By Helmut E. Graeb
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 concerning the projects of analog layout centering and sizing. particularly, worst-case eventualities are formulated and analyzed. This paintings is correct on the crossing aspect among strategy and layout know-how, and is either reference paintings and textbook for figuring out CAD equipment in analog sizing.
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Extra resources for Analog Design Centering and Sizing
Nxs of the individual parameters xs,k , k = 1, . . , nxs , and by the mutual correlations k,l , k, l = 1, . . , nxs , k = l, between parameters xs,k and xs,l in the following way: C = Σ·R·Σ (26) 36 ANALOG DESIGN CENTERING AND SIZING ⎡ σ1 0 ⎢ ⎢ 0 Σ = ⎢ . ⎣ .. 0 ⎡ ⎢ ⎢ R = ⎢ ⎣ σ2 . 0 1 1,2 2,1 1 .. σ12 ⎥ ⎥ ⎥ ⎦ 0 ... σ1 (27) σnxs .. ⎢ σ1 ⎢ σ C = ⎢ 2 2,1 .. ⎣ . nxs ,1 ⎤ 0 .. .. nxs ,1 ⎡ ... 1,nxs .. . nxs −1,nxs nxs ,nxs −1 1 1,2 σ2 ... σ22 .. ⎥ ⎥ ⎥ ⎦ σ1 . σnxs −1 nxs ,nxs −1 σk2 is the variance of parameter xs,k .
They lead to different behaviors of transistors in a circuit, a so-called mismatch. But analog circuits are formed of transistor pairs like current mirrors requiring an identical behavior of the transistors in a pair and are therefore very sensitive to mismatch. Local variations have always been an issue in analog design. But as the device dimensions become smaller and smaller, the significance of local variations compared to global variations grows critical for digital circuits as well. The statistical variation of critical paths’ delays for instance are strongly depending on the local and global process variations and their effect on the correlation of gate delays.
Range parameters xr = [xr,1 . . xr,k . . xr,nxr ]T ∈ Rnxr are parameters that are subject to a range of values they can acquire. Typical examples of range parameters are so-called operating parameters that model operating conditions, as for instance supply voltage or temperature. Range parameters differ from statistical parameters in that they do not have probability data in form of statistical distributions on top of their given ranges of values. For the temperature for instance, a range of -40◦ C to 125◦ C can be specified.
Analog Design Centering and Sizing by Helmut E. Graeb
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