Accession Number : AD0672987

Title :   NETWORK FUNCTION DETERMINATION FROM PARTIAL SPECIFICATION,

Corporate Author : MICHIGAN UNIV ANN ARBOR RADIATION LAB

Personal Author(s) : Braun,Arthur R. ; McMahon,E. Lawrence

Report Date : JUN 1968

Pagination or Media Count : 74

Abstract : In certain problems of network theory the real and imaginary parts of a driving-point impedance function may be independently given in a band of interest leaving its continuations to zero and infinity completely unspecified. By manipulating the Hilbert transforms, relating the real and imaginary parts of a function of a complex variable (p = sigma + j omega) having no poles on the j omega axis or in the right-half plane, this report shows that if the continuations exist they are unique and readily obtained. Three necessary conditions for the existence of the continuations to the given parts (of the driving-point impedance function) are obtained. Further, if these three conditions are satisfied the continuations may be obtained as a Fourier series. Four known impedances were used as examples and their continuations determined. The results obtained were excellent. The agreement between the Fourier series solution (using the first six terms at most) and the exact expression was good up to the second significant figure. In the appendix a computer program which obtains the Fourier coefficients of the unknown continuations, from the given real and imaginary parts, is furnished. (Author)

Descriptors :   (*RADAR CROSS SECTIONS, ELECTRICAL IMPEDANCE), (*ELECTRICAL NETWORKS, *ELECTRICAL IMPEDANCE), RADAR REFLECTORS, INTEGRAL TRANSFORMS, FOURIER ANALYSIS, CORRELATION TECHNIQUES, COMPLEX VARIABLES, COMPUTER PROGRAMS, SERIES(MATHEMATICS)

Subject Categories : Electrical and Electronic Equipment
      Active & Passive Radar Detection & Equipment

Distribution Statement : APPROVED FOR PUBLIC RELEASE