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Prof. D. Zhou UT Dallas Analog Circuits Design Automation 1

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Summary of performance variation Variations can be introduced from manufacture process and operation condition. Foundry usually provides distribution of manufacture process introduced variations. Therefore the MC simulation can use such distribution in the sampling. Variations introduced by operational condition usually need to be modeled. It often is modeled as “white- noise”, such as Vdd fluctuation. Analog Circuits Design Automation 2

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Summary of performance variation In general we need to run large amount of MC samplings to find the upper and lower bound. It is time consuming and in many cases impractical. Corners are widely used to get an estimation of the variation bounds. They can be computed in short time but not accurate. Analog Circuits Design Automation 3

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Summary of performance variation We can use Kharitonov’s theorem to compute the bounds. It can be applied to linear system. It provides the tight bounds when the coefficients in the Kharitoinov’s polynomials are independent with each other. Otherwise it provides a loser bound. We can use optimization method to find the upper and lower bounds. For non-linear system or un-convex function, it gives an estimation of the bound. Not guarantee to be the bound. Analog Circuits Design Automation 4

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Summary of performance variation We have discussed several optimization methods, such as SA, penalty function, GA, multi-start point, and etc. Under the frame of each optimization scheme, user can “modify” those scheme by inserting the property or “experience” related to the concerned problem to speed-up the computation. In the middle term-project, we shall connect the signed homework and apply the discussed issues to an Operational Amplifier. Analog Circuits Design Automation 5

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