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Subject to change without notice
c o n t r o l e l e m e n t s
3 measurement Principles and Basics
What does „measure“ mean:
the reproducible comparison of an unknown with a known
reference and the display of the result as a multiple of the
unit of the reference.
3.1 Display of measuring ranges
There are various methods to describe the display of a multi-
meter. The simplest one consists of just specifying the number
of available digits. The measuring range of a Digital Multimeter,
in short DMM, thus indicates how many steps the display can
show. Some examples will be the best method to describe the
definition of the range of display.
A 6-digit, a 6½-digit and a 6¾-digit DMM will be used for the
explanation.
6-digit DMM
6½-digit DMM
6¾-digit DMM
Range
of the display:
0 0 0 0 0 0
0
0 0 0 0 0 0
0
0 0 0 0 0 0
to to to
9 9 9 9 9 9
1
9 9 9 9 9 9
3
9 9 9 9 9 9
Availabe number
of digits:
1.0 0 0.0 0 0 digit
2.0 0 0.0 0 0 digit
4.0 0 0.0 0 0 digit
The „6“ indicates the number of digits which are always shown in
the display. The fraction ½ resp. ¾ indicates at which number in
the highest digit the range will be switched to the next (change
of decades). The switchover to the next higher range will cause
a loss of one digit in the display, hence also the resolution will
be reduced by one digit.
In the following an example will be given for the switching of
the number of digits of the display when the range is switched.:
Measuring result 1: 1 0 V
1 0 V
1 0 V
Display 1:
1 0,0 0 0
1 0,0 0 0 0 0
1 0,0 0 0 0 0
Measuring result 2: 2 0 V
2 0 V
2 0 V
Display 2:
2 0,0 0 0
2 0,0 0 0 0
2 0,0 0 0 0 0
Change of decades
Measuring result 3: 3 9,9 9 9 9 9 V
3 9,9 9 9 9 9 V
3 9,9 9 9 9 9 V
Display 3:
3 9,9 9 9
3 9,9 9 9 9
3 9,9 9 9 9 9
Measuring result 4: 4 0 V
4 0V
4 0 V
Display 4:
4 0,0 0 0
4 0,0 0 0 0
4 0,0 0 0 0
Change of decades
the display of the measurement range of 6½ digits
is only possible at a measuring time of 60s.
3.2 overranging
In the previous example our 6½ – digit DMM had a range of the
display of 2,000,000 digits. The switching of decades took place
when in the first digit the number 1 changed to 2. Another 6½ –
digit DMM may have a range of display of 1,250,001 digits. Here,
the switching of decades also happens in the highest digit, but
whenever the 3rd digit changes from 5 to 6.
6½-digits DMM1
6½-digits DMM2
Display range:
0
0 0 0 0 0 0
0
0 0 0 0 0 0
to
to
1
9 9 9 9 9 9
1
2 5 0 0 0 0
Measuring points:
2.0 0 0.0 0 0 digit
1.2 5 0 0 0 1 digit
Measuring result 1:
1 0 V
1 0 V
Display 1:
1
0,0 0 0 0 0
1 0,0 0 0 0 0
Measuring result 2:
1 2,5 0 0 0 0 V
1 2,5 0 0 0 0 V
Display 2:
1 2,5 0 0 0 0
1
2,5 0 0 0 0
Measuring result 3:
1 2,6 0 0 0 0 V
1
2,6 0 0 0 0 V
Display 3:
1 2,6 0 0 0 0
1
2,6 0 0 0
Change of decades
DMM no. 1 with 2,000,000 digits is able to display up to 1,999,999,
the DMM no. 2 with 1,250,001 digits can only display up to
1,250,000. .DMM no. 1 is hence specified with an „overrange
of 100 %“. In contrast DMM no. 2 has an overrange of 25 %. If
DMM no. 2 had a range of display of 1,400,000 digits, it would
have an overrange of 40 %.
the measuring range of a Dmm thus is given by the
full range minus overrange.
Example: 6½-digit DMM with 1,250,001 digits:
Full range:
12,50000 V
– Overrange:
2,50000 V
Measurement range:
10,00000 V
3.3 resolution of a measuring range
The resolution of a digital measuring instrument is equal to the
least significant digit of the display. The digitized measurement
value is hence quantized. In contrast to this, the resolution of an
analog measuring instrument is given by the smallest change
discernible by the viewer. With analog measurement each
measurement value corresponds to a unique display.
the resolution of a Dmm depends on the number
of available digits and is the reciprocal value of the
number of digits (without the overrange).
Example: 6½-digit DMM with 1.2 0 0.0 0 0 digit
the overrange amounts to 200,000 digits, hence the
resolution follows:
1
= 0,000001
1.200.000 – 200.000
this is equivalent to 0.0001 % of full range.
A Dmm has a resolution of 0.1 V in the 100 V range. if a voltage
of 100.05 V is to be measured, the Dmm can display either 100.0
V or 100.1 V (disregarding all other measurement uncertain-
ties). the Dmm can never measure more accurately than the
resolution allows which is here 0.1 %.
3.4 measurement accuracy
The measurement accuracy of a digital measuring instrument
is by its nature principally limited by its resolution. The theore-
tical maximum accuracy of a measurement and also the least
significant display digit are defined by the smallest quantizing
step (LSB = least sigificant bit) of the analog/digital converter.
The following factors influence the accuracy of a DMM:
– Active and passive component tolerances and their tempe-
rature dependence
– Stability of the reference voltage of the DMM
– Properties of the a/d converter
m e a s u r e m e n t P r i n c i p l e s a n d B a s i c s
