From 1c1abae6e920f02865844449a0bda8378872f835 Mon Sep 17 00:00:00 2001 From: Cahit Date: Fri, 30 Oct 2015 11:23:56 +0100 Subject: [PATCH] added conclusion and fixed some typos --- .../twepp2015_ugur.tex | 66 +++++++++++-------- 1 file changed, 39 insertions(+), 27 deletions(-) diff --git a/2015-twepp-cahit-tdc_with_stretcher/twepp2015_ugur.tex b/2015-twepp-cahit-tdc_with_stretcher/twepp2015_ugur.tex index 952ae3c..f825d94 100644 --- a/2015-twepp-cahit-tdc_with_stretcher/twepp2015_ugur.tex +++ b/2015-twepp-cahit-tdc_with_stretcher/twepp2015_ugur.tex @@ -35,8 +35,8 @@ circuits} High precision Time-to-Digital converters (TDCs) are mainly used in high energy physics, where timing plays a crucial part in particle identification. For this purpose setups with combinations of particle-sensitive materials (e.g. -Scintillator, Cerenkov) and photosensitive devices (photomultiplier, -multipixel photon counter) are used to measure the energy deposited in the +Scintillator, Cherenkov) and photosensitive devices (photomultiplier, +multi-pixel photon counter) are used to measure the energy deposited in the material by reconstructing a given property of the output pulse - the total charge collected, the pulse amplitude, etc \cite{tot}. Because of the recent developments of high precision TDCs and the superiority of the ToT measurements @@ -62,7 +62,8 @@ both edges of a signal for a ToT measurement with a novel approach. \section{Architecture} As explained in our previous paper the architecture of the TDC is based on the interpolation method \cite{kalisz}, where the interpolator is built as a tapped -delay line with the wave union laucher \cite{WUL} for the precision enhancement. +delay line with the wave union launcher \cite{WUL} for the precision +enhancement. The full architecture of the TDC and a diagram of the tapped delay line method can be seen in figure~\ref{fig:tdcArch}. The start signal for the delay line is the digital output signal from the front-end electronics (FEE), where as the @@ -151,14 +152,14 @@ the input pulse is larger than the dead time of a channel. \begin{figure}[tbp] \centering -\begin{subfigure}[b]{.75\textwidth} +\begin{subfigure}[b]{.7\textwidth} \includegraphics[width=1\linewidth] {../figures/tdc/stretcher_timing_semiAsync.eps} \caption{Timing diagram of the ToT method without the delay circuit} \label{fig:stretcherTimingSemi} \end{subfigure}% -\begin{subfigure}[b]{.75\textwidth} +\begin{subfigure}[b]{.7\textwidth} \includegraphics[width=1\linewidth] {../figures/tdc/stretcher_timing_fullAsync.eps} \caption{Timing diagram of the ToT method with the delay circuit} @@ -232,7 +233,7 @@ measurement time distributions we do not apply any cuts or curve fittings. \begin{figure}[tbp] \centering - \includegraphics[width=.6\textwidth] + \includegraphics[width=.5\textwidth] {../figures/tdc/9ps_res.eps} \caption{The precision of a sample channel for leading edge measurement.} \label{fig:precisionLeading} @@ -243,14 +244,14 @@ measurement time distributions we do not apply any cuts or curve fittings. \begin{figure}[tbp] \begin{subfigure}{.5\textwidth} \centering - \includegraphics[width=.9\linewidth] + \includegraphics[width=.8\linewidth] {../figures/tdc/t_diff_tot_alternating.eps} \caption{ToT measurement with conventional method.} \label{fig:precisionToTalt} \end{subfigure}% \begin{subfigure}{.5\textwidth} \centering - \includegraphics[width=.9\linewidth] + \includegraphics[width=.8\linewidth] {../figures/tdc/t_diff_tot_stretcher_high_precision.eps} \caption{ToT measurement with novel method.} \label{fig:precisionToTstretch} @@ -287,7 +288,7 @@ mean value relative to the oscilloscope results was observed as $38~ps$. \begin{figure}[tbp] \centering - \includegraphics[width=.69\textwidth]{../figures/tdc/tot_sweep.pdf} + \includegraphics[width=.6\textwidth]{../figures/tdc/tot_sweep.pdf} \caption{ToT sweep with $1.6~ns$ granularity.