Table 10. Wide-Range Parameters

Table 11. Wide-Range Measurement Values

8.2.1.2.1 Wide-Range Calibration

To begin calibration, select an object temperature (T_OBJ) and a value for the die temperature (T_DIE). With these system temperatures stable, take a statistically significant number of samples of V_Sensor (results shown in register 00h).

in this example, 64 samples were taken. Do not use the object temperature readings given in register 03h; these values are invalid before calibration.

To compensate for first order drift in system temperatures, it is often useful to normalize the data set. For this purpose, for each temperature set, the sensor voltage data (given in register 00h) is normalized by first finding the best fit line of the form shown in Equation 11:

Equation 11.

The normalized data for each data set is then calculated as shown in Equation 12:

Equation 12.

The normalized data, V_{Sensor_norm}, is centered on zero mean, and is first-order corrected for long-term drift. The standard deviation for each data set is then calculated to estimate the sensor noise, σ. Verify that the data are limited by white noise and no other effects. For a sensor-noise-limited data set, v_SENSOR σ is typically < 1 μV, and preferably < 0.5 μV after first-order correction for drift, as described previously. If this condition is not satisfied, then the calibration accuracy is limited by external system factors (for example, convection or conduction). Repeat this process for each combination of T_OBJ and T_DIE for which the calibration is to be performed. The normalized data are used only for evaluating the suitability of the data set for calibration, and not for the actual calibration itself.

For calibration, the mean value, <V_SENSOR>, is calculated for each combination of T_OBJ and T_DIE, as shown in Table 12. Using the mean value minimizes error introduced by random noise. Based on the means, a set of coefficients is generated based on a user-selected optimization criteria for Equation 7. Common criteria are minimizing the maximum error, minimizing the average error, and so on. For a detailed discussion of optimization methods, see SBOU142 — TMP007 Calibration Guide.

8.2.1.2.2 Verifying the Calibration

The next step is to use the generated coefficients to verify the calibration, and determine the accuracy of the system. For common calibration (C) , the same coefficients are used for all devices; in unit calibration (U) the coefficients are calculated for each device. Common calibration includes device-to-device variation, and thus is less accurate, but much easier to implement. Unit calibration is more accurate, and eliminates device variation, but requires more effort to implement. The choice depends on the application requirements for accuracy versus implementation effort.

Mean calibration error at each point is defined as shown in Equation 13:

Equation 13.

where

• T_{OBJ_PREDICT} is the temperature based on the calibration coefficients.
• T_{OBJ_ACTUAL} is the known object temperature, measured independently.
• N is the number of devices in the calibration set.

The mean error graph (see Figure 54) provides an efficient method of understanding how the systematic errors vary across the temperature ranges of interest. This graph also provides a means of weighing the benefits and efforts of common versus unit calibration for a particular application.

Note that calibration does not affect the temporal random noise observed, as shown in Figure 55. The standard deviation of the temperature error is independent of the calibration if the random error is dominated by the sensor noise and not external system factors, such as convection and conduction. For common calibration, the total standard deviation increases because of the effects of device-to-device variation. This standard deviation is calculated in the usual way, by substituting T_{OBJ_PREDICT} for the mean in the standard deviation formula.

The accuracy is then defined as the mean calibration error plus the random errors from all sources. For this example application, use the criteria shown in Equation 14:

Equation 14.

The resulting accuracy over T_OBJ and T_DIE is shown in Figure 10 and Figure 11 for the unit- and common-calibration approaches, respectively. Clearly, the unit calibration results in higher accuracy, though common calibration is applicable for many application requirements.

Table 13. Narrow-Range Requirements

Table 14. Narrow-Range Measurement Values

8.2.2.2.1 Narrow-Range Calibration

To begin calibration, select an object temperature (T_OBJ) and a value for the die temperature (T_DIE). With these system temperatures stable, take a statistically significant number of samples of V_Sensor (results shown in register 00h).

in this example, 64 samples were taken. Do not use the object temperature readings given in register 03h; these values are invalid before calibration.

To compensate for first order drift in system temperatures, it is often useful to normalize the data set. For this purpose, for each temperature set, the sensor voltage data (given in register 00h) is normalized by first finding the best fit line of the form shown in Equation 15:

Equation 15.

The normalized data for each data set is then calculated as shown in Equation 16:

Equation 16.

The normalized data, V_{Sensor_norm}, is centered on zero mean, and is first-order corrected for long-term drift. The standard deviation for each data set is then calculated to estimate the sensor noise, σ. Verify that the data are limited by white noise and no other effects. For a sensor-noise-limited data set, v_SENSOR σ is typically < 1 μV, and preferably < 0.5 μV after first-order correction for drift, as described previously. If this condition is not satisfied, then the calibration accuracy is limited by external system factors (for example, convection or conduction). Repeat this process for each combination of T_OBJ and T_DIE for which the calibration is to be performed. The normalized data are used only for evaluating the suitability of the data set for calibration, and not for the actual calibration itself.

For calibration, the mean value, <V_SENSOR>, is calculated for each combination of T_OBJ and T_DIE, as shown in Table 15. Using the mean value minimizes error introduced by random noise. Based on the means, a set of coefficients is generated based on a user-selected optimization criteria for Equation 7. Common criteria are minimizing the maximum error, minimizing the average error, and so on. For a detailed discussion of optimization methods, see SBOU142 — TMP007 Calibration Guide.

8.2.2.2.2 Verifying the Calibration

The next step is to use the generated coefficients to verify the calibration, and determine the accuracy of the system. For common calibration (C) , the same coefficients are used for all devices; in unit calibration (U) the coefficients are calculated for each device. Common calibration includes device-to-device variation, and thus is less accurate, but much easier to implement. Unit calibration is more accurate, and eliminates device variation, but requires more effort to implement. The choice depends on the application requirements for accuracy versus implementation effort.

Mean calibration error at each point is defined as shown in Equation 17:

Equation 17.

where

• T_{OBJ_PREDICT} is the temperature based on the calibration coefficients.
• T_{OBJ_ACTUAL} is the known object temperature, measured independently.
• N is the number of devices in the calibration set.

The mean error graph (see Figure 54) provides an efficient method of understanding how the systematic errors vary across the temperature ranges of interest. This graph also provides a means of weighing the benefits and efforts of common versus unit calibration for a particular application.

Note that calibration does not affect the temporal random noise observed, as shown in Figure 55. The standard deviation of the temperature error is independent of the calibration if the random error is dominated by the sensor noise and not external system factors, such as convection and conduction. For common calibration, the total standard deviation increases because of the effects of device-to-device variation. This standard deviation is calculated in the usual way, by substituting T_{OBJ_PREDICT} for the mean in the standard deviation formula.

The accuracy is then defined as the mean calibration error plus the random errors from all sources. For this example application, use the criteria shown in Equation 14:

Equation 18.

The resulting accuracy over T_OBJ and T_DIE is shown in Figure 57 for the unit- and common-calibration approaches. Clearly, the unit calibration results in higher accuracy, though common calibration is applicable for many application requirements.

Reduce the random temporal error by increasing the sample time. Figure 58 shows the effects of increasing the sample time on the standard deviation. As a result of device-to-device variation, the effects of increased sample time on the common-calibration scheme is negligible; however, an improvement is seen for the unit calibration scheme.

Finally, the resulting accuracy is shown for the different sample times as a function of T_DIE in Figure 59. Improve the accuracy by generating separate coefficient sets for T_DIE = 25°C and T_DIE = 30°C.