From b3d361499ba0d128b3ade2d496c9192b3420b756 Mon Sep 17 00:00:00 2001 From: Cahit Date: Thu, 12 Nov 2015 16:18:13 +0100 Subject: [PATCH] applied the corrections based on the objections of the refree --- .../editor_report_20151109.pdf | Bin 0 -> 23445 bytes 2015-twepp-cahit-tdc_with_stretcher/figures | 1 + .../twepp2015_ugur.tex | 191 ++++++++++-------- figures/tdc/stretcher_semiAsync.pdf | Bin 9269 -> 15673 bytes .../tdc/temp_TOToffset_vs_TOTshift_@43C.pdf | Bin 4919 -> 4913 bytes figures/tdc/temp_vs_tot.pdf | Bin 10453 -> 10446 bytes .../tdc/temp_vs_tot_with_bothCorrection.pdf | Bin 23023 -> 23006 bytes .../tdc/temp_vs_tot_with_tempCorrection.pdf | Bin 22858 -> 22842 bytes 8 files changed, 106 insertions(+), 86 deletions(-) create mode 100644 2015-twepp-cahit-tdc_with_stretcher/editor_report_20151109.pdf create mode 120000 2015-twepp-cahit-tdc_with_stretcher/figures diff --git a/2015-twepp-cahit-tdc_with_stretcher/editor_report_20151109.pdf 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zzL3X&BA+1;KsD(M8FT^(MJ&vk1l<&IL|m5jWMEPnNIsimj(V-s@7hp$qv!g>S51bVUf;a@^=udv)a;!f!CPzg6W#w6|02^M1FK~LVEWIlHT#O! zkqB9Ah#7%~pfF!Az!Cyl-~cx8S%$^pA-Id|0wO-k&}d6Ev_Id;P*|*tGcrYnh8Po5 zWGHBRrpmBr^bdMi97Lp<($^A&gD4!|+rUBmiYYP>hebmSn<;u|h>G#O3`7%T#GCK+ zu$BY{ literal 0 HcmV?d00001 diff --git a/2015-twepp-cahit-tdc_with_stretcher/figures b/2015-twepp-cahit-tdc_with_stretcher/figures new file mode 120000 index 0000000..699a0b3 --- /dev/null +++ b/2015-twepp-cahit-tdc_with_stretcher/figures @@ -0,0 +1 @@ +../figures/tdc \ No newline at end of file diff --git a/2015-twepp-cahit-tdc_with_stretcher/twepp2015_ugur.tex b/2015-twepp-cahit-tdc_with_stretcher/twepp2015_ugur.tex index 4910f06..e5c8f8f 100644 --- a/2015-twepp-cahit-tdc_with_stretcher/twepp2015_ugur.tex +++ b/2015-twepp-cahit-tdc_with_stretcher/twepp2015_ugur.tex @@ -1,10 +1,12 @@ \pdfoutput=1 % only if pdf/png/jpg images are used \documentclass{JINST} +\usepackage{caption} \usepackage{subcaption} +\usepackage{lineno} -\title{A novel approach for pulse width measurements with a high resolution -(8.7~ps) TDC in an FPGA} +\title{A novel approach for pulse width measurements with a high +precision (8~ps RMS) TDC in an FPGA} \author{C. Ugur$^a$\thanks{Corresponding author.}~, S. Linev$^b$, @@ -20,17 +22,21 @@ E-mail: \email{c.ugur@gsi.de}} \abstract{High precision time measurements are a crucial element in particle identification experiments, which likewise require pulse width information for -charge and Time-over-Threshold (ToT) measurements. In almost all of the -FPGA-based TDC applications, pulse width measurements are implemented using two -of the TDC channels for leading and trailing edge time measurements -individually. This method however, requires double the number of resources and -therefore this paper presents a novel way of measuring pulse width using a -single TDC channel, while still achieving high precision (as low as 12~ps RMS).} +Time-over-Threshold (ToT) measurements and charge measurements (correlated with +pulse width). In almost all of the FPGA-based TDC applications, pulse width +measurements are implemented using two of the TDC channels for leading and +trailing edge time measurements individually. This method however, requires +twice the number of resources. In this paper we present the latest precision +improvements in the high precision TDC (8~ps RMS ) developed before +\cite{tdc_ieee}, as well as the novel way of measuring ToT using a single TDC +channel, while still achieving high precision (as low as 11.7~ps RMS).} \keywords{Front-end electronics for detector readout; Digital electronic circuits} \begin{document} +\setpagewiselinenumbers +\linenumbers \section{Introduction} High precision Time-to-Digital converters (TDCs) are mainly used in high energy @@ -40,7 +46,7 @@ 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 +developments of high precision TDCs and the advantages of the ToT measurements over the amplitude and charge measurements in terms of cost and wider dynamic range, this method is becoming more attractive for the recent studies. @@ -55,9 +61,9 @@ on the precision, range, non-linearities, dead time, resource usage and environment variation effects. This study is based on the previous TDC design \cite{tdc_ieee} for single edge -measurements applying tapped delay line method, as its superiority in range, -dead time and especially in precision. The work is further developed to react -to both edges of a signal for a ToT measurement with a novel approach. +measurements applying tapped delay