Managing noise in the signal chain, Part 2: Noise and distortion in data converters
IntroductionThis is the second in a three-part series on noise in the signal chain. In Part 1, we identified the origins and characteristics of noise found in all semiconductor devices and explained how it is specified in device data sheets. We showed how to estimate the output noise of a voltage reference under real-world conditions that are not specified in the data sheet. In this article we focus on the sources of noise and distortion particular to ADCs and DACs. As before, we show how this noise is specified in a data sheet. Part 3 of the series will bring Parts 1 and 2 together, and show readers how to by optimize their noise budget and choose the most appropriate data converter for their application.
Noise in the signal chain
The sources of noise in a signal chain can be either internal or external. Managing noise in the signal chain requires meticulous examination of each circuit in the chain to minimize noise where possible. This is elementary and pivotal to our discussion because noise, once embedded in a signal, is very difficult or impossible to remove.
It is important that we start by briefly reviewing a few basic, but critically important, topics from the Part 1 article on Annoying Semiconductor Noise. Understanding electrical noise is more essential today than it has ever been. As 14- and 16-bit data converters become mainstream and 18- and 24-bit converters are increasingly available, noise is often the single factor that limits a system’s performance. There is no doubt that recognizing its origins and characteristics is key to achieving a signal chain’s greatest possible accuracy.
Generally speaking, noise is any electrical phenomenon that is unwelcomed in an electrical system. Depending on its origin, noise can be classified as external (interference) or internal (inherent). This article will focus on the noise inherent in all data converters and caused by the sampling process.
Figure 1. Noise in the signal chain.
In Figure 1 all external noise sources are combined into the term Vext. All internal noise sources are combined into the term Vint.
Now we will examine the four common types of noise and distortion in data converters: quantization noise, sample jitter, harmonic distortion, and analog noise.
Noise in Data Converters
Quantization noise is the most well-known source of noise in a data converter. It results from the errors inherent in the sampling and quantization process used in the converter. The magnitude of this noise is determined by three factors: resolution, differential nonlinearity, and bandwidth.
Quantization is the uncertainty that results from dividing a continuous signal into 2N discrete levels, where N is the resolution in bits. All analog voltages within a given quantum have the same code which results in a quantization uncertainty. This uncertainty is called the “quantization error.” The root mean square (RMS) value of the quantization error is the quantization noise. Quantization error is inversely proportional to 2N. The quantization error over time for an ideal ADC is shown in Figure 2, which also shows how quantization error reduces as the resolution increases.
Figure 2. Quantization error results from dividing a continuous signal into 2N discrete levels.
The RMS quantization noise of an ideal data converter of resolution N is given by:
Or in terms of LSB:
The differential nonlinearity (DNL) of a data converter is the deviation of any code width from an ideal 1 LSB step. An ideal data converter would have a DNL of 0, but most precision data converters today have a DNL < 1. The average DNL of a data converter increases its average quantization error and, therefore, its quantization noise (Figure 3).
Figure 3: Quantization error over time, DNL > 0.
The average DNL is usually not specified in a data converter data sheet, however, the typical DNL specification can be used in its place with reasonable accuracy.
The RMS quantization noise, including the effects of resolution (N) and DNL, is given by:
Or in terms of LSB: