User's Manual

Instruction Manual
748332-F
April 2003
3-6 Startup and Operation Rosemount Analytical Inc. A Division of Emerson Process Management
Model NGA2000 NDIR
3-6 LINEARIZATION
The NDIR Analyzer Module can be operated
in linear and non-linear mode. Linearization
can be toggled ON/OFF in the Expert
Controls menu. In the OFF position,
linearization is disabled for all ranges, and the
component of interest is measured in percent
of fullscale. In the ON position, measurement
is in engineering units: Either ppm or percent
of concentration.
The NDIR Analyzer Module is linearized with
the following fourth-order polynomial:
Y = A
o + A1X + A2X
2
+ A3X
3
+ A4X
4
Where:
X = the normalized non-linear input
A
O, A1, A2, A3, A4 = linearization
coefficients
Y = the normalized linear output
Linearization coefficients can be developed
and stored for each range through the Expert
Controls menu. The operating range is
selected by entering RANGE = 1, 2, 3 or 4 in
the Range Mode section that that menu.
Coefficients for each selected range are
automatically used when the module is in
Linearization Mode. The user instructs the
Analyzer Module as to which set of
coefficients are to be used for each range.
Maximum dynamic range is 3:1.
When ordered, special linearization
coefficients for non-standard fullscale ranges
are entered in the appropriate range(s) at the
factory. If a range is not specified, the set of
coefficients will be for Range 4.
The operator may want the module to output
measurement in engineering units (ppm).
This response is linear over the operating
range. The following coefficients will make no
correction to the non-linear response, but will
cause the NDIR Analyzer Module to output
gas measurement in engineering units:
A0 = 0.00000
A1 = 1.00000
A2 = 0.00000
A3 = 0.00000
A4 = 0.00000
To calculate linearization coefficients other
than those installed at the factory, take a
minimum of 11 data points. (A more accurate
curve can be obtained as the user
approaches 21 data points. If urgent, a curve
can be created with as few as four points, but
this is only a temporary fix. A more accurate
curve should be created as soon as possible.)
These data points can be obtained with an
accurate gas divider or other flow mixing
device. Before calculating coefficients, the
data must be normalized to ranges of 0 to 1
units for both percent and concentration
readings. Then, the axis must be reversed as
illustrated in Figure 3-7 on page 3-7 and
Figure 3-8 on page 3-7. A multiple linear
regression is then used to calculate
coefficients. (For example: If the range is 0
to 5000 ppm and readings are 0 to 100%,
then divide all of the concentrations by 5000
and the readings by 100. Put the normalized
concentrations on the Y-axis and the
normalized readings on the X-axis.)
These data points can be entered into any
program capable of computing a fourth-order
polynomial curve. This curve will be the
mirror image of the curve on the Calibration
and Data Sheet provided in the rear of this
manual; however, the linearization coefficients
will be different. Use the coefficients
calculated with the curve in the polynomial
shown on the previous page.
After taking the data points, the operator may
determine coefficients for user-specific gas by
either using any program capable of
calculating a fourth-order curve fit or calling
the factory to have the specific coefficients
calculated.
When entering the operator-determined
coefficients, note that the microprocessor only
recognizes five significant digits to the right of
the decimal point (e.g., 0.12345).