Novel Analysis and Synthesis Toolbox for Noise Characterization of Coupled Oscillator Systems

• Applicant: Professor Dr.-Ing. Viktor Krozer, Ph.D.
• Subject Area: Communication Technology and Networks, High-Frequency Technology and Photonic Systems, Signal Processing and Machine Learning for Information Technology ; Electronic Semiconductors, Components and Circuits, Integrated Systems, Sensor Technology, Theoretical Electrical Engineering
• Term: since 2019
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 423744006

Oscillatory behavior and noise properties of complex networks abounds on all scales and in a myriad of scientific areas. Modelling these complex, highly nonlinear networks is an inherently difficult task, especially when noise is involved in the study. Of special importance is the modelling of oscillator phase-dynamics. In free-running oscillating systems the concept of oscillator phase and amplitude is clear and well-defined geometrically and the resulting mathematical description is referred to as a phase-macro model (PMM). We have been at the forefront of this development. Free-running and coupled oscillating systems belong to the same class of dynamical systems, however, the PMM framework is not applicable to the coupled scenario and is hence incomplete. The knowledge on how to extend the original single-oscillator PMM methodology was limited due involvement of various mathematical approaches such as e.g. differential geometry, hyperbolic manifold theory, stochastic integration and linear algebra. Further, Perturbation Projection Vector/Impulse Sensitivity Function (PPV/ISF) analysis/synthesis tools are among the most influential and impactful ideas proposed in the field of single oscillator noise analysis over the past coupled decades. In our previous DFG project, we have proposed the novel PMM-C methodology, which represents the first unified description of amplitude/phase linear-response of both single and coupled oscillator systems in one closed expression. The PMM-C framework represents the first unified and physically complete (i.e. non-empirical, coordinate independent etc.) model representation of coupled oscillator response including noise. Using the PMM-C we are now in the unique position of being able to extend the PPV/ISF tools to the regime of coupled oscillators, involving coupled oscillator ensembles perturbed by noise. Examples include noise-modelling of super-/sub-harmonic injection-locked oscillator circuits and synthesis of optimal noise performance in coupled THz oscillator arrays. In addition, we have also introduced the novel SYM-OFD methodology demonstrating minimized phase-noise operation based on symmetry properties of steady-state solutions. This newly discovered phenomenon has been verified in several simulation trials. Our aim with this proposal is to leverage the novel SYM-OFD methodology in order to implement an entirely new class of algorithms capable of locating zero AM-PM points in the parameter space of a (coupled) oscillator system. These new simulation tools will introduce an entirely novel approach to minimization of coupled oscillator noise response and represent a breakthrough in modelling, analysis and numerical simulation of single and coupled oscillating systems. Both the PMM-C and SYM-OFD frameworks constitute paradigm shifts within their respective fields. We plan to implement these theoretical results into a novel CAD simulation framework and validate all results experimentally.

• DFG Programme: Research Grants