IEEE Instrumentation & Measurement - September 2023 - 16

TDCs [11], [13]. To implement this calibration, a Look-Up Table
(LUT) is used to map each binary code delivered by the
encoder to a new code that represents the estimated equivalent
time without PVT variations. The code density test method is
usually used to obtain the content of this table, which consists
of the following steps: estimation of bin width and obtaining
the calibration table.
Estimation of Bin Width: A periodic signal with N pulses (samples)
is taken as a test. N is usually on the order of more than
100,000 samples, allowing a low enough standard error
(σσE
= / N) to consider the measurements valid. The standard
deviation σ (quantified in picoseconds) represents the
TDC capability to obtain the same measurement over time intervals
of the same duration. The frequency of this signal must
be asynchronous with respect to CLK so that each capture represents
a different and unpredictable measurement for Tn
Tn
()1 and
()2 . A histogram accumulates the number of times each equal
measurement is made. In the end, the histogram must contain
an ideally uniform distribution of its values. The delay ω of the
bin i can be estimated as:
ωi = × ,
ni
N
T
(1)
where ni is the number of the histogram counts for the i th− bin,
and the average bin width w represents the TDC resolution.
Obtaining the Calibration Table: Content of CT is obtained by using
the procedure expressed as:
tk = +
ωk
2 ∑ ωi ,
k−1
i 0
=
where tk represents the total delay from the origin of the
TDL to the bin k. This CT can be used either offline or online.
When used in the offline mode, the content of CT is fixed.
(2)
Nonetheless, PVT variations cause bin delay changes. In general,
the temperature affects the TDC operation the most, due
to the wide range of ambient temperatures in which TDC can
work. To compensate for this, online calibration is used by updating
the content either for each measurement made or every
arbitrary time. Embedded temperature sensors are typically
used in FPGA devices to accomplish this task.
IS
CLK
(a)
Fine measurement
Capture Module
IS
CLK
(b)
IS
Fine measurement
IS
CLK
(c)
Capture Module
Capture Module
Capture Module
CLK
Complementary Strategies
Additional components have been used to improve the TDC
performance in terms of resolution, precision, and linearity.
(A detailed description of these and additional metrics can
be found in [14]). Examples of these strategies are the multichain
and multisampling methods. They can be incorporated
under the configuration shown in Fig. 6. For simplicity purposes,
CC and postprocessing components are not displayed.
Fig. 6a shows the strategy introduced in Fig. 3. Fig. 6b illustrates
the multichain method [15]. In multichain TDL, each
channel has more than one TDL [3]. Here, the signal generated
by the PS is propagated through multiple TDLs, and
each TDL has its corresponding capture module. The captures
made are encoded and averaged to obtain a FM. Garzetti
[16] uses the multichain method in combination with a WUA
launcher to explore a different number of parallel TDL arrays
(fOUT). When increasing fOUT, area occupancy and power
consumption also get incremented, whereas the improvement
in resolution and precision is saturated around fOUT=4. Fig.
6c represents the multisampling method in which several captures
of the pulse signals (PS output) propagated along the
TDL are made. For each sample, replicas of the clock signal are
created so that there is a phase shift between them. Again, the
captures are coded and averaged to obtain the FM. The last
case is shown in Fig. 6d, where the two methods are combined.
With these methods, it is possible to reach sub-picoseconds
precision. The drawback is that, despite the outstanding results
regarding resolution
and precision, the number
of implemented channels
is reduced proportionally
due to resource utilization
[17]. For this reason, the architecture
shown in Fig. 6b
may not be economical for
a large-scale measurement
system and has not been
explored yet.
Fine measurement
Capture Module
Fine measurement
Capture Module
Capture Module
Capture Module
(d)
Fig. 6. Popular configuration for multichain and multisampling methods.
16
IEEE Instrumentation & Measurement Magazine
Recent
Contributions
In the Table 1, some examples
of state-of-the-art TDC
architectures are shown.
The proposed architectures'
general configuration
(pulse shaper, TDL length
considering the active bins
September 2023
Pulse
Shaper
Pulse
Shaper
Pulse
Shaper
Pulse
Shaper
Pulse
Shaper
Pulse
Shaper

IEEE Instrumentation & Measurement - September 2023

Table of Contents for the Digital Edition of IEEE Instrumentation & Measurement - September 2023

Contents
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