Large analog circuit models are very expensive to evaluate and verify. New techniques are needed to shorten timeto-market and to reduce the cost of producing a correct analog integrated circuit. Model order reduction is an approach used to reduce the computational complexity of the mathematical model of a dynamical system, while capturing its main features. This technique can be used to reduce an analog circuit model while retaining its realistic behavior. In this paper, we present an approach to model order reduction of nonlinear analog circuits. We model the circuit using fuzzy differential equations and use qualitative simulation and K-means clustering to discretion efficiently its state space. Moreover, we use a conformance checking approach to refine model order reduction steps and guarantee simulation acceleration and accuracy. In order to illustrate the effectiveness of our method, we applied it to a transmission line with nonlinear diodes and a large nonlinear ring oscillator circuit. Experimental results show that our reduced models are more than one order of magnitude faster and accurate when compared to existing methods.
Analog and mixed signal (AMS) designs are important integrated circuits that are usually needed at the interface between the electronic system and the real world. Recently, several formal techniques have been introduced for AMS verification. In this paper, we propose a difference equations based bounded model checking approach for AMS systems. We define model checking using a combined system of difference equations for both the analog and digital parts, where the state space exploration algorithm is handled with Taylor approximations over interval domains. We illustrate our approach on the verification of several AMS designs including ∆Σ modulator and oscillator circuits.
Abstract-We model and verify analog designs in the presence of noise and process variation using an automated theorem prover, MetiTarski. Due to the statistical nature of noise, we propose to use stochastic differential equations (SDE) to model the designs. We find a closed form solution for the SDEs, then integrate the device variation due to the 0.18µm fabrication process and verify properties using MetiTarski. We illustrate the proposed approach on an inverting Op-Amp Integrator and a Band-Gap reference bias circuit.
Problem statement: Oil refineries are widely used to store various liquids and gases. Petroleum products are in high demand. Oil companies have abundant resources of petroleum products in pipelines and storage tanks. Approach: Included are storage tanks at retail gasoline station, home heating oil tanks, lubricant storage at automotive service facilities, propane tanks in all sorts of application, and oil company terminals across the world. The aim of this study is to present a model by which a decision maker should be able to choose the optimal number of tanks, tank size and truck arrival rate to maximize average total profit per week for an oil terminal operation. Results: In this study, oil terminal modeled by using a discrete event simulation program Arena for AL-Dura refinery, Baghdad, Iraq. Multifactor variance analysis is used to determine different levels of the three factors and their interactions significantly affect the terminal profit including the optimal number of tanks, size of tanks and trucks of the arrival rate to maximize total revenue on average per week. Conclusion/Recommendations: The result showed minimum cost of oil at the terminal and tanker truck fill rates and price and income structure, also predict with 90% confidence levels, a number of factors, which gives highest average total income per week
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