(Editor's Note: There are links to the previous parts of this series at the end, below the author's biography.)

The perfect analog-to-digital converter (ADC) was discussed in Part 3: Analog and the digital world (link at the end). As a mixed-signal device with analog input and digital output, the descriptive specifications can be expected to be analog and digital. The transfer function for the ideal ADC is shown in Figure 1.

Figure 1: ADC ideal transfer function

The transition from output code 000 to 001 should happen as the input analog voltage reaches half of one LSB. When that transition happens at some other input voltage, the difference is the offset. This is an analog voltage error located at the first switch point as shown in Figure 2.

Figure 2: Input voltage offset

Because the first switch point is shifted, the entire transfer function is shifted either right or left, depending on the polarity of the offset.

Gain error is the second transfer function error. Figure 3 shows the effect of this error is a change in the slope of the transfer curve.

Figure 3: Gain error

Gain error is seen as a shift in the full-scale code after the offset is corrected. This error can be caused by an error in the value of the reference voltage, as well as faults within the converter.

Notice that with all of the previous errors, the transfer function remains a straight line. While this is convenient for definition, there are two static parameters which describe the deviations from the ideal straight line, Figure 4.

Figure 4: INL and DNL

The integral non-linearity (INL) is a measure of the deviation of the transfer function from the ideal straight line. The differential non-linearity (DNL) is any one step size deviation from the ideal. Two cases of extreme DNL are shown in Figure 5.

Figure 5: Extreme DNL

These errors can be disastrous in systems where a closed-loop control system is searching for a position. In the case of a missing code, the system would continue to search about a point and never settle.

Monotonic systems are those whose output code either remains constant or always increases, with increasing values of input. Consider a system where the target value is 110 at an input of six-eighths of full scale. As the input is increased from three- to four-eighths, the output code increases. When the input is increased from four- to five-eighths, the output code decreases. The system concludes it has passed the target point and reverses. The system remains trapped in a local minima, with no chance of reaching the desired final point.

In the next part of this series, we will open the topic of specifications of dynamic performance for ADCs.

About the author



William P. (Bill) Klein is a Senior Applications Engineer with the High Performance Analog group at Texas Instruments. Bill joined TI through its acquisition of Burr-Brown in August 2000. His experience as an analog circuit designer covers over 40 years in fields ranging from mineral exploration to medical nuclear imaging. One current role Bill has is hosting the Analog e-LAB Web Cast, presenting real world solutions to real world problems in analog circuit design. In addition to a BSEE from Arizona State University and registration as a Professional Engineer in the State of Arizona, he has authored numerous magazine articles, application notes and conference papers.

Previous installments of this series:

• "SIGNAL CHAIN BASICS (Part 13): Putting the Bode plot to use", www.planetanalog.com/features/showArticle.jhtml;?articleID=207403561, click here
• "SIGNAL CHAIN BASICS (Part 12): The Bode plot, an essential ac-parameter display tool", www.planetanalog.com/features/showArticle.jhtml;?articleID=207403561, click here
• "SIGNAL CHAIN BASICS (Part 11): Introducing voltage- and power-conditioning circuits", www.planetanalog.com/features/showArticle.jhtml;?articleID=207001505, click here
• "SIGNAL CHAIN BASICS (Part 10): Exploring the Delta-Sigma Converter", www.planetanalog.com/features/showArticle.jhtml;?articleID=206903892, click here
• "SIGNAL CHAIN BASICS (Part 9): SAR Converter Operation Explored", www.planetanalog.com/features/showArticle.jhtml;?articleID=206901015, click here
• "SIGNAL CHAIN BASICS (Part 8): Flash- and Pipeline-Converter Operation Explored", www.planetanalog.com/features/showArticle.jhtml;?articleID=206504089, click here
• "SIGNAL CHAIN BASICS (Part 7): Op Amp Performance Specification--Bias Current", www.planetanalog.com/features/showArticle.jhtml;?articleID=206101908, click here
• "SIGNAL CHAIN BASICS (Part 6): Op Amp Input Voltage Offset", www.planetanalog.com/features/showArticle.jhtml;?articleID=205901111, click here
• "SIGNAL CHAIN BASICS (Part 5): Introduction to the Instrumentation Amplifier", www.planetanalog.com/features/showArticle.jhtml;?articleID=205208593, click here
• "SIGNAL CHAIN BASICS (Part 4): Introduction to analog/digital converter (ADC) types", www.planetanalog.com/features/showArticle.jhtml;?articleID=204803631, click here
• "SIGNAL CHAIN BASICS (Part 3): Analog and the digital world", www.planetanalog.com/features/showArticle.jhtml;?articleID=204400376, click here
• "SIGNAL CHAIN BASICS (Part 2): Op Amp--Basic operations", www.planetanalog.com/features/showArticle.jhtml;?articleID=203101699, click here
• "SIGNAL CHAIN BASICS: Operational Amplifier--The Basic Building Block", www.planetanalog.com/features/showArticle.jhtml;?articleID=202801320, click here