How to successfully calibrate an open-loop DAC signal chain? Here are two methods

Unipolar voltage DACs can only provide positive or negative outputs. This article will use the AD5676R as an example of a unipolar DAC to illustrate how to perform accurate calibration. The same method can be used to make the necessary adjustments to other types of DACs.

Bipolar voltage DACs, such as the AD5766, can achieve both positive and negative outputs.

Current-output DACs are often used in a multiplying configuration (MDAC) to provide variable gain, and they usually require an external amplifier to buffer the voltage developed across a fixed resistor.

Precision current source DACs (IDACs), such as the AD5770R and LTC2662, are a new class of DACs that can accurately set the output current within a predefined range without any additional external components.

An ideal digital-to-analog converter produces an analog output voltage or current that is strictly proportional to the input digital code, independent of disturbing external influences such as power supply and reference voltage variations.

For an ideal voltage output DAC, the input digital code increases by a single step.

The corresponding output increase is called LSB and is defined as follows:

in:

(VREF+) and (VREF-) are the positive and negative reference voltages, respectively. In some cases, (VREF-) is equal to ground (0 V).

n is the resolution of the DAC in bits.

LSB _SIZE (V) is the smallest increment of the DAC output in volts.

This means that for any given input code, once the LSB is known, the voltage output of the DAC should be accurately predicted.

In practice, the accuracy of a DAC output is affected by the DAC gain and offset errors (internal errors) as well as other components in the signal chain (system-level errors). For example, some DACs have integrated output amplifiers, while others require external amplifiers, which can be additional error sources.

In a data sheet, the most relevant specifications are defined in the terminology section. For a DAC, this section lists parameters such as offset error and gain error.

Zero-scale error is a measure of the output error when a zero-scale code (0x0000) is loaded into the DAC register.

Figure 1 shows the effects of offset and gain errors on the transfer function of a unipolar voltage DAC.

Gain error is a measure of the range error of the DAC and is shown as the purple line in Figure 1. Gain error is the deviation of the slope of the DAC transfer characteristic from the ideal value. The ideal DAC transfer characteristic is shown in black.

Offset error is the difference between the actual output and the ideal output in the linear region of the transfer function, shown as the blue line in Figure 1. Note that the blue transfer function is interpolated to intersect the y-axis, resulting in a negative V _OUT , thus determining the offset error.

• Zero error drift is a measure of the change in zero error with temperature.

• The gain error temperature coefficient is a measure of the variation of gain error with temperature.

• Offset error drift is a measure of the change in offset error over temperature.

Temperature changes have a significant impact on the accuracy of electronic systems. Although the internal gain and offset errors of a DAC are usually specified with respect to temperature, other components in the system may contribute to the total offset and gain of the output.

Therefore, even if the INL and DNL of a DAC are very competitive, other errors must be considered, especially with respect to temperature. The latest DACs specify a total unadjusted error (TUE) to measure the total output error including all errors—that is, INL error, offset error, delta error, and output drift over supply voltage and temperature. TUE is expressed in %FSR.

When the data sheet does not specify the TUE of a DAC, the TUE can be calculated using a technique called RSS or root sum square, which is used to sum uncorrelated error sources for error analysis.

There are other smaller error sources, such as output drift, which are usually ignored because their relevant effects are relatively small.

Every specification for every component in the system must be converted to the same units. This can be done using Table 2.

Table 2. Unit conversion matrix

TUE is a good metric that succinctly explains how accurate a DC DAC output is given all the internal errors. However, it does not take into account system-level errors, which can vary depending on the signal chain in which the DAC is located and its environment.

It is worth noting that some DACs have internal buffers/amplifiers in the output stage, in which case the data sheet specifications reflect the effects of both as part of the internal errors.

When trying to analyze the DAC signal chain error budget for a given application, system designers should consider and verify the contributions of the different components, paying attention to the expected operating temperature of the system. Depending on the end application, the signal chain may have many different building blocks, including power ICs, buffers or amplifiers, and different types of active loads, which can all introduce system-level errors.

Voltage Reference

Every DAC requires a voltage reference to operate. The voltage reference is one of the main factors affecting the accuracy of the DAC and the overall signal chain.

The key performance specifications of the voltage reference are also defined in a separate data sheet for the voltage reference, such as the ADR45XX series, or as part of the DAC data sheet if the device has an internal reference for user use.

Dropout voltage is sometimes also called supply voltage margin and is defined as the minimum voltage difference between the input voltage and the output voltage required to maintain an output voltage accuracy of 0.1%.

