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

2. 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

3. 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

4. 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

5. 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