Analog circuit start-up behavior analysis : an interval arithmetic based approach
- Analysis of electronic circuit start-up behavior is an interesting problem from both theoretical and practical viewpoints. Although the introduction of ternary logic has effectively solved the problem for digital circuits, we have not seen a similar solution for analog circuits. This work introduces a new method that efficiently solves this problem for small analog circuits. The proposed method treats electronic circuits as non-linear dynamical systems. Particularly, we introduce a novel reformulation of the dynamical systems theory and use this new framework to investigate the relationship between a circuit's start-up behavior and its DC solutions. These theoretical considerations culminate in a rigorous (i.e. non-heuristic) algorithm that effectively reduces the original problem into an equation solving problem. The practical side of our work is concerned with solving the resulting equations. In general, finding the complete solution set of a system of algebraical (i.e. non-differential) equations is an NP-hard problem, but some approaches do work well for certain types of problems. Our method uses an interval arithmetic based branch-and-bound algorithm that is known to be effective for solving equations with smooth non-linearities. We further enhanced this algorithm by incorporating (1) a novel affine relaxation procedure, (2) a graph based constraint propagation technique, and (3) a novel graph-decomposition algorithm to improve the scalability of the proposed method. With these improvements, the proposed method easily handles circuits with dozens of state variables.
|Type of resource
|electronic; electronic resource; remote
|1 online resource.
|Kabak, Mehmet Ozan
|Stanford University, Department of Electrical Engineering.
|Statement of responsibility
|Mehmet Ozan Kabak.
|Submitted to the Department of Electrical Engineering.
|Thesis (Ph.D.)--Stanford University, 2015.
- © 2015 by Mehmet Ozan Kabak
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
Also listed in
Loading usage metrics...