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ADDENDUM FOR SELECTABLE OUTPUT FUNCTIONS
2.0 POLYNOMIAL 1 (5th order)
Available for HART version
The polynomial function, applied to the transmitter input (x) expressed
in % of the calibrated span, has the following form:
Out =
±
A
0
±
A
1
(x)
±
A
2
(x
2
)
±
A
3
(x
3
)
±
A
4
(x
4
)
±
A
5
(x
5
)
where (x) and Out should be normalized in the range 0 to 1 for
calculation purpose, with following Out meaning:
Out = 0 means Analog out 4 mA
Out = 1 means Analog out 20 mA
This function can be used for linearization purpose: the user can plot the
characteristic curve of the input and find, using a mathematical method,
the parameters of the polynomium that better approximate the plotted
curve. Check, after the calculation, if the maximum error is compatible
with the application.
The following are some application examples.
2.1 CYLINDRICAL VESSEL
Using the polynomial function applied to a level transmitter installed in
a horizontal cylindrical vessel it is possible to transmit the measure of
level in term of partial volume. Some different cases should be
considered:
a) Cilindrical vessel with flat ends (not often used. Fig. 1a). Transmitter
measuring the whole vessel heigth.
The following polynomium gives the area of the circular section in
relation to the heigth h (heigth of the liquid in the vessel).
Out = - 0.02 + 0.297 h + 2.83 h
2
- 4.255 h
3
+ 3.5525 h
4
-1.421 h
5
Being both the input h and the output Out normalized, i.e. in the range
0 to 1 (or 0% to 100%), the vessel diameter corresponding to a circular
area equal to 1 (100%) will be "normalized" by a "K" factor of the
following value :
K = 2 •
√
1/
π
= 1.12838
The volume of the liquid contained in the vessel, at heigth = h will be
V = Out • (d/1.12838)
2
• L
where d = vessel diameter and L = vessel length.
The non conformity error is within 0.1% between 0.5% and 99.5% of h,
0.2% at 0% and 100%.
b) Cilindrical vessel with hemispherical ends (see Fig. 1b). Transmitter
measuring the whole vessel heigth.
The same polynomium can be used also for the cylindrical vessel with
hemispherical ends. To obtain the volume contained in the vessel can
be used the following empyrical formula:
V = Out • (d/1.12838)
2
• (L + 2/3 d)
Fig. 1a
Fig. 1b
d
GENERAL DESCRIPTION
The 2600T Series Pressure Transmitter can be selected with a linear, a "polynomial" output function, for input linearization
using a 5th order polynomial function, or for input linearization using 2 polynomial functions of 2nd order.
Also a Constant Current function can be choosen for loop or associated equipment test.
1.0 LINEAR
Using this function, the relationship between the input (measured value), expressed in % of the calibrated span and the output
is linear, e.g. at 0% input, corresponds 0% output (4mA), at 50% input corresponds 50% output (12mA) and at 100% input
corresponds 100% output (20mA). Available for analog and HART version.
Summary of Contents for 2600T EN Series
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