45
Subject to change without notice
4 Dc measurements
4.1 input resistance for dc measurements
In order to profit from the high linearity of the conversion me-
thod, the input resistance is extremely high for input voltages
up to 1 V (
>
1 GΩ). In this range, the instrument still allows pre-
cise measurements with a maximum of 1 ppm load error with
measuring objects with an internal resistance of 1 kΩ.
in the ranges 10 V, 100 V, 1000 V an internal resi-
stance of 100 Ω, with 100,000 digits resolution, will
already cause an error of one digit.
The values of the input resistance and the maximum number of
available digits in the various ranges are given in the following
table; the maximum number of digits is valid with an integration
time of 1 or 10s.
Maximum Maximum
number of
input
Maximum
Range
digits
resistance
resolution
100 mV
1 200 000
1 GΩ
100 nV
1 V
1 200 000
1 GΩ
1 µV
10 V
1 200 000
10 MΩ
10 µV
100 V
1 200 000
10 MΩ
100 µV
600 V
1
600 000
10 MΩ
1 mV
The influence of the source resistance is shown in the following
figure.
The error in % of a measurement comes about as follows:
example:
r
i
≥
1 GΩ; R
s
= 10 kΩ,
measurement error = 0,001% (10 ppm)
the often used unit ppm for errors can be calcula-
ted: error in (%) x 10,000.
4.2 series mode rejection
One of the main advantages of an integrating measuring me-
thod is the high series mode rejection of ac components (e.g.
interference from the line) which are superimposed on the
signal voltage. For frequencies for which the integration time
is a multiple of their period theoretically an infinite suppression
is achieved. Due to the integration the positive and negative
portions of the hum from the line will cancel. The interference
from the line thus can be almost completely eliminated. The
Multifunctionmeter HM8112-3 achieves a series mode rejection
of
>
100 dB for 50/60 Hz ± 5 %.
4.3 common mode rejection
Common mode rejection is the ability of a measuring instrument
to only display the desired difference signal between the „HI“ and
„LO“ input terminals while suppressing any signals referenced
to to ground common to both input terminals as far as possible.
In an ideal system there would be no error; in practice stray
capacitances, isolation resistances and ohmic unsymmetries
convert part the common mode signal to series mode.
4.4 thermal voltages
One of the most frequent causes of dc measurement errors
at low levels are thermoelectric voltages. They are generated
at the contact junctions between two different metals which
are at the same temperature or differring temperatures. The
drawing shows the various points in a measurement circuit
which are possible sources of thermoelectric voltages; those
may be at an external contact junction (contact 1/2) but also
within the terminals of the measuring instrument. Hence it is
necessary to make sure that junctions are either made of the
same material or at least to use materials which generate only
very small thermoelectric voltages when brought in contact.
The table below shows the different thermoelectric voltages für
diverse material combinations.
contact materials thermoelectric voltage (appr.)
Cu - Cu
<
0,3 µV/°C
Cu - Ag (Silver)
0,4 µV/°C
Cu - Au (Gold)
0,4 µV/°C
Cu - Sn (Tin)
2-4 µV/°C; depending on the composition
if, e.g. the material no. 1 is a silver conductor and
the material no. 2 a copper cable, a temperature
difference of only 1 degree will generate already a
thermoelectric voltage of 400 nV. this would cause
a ±40 digit error in the smallest range and 7½
digits resolution (10 nV sensitivity). For 6½ digits
of resolution the error would thus amount to ± 4
digits. With the Hm8112-3, 6½ digits resolution ,
the influence of this level of thermoelectric voltage
would affect the last digit.
DMM
R
s
V
V
s
R
i
V
m
R
i
= Max. Input resistance of the DMM
(10 MΩ oder >1 GΩ)
R
s
= Source resistance of the measurement object
V
s
= Voltage of the measurement object
contact 1
at T1
contact 2
at T2
contact 3
(HI connector)
contact 4
(LO connector)
Material 1
Material 2
Material 2
Material 1
DMM
V
m
V
V
s
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
D c m e a s u r e m e n t s
100 x R
s
Error (%) = ——————
R
s
+ R
i
