Ⅱ-9. Instrumentation

RIKEN Accel. Prog. Rep. 49 (2016)

Implementation of the TDC function in the GTO
T. Yoshida,∗1 H. Baba∗2 and K. Ieki∗1∗1∗2Department of Physics, Rikkyo University
RIKEN Nishina Center- 200 -GlobalClock
FF

FF

FF

Counter

EncoderFF
Signal In

DNL (LSB)

Fig. 1. Block diagram of TDC in the GTO.

21(a) LUT-DL TDC

0-1-2

DNL (LSB)

The ﬁeld-programmable gate array (FPGA) has become a popular device and has been widely adoptedfor physics measurements1) in recent years. An FPGAbased NIM logic module has been developed2) called aGeneric Trigger Operator (GTO). Advanced logic circuits have successfully been introduced in the GTO3,4) .
The present article describes the implementation of thetime-to-digital converter (TDC) function in the GTO.
There are several attempts to develop the TDC function in FPGAs5,6) . The conversion time of a conventional TDC is typically 10–100 µs, while that of anFPGA-based TDC is only tens of nanoseconds. The
block diagram of the TDC function in an FPGA isshown in Fig. 1. The shaded triangles are delay units.
FF denotes to the ﬂip-ﬂop component. The coarse timing value is obtained using the global clock. When a50-MHz clock is applied, the coarse timing value will
be a 20-ns step. To obtain the ﬁne timing value beyond the clock frequency, the tapped delay line (thecascade chain of the delay units in Fig. 1) and FF array are used. An input signal is delivered to the FF
components whenever the signal passes through the delay units. The value of the FF array is latched by theglobal clock which achieves mostly equal-length wiring.
The encoder seeks transitions of “0→1” and “1→0” inthe FF array. The former transition corresponds tothe leading edge of the input signal, and the latter one
is the trailing edge. Thus, this TDC is capable of measuring both the edges of the signal at the same time. In
this work, the look-up-table (LUT) and the carry-logic(CL) components are adopted as a delay unit. These
are called as LUT-DL TDC and CL-DL TDC, respectively. The LUT-DL TDC uses 45 LUT components
and a 50-MHz global clock. The CL-DL TDC consistsof 113 CL components and a 162.5-MHz global clock.
The conversion times are 40 ns (2 global clocks) for
the LUT-DL TDC and 18.5 ns (3 global clocks) for
the CL-DL TDC.
The diﬀerential non-linearity (DNL) has been measured to investigate the performance of the developed
TDC function. The linearity of the coarse timing isquite good as the global clock is generated from thequartz resonator that has a frequency stability of 10−6 .
However, the linearity of the ﬁne timing depends onthe variation of the propagation delay of the LUT/CLcomponents and the wiring length in the FPGA. Figure 2 shows the result of the DNL measurement for theﬁne timing. The measurement method is the same asthat in Ref. 6. The least signiﬁcant bit (LSB) of theLUT-DL TDC and CL-DL TDC is 446 ps and 54.6

2110203040

Bin Number(b) CL-DL TDC

0-1-2

204060

Bin Number

80100Fig. 2. The diﬀerential non-linearity of the developed TDC.

ps, respectively. The bin number corresponds to then-th LUT/CL components. The LUT-DL TDC has agood performance because the DNL is much less than
1 LSB in any bin. However, some bins of the CL-DL
TDC reach ±1 LSB, which implies there are missing
values in the converted result. This DNL for the CLDL TDC may be improved by ﬁne tuning the wiring
length in the FPGA.
Two types of TDC functions have successfully been
introduced in the GTO. Its conversion time is very
fast and the linearity is reasonable. Based on this result, the particle-identiﬁed trigger for future BigRIPS
experiments will be established by analyzing the timeof-ﬂight, position and delta-E information in the GTO.
References1) H. Sadrozinski and J. Wu : Applications of FieldProgrammable Gate Arrays in Scientiﬁc Research (CRCPress, 2011).
2) H. Baba et al.: RIKEN Acc. Prog. Rep. 46, 213 (2013).
3) H. Baba et al.: RIKEN Acc. Prog. Rep. 47, 235 (2014).
4) H. Baba et al.: In this report.
5) J. Wu and Z. Shi : 2008 IEEE Nuclear Science Symposium Conference Record, (2008) p. 19.
6) X. Qin et al.: IEEE Trans. Nucl. Sci. 60, 3550 (2013).