NETWORK FUNCTION DETERMINATION FROM PARTIAL SPECIFICATION,
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1968
- Accession Number
- AD0672987
Entities
People
- Arthur R. Braun
- E. Lawrence Mcmahon
Organizations
- University of Michigan