Rigorous analysis of quantization error of an A/D converter based on β-map

A non-binary analog-to-digital converter (ADC) based on β-expansion, called β-encoder, is so far reported to achieve robustness against large process variation and wide environment change. Quantization error of β-encoder is not uniformly distributed, which makes the mean squared error (MSE) evaluation difficult. An analysis method for giving the upper bound of MSE of the quantization error is provided. Signal-to-noise-ratio (SNR) is also evaluated and the result is effective for designing β-encoders.