By Helmut E. Graeb
What you’ll locate here's a attention-grabbing compendium of primary challenge formulations of analog layout centering and sizing. This crucial paintings presents a differentiated wisdom in regards to the initiatives of analog layout centering and sizing. particularly, worst-case situations are formulated and analyzed. This paintings is true on the crossing aspect among procedure and layout know-how, and is either reference paintings and textbook for realizing CAD tools in analog sizing.
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4 that the level curves of a Gaussian probability density function are ellipsoids. If the shape of a parameter region corresponds to the shape of the level contours of a probability density function, we are able to complement the parameter region with probability values for the occurrence. In this way, we allow a transition between range parameters and statistical parameters. (11), illustrated by Figure 19(d), finally provides the most general description of a nonlinear tolerance region described by single nonlinear inequalities, ϕnonlin,µ (xr ) ≥ 0, as nonlinear bounding surfaces, as indicated by the dashed line in Figure 19(d).
These dynamic variations during operation may also be larger or smaller, depending on the quality of the actual IC. Operating conditions are usually modeled as intervals of range parameters. Manufacturing fluctuations are modeled as statistical parameter distributions on the regarded design level. The calculation of the statistical parameter distribution is a difficult task that requires specific optimization algorithms and the consistent combination of measurements that belong to different design levels and design views [40, 29, 109, 87, 98].
It shows the typical bell shape of the probability density function of two parameters and the quadratic form of the equidensity contours determined by (24). The matrix C denotes the variance/covariance matrix, or covariance matrix, of the parameter vector xs . 5) that originates from a normal distribution with mean value xs,0 and covariance matrix C is also denoted as: xs ∼ N (xs,0 , C) (25) The covariance matrix C is formed by the standard deviations σk , k = 1, . . , nxs of the individual parameters xs,k , k = 1, .