Instruction Manual

748332-F April 2003

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 = Ao + A1X + A2X2 + A3X3 + A4X4

Where:

X = the normalized non-linear input

AO, 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).

3-6

Startup and Operation

Rosemount Analytical Inc. A Division of Emerson Process Management