Microwave Filter Design
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3.0 Literature Review
The discipline of filter theory is complicated, with a solid mathematical basis, and has
extensive literature dedicated to describing the numerous alternative approaches and
methods that can be implemented to realise particular filter functions. The derivation
and description of exact methods for filter synthesis goes back to the 1960’s and
1970’s. The papers published during and since this time are often hard to follow, and
therefore apply, and present a lot of high level maths very briefly. Additionally, few
have taken their work from the abstract theory stage to the actual filter physical design
of the filter. This combined with the often different approaches each author has to
similar processes makes the overall area somewhat incoherent.
Darlington, in 1939 developed the basic process of filter synthesis [4], and Cauer[5]
firstly identified the important filtering properties to produce optimum filters.
Cohn[6] developed the coupled-cavity structure for waveguide filters to realise a
physical filter at microwave frequencies. Reiter[7] outlined an equivalent circuit to
describe the physical structure and since this time there have been numerous articles
published on methods developed to solve this structure. J.D Rhodes [8,9], A.E Atia
and A.E. Williams[10,11], Dishal [12], Alseyab [13] are key figures responsible for
much of the literature on filter synthesis since 1950. Many of the methods described
use improved mathematical techniques to implement the Darlington synthesis method,
described in the 1939 paper [4]. The articles are written for other experts in the field,
and presume a solid background and understanding of the theory. The theory outlined
briefly in these papers is detailed in several books, two of the most useful references
being ‘Microwave Filters, Impedance Matching Networks and Coupling Structures’
(Matthaei,Young and Jones [14]), and ‘Introduction to Modern Network Synthesis’
(Valkenburg [15] ).
A reasonable summary and adaptation of the synthesis methods developed over the
last 40 years is a paper by Richard Cameron ‘General Coupling Matrix Synthesis
Methods for Chebyshev Filtering Functions’[1]. His paper offers a generalised
approach of the current technique of generating transfer polynomials and solving for
the filter function. The paper effectively follows the Darlington procedure combined