An unconstrained nonlinear programming approach to design centering

An algorithm for design centering linear electic networks with fixed tolerances is descibed. By assuming a linear relationship between the statistical deviations of the component values and the circuit response, an objective function based on failure probabilities ¿ the probabilities of violating specifications at the individual frequencies ¿ is introduced. The objective function is minimised by unconstrained optimisation in a least-squares or minimax sense. Although applications of the method at present are limited to problems where the errors introduced by the above linear relationship are reasonably small, the method has several advantages which rely on its deterministic foundation. For instance, it is easy to implement facilities which enable the designer to consider tracking variables and constrain toleranced variables not to change value during optimisation. Examples demonstrate applications of the method to small as well as large circuits, and, finally, proposals for improvement of the method are considered.