Approximation Theory for Filter-Networks

This paper presents a general design theory for filter-networks constructed on the basis of theory of the Abelian Integral. An ideal transmission function is defined to be an Anbelian Integral with the following properties: 1) in given regions , 2) is regular at any given point , and 3) otherwise is a harmonic function. The application of appropriate analytic transformation techniques to leads to a generalized characteristic function . All kinds of realizable transfer functions can be derived by the use of linear transformations of with respect to . Further, this treatise gives the design methods for filter-networks having one or two pass bands, in which they exhibit the Tchebycheff performance. Besides the method is also established to synthesize a reactance band-pass network with the order N using only coils. Three design examples, such that the band-pass filter comprising only 6 coils for and 4 coils for , and the double-pass-band filters with and 4 coils, are described in quite detail. All of the examples have the Tchebycheff performance in their pass bands.