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

Abstract

Summary In this paper, a new type of an oscillatory noise‐shaped quantizer (NSQ) for time‐based continuous‐time sigma‐delta modulators is presented. The proposed NSQ is composed of an oscillatory voltage‐to‐time converter and a polyphase sampler. Using Tustin's transformation method and through the approximation of the comparator gain, a linearized model of the NSQ is introduced. This way, a novel realization of the first‐ and second‐order NSQ is presented. Its implementation is based on fully passive continuous‐time filters without needing any amplifier or power consuming element. The ploy‐phase sampler inside the NSQ is based on the combination of a time‐to‐digital and a digital‐to‐time converter. The layout of the proposed NSQ is provided in Taiwan Semiconductor Manufacturing Company 0.18 μm complementary metal‐oxide‐semiconductor 1P6M technology. The verification of the proposed NSQ is done via investigating both the system level and postlayout simulation results. Leveraging the proposed NSQ in an Lth‐order time‐based continuous‐time sigma‐delta modulator enhances the noise‐shaping order up to L + 2, confirming its superior effectiveness. This makes it possible to design high performance and wideband continuous‐time SDMs with low power consumption and relaxed design complexity.

Analysis and design of an asynchronous pulse‐width modulation technique for switch mode power supply

“…ω c ≃ π/2T d ). Also, regarding to (1) and representing the delay unit with the Tustin's approximation, e −sT d ≃ 2 − sT d / 2 + sT d [22], the comparator gain k cmp is determined as (5) and (6) for first-order and second-order loop filters, respectively…”

“…However, this may be done at the expense of reducing the spurious-free dynamic range of the modulator. A conventional method for investigating this issue is to analyse the amplitude of the harmonics in the output signal as a function of the Bessel coefficients [20][21][22]31]. Another method, which is usually used in the class-D amplifiers, is to examine the effect of the carrier signal mean value fluctuations on the modulator [17].…”

“…It is worth mentioning that the average switching frequency of the modulators has been derived based on Section 3 explanation. According to this derivation, the ratio of the average frequency BAPWM to the average frequency HAPWM is given by (21) and (22) for first-and second-loop filter configuration, respectively f sw1, BAPWM f sw1, HAPWM = 4gT…”

“…The APWM structure, actually Hysteretic comparator based Asynchronous Pulse Width Modulation (HAPWM) here, is very similar to an asynchronous SDM. It is a good candidate to achieve high-frequency operation to generate high-precision single-bit signals without producing the quantisation noise [5,[16][17][18][19][20][21][22]. Eliminating the requirement for a high-quality carrier generator (sawtooth signal), this architecture provides a low-cost implementation [18][19][20][21][22][23][24].…”

“…It is a good candidate to achieve high‐frequency operation to generate high‐precision single‐bit signals without producing the quantisation noise [5, 16–22]. Eliminating the requirement for a high‐quality carrier generator (sawtooth signal), this architecture provides a low‐cost implementation [18–24]. For this attractive feature, the APWM modulators have attracted a lot of attention.…”