8.5.5 Error Due to Real External Resistance

R_EXT is a theoretical value and may not be available in standard commercial resistor values. It is possible to closely approach the theoretical R_EXT using two or more standard values in parallel. However, standard values are characterized by a certain tolerance. This tolerance will affect the accuracy of the time interval.

The accuracy can be evaluated using the following procedure:

1. Evaluate the min and max values of R_EXT (R_{EXT_MIN}, R_{EXT_MAX} with Equation 1 using the selected commercial resistance values and their tolerances.
2. Evaluate the time intervals (T_{ADC_MIN}[R_{EXT_MIN}], T_{ADC_MAX}[R_{EXT_MAX}]) with the T_ADC equation mentioned in Equation 3.
3. Find the errors using Equation 3 with T_{ADC_MIN}, T_{ADC_MAX}.

The results of the formula indicate the accuracy of the time interval.

The example below illustrates the procedure.

• Desired time interval, T_desired = 600 s,
• Required R_EXT from Equation 1, R_EXT= 57.44 kΩ.

From Table 3 R_EXT can be built with a parallel combination of two commercial values with 1% tolerance: R1 = 107 kΩ, R2 = 124 kΩ. The uncertainty of the equivalent parallel resistance can be found using Equation 4:

SPACER

The uncertainty of the parallel resistance is 0.82%, which means the value of R_EXT may range between R_{EXT_MIN} = 56.96 kΩ and R_{EXT_MAX} = 57.90 kΩ.

Using these value of R_EXT, the digitized timer intervals calculated by T_ADC equation mentioned in Equation 3 are respectively T_{ADC_MIN} = 586.85 s and T_{ADC_MAX} = 611.3 s, giving an error range of –1.88% / +2.19%. The asymmetry of the error range is due to the quadratic transfer function of the resistance digitizer.