“Any practical Electronic application is subject to multiple error sources that can cause the most delicate components to deviate from the behavior described in their data sheets. When the application signal chain has no built-in mechanism to self-adjust for these errors, the only way to minimize the effects of the errors is to measure the errors and calibrate them systematically.
Any practical electronic application is subject to multiple error sources that can cause the most delicate components to deviate from the behavior described in their data sheets. When the application signal chain has no built-in mechanism to self-adjust for these errors, the only way to minimize the effects of the errors is to measure the errors and calibrate them systematically.
Open loop systems do not use the output to adjust the control operation at the input in order to achieve the desired performance, whereas in a closed loop system the output is dependent on the control operation of the system and the system can automatically implement corrections to improve performance. Most digital-to-analog converter (DAC) signal chains are “set and forget” type systems, where the accuracy of the output depends on the accuracy of each block in the signal chain. A “set and forget” type system is an open loop system. For open loop systems requiring high accuracy, calibration is recommended and most likely required.
We will cover two types of DAC signal chain calibrations: TempCal (operating temperature calibration), which provides the best level of error correction, and SpecCal (calibration using specs), when TempCal cannot be used, It is a valid alternative, but not as comprehensive as the former.
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 for other types of DACs.
Bipolar voltage DACs such as the AD5766 can implement 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 precisely set the output current within a predefined range without any additional external components.
DAC Transfer Function Theory and Internal Errors
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 is incremented in a single step
The corresponding output increase is called LSB and is defined as follows:
(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.
LSBSIZE (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 the DAC output is affected by the DAC gain and offset errors (internal errors) as well as by other components in the signal chain (system level errors). For example, some DACs have an integrated output amplifier, while others require an external amplifier, which can be an additional source of error.
In the data sheet, the most relevant technical specifications are defined in the Terminology section. For DACs, this section lists parameters such as offset error and gain error.
Zero-scale error measures the output error when the zero-scale code (0x0000) is loaded into the DAC register.
Figure 1 shows the effect of offset and gain error on the transfer function of a unipolar voltage DAC.
Gain error measures the span error of the DAC, as shown by the purple line in Figure 1. Gain error refers to the deviation of the slope of the DAC’s conversion characteristics from the ideal. The conversion characteristics of an ideal DAC are shown in black.
The offset error is the difference between the actual output and the ideal output in the linear region of the transfer function, as shown by the blue line in Figure 1. Note that the blue transfer function uses interpolation to intersect the y-axis, resulting in negative VOUT to determine the offset error.
Figure 1. Representation of offset error and gain error for a unipolar DAC
The effect of gain error and offset error can be seen by the blue curve in Figure 4. The same parameter can also be defined in terms of its change with temperature.
Zero error drift measures the change in zero error with temperature.
The gain error temperature coefficient measures the change in gain error with temperature.
Offset error drift is a measure of the change in offset error with 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 overall offset and gain of the output.
Therefore, even if the INL and DNL of the DAC are very competitive, other errors must be considered, especially with regard to temperature. The latest DACs specify total unadjusted error (TUE) to measure the total output error including all errors—that is, INL error, offset error, incremental error, and output drift over supply voltage and temperature. TUE is expressed in %FSR.
When the data sheet does not specify the TUE of the DAC, it can be calculated using a technique called RSS or root of sum square, which can be 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 associated effects are small.
Every specification of every component in the system must be converted to the same unit. This can be done using Table 2.
Table 2. Unit Conversion Matrix
TUE is a good metric to explain succinctly how accurate the output of a DC DAC is given all the internal errors. However, it does not account for system-level errors, which vary depending on the signal chain in which the DAC is located and its environment.
It’s worth noting that some DACs have built-in buffers/amps in the output stage, in which case the data sheet specification reflects the effect of both as part of the internal error.
System level error
When attempting to analyze the DAC signal chain error budget for a given application, the system designer should consider and verify the contributions of different components, focusing on the expected operating temperature of the system. Depending on the end application, the signal chain can have many different building blocks, including power ICs, buffers or amplifiers, and different types of active loads, all of which can introduce system-level errors.
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 reference are also defined in the reference’s separate data sheet, such as the ADR45XX family, or as part of the DAC data sheet (if the device has a built-in reference for user use).
Dropout, also sometimes referred to as supply voltage headroom, is defined as the minimum voltage difference between the input voltage and the output voltage required to maintain 0.1% accuracy of the output voltage.
