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 pulses separated in time less than the total dead time
+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 pulses 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.
+compilations has to be tackled in order to obtain real time information.
% \subsection{Stretcher offset calculation and calibration}
% With the method mentioned above the time measured is the sum of the pulse width
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 possible to be
-generated. These pulses/patterns are sent to the TDC for leading edge and ToT
-measurements. The output of the pulser is split in fanout chips to fire every
-channel of the TDC. The observed non-linearities of the TDC \cite{tdc_ieee} are
-corrected by bin-by-bin calibration \cite{calibration} and the calibration table
-is automatically updated after every 200~000 events. In the measurement time
+This way, it is possible to generate pulses or patterns with 1.67~ns resolution.
+These pulses/patterns are sent to the TDC for leading edge and ToT measurements.
+The output of the pulser is split by fanout chips to fire every channel of the
+TDC. The observed non-linearities of the TDC \cite{tdc_ieee} are corrected by
+bin-by-bin calibration \cite{calibration} and the calibration table is
+automatically updated after every 200~000 events. In the measurement time
distributions we do not apply any cuts or curve fittings.
\begin{figure}[tbp]
\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. (The mean and
+methods. A negligible change in the precision is observed. (The mean and
precision values are in nanoseconds.)}
\label{fig:precisionToT}
\end{figure}
The precision of the ToT measurements is tested by sending a short pulse
(3.32~ns) from the pulse generator to each channel. With the conventional method
- two channels for the measurement - the precision is measured between 10.3~ps
-and 13~ps among the channels. The same test is repeated the with the novel
-method to measure the precision between 11.7~ps and 15.3~ps. The sample channel
-precisions are shown in figure~\ref{fig:precisionToT} for both measurements.
+and 13~ps among the channels. The same test is repeated with the novel method to
+measure the precision between 11.7~ps and 15.3~ps. The sample channel precisions
+are shown in figure~\ref{fig:precisionToT} for both measurements.
The measured ToT values with both methods do not match the generated pulse width
(3.32~ns) because of the offset between the channels and the offset induced by
\subsection{Effect of DC-DC converters over wide pulses}
-We also tested the quality of the long time interval measurements, as this is
-important for both time of flight (ToF) and ToT measurements. Tektronix AWG7000
-is used as the pulse generator with two outputs controlled over a general
-purpose interface bus (GPIB). Signals from two outputs are sent to two different
-channels of the TDC, where the time interval between the signals is measured.
-Starting with 0~s, time interval is incremented with 1~ns granularity until
-1~us. The precision is recorded for each measurement.
+Additionally the quality of the long time interval measurements was also
+tested, as this is important for both time of flight (ToF) and ToT
+measurements. Tektronix AWG7000 is used as the pulse generator with two outputs
+controlled over a general purpose interface bus (GPIB). Signals from two outputs
+are sent to two different channels of the TDC, where the time interval between
+the signals is measured. Starting with 0~s, the time interval is incremented
+with 1~ns granularity until 450~ns. The precision is recorded for each
+measurement.
% We also tested the quality of the long time interval measurements as this is
% both important for the long time of flight (ToF) and ToT measurements. The test
% interval of 1~us is reached. The precision is recorded for each measurement.
% The calibration of the channels is done only once at the beginning of the test.
-\begin{figure}[bp]
+\begin{figure}[tbp]
\begin{subfigure}{.5\textwidth}
\centering
- \includegraphics[width=.86\linewidth]
- {figures/rms_trb3_with_dcdc.pdf}
+ \includegraphics[width=0.95\linewidth]
+ {figures/rms_trb3_with_dcdc.eps}
\caption{With DC-DC converters.}
\label{fig:rmsWITHdcdc}
\end{subfigure}%
\begin{subfigure}{.5\textwidth}
\centering
- \includegraphics[width=.86\linewidth]
- {figures/rms_trb3_without_dcdc.pdf}
+ \includegraphics[width=0.95\linewidth]
+ {figures/rms_trb3_without_dcdc.eps}
\caption{With a linear power supply.}
\label{fig:rmsNOdcdc}
\end{subfigure}%
-\caption{The precision of the measurements is recorded over a microsecond time
-interval between two outputs of a pulse generator. The oscillation amplitude is
-reduced to 3~ps by powering the FPGA with a linear power supply instead of
-DC-DC
-converters.}
+\caption{The precision of the measurements is recorded over almost half a
+microsecond time interval between two outputs of a pulse generator. The
+oscillation amplitude is reduced to 3~ps by powering the FPGA with a linear
+power supply instead of DC-DC converters.}
\label{fig:rmsVSdcdc}
\end{figure}
In figure~\ref{fig:rmsWITHdcdc} the precision as the 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 noted that the oscillation amplitude was improved
-by a factor of $\sim$12. The exposed secondary oscillation has an amplitude of
-$\sim$3~ps and a frequency of 25~MHz (figure~\ref{fig:rmsNOdcdc}). This
-additional oscillation is not further investigated as the amplitude is
-negligible.
+interval is shown. It was observed that over half 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 of the
+converters and the FPGA was powered with a linear power supply (HMP4040). The
+oscillation amplitude was improved by a factor of $\sim$12 under the same test
+conditions. The exposed secondary oscillation has an amplitude of $\sim$3~ps
+and a frequency of 25~MHz (figure~\ref{fig:rmsNOdcdc}). This additional
+oscillation is not further investigated as the amplitude is negligible.
\subsection{Effect of temperature over ToT}
\section{Conclusion}
In this paper we presented our novel way of measuring ToT on an FPGA TDC using a
single channel. Based on the conducted tests, precision of the leading edge
-measurement is recorded as low as 8~ps, resulting in 5.66~ps error on a single
+measurement is recorded as low as 8~ps, resulting in a 5.66~ps error on a single
channel. The precisions for ToT measurements with the conventional method (using
two TDC channels for two edges) and novel method (using a single TDC channel for
both edges) are recorded as 10.3~ps and 11.7~ps respectively. The ToT values,
-measured with the novel method, differ maximum 38~ps from the oscilloscope
-measurements, once the stretcher offset is eliminated. It is also discovered
-that the deterioration in the long time interval measurement precision can be
-limited to 3~ps, if the FPGA is powered with a linear power supply.
+measured with the novel method, differ by a maximum of 38~ps from the
+oscilloscope measurements, once the stretcher offset is eliminated. It is also
+determined that the deterioration in the long time interval measurement
+precision can be limited to 3~ps, if the FPGA is powered with a linear power
+supply.
The effect of the temperature change on the ToT measurement is also assessed and
-the average relative effect of the temperature on delay line is calculated as
-$\sim$0.4$\%/^{\circ}$C. These results show, that the temperature effect is
-larger for the longer delay lines. This effect can be compensated by a factor of
-$\sim$10 and limited to $\sim$65~ps with the described correction model.
+the average relative effect of the temperature on the delay line is calculated
+as $\sim$0.4$\%/^{\circ}$C. These results show, that the temperature effect is
+larger for the longer delay lines. This effect can be compensated by a factor
+of $\sim$10 and limited to $\sim$65~ps with the described correction model.
For many practical cases the temperature effect can be neglected, as it is
possible to control the temperature change below 1$^{\circ}$C. Although in many
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