Software calibration reduces D/A converter offset and gain errors

One solution is to add extra components to remove the errors through post-manufacture trimming. Some D/A converters have internal trimming registers that allow the user to calibrate out whatever errors exist in the system so that a digital code sent to the D/A converter will produce the correct output voltage. This design note will explain the steps required to reduce the system error using a software solution rather than a hardware one.

The two error mechanisms common to all D/A converters are offset and gain error. Offset error is the deviation from the minimum voltage expected when the minimum code is applied. For example, for a unipolar D/A converter a code of 0x0000 should provide the lowest possible output voltage. While the D/A is likely to have been factory calibrated to have inherently low offset, amplifiers and other components in the signal chain will add to the total offset value. The total offset in a signal chain is called the system offset. The system offset can be removed using the on-chip registers, as described later.

Gain error is the deviation in the slope of the transfer function, when the offset error is removed, from the ideal. For example a D/A converter may be required to start at 0 V and finish at 5 V, the actual transfer function may start at 5 mV and finish at 5.015 mV. In this case the gain error is 10 mV, Figure 1.

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Figure 1: Offset and gain errors in converters.

Figure 2 shows a simple signal chain comprising one channel of the AD5390 16-channel, 14-bit D/A converter and an amplifier.

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Figure 2: One channel of the AD5390 shows signal path and registers.

The AD5390, as shown, includes trimming registers. The final output voltage in the signal chain is determined by both the digital code applied to the D/A and by the contributions of the gain and offset errors of the D/A and the amplifier. The c and m registers of the D/A can be used to reduce these errors. The registers work on the basis that a straight line can be described by the formula

Using this, and applying it to the transfer function for the D/A converter, it can be seen that the output voltage (y) of the D/A is not just related to the digital input code (x) but is also affected by the values of m and c. If the m and c registers are programmed so that they cancel out the system gain and offset errors, the system output voltage will become more accurate.

The transfer function of the AD5390 is given in the data sheet as:

where m = 16,382 and c = 8,192 by default, x2 is the value that will be loaded to the D/A, and

If the default values for m and c are used, the value loaded to the DAC register (x2) will be the same as the input value (x1); that is, there is no adjustment for offset and gain errors. The next sections describe how the m and c registers are used to reduce the system gain and offset errors.

Removing the system offset error
Before we can begin adjusting the c register, we must understand how much of a change each bit in that register makes. The output span of the AD5390 is given as 2 · V_REF. Thus, for a 2.5-V reference, the output span is 5 V. Since there are 16,384 code steps for a 14-bit D/A, each step gives a change of

This is 1 LSB. Using the correct value for the c register will reduce the offset error below this value.

To measure the system offset we must set the D/A channel to its minimum voltage. The system output voltage is then measured and compared to the expected output voltage. The offset error is the difference between the two.

If the system has an offset measured at +5 mV, then we require

to correct the offset.

This implies that to reduce the +5 mV offset as much as possible, we need to program the c register with 8,192 - 16 = 8,176. While the offset has not been eliminated completely, it has been reduced to:

Removing the gain error
With the system offset error reduced, we can now calibrate out the system gain error. As mentioned earlier, the gain error is the deviation of the slope of the transfer function from the ideal. Since the transfer function is a straight line, the worst-case excursion from the ideal will be at the top end of the transfer function, i.e., the highest voltage. Moving that voltage as close as possible to the ideal value will have the effect of ensuring that the system gives the most accurate output voltage for any given D/A code.

To calculate the value required by the m register, the user should write 0x03FFF to the D/A channel, which gives the maximum output voltage. In an ideal world, this would be:

If, in our example, the system output voltage is measured at 5.0067 V, then we have a gain error of approximately 7 mV. Using the same LSB value as before, we find that the m register needs to be reduced by:

Thus, setting the m register to (16,382 - 20) = 16,362 will reduce the gain error to within 1 LSB.

Typical example
The calibration routines described above can either be performed as part of a one-time factory calibration, where the values for the m and c registers can be stored in an E²PROM,and loaded as part of the system startup procedure, or the system can be designed to measure the output voltages periodically and adjust the m and c registers as required.

For the latter, a high-quality A/D converter is typically used. The outputs of each of the D/A channels would be connected in turn to the A/D input and the voltage is calculated. This is achieved using a multiplexer. The AD5390 has an on-chip multiplexer/monitor function that makes the designer's job easier and reduces the number of external components. Each of the 16 voltage outputs can be switched internally, so that they appear on a single output pin connected to the measuring A/D.

This will allow the designer to remove the errors in the D/A. To remove system errors, the AD5390 must have input pins connected to the multiplexer, allowing external voltages to be monitored in the same way. Figure 3 shows a typical application example.

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Figure 3:A typical application shows how errors across multiple applications are handled.

Conclusion
Using the methods described above, it is typically possible to reduce gain and offset errors from the tens-of-millivolts range to below 100 μVolts. This has the obvious advantage of providing much more accurate systems without the expense of more costly D/A converters or of adding extra components to accomplish the same task.

About the author
Ken Kavanagh is a senior applications engineer supporting the precision converter product line at Analog Devices, Inc., Limerick, Ireland. He received a national diploma in electronics from Waterford Institute of Technology in 1991 and a bachelor of engineering degree from the University of Limerick in 1996. He can be reached at ken.kavanagh@analog.com.