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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

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In this brief, a hardware-accelerated simulation environment for continuous-time (CT) ΣΔ modulators is presented. Due to the presence of the nonlinear quantizer, simulating ΣΔ modulators is a complicated task in general. The simulation of CT modulators is even more time consuming than that of their discrete-time counterparts, due to the analog loop filter. In particular, in an automated design environment, a large number of simulations have to be performed during the design process of ΣΔ modulators. In this brief, it is shown for the first time that the system-level emulation of CT ΣΔ modulators on an fieldprogrammable gate array results in a significant acceleration, reducing the simulation time by a factor of more than 10 5 compared to a commonly used Simulink simulation. This allows simulating 10 000 of modulators per second, enabling the use of heuristic search algorithms for real-time design for CT ΣΔ modulators.

This paper presents how the optimization of continuous-time (CT) Σ∆ modulators by scaling the loop filter coefficients affects the signal transfer function (STF) and in which way the method can be used to reduce peaking in the STF. It is shown that, depending on the initial design, it is possible to define optimized parameter sets with increased performance and remaining flat STF or sets with constant performance and reduced STF peaking. Therefore, the system is first described as switched system to analyse its behaviour in the state space. The different effects of the optimization method on the STF are demonstrated on two example systems with differently designed noise transfer functions (NTF).