A Unified, Integrated Approach to Generalized Circuit Optimization

Abstract

<p>This thesis offers a unified and integrated treatment of three essential aspects of computer-aided circuit design: effective use of the state-of-the-art optimization tools, efficient calculation of exact and approximate gradients, and adequate mathematical representation of the engineering problems.</p> <p>The recent advances in gradient-based ℓp optimization are reviewed. The essence of the trust region Gauss-Newton method and the quasi-Newton solution to optimality equations is described. A new algorithm for linearly constrained one-sided ℓ₁ optimization is presented.</p> <p>Efficient approaches to network sensitivity analysis are addressed. Useful formulas are derived for general multi-ports, especially two-ports. Novel proofs of an important result for lossless two-ports are given.</p> <p>The basic formulations of nominal circuit optimization are introduced through a hierarchy of simulation models. Variables, error functions and ℓp objectives are identified. Optimization of multi-coupled cavity filters is described and illustrated by examples of elliptic, self-equalized and asymmetric designs. Large-scale optimization of multiplexers is also discussed.</p> <p>Realistic consideration of tolerance and uncertainties is of prominent interest to circuit, especially integrated circuit designers. A multi-circuit approach to design centering, tolerancing, tuning and yield enhancement is presented. Techniques for statistical design are reviewed. A generalized ℓp centering algorithm is developed.</p> <p>A novel approach to device modeling which utilizes multiple circuits and exploits the theoretical properties of the ℓp norm is described. It emphasizes the uniqueness and consistency of an equivalent circuit model. Practical applications are formulated and illustrated through industrial examples.</p> <p>A new algorithm for optimization with integrated gradient approximations is offered. Implementations for the minimax and ℓp problems are shown. The efficiency and usefulness are demonstrated by a large variety of examples.</p>