Calculating the Error Budget in Precision Digital-to-Analog Converter
David Fry, 应用工程师经理
Abstract: This application note analyses the parameters that affect the errors in precision digital-to-analog converter (DAC) applications. The analysis focuses on
the factors introduced by both the data converter and the voltage reference. It describes the calculations required to select the data converter and the reference to meet the system’s target specifications. The calculations are available in a
When designing a digital-to-analog converter (DAC) system, the DAC specifications and its voltage reference work in tandem to produce the overall system performance. Consequently, selection of both DAC and reference should be made
together. The components' specifications can be traded off against each other to ensure that system specifications are met at the lowest cost.
This application note focuses on Maxim's 3-terminal voltage references and
precision DACs. To design a system, one must first understand how the parts are specified and then how their performance characteristics interact. Voltage references and DACs have many specifications. Only those factors relevant to the error budget will be discussed here.
Voltage Reference Specifications
This is the output voltage tolerance, ignoring any effects of temperature, input voltage, and load. Temperature is normally +25?C.
Output-Voltage Temperature Coefficient
This is the change in reference output voltage, measured for a given change in temperature and specified in ppm/?C. Maxim uses the box method. The shape of the change vs. temperature characteristic is not specified; only the limits of this function are specified. The limits of the output voltage do not necessarily coincide
with the limits of temperature. So, to calculate the maximum change, multiply the
temperature coefficient by the temperature range for the part. Thus to illustrate, if a part has a temperature coefficient of 5ppm/?C, specified from -40?C to +85?C, the
maximum deviation over temperature would be:
ΔV = (T - T) × TC = (85 + 40) × ?5 = ?625ppm MAXMIN
It is generally best to select a device that is specified over the required temperature range, rather than a broader range. For instance, the MAX6025A is specified as a
15ppm/?C reference over 0?C to +70?C. This reference value works out to 1050ppm over the range. If, however, one chose a reference specified over the -40?C to +85?C range, a reference that is 1050/125 = 8.4ppm/?C or better would be required. Note that some devices are specified over several temperature ranges.
A graphical example of the box method is shown in Figure 1. Two different example
curves are shown, both of which satisfy the 5ppm/?C specification over -40?C to
Figure 1. Example temperature characteristics.
With series references, therefore, it is generally not possible to relate voltage drift and temperature so that one can calculate the drift over a specific range other than that over which the part is specified.
This term defines the incremental change in output voltage for a change in input
voltage. It is normally defined in terms of µV/V.
This term defines the incremental change in output voltage for a change in load
current. Some DACs may not buffer the reference input. Therefore, as the code changes, the reference input impedance will also change, causing a change in reference voltage. This change is generally small, but should be considered in high-accuracy applications. Note that this is more important with some DAC topologies such as R-2R ladders, while resistive string topologies are less
This is the change in reference voltage at +25?C after the temperature is cycled from T to T. It is specified as a ratio of the two voltages and expressed in ppm: MINMAX
6TEMPHYST = 10 × (ΔV/V) REFREF
Where ΔV is the change in reference voltage caused by the temperature cycle. REF
This is the change in reference output voltage vs. time, specified in ppm/1000 hours. Cumulative drift beyond a 1000-hour interval is not generally specified, but
is usually much lower than the initial drift. An application's long-term stability can be
improved by PCB-level burn-in. A typical output-voltage long-term stability
characteristic is shown in Figure 2.