35
APPENDIX E. NON LINEARITY AND THE USE OF A SECOND ORDER
POLYNOMIAL TO IMPROVE THE ACCURACY OF THE CALCULATED
PRESSURE
Most vibrating wire pressure transducers are sufficiently linear (
±
0.2 % FS) that use of the linear
calibration factor satisfies normal requirements. However, it should be noted that the accuracy of
the calibration data, which is dictated by the accuracy of the calibration apparatus, is always
±
0.1% F.S.
This level of accuracy can be recaptured, even where the transducer is nonlinear, by the use of a
second order polynomial expression, which gives a better fit to the data then does a straight line.
The polynomial expression has the form:
Pressure = AR
2
+
BR
+
C
Equation 17 - Pressure Calculation with Second Order Polynomial
Where;
R is the reading (digits channel B)
A, B, and C, are coefficients
Figure 18 shows a typical calibration sheet of a transducer that has a very little nonlinearity. The
figure under the “Linearity (%FS)” column is:
Calculated Pressure
-True Pressure
Full
S
cale Pressure
x 100%=
G
(
R
1
-R
0
)
-
P
F.S.
x 100%
Equation 18 - “Linearity (%F.S.)” on Calibration Sheet
Note: The linearity is calculated using the regression zero for R
0
shown on the sheet.
For example, from the typical sheet shown in Figure 18:
P= 210 kPa, G (R
1
– R
0
) = - 0.1192(7223-8983)
Gives a calculated pressure of 209.8 kPa, the error is 0.2 kPa.
Whereas the polynomial expression gives a calculated pressure of:
A (7223)
2
+
B (7223) + 1053 = 209.9 kPa
The actual error is only 0.1 kPa.
This is an insignificant improvement, however, where the nonlinearity is higher, for example
± 0.25% F.S., the improvement could be significant.
