In my last post, “DAC Essentials: The pursuit of perfection,” I explained the concept of the ideal DAC and established the key idioms of its performance. Now we’ll explore how real devices deviate from the ideal DAC transfer function and how to quantify those deviations.
DAC specifications are divided into two basic categories: static and dynamic. Static specifications are behaviors observed at the DAC output at a steady output state, while dynamic specifications refer to behaviors observed during a code-to-code transition. When discussing linearity and the DAC transfer function, you only need to consider static specifications.
Let’s first start with a spec called offset error. Offset error describes how much the entire DAC transfer function is shifted up or down. The measurement is usually made from a line of best fit taken from a two-point measurement around 10% and 90% full-scale. We do this to avoid operating the output operational amplifier in the non-linear region near its power rails. If you were to consider slope-intercept form for a straight-line equation, y = mx + b, offset error would be the b term, as illustrated below.
Zero-code error is similar to offset error but describes a different and useful DAC behavior. Zero-code error is measured by loading the DAC with all 0’s and observing the DAC output voltage. In the ideal DAC, we would see 0V at the DAC output when loaded with all 0’s, but due to headroom requirements for the output buffer, we usually see some small offset from 0V.
Another important specification is called gain error. As you may expect, it compares how the real DAC transfer function’s slope relates to the ideal slope. In the ideal case, the slope of the transfer function is equal to exactly 1 LSB, but frequently this figure is slightly off. The measurement for gain error is taken from the same two-point line of best fit used in measuring offset error. If offset error is the b term in y = mx + b, then gain error is the m term.
Offset error, zero-code error, and gain error are all provided holistically for a DAC using the measurement techniques mentioned above, which should make sense given what they’re describing. The remaining specifications, INL and DNL, are measured for each and every code in the DAC’s transfer function, but a single number is provided in the electrical characteristics table that expresses the worst case observed across the entire transfer function. The datasheet will also include graphs showing the typical INL or DNL across all codes in the typical characteristics section.
DNL is differential non-linearity. It expresses the difference between measured LSB size and ideal LSB size for any two sequential DAC codes. DNL is often used to infer DAC monotonicity and to determine if the DAC has any missing codes. Since most modern ADCs and DACs are monotonic, DNL is usually not as useful as INL.
The last static linearity specification is INL – integral non-linearity, which is also referred to as relative accuracy. INL describes the deviation between the ideal output of a DAC and the actual output of a DAC, where offset error and gain error have been calibrated out of the measurement. In a lot of ways, INL is the most valuable specification to consider for an application that requires extremely high precision. Offset, gain, and zero-code errors can be compensated for externally, but there is no way we can reach inside the device package and correct internal mismatches to fix INL.
In our next couple of posts, we’ll take a look at the DAC architectures used to create precision DACs. I hope you’ll check back for them in the coming weeks!
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