Annex
9327C_002-477e-05.10
Page
43
Best straight line – mathematical definition
The minimization of maximum deviation is known as Che-
byshev’s approximation. The best straight line is deter-
mined as follows:
x
= measurand (reference)
Q
= sensor charge signal or output signal from the
charge amplifier
Q
(
x
) = calibration curve, rising and falling
s
= slope of the best straight lines
Best straight line:
y
i
=
s x
i
(with starting value for slope s)
Form residues:
res
i
=
Q
i
-
y
i
res
=
res
max
+
res
min
sum min. + max. deviation
Recursive minimization of
res
=
f
(
s
) by changing
s
un-
til
res
= 0
Linearity
a
=
res
max
=
res
min
Fig. 24: Best straight line, linearity and hysteresis
Hysteresis
Quartz itself has a scarcely measurable hysteresis. How-
ever, the mechanical construction of the sensor can result
in slight hysteresis, but this is below the specified value (%
FSO) in every measuring range. If a greater hysteresis oc-
curs, then the sensor has not been correctly installed.
Hysteresis (b%) is included in the linearity (
a%) and does
not have to be additionally taken into account in estimat-
ing the measurement uncertainty.
Charge amplifier linearity
The linearity of charge amplifiers is typically within the
range of
0,05 % of the measuring range selected. For the
accuracy of the measurement, this is usually negligible
compared with other influences.
