To better understand how the calibration process works, the following section steps through a weigh scale example using the load cell properties from Table 4-1 and the ADS1235. The example load cell has a nominal bridge sensitivity of 2 mV/V and the weight capacity is 2 kg. Assuming V_EXCITATION = 5 V, the ideal full-scale bridge output voltage, V_OUT(Ideal), is 2 mV/V • 5 V = 10 mV. This is the expected output from the bridge when a 2-kg weight is placed on the scale. V_OUT(Ideal) is also the input voltage, V_IN(Ideal), measured by the ADC.

The general formula for an ADC output code is given by Equation 32:

where:

• N is the ADC resolution
• A is a scaling factor related to the ADC analog voltage range (refer to Section 6.8.33 for more information)

For the ADS1235, N = 24 and A = 2. Using the ADS1235 with a ratiometric reference configuration
(V_REF = V_EXCITATION = 5 V) and a PGA setting of 128 V/V, a 10-mV signal yields the ideal ADC output code, ADC_Ideal, given by Equation 33:

Equation 33 reveals that an error-free system should provide an ADC code value of 2,147,483 when the 2-kg weight is applied and an ADC code value of 0 when the weight is removed (V_IN(Ideal) = 0 V). Figure 5-15 shows the ideal bridge response using the example parameters.

Figure 5-15 Ideal Response for the Example Bridge Measurement System

For this example, the input to the system (x-axis) in Figure 5-15 is the applied weight and the system output is the ADC code (y-axis). The system output used to determine the calibration coefficients should be ADC codes because the calibration process executed by the microcontroller uses an ADC code as an input (see Figure 5-12).

Unfortunately, a real system will always have some errors compared to the ideal response in Figure 5-15, reducing the system accuracy. For example, the ADC and amplification stage have inherent errors, while the choice of bridge connection can introduce a gain error. Even the load cell has an inherent offset (zero balance) and gain error (sensitivity tolerance), as per Table 4-1. The system-level offset and gain error are the combined error from all of these different sources. Figure 5-16 shows how each system error might impact the green, ideal bridge response from Figure 5-15, resulting in the actual bridge response in red with unknown slope and y-intercept.

Figure 5-16 Actual vs Ideal Response for the Example Bridge Measurement System

The important takeaway from Figure 5-16 is that there is no way to correlate the measured ADC output code to the actual applied weight without knowing the value of B_Actual and the slope of the red bridge response. When the user applies a 2-kg test weight to this example system, the resulting output code, ADC_Actual, is 2,684,355. An ADC code of 2,684,355 corresponds to an applied load of 2.5 kg because the user assumes the system follows the green, ideal response. This outcome results in a 25% error at full-scale. Ultimately, calibration is necessary to determine the actual bridge response, reduce these errors, and maintain high-accuracy results.

To calibrate this weigh scale, first perform an offset calibration. In this example, B_Actual is measured to be 214,748 codes with no applied weight. Equation 32 can be used to back-calculate that 214,748 codes is approximately 1 mV (or 0.2 kg) when V_EXCITATION = V_REF = 5 V. This value represents the total system offset from all error sources.

The value of B_Actual is used to adjust the displayed weight to 0 kg when no load is present on the scale. Figure 5-17 shows how the offset calibration in this example translates the red, uncalibrated bridge response down to the blue, offset-calibrated bridge response. The weigh scale images on the right side of the figure indicate how the scale display changes before (in red) and after (in blue) the offset calibration.

Figure 5-17 Performing an Offset Calibration for the Example Weigh Scale System

The blue response in Figure 5-17 still has a gain error relative to the green, ideal bridge response shown in Figure 5-15. This example corrects that gain error by performing a gain calibration using a calibrated 2-kg test weight, W_Calibrated. The ADC measures W_Calibrated and produces an output code, ADC_Calibrated, of 2,469,606, which is equal to 2.3 kg. Figure 5-18 compares the ideal response of the 2-kg test weight to the measured response in the offset-free system. The weigh scale images on the right side of the figure indicate how the scale display changes before (in blue) and after (in green) the gain calibration.

Figure 5-18 Performing a Gain Calibration for the Example Weigh Scale System

As Figure 5-18 shows, the scale displays a value of 2.3 kg even after the offset calibration, resulting in a 15% error at full-scale. This value represents the total system gain error from all error sources. To correct this gain error and accurately display the value of the 2-kg weight, it is necessary to derive the scaling factor, M. Equation 34 shows how to calculate M from the measured parameters:

One important takeaway from Equation 34 is that the value of W_Calibrated directly impacts the calculation of M and therefore the accuracy of the gain calibration. As a result, ensure that the test load used in the system is calibrated properly and handled with care such that its physical properties are not altered.

Using the values provided in this example yields the result in Equation 35:

Equation 89 combines these results to derive the corresponding applied weight, W, from any ADC output code, ADC_Result:

Using the values provided in this example yields the result in Equation 37:

Equation 37 can be used to determine the value of any arbitrary weight applied to the scale in this example. If ADC_Result = 1,000,000 for example, then W = 0.697 kg. Figure 5-19 shows how to apply the specific values derived in this example to the calibration block diagram shown in Figure 5-12.

Figure 5-19 Weigh Scale Block Diagram With Example Calibration Coefficients

The values used in this example are theoretical and not meant to represent the behavior of any specific system. It is also important to remember that real systems have multiple sources of offset and gain error that all need to be considered, though it is possible that one error source might dominate. In any case, this calibration process can be applied to any bridge measurement system to remove some of the most common error sources and maintain high-accuracy results.