A new hybrid method for optimal circuit design using semi-definite programming

Abstract

In this article a new method for yield optimization (design centring) is introduced. The method has a statistical-geometrical nature, hence it is called hybrid. The method exploits the semi-definite programming applications in approximating the feasible region with two bounding ellipsoids. These ellipsoids are obtained using a two phase algorithm. In the first phase, the minimum volume ellipsoid enclosing the feasible region is obtained. The largest ellipsoid that can be inscribed inside the feasible region is obtained in the second phase. The centres of these bounding ellipsoids are used as design centres. In the second phase, an additional polytopic region approximation is constructed. A comparison between the obtained region approximations is given. Saving in the number of circuit simulations needed for yield optimization is also considered. Practical examples are given to show the effectiveness of the new method.

Space mapping surrogate‐based microwave circuit design centering using a new statistical technique

“…Hence, the large computational effort required, in addition to the uncertainty involved in the estimation process, represents an obstacle against the statistical design centering approaches and needs some innovative treatments for such problems. The second approach is classified as a geometric approach [9,13,14,19,[35][36][37][38][39][40][41]. It treats the problem implicitly by finding the center of a body approximating the feasible region, with the assumption that the feasible region is bounded and convex.…”

“…However, as the optimization gets close to the optimum, the methods based on interpolation will be more accurate as expected. This explains why the proposed algorithm is well suited for objective functions that have some uncertainty in their values or subject to statistical variations like the yield function [19,24] given by Eqn (2). Also, the algorithm may be useful for surrogate-based system design [9][10][11].…”

“…Another SM surrogate‐based method having a statistical‐geometrical nature has been introduced in Hassan and Mohamed . The method exploits semidefinite programming and GSM surrogates to approximate the feasible region with two bounding ellipsoids, namely, the minimum volume ellipsoid enclosing the feasible region and the largest ellipsoid that can be inscribed within the feasible region. The centers of these ellipsoids are used as design centers.…”

Microwave systems design centering exploiting space mapping technology and modified trust region algorithm

“…Due to its importance, system design centering has been discussed and developed by many researchers in several publications. [1][2][3][4][5][6][7][8][9][10][11][12][13] Generally, design centering approaches can be categorized into two main classes, namely, geometrical and statistical approaches. For geometrical approaches, the yield function is implicitly optimized by fetching the feasible region center and use it to approximate the design center.…”

“…In this regard, the feasible region could be approximated by a convex body, eg, hyper-sphere, a hypercube or a hyperellipsoid, then use the center of this body as the design center. 1,[5][6][7][8][9][10]12 On the other hand, statistical approaches utilize statistical analysis approaches to explicitly optimize the yield function with no restrictions on the problem size. [1][2][3][4]11 In general, yield function value at a given nominal parameter values could be estimated by generating a set of sample points in the design parameter space using a predefined probability distribution of the system parameters.…”