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 concerning the projects of analog layout centering and sizing. specifically, worst-case situations are formulated and analyzed. This paintings is true on the crossing aspect among method and layout expertise, and is either reference paintings and textbook for realizing CAD tools in analog sizing.
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Additional info for Analog Design Centering and Sizing
Elementary RC circuit with performance features time constant τ and area A as a function of resistor value R and capacitor value C. 2 ANALOG DESIGN CENTERING AND SIZING Performance Evaluation The right side of Figure 14 displays the performance functions of the RC circuit. e. e. the resistor value R and the capacitor value C, can be explicitly evaluated in this case. 11). Please note that the RC circuit is a linear circuit because it consists of linear circuit elements, as opposed to nonlinear circuit elements like transistors.
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 . σk xs,k , xs,l . For the variance, we have: ⎤ k,l σl (28) 1,nsx σnxs ..
The circuit operating conditions usually are a part of the circuit specification, but as the operating quantities are parameters, this part of the specification is categorized as parameter tolerances within the numerical-simulation-based sizing process. 2 Parameter Tolerances We distinguish two types of parameter tolerances, parameter ranges and parameter distributions. Correspondingly, we have defined range parameters and statistical parameters. Typical examples of parameter tolerances and the essential sources of IC performance variation are the manufacturing fluctuations and the operating conditions.