line method, due its advantages in range, +dead time and especially in precision. The work is further developed to react to +both edges of a signal for a ToT measurement with a novel approach. \section{Architecture} @@ -70,19 +76,20 @@ delay line is the digital output signal from the front-end electronics (FEE), whereas the propagation of the signal is stopped with the next rising edge of the 200~MHz clock signal. The output of the delay line, as thermometer code, is then sent to the decoder for the conversion to binary code. This data, as well -as the time stamp from the epoch and coarse counters with 5~ns granularity, are -saved in a ring-buffer. The readout and slow control of the TDC is based on the -TRBNet protocol \cite{trbnet}. +as the time stamp from the coarse and epoch (extension of the coarse counter) +counters with 5~ns granularity, are saved in a ring-buffer. The readout and slow +control of the TDC is based on the TRBNet protocol \cite{trbnet} developed for +TDC Readout Boards (TRB \cite{trb3}). \begin{figure}[tbp] \begin{subfigure}{.45\textwidth} \centering - \includegraphics[width=.9\linewidth]{../figures/tdc/tdc_arch.pdf} + \includegraphics[width=.9\linewidth]{figures/tdc_arch.pdf} \caption{TDC architecture} \end{subfigure}% \begin{subfigure}{.55\textwidth} \centering - \includegraphics[width=.9\linewidth]{../figures/tdc/tappedDelayLine.eps} + \includegraphics[width=.9\linewidth]{figures/tappedDelayLine.pdf} \caption{Tapped delay line} \end{subfigure}% \caption{The architecture of the TDC and the tapped delay line method.} @@ -102,7 +109,7 @@ With this stretcher method 500~ps wide pulses were measured successfully \begin{figure}[tbp] \centering \includegraphics[width=.5\textwidth] - {../figures/tdc/stretcher_semiAsync.eps} + {figures/stretcher_semiAsync.pdf} \caption{Semi-asynchronous stretcher logic is implemented before the delay line in order to keep the timing of the leading edge of the input signal ($hit$) and stretch the trailing edge beyond the clock period. The $hit_{in}$ signal to @@ -123,14 +130,14 @@ threshold crossings of the analogue signal. In conventional TDCs the input pulse is internally split and the leading and trailing edges are measured in two separate TDC channels. Although this method is straightforward and easy to implement, it is not resource efficient. For both -edges double the amount of resources in the FPGA must be used. +edges twice the amount of resources in the FPGA must be used. \subsection{Semi-asynchronous stretcher for ToT measurements} As the TDC channels are once again active as soon as the dead time after a successful measurement is over (in our case this value is 20~ns), for pulses -longer than this dead time the channel resources are active again. With this -way, a channel first measures the leading edge of the input pulse and then, when -the channel is active again, it measures the trailing edge. +longer than this dead time the channel resources are active again. In this way, +a channel first measures the leading edge of the input pulse and then, when the +channel is active again, it measures the trailing edge. As our TDC architecture is sensitive to the rising edges of positive input pulses, we generate two short positive pulses (still longer than a clock period) @@ -145,7 +152,7 @@ measured in the same channel, as long as the time gap between them is larger then the dead time. At the end, the data are written in the ring-buffer with one extra bit as an edge type marker. -Reusing the resources in this manner enables a compacter design with double the +Reusing the resources in this manner enables a compacter design with twice the number of channels in an FPGA. However, this is only possible, if the width of the input pulse is larger than the dead time of a channel. @@ -153,14 +160,14 @@ the input pulse is larger than the dead time of a channel. \centering \begin{subfigure}[b]{.7\textwidth} \includegraphics[width=1\linewidth] - {../figures/tdc/stretcher_timing_semiAsync.eps} + {figures/stretcher_timing_semiAsync.pdf} \caption{Timing diagram of the ToT method without the delay circuit} \label{fig:stretcherTimingSemi} \end{subfigure}% \begin{subfigure}[b]{.7\textwidth} \includegraphics[width=1\linewidth] - {../figures/tdc/stretcher_timing_fullAsync.eps} + {figures/stretcher_timing_fullAsync.pdf} \caption{Timing diagram of the ToT method with the delay circuit} \label{fig:stretcherTimingFull} \end{subfigure}% @@ -180,24 +187,24 @@ successfully. The full-asynchronous stretcher consists of two semi-asynchronous