BLA-based Design and Analysis of VCO-based Sigma-Delta Modulators (FWOTM823)

Two complementary methods have been developed in the past to design, analyse, and model nonlinear systems: the Describing Functions (DF) and the Best-Linear Approximation (BLA). The DF research started in the sixties. It assumes that the input and output signals are a combination of a constant, one or two sinusoid(s) and/or noise. It results in a powerful framework to describe both autonomous systems (limit cycles) and non-autonomous systems (input-output behaviour). However, the DF does not characterise/analyse the unmodelled residual (the nonlinear distortion) to its full extend. The more recent research on the BLA framework starts from a linear approximation and intensively uses multisine excitations to approximate the linear frequency dynamics of the nonlinear system. Additionally, it characterises the nonlinear distortions. The objective is to develop a uniform theory for the linear approximation of nonlinear (non-)autonomous dynamical systems. The envisioned theory will be able to produce distortion analyses and handle composite signals that combine multisines with a constant, sinusoid(s), or a random excitation. The theoretical results of the developed framework (excitation design, model extraction and analysis methods to get insight into nonlinear systems) will be demonstrated on a large class of nonlinear, autonomous and non-autonomous systems. The VCO-based sigma-delta modulator will serve as a demonstrator and guarantees the development of a uniform framework.

Keywords:modulators, BLA-based design

Disciplines:Optics, electromagnetic theory