1.1.1 Calibration Step

ADCT1 and ADCT2 define a straight line. A straight line that intersects the points (h,k) and (p,q) is represented by Equation 1. The output (y) is the temperature output from the ADC, while the input (x) is the actual temperature.

Equation 1: Straight line.

y - k = q - k p - h × ( x - h )

An ideal output from the ADC is a straight line defined by Equation 2.

Equation 2: Ideal output.

y = x
Figure 1-1. ADC and Ideal Output

The solid line in the figure above is an arbitrary ADC characteristic, while the dashed line represents the ideal result from the temperature measurement. The line defined by our two calibration points has the following equation:

Equation 3: Line defined by the calibration points.

y − A D C T 1 = A D C T 2 − A D C T 1 T 2 − T 1 ( x ⁢ − T 1 )
Figure 1-2. ADC Output with Line Defined by Calibration Points

The offset error is the distance between the origin of coordinates and the point where the line defined by the two calibration points intersects the y-axis. It’s found by setting x = 0 in Equation 4.

Equation 1-4 : Offset error.

T o f f s e t = A D C T 2 ⁢ −   A D C T 1 T 2 − T 1 ( − T 1 ) + A D C T 1
Figure 1-3. ADC Output with Offset Error Removed

It is necessary to find a gain factor k to apply to the ADC output values after the offset error has been removed. To find this factor, the following equation is used.

Equation 5: Gain factor.

k = T 2 A D C T 2 − T o f f s e t