Analytical Expressions for the Distortion of Asynchronous Sigma–Delta Modulators

Babaie-Fishani, Amir; Keymeulen, Bjorn Van; Rombouts, Pieter

doi:10.1109/tcsii.2013.2268352

Cited by 8 publications

(13 citation statements)

References 12 publications

(31 reference statements)

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“…According to [8], the third harmonic distortion of an ADSM, as in Fig.1 (a), with a loop-filter of F(ω) and an input voltage of v = A sin(µt) is (all voltages normalized to ±1):…”

Section: Previous Theory and Its Limitationsmentioning

confidence: 99%

“…Then, given a schmitt trigger threshold voltage of ±V th we will have ω c = π 2τi·V th . The theory in [8] only applies to a certain category of ASDMs where the schmitt trigger is ideal (has no delay). But in an actual circuit, the schmitt trigger always has a delay, modelled as T D in Fig.…”

Section: Previous Theory and Its Limitationsmentioning

confidence: 99%

“…In this paper we study a very popular form of PWM, known as Asynchronous Sigma Delta Modulation (ASDM), which uses a closed loop with a schmitt-trigger (or a comparator) and a continuous time loop filter. We build forth on our previous work [8] where we have already analyzed the distortion for the case without loop delay. The theory in [8] was an improvement to a prior work by Roza [9].…”

Section: Introductionmentioning

confidence: 99%

“…We build forth on our previous work [8] where we have already analyzed the distortion for the case without loop delay. The theory in [8] was an improvement to a prior work by Roza [9]. Unfortunately in practice, some loop delay (e.g.…”

Section: Introductionmentioning

confidence: 99%

“…to control the PWM carrier frequency. Therefore, here the theory of [8] is generalized to cover the case of a loop with delay as well.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Analyzing distortion in ASDMs with loop delay

Babaie-Fishani

Bock

Rombouts

2014

2014 IEEE International Symposium on Circuits and Systems (ISCAS)

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Abstract-Recently nearly exact expressions for the distortion in a commonly used family of Pulse Width Modulators (PWMs) known as Asynchronous Sigma Delta Modulators (ASDMs) were presented. Such an ASDM consists of a feedback loop with a schmitt-trigger (or a comparator), and a continuous time loop filter. However these previous results are not yet practically applicable because the effect of unavoidable loop delay (e.g. in the schmitt trigger) was not taken into account. Therefore we now present a more general theory that is also valid when there is a nonzero loop delay. A comparison of the resulting equations with computer simulations demonstrated a very good matching, confirming the validness of the theory. This way, a designer can now easily understand the relationship between the loop filter dynamics and the linearity of an ASDM.

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“…According to [8], the third harmonic distortion of an ADSM, as in Fig.1 (a), with a loop-filter of F(ω) and an input voltage of v = A sin(µt) is (all voltages normalized to ±1):…”

Section: Previous Theory and Its Limitationsmentioning

confidence: 99%

Section: Previous Theory and Its Limitationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…to control the PWM carrier frequency. Therefore, here the theory of [8] is generalized to cover the case of a loop with delay as well.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Analyzing distortion in ASDMs with loop delay

Babaie-Fishani

Bock

Rombouts

2014

2014 IEEE International Symposium on Circuits and Systems (ISCAS)

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

Tamaddon

Yavari

2017

Circuit Theory & Apps

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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.

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