W orst Case Analysis of Resistive Networks Using Linear Programming Approach zyxwvutsrqponmlkjihgfed by MONA ELWAKKAD ZAGHLOUL Department of Electrical Engineering and Computer Science, The George Washington University, Washington, D.C., U.S.A. ABSTRACT : It zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA is shown thatfor DC networks in which certain components are allowed to vary, the worst case DC problem can be solved by solving a linear programming problem. The constraints used in the linear programming problem are determinedfrom the elements tolerance regions. This enables us to obtain the worst case solution without having to compute the gradient of the network functions. I. Introduction In the design of electronic circuits the characteristics of some or all of the circuit components vary due to thermal, chemical or optical processes used in the environment. In these situations, we may assume that the actual physical behavior of the elements in the electronic circuit lie within some given tolerance region. These element tolerance regions then translate into some solution tolerance regions. This means that for certain networks, given that the parameter values lie within a certain range, it is necessary to determine the worst case values of certain response functions in the network. This problem is of considerable recent interest because of its importance to the design of integrated circuits. The worst case tolerance optimization problems in electronic circuits have been studied by various authors where several algorithms were proposed. Each of these algorithms has its advantages and disadvantages. Recently new algorithms for the zero tolerance problem (ZTP), the worst case problem (WCP), the fixed tolerance problem (FTP), and the variable tolerance problem (VTP) have been presented (l), where the applications of the interval arithmetic, linear programming techniques and other alternative optimization methods were suggested. The basic properties of these algorithms were studied and simple examples displayed. In all of these algorithms, the gradients of the circuit functions are to be calculated for each step of the optimization process, which is a costly procedure. In another technique (Z), the worst case DC problem has been solved by the use of inverses of convex sets of real matrices. Using this technique, the problem was solved by solving 2” sets of equations which represent the two extreme points associated with each of the n elements that are varying in the circuit. Although the results in (2) can be useful for networks with few elements, its usefulness becomes doubtful as n becomes very large. In this paper we use linear programming techniques to compute the worst case problem. The principle used is to start from the component’s assumed known zyxwvutsrqpo 0 The Franklin Institute 0016-0032/83 $3.00+0 00 339