Calculating transfer functions of CT sigma-delta modulators with arbitrary DAC waveforms

Brückner, Timon; Kiebler, Martin; Lorenz, Matthias; Zorn, Christoph; Mathis, Wolfgang; Ortmanns, Maurits

doi:10.1109/iscas.2013.6572083

Cited by 9 publications

(6 citation statements)

References 7 publications

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“…Compared with the DT SDMs, it is a demanding task to calculate the NTF in CTSDMs. 5 Some generalized approaches in the context of automated control systems have been already developed to introduce a semilinear model for the comparator-based closed-loop systems. Describing function (DF), the frequently used method, is a simple approach that can provide sufficiently accurate estimations of the frequency and amplitude of a possible periodic oscillation.…”

Section: Discussionmentioning

confidence: 99%

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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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Section: Discussionmentioning

confidence: 99%

“…On the other hand, calculating the NTF is required to use the NC approach in conventional CTSDMs. Compared with the DT SDMs, it is a demanding task to calculate the NTF in CTSDMs …”

Section: Introductionmentioning

confidence: 99%

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

Tamaddon

Yavari

2017

Circuit Theory & Apps

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“…For this purpose, in [7] the lifting method is used [8]. In [9] CT SDMs with arbitrary feedback digital-to-analog converters (DACs) and the CT filter function H CT (s) including non-idealitiessuch as finite DC gain and GBW -can be transformed by the lifting method to a DT filter H(z). The analytically derived, equivalent DT model behaves exactly as the CT model at the sampling instants and serves as basis for the incremental NTF in the same way as the filter of a genuine DT ADC.…”

Section: A Lifting Methods For Ct I-sd Adcsmentioning

confidence: 99%

Performance Evaluation of Incremental Sigma-Delta ADCs Based on their NTF

Wagner

Vogelmann

Ortmanns

2020

IEEE Trans. Circuits Syst. II

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In this paper the performance of I-SD ADCs based on the spectral description is discussed. It is based on the modulator and the reconstruction filter and accounts for the applied reset. The definition of the overall noise transfer function (NTF) enables the analysis of the performance of I-SD ADCs in frequency domain and consequently makes it possible to explain the inherent behavior of this type of ADC including reconstruction filter and non-idealities. In the state of the art, the performance of an I-SD ADC is either obtained by simulations or predicted via time-domain considerations. However, these simulations can become time consuming and time-domain considerations neglect non-idealities, especially in the case of a CT modulator. Only recently, a general way to describe the NTF of DT and CT I-SD ADCs was introduced. This work gives a detailed analysis of the NTF of I-SD ADCs and the impact of its properties on the resulting SQNR. It discusses the influence of common reconstruction filters and based on this analysis, it introduces as an example a modified CoI filter that allows to improve the ADC's performance.

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“…Therefore, it is also an accurate method to simulate a CT modulator with the high speed solvers of its DT counterpart. Finally, in [11] it was shown that the lifting method can be utilized to obtain the NTF and STF of freely running CT SDMs including arbitrary DAC feedback waveforms and non-ideal loopfilter behavior -which is shortly reviewed in the following as reference.…”

Section: A Lifting Methods For Freely Running Sdmsmentioning

confidence: 99%

“…The function H DTn (z) accounts for the non-delayed signal part in the current clock cycle, whereas the delayed function H DTn−1 (z) accounts for the signal part that is shifted into the next clock cycle by ELD. A more detailed description of how lifting is used to calculate the STF on non-ideal CT loopfilters can be found in [11]. With the equivalent DT filter H(z) in (13), the NTF of the freely running CT modulator can be expressed by…”

Section: A Lifting Methods For Freely Running Sdmsmentioning

confidence: 99%

On the Signal Filtering Property of CT Incremental Sigma–Delta ADCs

Wagner

Vogelmann

Ortmanns

2019

IEEE Trans. Circuits Syst. II

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In this paper the calculation of the signal behavior and the achievable signal-to-quantization-noise ratio of continuous-time (CT) incremental Sigma-Delta (I-SD) ADCs is described. The presented method allows for the analysis of I-SD ADCs in frequency domain including the specific non-idealities of the CT modulator. In the state of the art, it is described that the omission of the preceding sample-and-hold for the I-SD ADC alters the transfer characteristic compared to a Nyquistrate converter. So far, for CT I-SD ADCs this behavior is only investigated via simulations. In this work the model of a discretetime I-SD ADC is generalized and adapted for the CT case. This allows to analytically obtain the signal and noise transfer function of the I-SD ADC in frequency domain in combination with arbitrary reconstruction filters due to the utilization of the lifting method in a fast and accurate way.

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Calculating transfer functions of CT sigma-delta modulators with arbitrary DAC waveforms

Cited by 9 publications

References 7 publications

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

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

Performance Evaluation of Incremental Sigma-Delta ADCs Based on their NTF

On the Signal Filtering Property of CT Incremental Sigma–Delta ADCs

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