The theory of two-port three-terminal lumped linear RC networks has not yet been fully explored. In particular, there are no general 'necessary and sufficient' conditions for network synthesis, nor standard synthesis techniques for 'non-series-parallel' topologies. By using a digital computer and a technique of coefficient matching, allied with an optimisation routine, 'non-series-parallel' topologies can be synthesised as readily as 'series-parallel' topologies. Coefficient matching involves the construction of individual error functions, to measure the departure of the coefficients required from those currently achieved. The effect of modifying the method of function representation is investigated and it is demonstrated that for the best method the efficiency of the optimisation algorithm is greatly improved. The properties of closed form expressions for the normalising variable are examined. The network topology may require alteration as part of the design process. Criteria for the removal and addition of elements are discussed and their implementation in a computer program for network design without user interaction is described. The effectiveness of the approach is illustrated by the synthesis of a new 'non-series-parallel' network. Only one 'non-series-parallel' network with no 'series-parallel' equivalent has previously been published. It is demonstrated that there are many equivalent realizations with different topologies. The existence of 'non-series-parallel' networks, with no 'series- parallel' equivalents, containing as few as nine elements is verified. Analytical techniques for synthesising 'non-series-parallel.' networks must be developed before 'necessary and sufficient' conditions for all sets of admittance functions can be obtained. The properties of admittance functions with two finite poles are discussed. Several useful topological theorems are derived. Two simple 'non-series-parallel' networks are analysed, and their element values are obtained as expressions in terms of the residues at the poles of the required admittance functions. The existence of many other possible realizations is demonstrated by the use of equivalence transformations.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:737263 |
| Date | January 1976 |
| Creators | Krzeczkowski, A. J. |
| Publisher | University of Leicester |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://hdl.handle.net/2381/34792 |
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