} \label{fig:totSweep} \end{figure} @@ -307,24 +308,25 @@ calibration of the channels is done only once at the beginning of the test. In figure~\ref{fig:rmsWITHdcdc} the precision of a channel as a function of the measured interval is shown. It was observed that over a microsecond time interval the precision value oscillates with an amplitude of $48~ps$ and this -effect was thought to be from the DC-DC converters. Next, the board was stripped -down of the converters and the FPGA was powered with a linear power supply -(HMP4040). The test was repeated to be observed that the main oscillation had -disappeared but there was a secondary oscillation with an amplitude of -$\sim3~ps$ and a frequency of $25~MHz$ (figure~\ref{fig:rmsNOdcdc}). This -trivial oscillation is not further investigated as the amplitude is negligible. +effect was thought to be from the DC-DC converters. Next, the board was +stripped down of the converters and the FPGA was powered with a linear power +supply (HMP4040). The test was repeated to be noted that the oscillation +amplitude is improved by a factor of $\sim12$. The exposed secondary oscillation +has an amplitude of $\sim3~ps$ and a frequency of $25~MHz$ +(figure~\ref{fig:rmsNOdcdc}). This trivial oscillation is not further +investigated as the amplitude is negligible. \begin{figure}[tbp] \begin{subfigure}{.5\textwidth} \centering - \includegraphics[width=.9\linewidth] + \includegraphics[width=.8\linewidth] {../figures/tdc/rms_trb3_with_dcdc.eps} \caption{With DC-DC converters to power the FPGA.} \label{fig:rmsWITHdcdc} \end{subfigure}% \begin{subfigure}{.5\textwidth} \centering - \includegraphics[width=.9\linewidth] + \includegraphics[width=.8\linewidth] {../figures/tdc/rms_trb3_without_dcdc.eps} \caption{Linear power supply to power the FPGA.} \label{fig:rmsNOdcdc} @@ -395,7 +397,7 @@ change, when both - temperature and offset - corrections are applied. \caption{ToT shift $@42.8^{\circ}C$ as a function of stretcher offset.} \label{fig:totVSoffset} \end{subfigure}% -\caption{The effect of temperature is seen more drasticall on channels with +\caption{The effect of temperature is seen more drastically on channels with longer stretcher offsets.} \label{fig:temp} \end{figure} @@ -423,8 +425,18 @@ temperature change.} \section{Conclusion} - - +In this paper we presented our novel way of measuring ToT on an FPGA TDC using +a single channel. Based on the conducted tests precision of the leading edge +measurement is recorded as low as $8.7~ps$, suggesting $6.15~ps$ error on a +single channel. The precisions for ToT measurements with the conventional and +novel methods are recorded as $12.2~ps$ and $12.1~ps$ respectively. The novel +method is investigated further to find out, that the ToT value differs maximum +$38~ps$ from the oscilloscope measurements once the stretcher offset is +eliminated. It is also discovered that the deterioration in the long time +interval measurement precision can be limited to $3~ps$, if the FPGA is powered +with a linear power supply. The effect of the temperature change on the ToT +measurement is also assessed and the degeneration is improved by a factor of +$\sim10$ and limited to $\sim50ps$ with a correction model. @@ -443,6 +455,13 @@ F. Gonnella et al., \href{http://arxiv.org/abs/1412.1743} {\emph{arXiv:1412.1743}} (2014). +\bibitem{WUL} +J. Wu, Z. Shi, +\emph{The 10-ps wave union TDC: Improving FPGA TDC resolution beyond its cell +delay} +\href{http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4775079} +{\emph{Nuclear Science Symposium Conference Record}, 3440-3446, (Oct., 2008).} + \bibitem{tdc_counter} M. Buchele et al., \emph{A 128-channel time-to-digital converter (TDC) inside a Virtex-5 FPGA on @@ -464,13 +483,6 @@ resolution} \href{http://stacks.iop.org/0026-1394/41/i=1/a=004} {\emph{Metrologia}, 41, 17, (2004).} -\bibitem{WUL} -J. Wu, Z. Shi, -\emph{The 10-ps wave union TDC: Improving FPGA TDC resolution beyond its cell -delay} -\href{http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4775079} -{\emph{Nuclear Science Symposium Conference Record}, 3440-3446, (Oct., 2008).} - \bibitem{trbnet} J. Michel et al., \emph{The HADES trigger and readout board network (TrbNet)} -- 2.43.0