Applications that are a perfect fit for 12-bit analog-to-digital converter (ADC) systems are multiplexed circuits, handheld meters, data loggers, automotive systems, and monitoring systems. In these systems, a 12-bit ADC that produces 4096 possible digital outputs usually supplies ample information for most system designers. When accomplishing this level of digital output resolution, it is possible to use either a 12-bit SAR or 24-bit delta-sigma ADC. This article helps to determine the key specifications for ADCs, as you compare the performance of SAR and delta-sigma converter systems.

The first step to identifying the correct ADC is to inspect the respective product datasheet. Once you embark on this type of activity, you will find that the number of these specifications can quickly overwhelm you; especially if you are just learning the ropes about the ADC. Letâ€™s narrow down that list to a handful of the key characteristics and specifications by setting a few priorities, keeping in mind that we are working on a system as opposed to an individual device. If you want to go deeper, reference 1 gives you a summary of most of the primary ADC specifications and characteristics.

Several specifications can be critical in a particular application. However, for these systems one needs to know the following ADC characteristics:

- Basic transfer function
- Full-scale-input-range
- Number of bits
- Analog and/or digital gain capability
- Power consumption
- Through-put timing
- Output noise

**ADC transfer function, full-scale input range, number of bits**

Theoretically, an ADCâ€™s ideal transfer function is a straight line with the input voltage on the x-axis and the digital output code on the y-axis. The practical ideal transfer function (**Figure 1** ) has a uniform staircase formation. **Figure 1** shows the ideal transfer function of a 3-bit ADC. **Equation 1** describes the code width in this diagram (for an â€śnâ€ť bit converter):

(ideal code width) = FS / (2^{n} )Â Â Â Eq. 1

**Click on image to enlarge.****Figure 1. Unipolar ideal ADC transfer function**

This ideal ADC relates all analog inputs to a limited number of digital output codes. In Figure 1, there are 23 or eight output codes. Given that the analog input scale is continuous and the digital codes are discrete, this conversion process introduces a quantization error.

If you increase the number of discrete codes (or increase the number of ADC bits), the corresponding code widths become smaller. Notice that if the desired number of output codes continues to be eight, the analog input range decreases.

**ADC gain capability**

Analog and/or digital gain within the ADC circuit is sometimes obvious and other times not so obvious. For instance, a basic SAR-ADC does not have analog gain capability. This is easy to know as long as you read the front page of the datasheet and examine the simplified ADC circuit diagram. On the other hand, some SAR-ADCs have internal programmable-gain-amplifier (PGA) circuits. This PGA function supplies an analog gain inside the device. This is a convenient gain block, however, it is important to note that the number of bits do not change with PGA gain changes. The only visible change is the input range of the ADC and the code width (or LSB) voltage. As the PGA gain increases, the ADCâ€™s input range decreases.

If the converter has more that 12-bits, it is possible to implement digital (or process) gain with the converter (**ref 2** ). If you are using a 24-bit delta-sigma ADC, you will find 4096 places in the output code that will produce 12 bits of codes. The number of output codes with a 24-bit ADC is 224, or 16,777,216 codes.

**Power consumption**

In terms of power consumption, you can exercise power-down capability with SAR-ADCs. When the SAR-ADC is converting a signal, there is a power consequence. The SAR-ADC takes a â€śsnap-shotâ€ť of the input analog signal to produce one digital output code. When the SAR-ADC is not converting, the device goes into a sleep mode. This characteristic is useful in battery-powered applications.

The power consumption model of delta-sigma converters is different than the SAR-ADC. A delta-sigma converter acquires numerous samples of the input signal and combines those samples into one output code representation. During the time that the output is available, the converter continues to sample in preparation for the next output code. Delta-sigma converters do not have the convenient SAR-ADC, power-down function.

**Throughput timing **

Although the SAR-ADC and delta-sigma converter both transmit a serial output data stream that represents their conversion, the two devices have significant differences during their conversion times. A SAR-ADC samples the input signal and converts that one signal to a serial digital output. **Figure 2** shows an example the conversion timing of a SAR-ADC. In this diagram, the throughput time includes the conversion time (tCONV) and a quiet time (tq). The converter transmits a serial 12-bit stream of data at its output (SDO).

**Click on image to enlarge.****Figure 2. 12-bit SAR-ADC conversion timing diagram using the ADS7886.**

One can view the SAR-ADC as a one-shot converter where the output data represents a single analog sample.

**Figure 3** illustrates a possible delta-sigma converter timing scenario. In this figure, the converter acquires multiple samples and internally produces intermediate conversions.

**Click on image to enlarge.****Figure 3. 24-bit delta-sigma conversion timing diagram using the ADS1258.**

This figure shows the intermediate, internal conversions of the delta-sigma converter with a fifth-order digital filter. Notice the â€śhidden conversionsâ€ť are an artifact of the internal digital filterâ€™s order. The user never sees these hidden conversions.

**Output noise**

The noise magnitude produced by the SAR-ADC and delta-sigma converter, as compared to the number of bits, is dramatically different. Typically, the noise generated by the 12-bit SAR-ADC is well below the voltage size of the converterâ€™s LSB. For instance, a 12-bit SAR-ADC with a 4.096V full-scale input range has an LSB size of 1 mV. In contrast, a 24-bit delta-sigma converter with a 4.096V full-scale input range has an approximate LSB size of 244 nV.

Device or converter noise is a random event, but it does follow probability theories. **Figure 4** illustrates a group of a delta-sigma converter results with a DC input. There are three points of interest.

**Click on image to enlarge.****Figure 4. Continuous output data from a delta-sigma converter.**

First is the mean value. The mean, or average value of the data, is a reference point needed when you calculate the dataâ€™s standard deviation. The second point of interest is the volts-RMS or bits-RMS label. These labels are equivalent to a span from the dataâ€™s negative to the positive standard deviation. Third, if you are going to place the converter results in a display, volts p-p or bits p-p determine how often the lower digits in your display change.

**Figure 5** shows how the output data in Figure 4 translates into a histogram. The RMS value is equal to the standard deviation of this data. Between the two standard deviations or RMS lines in this graph, a significant number of the noise occurrences are captured. The probability that an ADC produces one output value that lands between the two RMS lines is equal to about 68 percent.

**Click on image to enlarge.****Figure 5. Unipolar Ideal ADC Transfer Function**

With the Gaussian distribution in our histogram plot, you can see that your RMS limits exclude a lot of data. If you look at the number of converter output results between the two standard deviation limits, you account for 68 percent of the occurrences. But if you multiply the doubled standard deviation by a constant or crest factor, you can expand the percentage of occurrences underneath the curve. The crest factor allows you to define your peak-to-peak limits as well as determine which of the converter bits are useful in your 12-bit system.

**Conclusion**

The discussion in the article excludes a signification number of ADC specifications. These other specifications are important as you hone in on your finished solution, however, the topics mentioned here can be used to quickly prove or disprove the appropriate direction for your system design. The 12-bit applications that we are exploring include multiplexed circuits, handheld meters, data loggers, automotive systems, and monitoring systems.

**References**

1. â€śA Glossary of Analog-to-Digital Specifications and Performance Characteristics (SBAA147B),â€ť B. Baker, Texas Instruments, October 2011.

2. â€śDelta-sigma ADCs in a nutshell, part 3: the digital/decimator filter,â€ť Baker, EDN, February 21, 2008.

For more information, see **Part 4** and **links to Parts 1,2,3** here.

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