Decimation Resolution Gain

Formula

Description

Oversampling by the oversampling ratio (OSR) and then decimation (low-pass filtering and downsampling) improves the effective number of bits by half a bit per doubling of the sample rate. This is equivalent to the decimation-enob formula but uses OSR (oversampling ratio) as the input parameter. OSR = Fs_actual / (2 × Fsignal_max), the ratio of actual sampling rate to the minimum Nyquist rate. Sigma-delta ADCs combine extreme oversampling (OSR = 64 to 1024) with noise shaping to achieve 16-24 bit resolution from a simple 1-bit quantizer.

Variables

• ENOB_gain — Improvement in effective number of bits
• OSR — Oversampling ratio

Practical Notes

OSR of 4 = +1 bit, 16 = +2 bits, 64 = +3 bits, 256 = +4 bits. With noise shaping (as in sigma-delta converters), the gain is much higher: a first-order modulator gains 1.5 bits per doubling of OSR, a second-order gains 2.5 bits. This is why sigma-delta ADCs achieve very high resolution without extremely fast sampling rates.