By Helmut E. Graeb
What you’ll locate here's a interesting compendium of primary challenge formulations of analog layout centering and sizing. This crucial paintings offers a differentiated wisdom concerning the initiatives of analog layout centering and sizing. particularly, worst-case situations are formulated and analyzed. This paintings is true on the crossing element among method and layout know-how, and is either reference paintings and textbook for figuring out CAD tools in analog sizing.
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Additional info for Analog Design Centering and Sizing
For β = 0, the maximum value of pdfN , given by √2π nxs1·√det C , is obtained at the mean value xs,0 . Increasing values β > 0 determine concentric ellipsoids centered around the mean value xs,0 with increasing value of β and decreasing corresponding value of pdfN . Figure 22(a) illustrates the situation if the two parameters are positively correlated. The major axes of the ellipsoids then have a tilt in the parameter space. Note that the equidensity ellipsoids denote a tolerance region corresponding to (10).
E. a finite set of sample elements, is generated, which is originating from a certain statistical distribution. In the next section, the generation of sample elements from a normal distribution will be described. e. zk ∼ U (0, 1), k = 1, . . , nxs . This step is based on methods to create pseudo-random sequences of real numbers between 0 and 1. This is implemented for instance by a linear feedback shift register, where the XOR operation of several bits is fed back to the input. Another approach is a multiple recursive generator zk = wn /ν, wn := (a1 wn−1 + .
Local variations lead to an increase in the number of statistical parameters that corresponds to the number of transistors in a circuit. In a circuit with 100 transistors for instance there will be one global threshold voltage Vth,glob that affects all transistors equally and 100 local threshold voltages Vth,loc,i , i = 1, . . , 100 that affect each transistor individually and independently from the others. According to the assumptions that global statistical parameters are not correlated with local statistical parameters and that local statistical parameters are not correlated with each other, the covariance matrix has the following structure: xs = xglob xloc , C= Cglob 0 0 Σloc , Σloc = diag(σloc,1 .