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Hello, and welcome to the TI Precision Lab covering data converter error sources. Overall, this video will discuss how gain and offset errors can be calculated and eliminated through calibration. We will start by doing an offset and gain error calculation for a data converter system. Next, we will discuss a few methods for calibrating out this error. And finally we will introduce some different error sources that are difficult to calibrate out.

In this slide, we repeat the offset calculation from the Precision Lab's video titled, Statistics Behind Error Analysis. Here, we are looking at the typical offset for each of the two amplifiers and the ADC in the signal chain. All the offset values are referred to the input of the data converter. So the gain of each amplifier needs to be taken into account. In this example, U1 has a gain of 20, so its offset will be multiplied by this factor.

All three offsets are combined using the square root sum of the squares because they are uncorrelated, Gaussian distributions. The total offset here represents a typical offset for the system, which is plus or minus 1 standard deviation. To set a worst case limit, we can multiply the standard deviation by the appropriate factor from the table according to the system requirements.

For example, if we set the system maximum specification to plus or minus 3 standard deviations, then 99.73% of the population will be inside that limit and 0.27% of the population will fail the limit. Depending on the requirement, a more conservative element can be set.

Here, we show a similar statistical analysis can be done for gain error. In this case, the current shunt resistor, current shunt amplifier, buffer, and data converter will contribute gain error. We will ignore the gain error of the buffer as it is very small and related to the open loop gain of the amplifier.

In this case, some of the parameters don't have a typical value, so we have to use the worst case for the analysis. The equations at the top of the slide show an absolute, worst case analysis where the errors are directly added and a statistical worst case where the errors are added as the sum root sum of the squares. The statistical worst case is a more reasonable estimate of worst case, whereas the absolute worst case is more conservative.

In this example, the error for the current shunt amplifier, U1, is the dominant source of error. For many circuits, the gain is set by external, discrete resistors. For this type of circuit, a Monte Carlo analysis is a good approach for finding gain error. The Precision Labs video, titled Gain Error and Monte Carlo Analysis, covers this topic. The transfer characteristic for most signal chains is a linear function in the form y equals mx plus b. Technically, there will be some nonlinear terms, but assume linearity is a good first order approximation.

Offset and gain calibration are based on the idea that we can solve the straight line equation for the slope and intercept. Note that the slope error is the gain error, and the intercept is the offset error. Applying two different input signals and measuring the associated output code will allow you to solve for the slope and intercept. However, you have to be careful to make sure that the amplifiers are all operating in the linear region of the curve.

Looking at the input/output relationship, you can see how it would not be possible to determine the slope of the transfer function in the nonlinear region. In this example, we apply 0 amps and 20 amps and measure the associated output codes. Note that 0 amps drives the output of U1 to 0.5 volts, and 20 amps drives the output to 4.5 volts. So these test signals keep the system in the linear range.

It is very important that the test signals used are very accurate. Any error in the test signal will introduce error in the calibration coefficients and minimize the effectiveness of the calibration. After calibration, the measured slope and measured offset, called calibration coefficients, are generally stored in the microcontroller's memory. These coefficients are then used during normal device operation to compensate for the gain and offset error. On the next slide, we will look at the math for this example.

This is an example calibration based on the circuit from the previous slide. In this case, the calibration test signals are at 0.5 volts and 4.5 volts. Notice that the ideal graph is shown in blue and the measured graph is shown in red. The measured graph has an offset and different slope than the ideal function.

The slope can be calculated by taking the change in output code divided by the change in input voltage. The offset is determined by solving the y equals mx plus b equation for b and substituting one input and its associated output signal. Once you have the offset and slope, you can correct the error for any input.

In this example, we apply a 2.0 volt input signal. The uncalibrated reading for this is 2.002 volts, so there is a 2 millivolt error from gain and offset. Applying the correction using the calibration coefficients, we can eliminate the error and determine the actual input signal of 2 volts.

Some calibration schemes apply external calibration signals during initial production to calibrate the system. In other cases, the system will have onboard precision references to generate the calibration signal. However, for some applications, generating the precision calibration input signals may not be practical because the cost may be too high. In the example we just considered, the calibration signals were 0 amps to 20 amps. Generating a precision, 20-amp signal to calibrate the system is challenging and expensive.

