Increasing SQNR by Increasing Bits Per Sample
December 3, 2019
Increasing the number of bits per sample will decrease the quantization noise and, therefore, increase SQNR. Theorem 3 quantifies this qualitative relationship for a full-scale sine waveform input. Take note that the SQNR increases approximately 6dB for every additional bit.
Let SQNR be the signal to quantization noise ratio for a full-scale sinusoid input.
Let b be the number of bits used by a converter. Then:
(1) The power 𝑃𝑠 of a sine waveform Asin(2𝜋𝑓c 𝑡 + 𝜙) is A2/2
Proof: Let 𝜏 = 1/𝑓c be one period of the sine waveform.
(2) For SQNR:
(3) For SQNRdB:
Over-Sampling with Quantization Uniformly Distributed White Noise
Theorem 3 is a theoretical ideal. In practice, an N bit converter has issues with inherent noise and doesn’t provide N bits of precision. Given this, system engineers want to know how many effective bits they can achieve. The b in Theorem 3 is equated in terms of SQNRdB to yield the following quantity called ENOB.
Let SINAD be the signal-to-noise-and-distortion ratio. Then: