MMSE Estimator for Linearized Analysis and SNR of ADCs Tested with Sinusoidal Inputs

The classical formula for the signal-to-noise ratio (SNR) of an analog-to-digital converter (ADC), SNR=6.02N + 1.76dB, is derived by assuming a full-scale sinusoidal input that is uncorrelated with the quantization error (QE) arising from the N-bit ADC quantizer. This premise is inaccurate, particularly for the ADCs backed off to have a limited number of bits, N = 1,2, $\ldots$, 5. This paper uses the minimum mean square error (MMSE) estimator to perform a linearized analysis for a generic N-bit ADC, which takes into account the interaction between the ADC quantization characteristic and the probability distribution of the sinusoidal input. The estimated linearized gain guarantees the uncorrelation between the input and the QE. We compare the derived SNR with the classical formula to demonstrate their differences.