The temperature coefficient (TC or TCV _OUT ) is the relationship between the change in the output voltage of the device and the change in ambient temperature, normalized by the output voltage at 25°C. The TCV _OUT of the ADR4520/ADR4525/ADR4530/ADR4533/ADR4540/ADR4550 A and B grades are fully tested at three temperatures: −40°C, +25°C, and +125°C. The TCV _OUT of the C grade is fully tested at three temperatures: 0°C, +25°C, and +70°C. This parameter is specified using the following two methods. The black box method is the most common method and considers the temperature coefficient over the entire temperature range; the bow tie method calculates the worst case slope at +25°C and is therefore more useful for systems calibrated at +25°C.

For some DACs, an external reference can provide better performance than an integrated reference. The reference voltage directly affects the transfer function, so any change in this voltage results in a proportional change in the slope of the transfer function (i.e., gain).

It is worth noting that some DACs have internal buffered references, in which case the data sheet specifications reflect the effects of these internal blocks as part of the internal errors.

Voltage Regulation

Every independent IC that acts as a power supply defines line regulation, which represents the change in output in response to a given change in input. This applies to power supplies, buffers, and voltage reference ICs, which should keep the output voltage stable regardless of the input. In the data sheet, line regulation is usually specified at ambient temperature.

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Load regulation is defined as the incremental change in output voltage with a change in load current. The voltage output is usually buffered to mitigate the effects of this change. Some DACs may not buffer the reference input. Therefore, when the digital code changes, the reference input impedance also changes, causing the reference voltage to change. The effect on the output is generally small, but should be considered in high-precision applications. In the data sheet, load regulation is usually specified at ambient temperature.

Change of soldering thermal resistance

The solder thermal resistance (SHR) change is most relevant to the voltage reference. It is the permanent change in output voltage due to reflow of the device and is expressed as a percentage of the output voltage. For more information, refer to the ADR45xx family data sheet. In general, all ICs are affected to some degree by SHR changes, but this is not always quantifiable and depends greatly on the specific system setup of the application.

Long-term stability

Long-term stability defines the change in output voltage over time and is expressed in ppm/1000 hours. A PCB-level aging treatment can improve the long-term stability of an application.

A simplified diagram of the DAC signal chain is shown in Figure 2. The blocks shown in black boxes show a simplified open-loop signal chain, while the blocks shown in gray boxes are examples of the additional components required to implement a closed-loop signal chain.

Closed-loop solutions require additional components and software manipulation of digital data to provide a more accurate output. If these additional resources cannot be added for various reasons (space, cost, etc.), an open-loop solution will still work - as long as it can provide the required accuracy. This article explains how to perform open-loop calibration to help deal with this situation.

In theory, it is a simple procedure to calibrate out the gain and offset errors (which are constant in the absence of external influences). The linear region of the DAC transfer function can be modeled as a straight line described by the following equation:

in:

y is the output.

m is the slope of the transfer function after accounting for gain error (shown as the purple line in Figure 1).

x is the DAC input.

c is the offset voltage (shown as the blue line in Figure 1).

Ideally, m is always 1 and c is always 0. In practice, the gain and offset errors of the DAC are taken into account, and once known, corrections can be made at the DAC input to achieve a digital output that is closer to the ideal DAC output. The gain error can be removed by multiplying the digital DAC input by the inverse of the gain error. The offset error can be removed by adding the inverse of the measured offset error to the digital DAC input.

The following formula shows how to calculate the correct DAC input to produce the desired voltage:

in:

Note that offset error can be either positive or negative.

This section uses the AD5676R as an example to show how to actually calibrate the offset and gain in a DAC signal chain. All measurements were made using the EVAL-AD5676 evaluation kit with the AD5676R internal reference enabled. The EVAL-AD5676 board and the measurement setup are part of the signal chain we measure in our example. Each component of this signal chain (power IC, AD5676R on the board, parasitics introduced by the layout and connectors, etc.) contributes to the system error. Our intention is to show how to calibrate this system to provide an example for any other system.

The EVAL-SDP-CB1Z Blackfin ^® SDP controller board (SDP-B) is used to communicate with the AD5676R on the EVAL-AD5676 evaluation kit, and an 8-bit DMM is used to measure the output voltage of V _OUT 0. A climate chamber is used to control the temperature of the entire system consisting of the EVAL-SDP-CB1Z, EVAL-AD5676, and the AD5676R with internal reference.

The EVAL-AD5676 was powered up as described in the user guide and the link was configured as shown in Table 3.

Table 3. EVAL-AD5676 Evaluation Board Jumper Configurations for Described Measurements

First, the signal chain error without calibration (NoCal) at different temperatures is evaluated. The output error is calculated considering the LSB difference between the ideal and measured values ​​for a specific input code. This error includes both internal and external errors of the DAC and the overall signal chain on the EVAL-AD5676 board. The output error without calibration is shown in Figure 3.

