Kaman KD-5100 - Manual (Page 38)

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Method of Computing Performance
These results are based mainly on simulations. First the sensor inductance and resistance was
computed using a modeling program. Then the effect of 2 meters of cable was factored in taking
in consideration the transmission line effects of the cable. After that the resultant inductance and
resistance was put in a model to simulate the circuit bridge network. The performance in each
case was optimized to provide temperature coefficient as close to .02%FR as possible while
adjusting the parameters for optimal linearity and reasonably good output. The resulting data
was then fit to exponential curves to provide a continuous function of non-linearity and
temperature coefficient vs. coil diameter (and the fit was very good). Finally, the results were
then adjusted slightly based on data from actual systems and engineering judgement.
This does mean that you can adjust for better temperature coefficient if you are not concerned
with linearity and resolution. You can also get better resolution if you are willing to have a bad
temperature coefficient. The tradeoffs were made to provide the best overall accuracy. What
good is excellent resolution if the temperature coefficient causes the output to drift out of range?
In general the results will be reasonably accurate from about 10-50% of the coil diameter.
Ranges of less than 10% will have additional errors not accounted for such as thermal expansion
of the sensor body. Ranges less than 10% and greater than 50% will also have errors due to
mismatch in the sensors and electronics.
A Note about Small Ranges
There is a point of diminishing returns when the range gets small relative to the coil diameter.
At a range of about 20% of the coil diameter, the amount of change in the measured variable
starts to get small rapidly. This causes the inherent output of the system to be reduced such that
as you add more gain in the electronics to compensate your effective resolution does not increase
(and in fact your noise as a % of the range starts to increase). Also you start to get significant
errors from sensor body thermal expansion and component matching in the electronics. The
‘break even’ point is at a range of about 5% of the coil diameter. This means that reducing the
range will not help your effective performance and your dynamic range will be reduced. A range
that is too small also makes it more difficult to set up the sensor within its measurement range.
Other Observations
1) Performance degrades rapidly when the range is past 50% of the coil diameter.
2) There is a limit (floor) to the resolution and accuracy when operating over very small ranges
(<5% of the coil diameter).
3) The optimum performance will be when operating with a measuring range of approximately
35% of the coil diameter. This is where the best tradeoff between resolution, non-linearity,
and temperature coefficient will be achieved.