An investigation into a method of designing insertion loss ladder filters avoiding incompatibilities

摘要

In this thesis Saraga’s design method for insertion loss filters is investigated, and an attempt made to assess its practicality. The basic filter design method (Darlington, Cauer) leads to numerical accuracy problems. Accepted methods for dealing with inaccuracy either replace the independent variable (frequoncy) by the more suitable "z-variable" (Szentirmai, Bingham) or introduce rules for polynomial manipulation based on multiplication in preference to summation (Musson, Norek). In contrast to these approaches, Saraga chooses the dependent variables (network functions) so as to avoid "incompatibilities". Saraga’s method, applicable so far only to symmetrical filters (i.e. of odd degree n), had in the past been investigated only for n=7. In this thesis the mathematical results obtained by Saraga are extended and generalised.ududPractical design tests carried out for n=7 (using artificially introduced inaccuracies to test the power of the method to overcome inaccuracies) are supplemented and extended to n=9. Various ways of comparing the practical results of different methods for overcoming numerical accuracy problems are discussed, and one particular method is chosen: to use the different methods to design the same nominal filter, with the same numerical accuracy which is reduced until one method breaks down. A comparison of Saraga’s method with Szentirmai’s/Bingham’s is carried out (and also with Orchard’s earlier method). The results are not conclusive; other methods of comparison may have to be used and the comparison will have to be applied to other filters (proposals for further work are made). Some programsudDeveloped previously (in a now obsolete language) had to be rewritten and some new filter design programs had to be developed. A sub-program for adjusting the numerical accuracy of any design program to a specified number of significant figures was also developed.