Studies in optimisation as an aid to circuit synthesis and design.

This research is broadly concerned with the application of optimisation techniques in the design of lumped, linear, passive, two port networks. In particular it considers the problem where the trial, starting network is remote from any acceptable solution and, possibly, unable to realise the design requirements without substantial topological alterations. The early aims of the research set out to automate these topological modifications using a logical sequence of changes --- an approach initially motivated by the ease with which virtual element sensitivities could be computed. A prerequisite for this type of study was that there existed a reliable optimisation algorithm for integrating into the design process. To meet this need, an on-line Marquardt-Levenberg non-linear least squares algorithm was developed where decisions involving the more nebulous aspects of optimisation could be made at run-time, (eg. linear search qualities, convergence criteria etc). Pole-zero matching was used to study a new network modification process known as the 'generalised growth strategy' and adapted for an on-line environment. A little qualitative progress was made towards an understanding of network modification processes but most of the results concerned the generation of novel network equivalents. Attempts to quantify the notion of problem ill-conditioning and the dangers of variable transformations (used to produce realisable solutions) were also tried. A final study involved the lumped element simulation of a coaxial cable in the frequency domain (1/2MHz-lGHz) where no obvious trial starting network existed. The on-line approach in this instance, proved to be a vital asset --- particularly for allowing run-time changes to the error weighting strategy. The results obtained were impressive but the design approach was difficult to formulate and acted as an aid to the manual design rather than a replacement of it. In conclusion, it was felt that, in the long term, greater consideration should be given to a study of multimodality and non-deterministic processes. In the short term, on-line working is worth further exploitation --- possibly incorporating use of graphical terminals for monitoring frequency characteristics.