stretchers (sensitive to two different edges as explained above) and a delay circuit for the trailing edge. The timing diagram for this method is shown in -figure~\ref{fig:stretcherTimingFull}. The pulse $hit_l$ is measured as normal in -the TDC channel, while the $hit_t$ pulse is delayed in the FPGA ($hit_d$) and -injected back in to the channel. The delay circuit is a chain of several +figure~\ref{fig:stretcherTimingFull}. The pulse $hit_l$ is measured as normal +in the TDC channel, while the $hit_t$ pulse is delayed in the FPGA ($hit_d$) +and injected back in to the channel. The delay circuit is a chain of several inverters connected one after another. The inverters are placed far away from each other in the FPGA in order to take advantage of the long propagation time of the normal routing through the switching circuitry, buffers and metal interconnects. In the FPGA that we use - Lattice ECP3 FPGA with 150K logic elements - the routing from one corner to the diagonally opposite corner takes -approximately 10~ns. By increasing the number of laps between the corners delays -longer than the intrinsic TDC dead time are achievable. +approximately 10~ns. By increasing the number of laps between the corners +delays longer than the intrinsic TDC dead time are achievable. Using this circuitry allows us to measure both edges of pulses shorter than the -dead time of the TDC on a single channel. The disadvantage of this method is the -extra dead time after the measurement of the trailing edge, which limits the -measurement of double pulse with offsets less than the total dead time (pulse -length + stretcher delay + conversion dead time). Also, the non-deterministic -stretching time between the channels and the design compilations has to be -tackled to get the real time information. +dead time of the TDC on a single channel. The disadvantage of this method is +the extra dead time after the measurement of the trailing edge, which limits +the measurement of double pulse which are separated in time less than the total +dead time (pulse length + stretcher delay + conversion dead time). Also, the +non-deterministic stretching time between the channels and the design +compilations has to be tackled to get the real time information. % \subsection{Stretcher offset calculation and calibration} % With the method mentioned above the time measured is the sum of the pulse width @@ -218,8 +225,8 @@ tackled to get the real time information. \section{Tests} The test setup consists of two FPGA boards; one as the pulse generator and the -other as the TDC board (TRB3 \cite{trb3}). The pulse generator board uses an -ecp2m-100 FPGA, where as the TDC is implemented in an ecp3-150 FPGA both from +other as the TDC board (TRB3). The pulse generator board uses an +ECP2M-100 FPGA, where as the TDC is implemented in an ECP3-150 FPGA both from Lattice. The pulse generator design generates groups of 4 bit data with 150~MHz and this data is serialised with a DDR2 module from the FPGA vendor at 600~MHz clock frequency. This way, pulses or patterns with 1.67~ns resolution are @@ -232,9 +239,11 @@ apply any cuts or curve fittings. \begin{figure}[tbp] \centering - \includegraphics[width=.5\textwidth] - {../figures/tdc/9ps_res.eps} - \caption{The precision of a sample channel for leading edge measurement.} + \includegraphics[width=.48\textwidth] + {figures/tdiff_8ps.pdf} + %{figures/9ps_res.pdf} + \caption{The precision of a sample channel for a leading edge measurement. +(The mean and precision values are in nanoseconds.)} \label{fig:precisionLeading} \end{figure} @@ -244,20 +253,20 @@ apply any cuts or curve fittings. \begin{subfigure}{.5\textwidth} \centering \includegraphics[width=.8\linewidth] - {../figures/tdc/t_diff_tot_alternating.eps} + {figures/tot_alternating_10psRMS.pdf} \caption{Conventional method.} \label{fig:precisionToTalt} \end{subfigure}% \begin{subfigure}{.5\textwidth} \centering \includegraphics[width=.8\linewidth] - {../figures/tdc/t_diff_tot_stretcher_high_precision.eps} + {figures/tot_stretcher_12psRMS.pdf} \caption{Novel method.} \label{fig:precisionToTstretch} \end{subfigure}% \caption{The width of a pulse is measured both with the conventional and novel methods. A negligible change in the precision is inspected between the two -methods.} +methods. (The mean and precision values are in nanoseconds.)