Read e-book online Analog Design Centering and Sizing PDF

By Helmut E. Graeb

ISBN-10: 1402060033

ISBN-13: 9781402060038

ISBN-10: 1402060041

ISBN-13: 9781402060045

What you’ll locate here's a attention-grabbing compendium of basic challenge formulations of analog layout centering and sizing. This crucial paintings offers a differentiated wisdom in regards to the projects of analog layout centering and sizing. particularly, worst-case situations are formulated and analyzed. This paintings is correct on the crossing element among approach and layout know-how, and is either reference paintings and textbook for realizing CAD equipment in analog sizing.

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Only that part of the probability density function that corresponds to acceptable values of R and C is given. We can think of the probability density function as a bell-shaped “cake” that describes the variation of the actual parameter vectors due to the manufacturing process. A portion of varying parameter vectors are cut away by the performance specification. An optimal design will lead to a maximum remaining volume of the “cake,” which is equivalent to a maximum parametric yield Ymax . The part of the design process that targets at maximum yield is equally called yield maximization or design centering.

Nxs , are collected in a random vector y of normally distributed, pseudo-uncorrelated vector elements. e. xs ∼ N (xs,0 , C). 13) we obtain: E {xs } = A · E {y} + b = b (54) V {xs } = A · V {y} · AT = A · AT (55) element is represented by a vector of parameter values x. It refers to the stochastic event of an infinitesimal range of values dx around x. 3A sample 44 ANALOG DESIGN CENTERING AND SIZING Comparison of (52) and (53) with (54) and (55) finally yields y ∼ N (0, I) → xs ∼ N (xs,0 , C), C = A · AT (56) xs = A · y + xs,0 (57) y = A−1 · (xs − xs,0 ) (58) Transformation formulas (57) and (58) can be verified by showing that they transform the probability density function of the multivariate standard normal distribution (36) into the probability density function of the general multivariate normal distribution (23) Exercise.

The tolerance region Tr is the intersection of Parameters & Tolerances, Performance & Specification 31 all these halfspaces. Inequalities may be redundant, leaving them out would not alter the tolerance region Tr . The bounding line at the top of Figure 19(b) corresponds to such a redundant inequality. (10) defines a tolerance region that is shaped as an ellipsoid, as illustrated by the ellipse in Figure 19(c). 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.

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Analog Design Centering and Sizing by Helmut E. Graeb


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