A novel optimization method for CT sigma-delta-modulators using a switched system model

Abstract

This paper presents an approach to analyse the stability of continuous time Σ∆ data converters and shows a new method to define optimized parameter sets without a large number of simulations. Thereby the converter is described as a switched system. The presented analysis is based on a state space description which is utilized to express the properties of a stable behaviour. It is shown how the analysis method can be used to optimize the filter coefficients of the modulator by scaling the integrators outputs

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

“…Dazu wurde zunächst eine Modellierung des Modulators als SwitchedSystem (Zorn et al, 2010) eingeführt, die der Skalierungsmethode (Zorn et al, 2011) (Maeyer et al, 2005). Dadurch wird die Ordnung des STFTiefpassverhaltens beibehalten.…”

“…Daher wird der Modulator in dieser Arbeit als Switched-System (Gonçal-ves et al, 2001) betrachtet. Außerdem wird gezeigt, wie die Optimierungsmethode aus Zorn et al (2011) (Lunze, 2000). Das Schleifenfilter kann daher als ein äquivalentes System mit den Eingangssignalen r(t) und u(t) betrachtet werden, wie es in Abb.…”

STF optimization of 1-bit CT ΣΔ modulators based on scaled loop filter coefficients

“…In [7] it was shown how scaling the components of the MSPs and therewith the loop filter coefficients by a factor ξ < 1 can be used to reduce the overall time of the integrators in saturation. As a result, it was shown that the scaling method can lead to an optimized performance regarding SNR and DR of a Σ∆ modulator.…”

“…Thereby, the kind of improvement is depending on the initial NTF design. In case of a design with a conservative NTF with a flat STF right from the beginning, it was shown in [7] that it is possible to increase the SNR and DR by scaling the filter coefficients. In this case it can be observed that the optimization will just slightly affect the STF.…”

“…Therefore, the modulator will be described as switched system [6] in this paper. Furthermore, we will present how the optimization method [7] can also be use to reduce the STF peaking while the performance of the modulator is nearly not effected. Thereby, the filter coefficients are scaled to reduce the dynamic of the internal states in the state space.…”