Nabawi, Asim Adbul-Fattah
(1980)
Frequency-domain analysis and optimisation of linear networks.
*University of Southampton, Doctoral Thesis*.

## Abstract

The objective of the research conducted in this thesis is the development of a package for computer-aided frequency-domain analysis and optimisation of large-scale linear electrical networks on a small interactive computer. To enable the implementation of such a package on asmall machine, and for efficient analysis, the network under consideration must be described in terms of nested subnetworks. In this case the required network analysis may be carried in a hierarchical fashion; starting with the smallest (or deepest) subnetwork and ending with the whole given network. The calculation of the admittance parameters of the equivalent three-pole of each de-nested subnetwork is central to the scheme. This is achieved in an efficient manner by using a suitable partitioning strategy whereupon an L-U factorisation technique, with its attendant forward and backward substitutions, is used to solve for the required admittance parameters. From these admittance parameters many other network functions are readily derived. The other possible analysis using the present package is the first-order linear network sensitivity analysis. A new scheme to allow this analysis to be carried out for networks including nested subnetworks is described. This scheme relies, for its efficiency, on the results of the a.c. analysis using the L-U factorisation technique, and on the use of the adjoint network concept. The implementations of this integrated scheme of analyses proved it to be both efficient and reliable optimisation of this category of networks to voltage-gain Modulus and/or Phase output specifications is carried out using an existing nonlinear programming algorithm. An appropriate transformation of design variables enables the use of an unconstrained minimisation of a least-square type of error function, to solve the optimisation problem. The user is allowed to define the performance specifications either as an upper and lower bound, or as a spot-on value, at each frequency point of interest. Since the use of gradient information enhances the speed of convergence of the minimisation process, the analyses algorithm in our package calculates the gradient vector and passes this information to the optimisation routine. From this gradient information, the latter calculates an initial estimate of the Hessian matrix. Several examples of network simulation and optimisation are introduced to demonstrate both the capababilities and efficiency of the package.

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