Spurious-Free Dynamic Range of a Uniform Quantizer

• Published in: IEEE transactions on circuits and systems. II, Express briefs Vol. 56; no. 6; pp. 434 - 438
• Main Authors: Oude Alink, M.S., Kokkeler, A.B.J., Klumperink, E., Rovers, K.C., Smit, G., Nauta, B.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.06.2009; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Additive noise; Additives; Analog-digital conversion; Analog-to-digital conversion; Counters; Digital-analog conversion; digital-to-analog conversion; Dynamic range; Dynamical systems; Dynamics; Errors; Gaussian noise; Harmonic distortion; intermodulation distortion; Noise; Noise levels; polynomial approximation; Quantization; quantization noise; Signal resolution; Signal to noise ratio; spurious-free dynamic range (SFDR); White noise
• ISSN: 1549-7747; 1558-3791
• DOI: 10.1109/TCSII.2009.2020929

Quantization plays an important role in many systems where analog-to-digital conversion and/or digital-to-analog conversion take place. If the quantization error is correlated with the input signal, then the spectrum of the quantization error will contain spurious peaks. Although analytical formulas describing this effect exist, numerical evaluation can take much effort. This brief provides approximations for the spurious-free dynamic range (SFDR) of a uniform quantizer with a single sinusoidal input, with and without additive Gaussian noise. It is shown that the SFDR increases by approximately 8 dB/bit, in case there is no noise. Generalizing this result to multitone inputs results in an additional 2 dB/bit per additional tone. Additive Gaussian noise decorrelates the sinusoid(s) and the quantization error, which results in a dramatic increase in SFDR.