BRONKHORST E-7000 Series, Инструкция по эксплуатации

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BRONKHORST HIGH-TECH B.V.
page 32 9.17.017
2.11 Calibration with polynomial functions
2.11.1 General information
A normally calibrated device will have linearized transfer functions within 1% accurate. This means that the
real temperature is proportional to the output signal (0-5 V, 0-10 V, 0-20 mA or 4-20 mA) within 1%.
A polynomial function is a method of approximation which mathematically describes a continue transfer
function.
By means of a few samples, a polynomial function can be obtained. After determining the polynomial
function, the original calibration points and an infinite amount of values in between, can be calculated with
high accuracy.
In a system where pressure- and/or flow meters and -controllers should be readout and set with high
accuracy, these polynomial functions often are used for approximation of their transfer function. For instance
the function which describes the relation between output voltage and measured temperature.
2.11.2 General form
The general form of a polynomial function of the n-N.D. degree is as follows:
y a0 a1 X a2 X a3 X ..... an X
2 3 n = + ⋅ + ⋅ + ⋅ + + ⋅
Where 'a0' to 'an' are polynomial parameters, which can be calculated.
When you have 'n + 1' measure-points, they can be approximated by means of a 'n-N.D.' degree polynomial
function.
2.11.3 Polynomial functions of sensor signal and setpoint
By means of a calibration at Bronkhorst HIGH-TECH B.V. several measure points will be used to obtain a
polynomial function.
The form of this function is:
Y a b X c X d X
2 3
= + ⋅ + ⋅ + ⋅
In which 'Y' is the measured value in correct unit (e.g. temperature in [
°
C]) and 'X' is the value of output signal
in correct unit (e.g. Uout in [V]).
Characters 'a - d' are polynomial parameters, which can be obtained by a mathematical program. These
parameters can be filled in and the polynomial function is completed.
Now a flow can be calculated out of the sensor output signal of the device.
2.11.4 Presentation of parameters
Parameters 'a - d' are polynomial function parameters, which can be obtained with a mathematical program
out of measured calibration points.
All parameters will be printed on the calibration certificate. They will be presented in scientific notation with 3
significant digits, where the last digit is obtained by rounding-off. Parameter 'b’ (the linear factor) however, are
exceptions: they are the most important parameters and therefore will be presented in 5 significant digits.
Example:
a = 7.67 · 10
-2
b = 4.3076
c = 1.11 · 10
-1
d = 1.73 · 10
-2
Polynomial function for sensor signal:
Y = 7.67 · 10
-2
+ 4.3076 · X - 1.11 · 10
-1
· X
2
+ 1.73 · 10
-2
· X
3