# ADC Signal-to-Noise Ratio (SNR)

If an Alternate Current (AC) signal is applied to an ideal Analog-to-Digital Converter (ADC), 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 Least Significant Bit (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 accompanying image:

The Root-Mean-Square (RMS) amplitude of the error output can be approximated by the equation below.

(1) ERRORRMS=1/(12−−√)∙1LSB

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 ADC is increased by 3 dB each time the fs is doubled.

(2) SNR=6.02∙N+1.76dB