Electrical Engineering and Systems Science > Systems and Control
[Submitted on 5 Mar 2024 (v1), last revised 7 Mar 2024 (this version, v2)]
Title:Faithful Dynamic Timing Analysis of Digital Circuits Using Continuous Thresholded Mode-Switched ODEs
View PDF HTML (experimental)Abstract:Thresholded hybrid systems are restricted dynamical systems, where the current mode, and hence the ODE system describing its behavior, is solely determined by externally supplied digital input signals and where the only output signals are digital ones generated by comparing an internal state variable to a threshold value. An attractive feature of such systems is easy composition, which is facilitated by their purely digital interface. A particularly promising application domain of thresholded hybrid systems is digital integrated circuits: Modern digital circuit design considers them as a composition of Millions and even Billions of elementary logic gates, like inverters, GOR and Gand. Since every such logic gate is eventually implemented as an electronic circuit, however, which exhibits a behavior that is governed by some ODE system, thresholded hybrid systems are ideally suited for making the transition from the analog to the digital world rigorous.
In this paper, we prove that the mapping from digital input signals to digital output signals is continuous for a large class of thresholded hybrid systems. Moreover, we show that, under some mild conditions regarding causality, this continuity also continues to hold for arbitrary compositions, which in turn guarantees that the composition faithfully captures the analog reality. By applying our generic results to some recently developed thresholded hybrid gate models, both for single-input single-output gates like inverters and for a two-input CMOS NOR gate, we show that they are continuous. Moreover, we provide a novel thresholded hybrid model for the two-input NOR gate, which is not only continuous but also, unlike the existing one, faithfully models all multi-input switching effects.
Submission history
From: Arman Ferdowsi [view email][v1] Tue, 5 Mar 2024 07:50:58 UTC (1,586 KB)
[v2] Thu, 7 Mar 2024 07:53:25 UTC (1,389 KB)
Current browse context:
eess.SY
References & Citations
Bibliographic and Citation Tools
Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)
Code, Data and Media Associated with this Article
alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)
Demos
Recommenders and Search Tools
Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.