The information needed to calculate the offset and gain errors, along with the corresponding correction codes, is located in the transfer function. Two points are needed for this: one data point close to zero (ZS _LIN ) and another close to full scale (FS _LIN ). The idea behind this is to operate in the linear region of the DAC. This information is usually provided along with the INL and DNL specifications, most likely in the footnotes of the specification sheet. For example, for the AD5676R, the linear region is from digital code 256 to digital code 65280.

Figure 4 explains the linear region of the DAC.

Once the ZS _LIN and FS _LIN codes are determined, we can collect the measurements needed for calibration, which are the DAC voltage outputs at these two digital codes ( V _OUT at ZS _{LIN and V OUT} at FS _LIN ), plus several other digital codes in between (¼ scale, mid-scale, and ¾ scale).

Measurements should be collected at the operating temperature of the application. If this is not possible, once these two key data points are collected at ambient temperature, the data sheets for the devices in the signal chain can be used to derive the required information.

Each device in the signal chain contributes errors, and every board is different, so they should be calibrated individually.

An optimum level of calibration can be achieved by measuring the error in the application environment at operating temperature and making systematic corrections when writing to the DAC to update the output.

To calibrate the DAC using this method, measure the DAC output corresponding to digital codes ZS _LIN and FS _LIN at the expected operating temperature of the system . The transfer function is constructed as follows:

in:

V _OE = offset error (V)

V _FS,LIN,ACT = Actual output of FS _LIN

V _ZS,LIN,ACT = Actual output of ZS _LIN

V _FS,LIN,IDEAL = FS _LIN ideal output

V _ZS,LIN,IDEAL = ideal output of ZS _LIN

Note that offset error can be either positive or negative.

Figure 5 shows the output error achieved using the TempCal method for the EVAL-AD5676 evaluation kit.

If it is not possible to measure the error in the application environment at operating temperature, a high level of calibration can still be achieved using the AD5676R data sheet and the DAC transfer function calibrated at ambient temperature.

_{To calibrate the DAC using this method, the DAC output for digital codes ZS LIN} and FS _LIN should be measured at ambient temperature . The transfer function is constructed as described in the TempCal section by calculating the gain and offset errors at ambient temperature and applying Equation 14.

in:

GE _amb = Gain error at ambient temperature

V _OE,amb = offset error at ambient temperature (V)

Calibrating the DAC signal chain at ambient temperature addresses system-level errors. However, external error changes due to temperature changes are not accounted for; therefore, this calibration method is not as accurate as the TempCal method.

The drift of the DAC internal errors (i.e., offset and gain errors) due to changes in operating temperature can be addressed using the data sheet specifications. This is what we call SpecCal. Typical values ​​for offset error drift are listed in the technical specification table of the AD5676R data sheet, and the typical performance parameter (TPC) for offset error vs. temperature indicates the direction of the error drift, depending on whether the ambient temperature is increasing or decreasing.

The change in gain error due to temperature is represented by TPC, the gain error vs. temperature relationship. Determine the % FSR of the gain error from the graph and then apply Equation 16.

Once we have estimated the offset and gain errors at operating temperature, we can use Equation 17 to determine the input code that corresponds to the SpecCal output.

in:

Figure 6 shows the output error achieved using the SpecCal method for the EVAL-AD5676 evaluation kit.

In this example, an internal reference is used. An external reference may add to the overall error. Errors due to the reference can be accounted for by using the reference data sheet and accounting for reference drift at the target temperature. Changes in the reference voltage change the actual output range, thus changing the LSB size. Using an external reference should resolve this issue. The TPC of temperature vs. output voltage can be used to determine changes in output range due to reference drift.

in:

This article outlines some of the main causes of DAC signal chain errors, including DAC internal errors defined in the data sheet, as well as system-level errors that vary with the system and must be considered in open-loop applications.

This article discusses two calibration methods: one for when the DAC can be calibrated at the system operating temperature and the other for when calibration at operating temperature is not possible but measurements can be made at ambient temperature. The second method uses the TPC and technical specifications provided in the data sheets of the DAC and other ICs in the signal chain to account for gain and offset error drift.

The TempCal method can achieve much better accuracy than SpecCal. For example, for the EVAL-AD5676 board at 50°C, Figure 7 shows that the TempCal method achieves accuracy very close to the ideal accuracy, while the SpecCal method still shows some improvement over the NoCal data.

Temperature variations have a significant impact on the accuracy of electronic systems. Calibrating at the system operating temperature can eliminate most errors. If this is not possible, information provided in the data sheets of DACs and other ICs can be used to account for temperature variations and achieve acceptable accuracy.