} \label{fig:precisionToT} \end{figure} @@ -265,21 +274,21 @@ First, the precision of the leading edge measurements between the channels are tested by selecting one of the 64 channels as the reference channel and calculating the time difference between each channel and the reference channel. The precision is calculated as the RMS of the time distribution of the -measurement and among 64 channels precision values fluctuate between 8.7~ps and +measurement and among 64 channels precision values fluctuate between 8~ps and 10.9~ps. In figure~\ref{fig:precisionLeading} an exemplary measurement shows a -precision of 8.7~ps. As this value combines the precision of two channels, the -single channel precision can be determined as 6.15~ps. +precision of 8~ps. As this value combines the precision of two channels, the +single channel precision can be determined as 5.66~ps. The same test is applied for the ToT measurement by generating a short pulse -(1.67~ns) at the pulse generator and splitting to each channel. First the -conventional method - two channels for the measurement - is used and the best -precision is calculated as 12.2~ps (figure~\ref{fig:precisionToTalt}). The same -test is done the with the novel method for comparison and the best precision is -calculated as 12.1~ps (figure~\ref{fig:precisionToTstretch}). The precision -among the channels varied between 12.1~ps and 17.9~ps. +(3.32~ns) at the pulse generator and splitting to each channel. First the +conventional method - two channels for the measurement - is used and the +precision is measured between 10.3~ps and 13~ps among the channels. The same +test is done the with the novel method for comparison and the precision is +calculated between 11.7~ps and 15.3~ps. The sample channel precisions are shown +in figure~\ref{fig:precisionToT} for both measurements. The mean values of the histograms with the conventional and novel method do not -match with the measured pulse width - (1.67~ns) - because of the offset between +match with the measured pulse width - (3.32~ns) - because of the offset between the channels and the offset induced by the stretcher respectively, which have not yet been accounted for. In order to test the pulse width measurement we applied a pulse width sweep and measured the shift in the mean value with both @@ -289,7 +298,7 @@ in the measured mean value relative to the oscilloscope results was observed as \begin{figure}[tbp] \centering - \includegraphics[width=.6\textwidth]{../figures/tdc/tot_sweep.pdf} + \includegraphics[width=.6\textwidth]{figures/tot_sweep.pdf} \caption{ToT sweep with 1.6~ns granularity.} \label{fig:totSweep} \end{figure} @@ -321,14 +330,14 @@ negligible. \begin{subfigure}{.5\textwidth} \centering \includegraphics[width=.8\linewidth] - {../figures/tdc/rms_trb3_with_dcdc.eps} + {figures/rms_trb3_with_dcdc.pdf} \caption{With DC-DC converters.} \label{fig:rmsWITHdcdc} \end{subfigure}% \begin{subfigure}{.5\textwidth} \centering \includegraphics[width=.8\linewidth] - {../figures/tdc/rms_trb3_without_dcdc.eps} + {figures/rms_trb3_without_dcdc.pdf} \caption{With a linear power supply.} \label{fig:rmsNOdcdc} \end{subfigure}% @@ -342,8 +351,8 @@ converters.} \subsection{Effect of temperature over ToT} The effect of the temperature on the ToT measurements are observed by building a -setup consisting of a ventilator and a TRB3 board. The temperature of the FPGA -is varied by adjusting the ventilator speed. The temperature of the FPGA is +setup consisting of a ventilator and a TRB3. The temperature of the FPGA is +varied by adjusting the ventilator speed. The temperature of the FPGA is measured by a temperature sensor on the board close to the FPGA. 14 different measurements are done in the temperature range of 36.8$^{\circ}$C and 42.8$^{\circ}$C. The mean of the ToT measurements are plotted as a function of @@ -355,17 +364,17 @@ corrected. One is the change in the ToT on a single channel with the changing temperature. The other is the secondary effect of the temperature change on different ToT offsets, as the effect of temperature is higher on the longer stretcher offsets due to larger intrinsic delays of the electronic components -on the delay lines. +on the delay lines. The average relative effect of the temperature on delay +line is calculated as $\sim$1.3$\%/^{\circ}$C. -The temperature correction is done by fitting a linear line to the temperature -curve of a channel (e.g. channel 12) - which lies in the middle of the spread - -and using the slope for correction. By selecting a channel in the middle the -absolute deviations of the ToT of the channels from the initial values are -minimised. +The temperature correction coefficient is calculated iteratively until the +smallest ToT deviation among every channel at the measured temperatures is +reached. -The secondary effect of the temperature change is corrected by applying another -linear fit on the curve of the shift in ToT as a function of the stretcher -offset (figure~\ref{fig:totVSoffset}). The slope of the linear fit is used as a +The secondary effect of the temperature change is corrected by applying a +linear fit on the curve of the shifts in ToT as a function of the stretcher +offsets at the maximum temperature (42.8$^{\circ}$C) +(figure~\ref{fig:totVSoffset}). The slope of the linear fit is used as a correction coefficient. Both corrections can be written in a single equation as: @@ -383,21 +392,21 @@ in the temperature and the initial ToT value, independent of the channel. Applying only the temperature correction of the above equation, the maximum ToT shift can be corrected by a factor of $\sim$4 (figure~\ref{fig:totVStemp_tempCorr}). This correction factor increases to -$\sim$10 limiting the ToT shift with $\sim$50~ps over 6$^{\circ}$C temperature +$\sim$10 limiting the ToT shift with $\sim$65~ps over 6$^{\circ}$C temperature change, when both - temperature and offset - corrections are applied. \begin{figure}[tbp] \begin{subfigure}{.5\textwidth} \centering \includegraphics[width=1\linewidth] - {../figures/tdc/temp_vs_tot.pdf} + {figures/temp_vs_tot.pdf} \caption{The shift of the ToT with temperature.} \label{fig:totVStemp} \end{subfigure}% \begin{subfigure}{.5\textwidth} \centering \includegraphics[width=1\linewidth] - {../figures/tdc/temp_TOToffset_vs_TOTshift_@43C.pdf} + {figures/temp_TOToffset_vs_TOTshift_@43C.pdf} \caption{ToT shift @42.8$^{\circ}$C as a function of stretcher offset.} \label{fig:totVSoffset} \end{subfigure}% @@ -410,14 +419,14 @@ longer stretcher offsets.} \begin{subfigure}{.5\textwidth} \centering \includegraphics[width=1\linewidth] - {../figures/tdc/temp_vs_tot_with_tempCorrection.pdf} + {figures/temp_vs_tot_with_tempCorrection.pdf} \caption{Correction only with temperature coefficient.} \label{fig:totVStemp_tempCorr} \end{subfigure}% \begin{subfigure}{.5\textwidth} \centering \includegraphics[width=1\linewidth] - {../figures/tdc/temp_vs_tot_with_bothCorrection.pdf} + {figures/temp_vs_tot_with_bothCorrection.pdf} \caption{Correction with temperature \& offset coefficients.} \label{fig:totVStempCorrected2} \end{subfigure}% @@ -431,17 +440,27 @@ 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 +measurement is recorded as low as 8~ps, resulting in 5.66~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 +methods are recorded as 10.3~ps and 11.7~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 $\sim$10 and limited to -$\sim$50~ps with a correction model. +supply. + +The effect of the temperature change on the ToT measurement is also assessed and +the average relative effect of the temperature on delay line is calculated as +$\sim$1.3$\%/^{\circ}$C. This result shows that the with the increasing length +of the delay line and temperature difference the shift in the mean value +increases. This degeneration is corrected by a factor of $\sim$10 and limited to +$\sim$65~ps with a correction model. +With correct environmental conditions and controlling, the temperature change +can be minimised to less then 1$^{\circ}$C. Although in many high energy +physics applications high precision ToT measurements are not required, if +necessary, the conventional method should be used, as the temperature effect +plays a minimal role. @@ -452,6 +471,14 @@ $\sim$50~ps with a correction model. \begin{thebibliography}{9} +\bibitem{tdc_ieee} +C. Ugur et al., +\emph{264 Channel TDC Platform applying 65 channel high precision (7.2~ps~RMS) +FPGA based TDCs} +\href{http://ieeexplore.ieee.org/xpl/abstractKeywords.jsp?arnumber=6658234} +{\emph{2013 IEEE Nordic Mediterranean Workshop on Time-to-Digital Converters +(NoMe TDC)}, 1-5, (Oct., 2013).} + \bibitem{tot} F. Gonnella et al., \emph{Time over threshold in the presence of noise}, @@ -472,14 +499,6 @@ M. Buchele et al., the GANDALF module}, \emph{Topical workshop on electronics for particle physics 2011}, (Sep., 2011). -\bibitem{tdc_ieee} -C. Ugur et al., -\emph{264 Channel TDC Platform applying 65 channel high precision (7.2~ps~RMS) -FPGA based TDCs} -\href{http://ieeexplore.ieee.org/xpl/abstractKeywords.jsp?arnumber=6658234} -{\emph{2013 IEEE Nordic Mediterranean Workshop on Time-to-Digital Converters -(NoMe TDC)}, 1-5, (Oct., 2013).} - \bibitem{kalisz} J. 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