On the stability of sigma delta modulators

Hein, S.; Zakhor, Avideh

doi:10.1109/78.224243

Cited by 109 publications

(71 citation statements)

References 25 publications

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“…A Σ∆ algorithm which has such uniform bounds on the "internal state variables" is called "stable" in the electrical engineering literature; see e.g. [13]. We are thus concerned here with establishing the existence of stable Σ∆ schemes of arbitrary order.…”

Section: More Refined Boundsmentioning

confidence: 99%

Approximating a bandlimited function using very coarsely quantized data: A family of stable sigma-delta modulators of arbitrary order

2003

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Section: More Refined Boundsmentioning

confidence: 99%

Approximating a bandlimited function using very coarsely quantized data: A family of stable sigma-delta modulators of arbitrary order

2003

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“…Sobald der Unterschied zwischen der Größe der invarianten Mengen des realen und des idealen Systems für eine festgelegte Amplitude des Eingangssignals zu groß wird, kann der Modulator das Signal nicht mehr richtig verarbeiten. In diesem Fall kann das System nicht dem Eingangssignal folgen und der Quantisierungsfehler wird zu groß, wodurch das SNR abnimmt (Hein and Zakhor, 1993).…”

Section: Maximaler Integratorpegelunclassified

STF Optimierung von single-bit CT ΣΔ Modulatoren basierend auf skalierten Filterkoeffizienten

Widemann

Zorn

Brückner³

et al. 2012

Adv. Radio Sci.

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Abstract. Die vorliegende Arbeit beschäftigt sich mit dem Signalübertragungsverhalten von single-bit continuous-time (CT) ΣΔ Modulatoren. Dabei liegt der Fokus der Untersuchung auf dem Peaking der Signaltransferfunktion (STF). Dieser Effekt kann die Performance und die Stabilität des Gesamtsystems negativ beeinflussen, da bei auftretendem STF-Peaking Signale außerhalb des Signalbands verstärkt werden. In dieser Arbeit wird ein neuer Ansatz zur Reduktion des Peakings vorgestellt, der auf der Optimierung der Systemdynamik basiert. Dabei werden die Filterkoeffizienten des Modulators systematisch angepasst. Anhand eines Beispielsystems wird gezeigt, dass der Ansatz genutzt werden kann, um das Übertragungsverhalten des Modulators abhängig vom Ausgangssystem zu verändern. So kann entweder die Systemsperformance verbessert werden, ohne Peaking in der STF zu erzeugen, oder das STF-Peaking reduziert werden, ohne die Systemperformance stark zu beeinflussen.

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“…The result is further generalized in (Hein and Zakhor, 1993) with different feedback gains. (Wang, 1993) provided state bounds analysis for the third order Δ∑ Modulators.…”

Section: Clipping In a δ∑ Modulatormentioning

confidence: 99%

“…(Zorn, et al, 2013). Such a modification can be referred as the functional scaling method, which does not necessarily maintain the characteristics of the system, but provides trade-off between the SNR performance and stability (Hein and Zakhor, 1993). The functional scaling method is easier to implement than the direct scaling method.…”

Section: Scaling the Input Signalmentioning

confidence: 99%

1-Bit processing based model predictive control for fractionated satellite missions

Bai

2014

Acta Astronautica

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In this thesis, a 1-bit processing based Model Predictive Control (OBMPC) structure is proposed for a fractionated satellite attitude control mission. Despite the appealing advantages of the MPC algorithm towards constrained MIMO control applications, implementing the MPC algorithm onboard a small satellite is certainly challenging due to the limited onboard resources. The proposed design is based on the 1-bit processing concept, which takes advantage of the affine relation between the 1-bit state feedback and multi-bit parameters to implement a multiplier free MPC controller.As multipliers are the major power consumer in online optimization, the OBMPC structure is proven to be more efficient in comparison to the conventional MPC implementation in term of power and circuit complexity. The system is in digital control nature, affected by quantization noise introduced by Δ∑ modulators. The stability issues and practical design criteria are also discussed in this work.Some other aspects are considered in this work to complete the control system. Firstly, the implementation of the OBMPC system relies on the 1-bit state feedbacks. Hence, 1-bit sensing components are needed to implement the OBMPC system. While the ∆∑ modulator based Microelectromechanical systems (MEMS) gyroscope is considered in this work, it is possible to implement this concept into other sensing components.Secondly, as the proposed attitude mission is based on the wireless inter-satellite link (ISL), a state estimator is required. However, conventional state estimators will once again introduce multi-bit signals, and compromise the simple, direct implementation of the OBMPC controller. Therefore, the 1-bit state estimator is also designed in this work to satisfy the requirements of the proposed fractionated attitude control mission.The simulation for the OBMPC is based on a 2U CubeSat model in a fractionated satellite structure, in which the payload and actuators are separated from the controller and controlled via the ISL. Matlab simulations and FPGA implementation based performance analysis shows that the OBMPC is feasible for fractionated satellite missions and is advantageous over the conventional MPC controllers. V VI

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On the stability of sigma delta modulators

Cited by 109 publications

References 25 publications

Approximating a bandlimited function using very coarsely quantized data: A family of stable sigma-delta modulators of arbitrary order

Approximating a bandlimited function using very coarsely quantized data: A family of stable sigma-delta modulators of arbitrary order

STF Optimierung von single-bit CT ΣΔ Modulatoren basierend auf skalierten Filterkoeffizienten

1-Bit processing based model predictive control for fractionated satellite missions

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