# 1.2 Data converters  (Page 3/3)

Accuracy

Many people confuse resolution with accuracy. Just because you have a converter with 16 bits of resolution doesn’t mean you always have 16 bits (or 15 ppm) of accuracy. Recall that a data converter requires a reference, and accuracy is the degree to which the result conforms to the correct value measured against a standard or reference. If you put exactly 1 V into an ADC and could resolve exactly that value with 16 bits, but the ADC tells you that it’s 1.2 V, that’s only 20 percent accuracy – a far cry from 15 ppm.

At a system level, the accuracy of the reference voltage will be one of the primary factors in the overall accuracy of the system. But the data converter itself contributes some errors. Some data converters will express an overall accuracy specification – often called total unadjusted error – but it is more common to see specifications for offset error, gain error and linearity.

The ideal transfer function for a data converter is shown in Figure 4, as a blue line. It appears as a staircase because the quantizer can only represent a range of voltages with a single code. The location of the transition point from one code to another is key to describing the converter's accuracy.

Offset error is the difference between the actual transition point and the ideal transition point – resulting in a translation of the transfer function left or right. Although this error is measured around a near-zero voltage input or output, the error continues throughout the entire transfer function from zero to a full-scale (FS) voltage. Consequently, the offset error near zero is the same as the offset error with a near FS voltage.

Gain error is the difference between the actual last transition point and the ideal last transition point – resulting in a rotation of the transfer function. It is the difference between the ideal slope of the transfer function and the actual slope between the measured zero point to FS, minus the converter’s offset error. This is actually measured by looking at where the last transition point at full scale occurs, as shown in Figure 5.

As you might imagine from the use of the term “error,” smaller gain and offset errors imply a more accurate converter. Gain and offset errors can often be corrected for in the digital domain, using the system microcontroller or DSP.

Linearity errors , on the other hand, are much more difficult to correct. While the transfer functions in Figure 4 and Figure 5 show steps that are exactly the same size, in actual converters the width of these steps will vary. Figure 6 shows how differential nonlinearity (DNL) is measured. DNL is the deviation in code width from the ideal 1LSB code width.

A DNL error less than –1 LSB can cause an entire code to “disappear,” resulting in what is called a missing code . The smaller the range of the DNL specification, the better.

Integral nonlinearity (Figure 7) is the cumulative effect of all of the differential nonlinearity errors, and is the maximum deviation between the actual code transition points and the corresponding ideal transition points after gain and offset error have been removed. The smaller the INL specification, the more accurate the data converter will be.

Speed, resolution and accuracy are important considerations in selecting a data converter, and you will often find what you need to know about these on the front page of the converter data sheet. But other important factors, such as the details of the digital interface and mechanical drawings of the package, are further inside the data sheet. You need to read the entire data sheet to effectively use a data converter.

Choosing the right data converter

A multitude of data converters are available for your design. While the three main specifications of speed, resolution and accuracy will help in the final selection process, narrowing down the options to choose from is the first step.

When selecting an ADC for a particular application, a good first selection criteria is to look at the topology of the ADC. Figure 8 is a simple comparison of ADC architectures that can help you find the right place to start when selecting a converter for your application. Delta-sigma converters are most suitable for higher-resolution tasks, while successive-approximation-register and pipeline architectures are the ones to look to for higher-speed applications.

Digital-to-analog converters have similar trade-offs in architecture: delta-sigma DACs tend to be slower, while R-2R, string and multiplying DACs all provide good general-purpose performance. High-frequency, fast-settling DACs are generally for current-steering architectures.

Knowing the speed and resolution requirements of your application, you can anticipate which architecture of converter will most likely suit your needs. Then you can look more closely for the converter that matches the accuracy requirements and other features that the application demands.

Table 1 lists some applications where data converters are used, as well as the selection criteria and some examples of actual converter products suitable for those applications.

Application Required sample rate Required resolution Architecture Example part Comments
Temperature measurement <10 sps 8-18 bits Delta-sigma ADS1146 High accuracy
Waveform analysis/synthesis <100 Msps 8-16 bits Pipeline ADS6445, DAC2902 High speed and good linearity (low distortion) required
Test and measurement <1 Msps 12-24 bits SAR ADC, multiplying DAC ADS7824, ADS8326, DAC8820 High accuracy and throughput, multiple channels
Ultrasonic imager <100 Msps 12-14 bits Pipeline ADS6445 High speed, good resolution
Motor control and positioning <500 ksps 12-18 bits SAR ADC, multiplying DAC ADS8361, DAC8811 High accuracy and throughput, multiple channels

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x-2y+3z=-3 2x-y+z=7 -x+3y-z=6
Need help solving this problem (2/7)^-2
x+2y-z=7
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-1
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