An NTF-enhanced time-based continuous-time sigma-delta modulator

An oscillatory noise‐shaped quantizer for time‐based continuous‐time sigma‐delta modulators

“…In this case, the SDM works at the limit-cycle mode. [10][11][12][13][14] This way, a linearized model may be attributed to the SDM for the sake of a simple mathematical analysis. This makes it possible to develop a new method for applying the NC technique in CTSDMs.…”

“…It is proven in Lee et al and Wang and Temes that by using this technique, the new NTF is enhanced as (1 − G ( z )) × NTF old . Although it is difficult to take advantage of this idea in the conventional CTSDMs, in this paper, a new approach is introduced for this technique to make it applicable to the proposed time‐based quantizer.…”

“…The TDC is clocked at the rate of f s , where f s = f Q / N . Applying a double‐sampled DFFs in the TDC gives the possibility of reducing f s as f s = f Q /2 N . The behavioral schematic of the double‐sampled DFF is shown in Figure B.…”

“…The signal‐to‐noise ratio (SNR) within the signal bandwidth of f BW for the TCSDM has been previously developed in Tamaddon and Yavari as where U p is the input signal amplitude, L eff is the effective noise‐shaping order, and OCR is the overcycling ratio defined as f c /2 f BW . The proposed NSQ can be conceived as a time‐based sub‐ADC with the shaping order of L NS .…”

“…If a comparator is located inside an oscillatory closed‐loop system, its associated gain and phase can be calculated through the Barkhausen's criteria. In this case, the SDM works at the limit‐cycle mode . This way, a linearized model may be attributed to the SDM for the sake of a simple mathematical analysis.…”