Page 78 of 82
Date: 27.01.06
10.2.
Display of measurement results
10.2.1
Introduction
Unlike analog displays of measurement signals in which the measured quantities
are represented continuously as electrical signals, only discrete values
representing the result of the quantization (digitization) exist when measurement
signals are shown on a digital display. Information loss is inevitable as a result of
quantization.
In this case, the analog-digital conversion is performed with a bipolar 16-bit ADC
(analog-digital converter), which means that 13-digit binary numbers are assigned
to the quantization levels obtained by quantization.
A thirteen-digit binary number can represent a range from 0 to 2
15
-1 = 32767. The
relative quantization error for a thirteen-bit digital signal equals
2
-15
= 1 / 32768 = 0.0031 %. This assumes, however, that the full input range of
the ADC is always used.
10.2.2
Dependence of the quantization error on input drive level
Let us assume that a load cell with an upper range value of 50 kN and a
sensitivity of 2 mV/V is connected to a Sensor Profibus Module 9221, whose input
range is set to 12.5 mV and which supplies the load cell with an excitation voltage
of 5 V.
For an applied force of 14 kN, the output signal of the load cell can be calculated
as
mV
V
V
mV
kN
kN
Us
8
.
2
5
/
2
50
14
=
⋅
⋅
=
Hence the input of the Sensor Profibus Module 9221 is driven at
%
4
.
22
5
.
12
8
.
2
=
mV
mV
This means that the quantization error should be taken into account when
assessing the maximum achievable measurement quality, because the displayed
value range now only extends from 0 to 7340 (32768 * 22.4 % / 100 %). In this
case the relative quantization error now equals 1 / 7340 = 0.014 %.
If one had selected the input range of the Sensor Profibus Module 9221 to be
5 mV , the relative digitization error would be much lower, namely
1 / 18350 = 0.0054 %.
•
It is fundamentally important to select the smallest possible input
measurement range in order to drive the ADC optimally.
•
The input measurement range is
not
based on the upper range limit of the
sensor but on the actual output voltage from the sensor for the expected load.
