SlimLine 9173B, Instruction Manual

Page: 40 / 44

SlimLine Force Sensor, Type 9173B to 9177B
Page 38 9173B_002-286e-07.10
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. 16:
Best straight line, linearity and hysteresis
Hysteresis
The maximum difference in output, at any measurand va-
lue within the specified range, when the value is ap-
proached first increasing and then decreasing measurand
(source: ANSI/ISA-S37.1).
Note: The quartz crystal itself has a scarcely measurable
hysteresis. However, the mechanical construction of the
sensor can result in slight hysteresis. If the hysteresis is
above the specified values (in %FSO), then the sensor is
faulty or has not been correctly installed.
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.