مرکز منطقه ای اطلاع رساني علوم و فناوري

Abstract :

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 $w(\\lambda )$ with the following properties: 1) $\\Re w(\\lambda ) = u(\\lambda ) = A_k$ in given regions $B_k$ , 2) ${u(\\lambda ) - \\log | \\lambda + a_i|}$ is regular at any given point $a_i$ , and 3) otherwise $u(\\lambda )$ is a harmonic function. The application of appropriate analytic transformation techniques to $w(\\lambda )$ leads to a generalized characteristic function $\\phi(\\lambda ))$ . All kinds of realizable transfer functions can be derived by the use of linear transformations of ${\\phi(\\lambda )}^2$ with respect to $\\lambda ^2$ . 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 $[(N - 1)/2]$ coils. Three design examples, such that the band-pass filter comprising only 6 coils for $N = 13$ and 4 coils for $N = 10$ , and the double-pass-band filters with $N = 8$ and 4 coils, are described in quite detail. All of the examples have the Tchebycheff performance in their pass bands.