# analog design size tuning

Design parameters must be appropriately changed to meet the new design specifications. The design specifications should be considered here in a wide sense, including restrictions on the performance of a circuit, and/or design objectives. The meaning of these two terms is clear if we consider, for example, an amplifier whose specifications could be: DC-gain > 70dB; gainbandwidth product > 5MHz; phase margin > 60degrees; input-equivalent noise < 3mV, with minimum power consumption and occupation area. Restrictions are those specifications that include inequalities, and objectives those whose intention is to maximize or to minimize some figure. Observe that the definition of the specifications introduces a character of subordination of the objectives in respect to the restrictions that must be considered in the formulation of the sizing problem. We will denote acceptability regions those within the multidimensional design space where all design restrictions are met. Basically two kinds of approaches have been formulated to the sizing problem: knowledge-based and optimization-based. Knowledge-based approaches capture designers´ expertise in the form of some kind of design plans . Knowledge addition is a costly effort, necessary for each particular circuit and not always reusable. Optimization-based approaches have become much more popular . They formulate circuit sizing as a constrained optimization problem. There are basically two alternatives for the implementation of the iterative process: • Deterministic incremental techniques, where updating requires information on the cost function and on their derivatives. An important disadvantage is that only changes of design parameters that make the value of the cost function decrease are permitted − the optimization process is quickly trapped in a local minimum of the cost function, so the utility of these techniques concentrates on the fine tuning of suboptimal sizings. • Statistical techniques, where design parameters are varied randomly and hence it does not require information on the derivatives of the cost function. The main advantage of the statistical techniques in respect to the deterministic ones is the capability to escape from local minima, thanks to a nonzero probability of accepting movements that increase the cost function. The price to pay is a larger computational cost.

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