Managing noise in the signal chain, Part 3: Select the best data converter for your noise budget
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, Vext, and all internal noise sources are merged into a single term, Vint.
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
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.
Tj is the ratio of the RMS jitter of the sample period to the period of sine-wave signal, in ppm.
Vn is the analog noise, in LSBRMS.
THD is the total harmonic distortion, in percentage.
SINAD reduces to the familiar, “rule-of-thumb” equation:
SNR = 6.02N + 1.76 dB LSBRMS
Equation 2: SNR rule-of-thumb equation
BW = 100 %
DNL = 0LSB
Tj = 0ppmRMS
Vn = 0LSBRMS
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.