Instrumentation & Measurement Magazine 25-3 - 9
Fig. 10. Shows the differences between the uncertainty calculated by the
proposed approach and the conventional uncertainty at constant N and variable b.
Fig. 12. DMP41 used for investigation.
instrument and hence the difference between the uncertainty
value calculated by the proposed algorithm and the conventional
uncertainty.
This algorithm is an important milestone for metrologists
to evaluate the effects of quantization error of the displayed
and measured values. With high-precision measurements, as
in international comparisons, the error, even if it is less than
1 ppm, may lead to a change in the direction of the results
of this comparison regarding satisfactory or unsatisfactory
results. This error is greatly affecting the displayed results, especially
at readouts with low N-bit wordlengths where it can
increase the uncertainty by more than 13 ppm at N= 16 and
4500 ppm at N=8, as shown in Table 2 and Table 3.
Fig. 11. The differences between the uncertainty calculated by the proposed
approach and the conventional uncertainty at constant b and variable N.
the upper bounds (a, and b) of the visible zone, while considering
that both a and b are defined according to the physical limits of
the measurand and the resolution r of the device display.
Fig. 10 and Fig. 11 show that the quantization error is
greatly affected by the N-bit wordlengths of the digital display
Verification Example
To verify the applicability of this approach, an example used
for the investigation is a load cell readout apparatus DMP41
ADC instrument with N-bit wordlengths of 24, the interval of
measuring range [a-b] is from 0 to 2 mv/v and has a resolution
r of 0.0000001 mv/v, and it is evaluated at reading Xj
= 1 mv/v
(Fig. 12). The DMP41 is evaluated according to the proposed
model using (1) to (13), and the results are compared with
those obtained according to the method proposed in [19]. For
the same input data, the results are summarized in Table 4.
Item
δ (mV/V)
qioXj
qicXj
Lmin
Lmax
u (mV/V)
(mV/V)
rj
ur
Es
( )
uur
Xj
rj
May 2022
10 6
(ppm)
(mV/V)
(mV/V)
(mV/V)
(mV/V)
Table 4 - Comparative results of DMP41
The proposed approached
1.1920929666E-07
0.99999950000
1.00000050000
0.999999440395
1.0000005596047
3.23087894296E-07
2.8867513E-07
0.0344
IEEE Instrumentation & Measurement Magazine
Ref [19]
0.00000011920929
0.9999995827674
1.0000004172325
0.999999523163
1.000000476837
0.0000002753021
0.000000288675135
- 0.013
9
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