Campbell Scientific CR9000X Measurement and Control System - Manual (Page 364)

Section 9. Program Control Instructions
Removing the Mystery from a 2 point Calibration: Y=MX+B
Many data acquisition systems available today make a raw measurement of the
output voltage, current, or resistance of a sensor, and scale the measurement to
the desired engineering units. You must know how a sensor behaves in order
to apply the proper scalars. The following paragraphs deal with determining
how a particular sensor might behave. The sensor output need only be linear
over the desired range and to have good repeatability. In other words, it needs
to be a precision instrument, but it does not necessarily need to be accurate.
The entire measurement system, from the sensor to the display device, gets
calibrated using the following procedure.
The following describes how to use a two point calibration method to solve for
the multiplier and offset for a linear relationship.
Solving for the Multiplier: Assume that a pressure sensor experienced a
change of 20 psi resulting in an output change of 3 mV. The important factors
are the changes (
Δ) and not the absolute values of the measurements. If we
want to scale the output to read the same as the known input (the standard), it
is necessary to multiply the output millivolts by some factor (M). In other
words, when the change in the output (
ΔX) is multiplied by the multiplier (M),
the resultant product should be equal to the change in the input ( ΔY):
ΔY = M • ΔX
M = ΔY / ΔX = 20 / 3 = 6.66667
Solving for the Offset: Now assume that the 2 different standard values
applied to the sensor were exactly 0 psi and 20 psi. When zero psi was applied
the output was 3 mV, and when 20 psi was applied the output was 6 mV.
y = mx + b to solve for b yields
b = y - (mx). Therefore
b = 20 - (6.66667 x 6);
= 20 - 40
= -20.
If x = 5 mV then:
y = 6.66667 • 5 + (-20) = 13.33335 psi (as shown in the chart)
In essence, these are the calculations used in the logger when using the
FieldCal instruction set up for two point calibrations.
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