# SIGNAL CHAIN BASICS Series (Part 3): Analog and the digital world

Post a comment

*( Editor's Note: there is a listing of the previous parts of this series, with hot links, at the end, right after "About the author".)*

Up to this point in this series, we have examined the operational amplifier (op amp) and its use in several applications. To emphasize the diversity of the entire signal chain, this article opens the door to the world of analog-to-digital converters (ADC) where we cross over into the digital world.

To appreciate the transition from analog to digital, we need to define a few terms unique to the digital area. These concepts form the foundation of the analog-to-digital transform and are independent of the method used to digitize the signal. It is necessary to understand that a digital representation of an analog signal is an approximation. The analog signal can assume any value within a range while the digital signal is constrained to distinct values.

As the output from the converter is a digital word it is characterized by the number of bits it contains. This defines the resolution available, but does not speak to the accuracy of the conversion. Resolution is commonly considered in terms of the least significant bit (LSB). For any converter this is calculated by:

_{fs}is full-scale voltage, and N is number of bits.

For example, a 16-bit converter operating with a full scale range of 5 V would have a LSB calculated as:

The various accuracy terms are usually expressed in terms of the LSB value. To understand the accuracy versus resolution exchange, consider the graphic in

**Figure 1**, which shows four possible combinations that can come from these options.

*Figure 1: Accuracy versus resolution*

*Target A* shows low resolution and poor accuracy. There is a large distance between shots and they are not near the center of the target. *Target B* shows good accuracy as all of the shots are around the center of the target, but the space between the shots indicates low resolution. *Target C* and *Target D* show a much higher resolution as the shots are in tighter groups. The shots in Target C are in a tight group, but they are not in the center ring compared to Target D, which has the highest accuracy, since all shots are in the center ring.

Another term necessary for understanding the digitization process is quantization noise, or quantization error. **Figure 2** shows the ideal transfer function for a three-bit ADC.

*Figure 2: Ideal transfer function for an ADC*

The straight line through the origin going to the upper right represents the transfer function for an analog-in and analog-out system. The independent variable is the continuous analog input voltage. It may assume any value along the X-axis. The dependent variable is the output code. It is constrained to one of the discrete values along the Y-axis.

Since the output must assume one of the discrete codes, a deviation from ideal will exist whenever the input is not at the exact value of a code. This error is shown in **Figure 3**:

*Figure 3: Quantizing error*

With this figure in mind, one can imagine the errors that could be created if the code transition values were not ideal. We will revisit this concept in a future installment and develop a mathematical model to predict the impact of this noise on the overall performance of an ADC.

In the next installment, we will examine different techniques used to render a digital value for an analog input.

** 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 Series (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