On incremental sigma-delta modulation with optimal filtering

Abstract

The paper presents a quantization-theoretic framework for studying incremental Σ∆ quantization systems. The framework makes it possible to efficiently compute the quantization intervals and hence the transfer function of the quantizer, and to determine the mean square error (MSE) and maximum error for the optimal and conventional linear filters for first and second order incremental Σ∆ modulators. The results show that the optimal filter can significantly outperform conventional linear filters in terms of both MSE and maximum error. The performance of conventional Σ∆ quantizers is then compared to that of incremental Σ∆ with optimal filtering for bandlimited signals. It is shown that incremental Σ∆ can outperform the conventional approach in terms of signal to noise+distortion ratio (SNDR) and the characteristics of the power spectral density (PSD). The framework is also used to provide a simpler and more intuitive derivation of the Zoomer algorithm.

An extended-range incremental CT ∑Δ ADC with optimized digital filter

“…Although several optimal filters have been derived for DT IΣ∆ ADCs [5,15,16], to the authors' knowledge, the digital filter optimization for CT ER-IΣ∆ ADCs has not been treated yet. In this section, optimization tools are employed as an alternative approach to design such filter so as to counteract analogdigital mismatches.…”

A low-power continuous-time incremental 2nd-order-MASH ΣΔ-modulator for a CMOS imager

“…Input values that cause changes in the output sequence are called transition points. They are non-uniformly distributed and [16]. It can be shown that the relevance of the output value of a cycle decreases with each cycle [11].…”

High dynamic range adaptive ΔΣ-based focal plane array architecture

“…Filter Design: Sophisticated filters such as triangular, zoomer [19], recursive [12], optimal [20], etc. can enhance the SNR performance at the low end of Photo-diode current, at the cost of more circuit complexity and higher power consumption [13].…”