TOPOLOGICAL FORMULAE FOR SENSITIVITY COEFFICIENTS OF NETWORK FUNCTIONS

Abstract

This chapter focuses on topological formulae for sensitivity coefficients of network functions. Sensitivity coefficients play an important role in the analysis of dynamical accuracy of networks. They are related to network functions determined under open-circuit or short-circuit conditions at some terminal pairs. Knowledge of network open-circuit or short-circuit functions is essential for the evaluation of sensitivity coefficients. The chapter presents the application of graph theory to the evaluation of sensitivity coefficients of network functions. It also discusses the derivation of sensitivity coefficients for the function of a 3-terminal-pair network with respect to variations of one imittance in terms of open-circuit impedance functions. The sensitivity coefficients are then expressed in terms of determinant and cofactors of the original network from which 3-terminal-pair network was derived. Finally, the determinant and cofactors are expressed topologically, first for ordinary element networks, and then for networks containing both ordinary and multiterminal elements.