# Managing noise in the signal chain, Part 1: Annoying semiconductor noise, preventable or inescapable?

**Introduction**

This is the first in a three-part series on managing noise in the signal chain. In this article we will focus on the characteristics of semiconductor noise found in all ICs, explain how it is specified in device data sheets, and show how to estimate the noise of a voltage reference under real-world conditions not specified in the data sheet. In Part 2 we focus on sources of noise and distortion particular to data convertors and show how it is specified in those data sheets. Our concluding Part 3 brings together Parts 1 and 2, and shows readers how to optimize their noise budget and choose the most appropriate data converter for their application.

Understanding electrical noise is more important today than it has ever been. As 14- and 16-bit data converters are becoming mainstream and 18- and 24-bit converters are increasingly available, noise is often the single factor that limits a system’s performance. Clearly, understanding the origins and characteristics of noise generated within an IC is key to achieving a system’s greatest possible accuracy.

Noise can irritate everyone, but it is especially annoying to analog design engineers. Generally speaking, noise is any unwelcome electrical phenomenon in a signal chain. Depending on its origin, it may be classified as external (interference) or internal (inherent). This is illustrated in the signal-chain diagram below (**Figure 1**). All all internal noise sources (V_{int}) have been combined at the output and all external noise sources (V_{ext) }have been combined at the input to the signal chain.

**Figure 1. Noise in the signal chain.**

To a designer it is important to understand the origin and characteristics of this internal semiconductor noise. These include thermal, shot, avalanche, flicker, and popcorn noise, as well as noise particular to data convertors, such as quantization, aperture jitter, and harmonic distortion. Designers must also know how, or if, this noise is preventable or inescapable.

**Noise in Semiconductor Devices**

All electrical components intrinsically generate noise. This includes all semiconductor devices and resistors. We begin by discussing the general properties of noise and then discuss the types and characteristics of common noise sources. Next, we will learn how to find and interpret noise specifications in a data sheet. We conclude by using all this information to calculate the output noise of a voltage reference under conditions not specified in its data sheet.

**Properties of Noise**

The follow section examines the nature of semiconductor noise and how it is specified in semiconductor devices.

**Noise Amplitude**

All the semiconductor noise sources have their origin in random processes, so the instantaneous amplitude of noise is unpredictable. The amplitude exhibits a Gaussian (normal) distribution.

**Figure 2. Gaussian noise distribution.**

Note that the RMS value of noise (V_{n}*)* is the standard deviation (σ) of the noise distribution. The relationship between the RMS and peak voltages of a random noise source is:

The ratio of the peak-to-peak to RMS voltage (V_{nP-P}/V_{nRMS}) of any signal is called the crest factor. The 6.6 in Equation 1 is a commonly used crest factor and comes from the fact that, statistically, a Gaussian noise source produces a peak-to-peak voltage 6.6 times the RMS voltage 0.10% of the time. This is the shaded area under the Noise Voltage Density curve shown in **Figure 2** where the probability of exceeding ±3.3σ is 0.001. It is important to remember that correlated signals add linearly, and random signals (like noise) add geometrically in root sum square (RSS) fashion.

**Noise Spectral Density**

Semiconductor noise sources can be placed in one of two categories, based on the shape of their spectral density curves. White noise dominates at high frequencies and pink noise dominates at low frequencies.

White noise is characterized by a uniform spectral density (**Figure 3**), having equal energy in any given bandwidth interval.

**Figure 3. White noise spectral density.**

Pink noise contains equal amounts of energy in each decade. It is characterized by a power spectral density (**Figure 4**) that is inversely proportional to frequency, thus the common name “1/f” noise.

**Figure 4. Pink noise spectral density.**

In Figure 4, K_{v} is a proportionality constant representing the extrapolated value of e_{n} at f = 1Hz. It is plotted on a log-log scale.

All noise found in semiconductor devices is a combination of white and pink noise, resulting in the noise spectral density curve shown in **Figure 5**, plotted on a log-log scale. The corner frequency (F_{C}) is the boundary between white and pink noise.

**Figure 5. Noise spectral density.**

The noise voltage present over any bandwidth is the area under the square of the noise spectral density curve, between the upper (F_{h}) and lower (F_{l}) frequencies of the band. Mathematically, this is written as:

Simplifying:

As can be seen, noise amplitude specifications must always be qualified by a frequency range.

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