The temperature coefficient (TC or TCVOUT) refers to the relationship between the change in the output voltage of the device and the change in ambient temperature, normalized to the output voltage at 25°C. The TCVOUT of the ADR4520/ADR4525/ADR4530/ADR4533/ADR4540/ADR4550 grades A and B is fully tested at three temperatures: −40°C, +25°C, and +125°C. Grade C TCVOUT is fully tested at the following 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 can calculate the worst-case slope at +25°C and is therefore more useful for systems that are calibrated at +25°C.
For some DACs, an external reference can perform better than an integrated reference. The reference voltage directly affects the transfer function, so any change in this voltage causes a proportional change in the slope (i.e. gain) of the transfer function.
It’s worth noting that some DACs have built-in buffered references, in which case the data sheet specification reflects the effects of these internal blocks as part of the internal error.
Each independent IC acting as a power supply defines a voltage regulation, which represents the change in the output in response to a given change in the input. This applies to power supply, buffer, and reference ICs, which should maintain output voltage regulation regardless of the input. In data sheets, voltage regulation is usually specified at ambient temperature.
Load regulation is defined as the incremental change in output voltage as the load current changes. 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. Its effect on the output is generally small, but should be considered in high-precision applications. In data sheets, load regulation is usually specified at ambient temperature.
Soldering Thermal Resistance Variation
Solder thermal resistance (SHR) variation is most dependent on the reference. It refers to the permanent change in the output voltage of the device due to reflow soldering, expressed as a percentage of the output voltage. For more information, see the ADR45xx family data sheet. In general, all ICs are affected to some extent by changes in SHR, but this is not always quantifiable and depends largely on the specific system assembly of the application.
long term stability
Long-term stability defines the change in output voltage over time, expressed in ppm/1000 hours. A PCB-level burn-in treatment can improve the long-term stability of the application.
Open Loop Calibration Theory
A simplified diagram of the DAC signal chain is shown in Figure 2. The block shown in the black box shows a simplified open-loop signal chain, while the block shown in the gray box is an example of the additional components required to implement a closed-loop signal chain.
Figure 2. Simplified DAC signal chain diagram
A closed-loop approach requires additional components and software to manipulate the 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 still works—as long as it provides the required accuracy. This article explains how to perform an open loop calibration to help with this situation.
In theory, calibration to remove gain and offset errors (which are constant in the absence of external influences) is a simple procedure. The linear region of the DAC transfer function can be modeled as a straight line described by the following equation:
y is the output.
m is the slope of the transfer function after accounting for gain error (shown by 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 considered, and once known, corrections can be made at the DAC input to achieve a figure that is closer to the ideal DAC output. The gain error is 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 formula below shows how to calculate the correct DAC input to produce the desired voltage:
Note that the offset error can be positive or negative.
How to successfully calibrate a DAC signal chain
This section uses the AD5676R as an example to illustrate how to actually calibrate the offset and gain in the DAC signal chain. All measurements were performed using the EVAL-AD5676 evaluation kit with the AD5676R internal reference enabled. Both the EVAL-AD5676 board and the measurement setup are part of the signal chain we measured in the example. Every component of this signal chain (power IC on the board, AD5676R, parasitics introduced by layout and connectors, etc.) contributes to the systematic error. Our intention is to show how to calibrate this system, thereby providing an example for any other system.
The EVAL-SDP-CB1Z Blackfin® SDP Control Board (SDP-B) was used to communicate with the AD5676R on the EVAL-AD5676 evaluation kit, and an 8-bit DMM was used to measure the output voltage of VOUT0. A climate box is used to control the temperature of the entire system consisting of the EVAL-SDP-CB1Z, EVAL-AD5676, and AD5676R with built-in reference.
The EVAL-AD5676 was powered up as described in the user guide with the link configuration shown in Table 3.
Table 3. EVAL-AD5676 Evaluation Board Jumper Configurations Used for the Measurements Described
First evaluate the signal chain error without calibration (NoCal) at different temperatures. The output error is calculated taking into account the LSB difference between the ideal and measured values for a particular input code. This error includes the internal and external errors of the DAC and the overall signal chain on the EVAL-AD5676 board. The uncalibrated output error is shown in Figure 3.
Figure 3. EVAL-AD5676 output error (LSB) without calibration.
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 required for this: one data point near zero (ZSLIN) and one near full scale (FSLIN). The rationale behind it is to work in the linear region of the DAC. This information is usually provided with the INL and DNL specifications, most likely in the endnotes of the spec sheet. For example, for the AD5676R, the linear region is from digital code 256 to digital code 65280.
Figure 4 illustrates the linear region of the DAC.
Figure 4. Transfer function and error of a unipolar voltage DAC.
Once the ZSLIN and FSLIN codes are determined, we can collect the measurements required for calibration, which are the DAC voltage outputs (VOUT at ZSLIN and VOUT at FSLIN) for these two digital codes, plus a few others in between Digital code (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 main data points have been collected at ambient temperature, the data sheets for the devices in the signal chain can be used to derive the required information.
Every device in the signal chain contributes error, every board is different and should be calibrated individually.
TempCal: Operating temperature calibration
The best level of calibration can be achieved by measuring the error of the application environment at operating temperature and making a system correction when writing to the DAC to update the output.
To calibrate the DAC using this method, measure the DAC outputs corresponding to the digital codes ZSLIN and FSLIN at the expected operating temperature of the system. Build the conversion function as follows:
VOE = Offset Error (V)
VFS,LIN,ACT = actual output of FSLIN
VZS,LIN,ACT = actual output of ZSLIN
VFS,LIN,IDEAL = ideal output for FSLIN
VZS,LIN,IDEAL = ideal output for ZSLIN
Note that the offset error can be positive or negative.
Figure 5 shows the output error achieved by the EVAL-AD5676 evaluation kit using the TempCal method.
Figure 5. System Output Error (LSB) Using TempCal at Different Temperatures
SpecCal: Calibrate Using Specs
If it is not possible to measure the error of 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 outputs corresponding to the digital codes ZSLIN and FSLIN should be measured at ambient temperature. Construct the transfer function as described in the TempCal section by calculating the gain and offset errors at ambient temperature and applying Equation 14.
GEamb = gain error at ambient temperature
VOE,amb = offset error at ambient temperature (V)
Calibrating the DAC signal chain at ambient temperature resolves 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.
DAC internal errors (i.e. offset and gain errors) drift due to operating temperature changes and can be accounted for using data sheet specifications. This is what we call SpecCal. Typical values for offset error drift are listed in the Specifications table in the AD5676R data sheet, and the typical performance parameter (TPC) for offset error versus temperature indicates the direction of error drift, depending on whether the ambient temperature increases or decreases.
The change in gain error due to temperature is represented by the TPC of the gain error versus temperature. Determine the % FSR of the gain error from the graph, then apply Equation 16.
After estimating the offset error and gain error at operating temperature, we can use Equation 17 to determine the input code corresponding to the SpecCal output.
Figure 6 shows the output error achieved by the EVAL-AD5676 evaluation kit using the SpecCal method.
Figure 6. System output error (LSB) using SpecCal at different temperatures.
The internal reference is used in this example. An external reference may add to the overall error. Errors due to the reference can be accounted for using the reference data sheet and considering the reference drift over the target temperature. Changes in the reference voltage will change the actual output range and thus the LSB size. Using an external reference should resolve this issue. The TPC of temperature versus output voltage can be used to determine the output range change due to reference voltage drift.
This article provides an overview of some of the main causes of DAC signal chain errors, including DAC internal errors as defined in the data sheet, and system-level errors that vary with the system and must be considered for open-loop applications.
This article discusses two calibration methods: one for situations where the DAC can be calibrated at system operating temperature, and one for situations where it cannot be calibrated at operating temperature, but can be measured at ambient temperature. The second method uses the TPC and specifications provided in the data sheets of the DACs and other ICs in the signal chain to account for gain and offset error drift.
The TempCal method can achieve much better precision than SpecCal. For example, for the EVAL-AD5676 board at 50°C, Figure 7 shows that the accuracy achieved by the TempCal method is very close to the ideal accuracy, while the SpecCal method still shows some improvement over the NoCal data.
Figure 7. System Output Error (LSB) for NoCal, SpecCal, and 50°C TempCal
Temperature changes have a significant impact on the accuracy of electronic systems. Calibrating at system operating temperature removes most errors. If this is not possible, the information provided in the data sheets of DACs and other ICs can be used to account for temperature variations and achieve acceptable accuracy.