, Rev. 4278B–8051–08/03}\r
+% \bibitem{resolution}\r
+% Atmel, ``Guidelines to Keep ADC Resolution within Specification'',\r
+% \href{http://stats.oecd.org/glossary/detail.asp?ID=3791}{\emph{8051\r
+% Microcontrollers Application Note}, Rev. 4278B–8051–08/03}\r
\r
\r
\r
jspc29 / publication.git / commitdiff