One way to simplify a calibration scheme is to do an offset-only calibration. The nice thing about the offset calibration is that it can generally be done by shorting the input to ground. Shorting the input to ground provides a very accurate 0 volt input signal. The 0-volt input signal does not have the accuracy and drifters inherent in a typical reference circuit that would be used for a two-point gain and offset calibration.

The circuit here shows a simple calibration scheme where the input signal can be disconnected and the input can be grounded for offset calibration. When 0 volts is applied to the input, the offset is directly read to be negative 30 codes. This offset includes the ADC offset, as well as the offset for amplifiers U1 and U2. Also, this calibration can be run periodically to account for offset drift. Ideally, it would be good if we could also calibrate the gain error, but this would require a precision calibration source.

So in order to minimize cost and complexity, some systems use the single one-point calibration. It is important to realize that this type of calibration can only be done on an ADC with a bipolar range or a differential input range. In the next slide, we will see why this method cannot be used on unipolar ADCs.

This slide shows the effect of positive and negative offset on a unipolar data converter. By unipolar, we mean that the input signal is always positive. That is, it ranges from 0 to the Full Scale Range, denoted as FSR. The output codes for this example range from 000 hex to FFF hex. Although there are no negative output codes for a unipolar converter, there can be a negative offset.

The graph on the left shows how negative offset would affect the ADC transfer function. The ideal curve is shown in blue, and the measured curve is shown in red. Notice that the measured curve is shifted downward by the negative offset, but the transfer function is truncated at 000 hex.

So for this example, applying a 0-volt input would generate a 000 hex output code, even though the actual offset error is negative 003 hex. Therefore, you are not able to calibrate for a negative offset using a 0-volt calibration signal for unipolar ADCs. However, as shown on the right-hand curve, you can measure a positive offset using a 0-volt input for unipolar ADCs.

In this example, applying 0 volts to the input, you would measure an offset of positive 003 hex. Nevertheless, this doesn't really help from a calibration perspective because the offset of an ADC will always range from negative to positive values. In the next slide, we will see why a bipolar ADC offset calibration works for a 0-volt input.

Here, we show the offset error for a bipolar ADC, or an ADC with a differential input range. The term "bipolar" means that the input can accept both negative and positive voltages. These curves can also apply to a unipolar input that has a differential input range.

The example shown earlier used the ADS 9110, which is a unipolar device that has a differential input range of plus or minus b-ref. The range starts at the Negative Full Scale, denoted as NFS, and ends at the Positive Full Scale, denoted as PFS. In this case, it is possible to apply 0 volts to the input and directly read the output.

Shorting the inputs to determine offset is often used as a simple approach for measurement and calibration of offset. Some data converters have a convenient feature that allows automatic offset calibration. In general, this calibration is initiated by sending the ADC a digital command. This can be done periodically so that offset drift is also accounted for.

During calibration, the ADC's inputs are disconnected from the rest of the circuit so special calibration test signals are not required. Note that in this case, the calibration only applies to the data converter. And offset errors from the rest of the signal chain are not corrected for in this automatic calibration.

The digital value for the offset is stored in a register after calibration. The offset register is automatically subtracted from readings after calibration to correct for the offset error. This correction can significantly reduce offset error. For example, the ADS 7042 typical offset is reduced from plus or minus 12 LSB to plus or minus 1/2 LSB through calibration.

Finally, it is important to note that this automated calibration corrects for offset error but does not correct for gain error. Gain and offset errors are two common error sources that can be eliminated using calibration. Some other error sources can be difficult or impossible to calibrate out. A few examples are noted here.

Offset and gain error can have a temperature drift. Integral non-linearity is a measurement of deviation of the transfer function from an ideal transfer function. Long-term shifter aging is a measurement of how the performance of the device degrades with time. Historesis indicates how the behavior of the device can be changed by temperature cycling the device. This is different from temperature drift in that the room temperature operation of the device can be altered, for example, by cycling the temperature from hot to cold and back to room temperature.

After the temperature cycle, the offset and gain can be shifted by stress induced inside the device from the temperature extremes. Note that these types of errors are very difficult to correct for in calibration. So ideally, they should be low compared to your system's error requirements.

That concludes this video. Thank you for watching. Please try the quiz to check your understanding of this video's content.

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