# Managing noise in the signal chain, Part 3: Select the best data converter for your noise budget

**Introduction**

This is the last of a three-part series on noise in the signal chain. In Part 1 about **Annoying Semiconductor Noise**, we identified the origins and characteristics of semiconductor noise found in all IC. We explained how it is specified in device data sheets and showed how to estimate the noise of a voltage reference under real-world conditions not specified in the data sheet. In Part 2 on **Noise and Distortion in Data Converters** , we focused on sources of noise and distortion particular to data converters. We showed how their noise is specified in a data sheet. We conclude in this article by bringing Parts 1 and 2 together. Now we will help readers choose the most appropriate data converter for their noise budget.

**Noise in the Signal Chain**

We begin with a brief review of concepts covered in Part 1 of the series. Noise is any unwelcome electrical phenomenon in an electrical system. Depending on its origin, noise can be classified as external (interference) or internal (inherent) to the signal chain. In **Figure 1** all external noise sources are combined into a single term, V_{ext}, and all internal noise sources are merged into a single term, V_{int}.

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

A noise budget is the allocation of the noise in a signal chain that results in an acceptable signal-to-noise ratio (SNR) at the output. The SNR is defined as the ratio of the full-scale RMS signal level to the total RMS noise. Therefore, to determine the acceptable distribution of noise within a signal chain you must evaluate its effect on total SNR. To this end, two specifications unique to data converters will be introduced: signal-to-noise and distortion (SINAD) ratio and effective number of bits (ENOB).

**Signal-to-Noise and Distortion**

Data converters expand the definition of SNR to include distortion, and use the term signal-to-noise and distortion (SINAD). The added distortion includes all undesired spectral components, excluding DC. SINAD is the ratio of the full-scale RMS signal to the RMS sum of all other noise and distortion components.

SINAD, in dBFS, can be expressed in terms of the quantization noise, sample jitter, analog noise, and THD as:

**Equation 1: SINAD expression in dBFS**

Where:

N is the resolution, in bits.

DNL is the average differential nonlinearity, in LSB.

BW is the fraction of the full Nyquist bandwidth used, in percent.

T_{j }is the ratio of the RMS jitter of the sample period to the period of sine-wave signal, in ppm.

V_{n }is the analog noise, in LSB_{RMS}.

THD is the total harmonic distortion, in percentage.

SINAD reduces to the familiar, “rule-of-thumb” equation:

SNR = 6.02N + 1.76 dB LSB_{RMS}

**Equation 2**: **SNR** **rule-of-thumb equation**

When:

BW = 100 %

DNL = 0LSB

T_{j }= 0ppm_{RMS}

V_{n} = 0LSB_{RMS}

THD = 0%

Together, these parameter values describe the *ideal* data converter in which the only noise source is the full bandwidth quantization noise inherent in the sampling processes.

In this case, ENOB = N bits.

**Next: Effective Number of Bits**

System level design and integration challenges with multiple ADCs on single chip

Understanding the basics of setup and hold time

Product How-to: Digital isolators offer easy-to-use isolated USB option

Managing noise in the signal chain, Part 2: Noise and distortion in data converters

War of currents: Tesla vs Edison

Simple reverse-polarity-protection circuit has no voltage drop

Control an LM317T with a PWM signal

Start with the right op amp when driving SAR ADCs