ADC Signal-to-Noise Ratio (SNR)

If an AC signal is applied to an ideal A/D converter, noise present in the digitized output will be due to quantization error. For the ideal converter, the maximum error for any given input will be +/- ½ LSb. If a linear ramp signal is applied to the converter input and the output error is plotted for all analog inputs, the result will be a sawtooth waveform with a peak-to-peak value of 1 LSb as shown in the figure below:


The root-mean-square (RMS) amplitude of the error output can be approximated by the equation below.

\begin{align} ERROR_{RMS} = 1/( \sqrt{12}) • 1 LSB \end{align}

The maximum theoretical signal-to-noise ratio (SNR) for an ADC can be determined based on the RMS quantization error determined above. If a full-scale (FS) sine wave is applied to the input of the ADC, the maximum theoretical SNR is determined by the equation below, where N is the resolution of the ADC in bits. The above formula assumes that the signal noise is measured over the entire usable bandwidth of the ADC (0 - fs/2), where fs = sampling frequency. For the case of oversampling where the signal bandwidth is less than the Nyquist bandwidth, the theoretical SNR of the A/D converter is increased by 3 dB each time the fs is doubled.

\begin{equation} SNR = 6.02 • N +1.76dB \end{equation}

20th Annual
Microchip MASTERs Conference 2016
Register now - Deadline: July 29

JW Marriott Desert Ridge Resort-Phoenix, AZ

© 2016 Microchip Technology, Inc.
Information contained on this site regarding device applications and the like is provided only for your convenience and may be superseded by updates. It is your responsibility to ensure that your application meets with your specifications. MICROCHIP MAKES NO REPRESENTATIONS OR WARRANTIES OF ANY KIND WHETHER EXPRESS OR IMPLIED, WRITTEN OR ORAL, STATUTORY OR OTHERWISE, RELATED TO THE INFORMATION, INCLUDING BUT NOT LIMITED TO ITS CONDITION, QUALITY, PERFORMANCE, MERCHANTABILITY OR FITNESS FOR PURPOSE. Microchip disclaims all liability arising from this information and its use. Use of Microchip devices in life support and/or safety applications is entirely at the buyer's risk, and the buyer agrees to defend, indemnify and hold harmless Microchip from any and all damages, claims, suits, or expenses resulting from such use. No licenses are conveyed, implicitly or otherwise, under any Microchip intellectual property rights.