Error Analysis of the Normalized Sine-Wave Histogram Test Algorithm for ADC Linearity Test

The sine-wave histogram test (SHT) is a prevalent method for characterizing the static linearity of analog-to-digital converters (ADCs). The normalized SHT (NSHT) algorithm has gained wide adoption in histogram data processing owing to its conceptual simplicity and intuitive extension from the classic ramp histogram test (RHT). However, this article reveals a fundamental and long-overlooked algorithmic error inherent in the NSHT, which degrades the accuracy of integral nonlinearity (INL) estimation. This error originates from the normalization process, where the measured nonuniform histogram is divided by an ideal sine-wave distribution to estimate code bin widths. This process erroneously assumes a proportional relationship between histogram count and code bin width. This assumption holds only for linear stimuli or ideal ADCs in the SHT. Consequently, estimation errors are introduced in code bin widths, systematically accumulated in code transition levels (CTLs), and ultimately propagated to differential nonlinearity (DNL) and INL. Critically, since this error does not scale linearly with the ADC intrinsic nonlinearity, it persists even after applying standard static gain and offset correction. To isolate this error, the IEEE standard SHT (SSHT) algorithm and the RHT are employed as reference methods in our comparative analysis. Simulation and experimental results show that although the NSHT yields a DNL estimation error on the order of 10⁻³ least significant bit (LSB), its accumulated INL error reaches −1.99 LSB, a magnitude that is 1.27 times the reference INL. Therefore, this article exposes a critical flaw in the NSHT and calls for a reevaluation of any normalized histogram-based test that employs nonlinear stimuli.