FUNCTIONAL NETWORK ANALYSIS AND SYNTHESIS.
Abstract
The primary motivation for this research has been to obtain analysis and synthesis methods for time-varying networks through functional techniques. The original attempts were to generalize Mikusinski's operational calculus to a form usable for time-varying networks. Although this still seems possible, these attempts led to investigations of zero-divisors (in an algebra based upon Volterra composition), which in turn led to the discovery of a time-variable scattering matrix. This research has shown that every linear, passive, solvablenetwork has such a scattering matrix, s(t, tau), and several of the key properties have been obtained. Since the scattering matrix for a lossless network takes a particularly interesting form (the adjoint is an inverse) and since the synthesis of lossless networks seems to form the foundation for the synthesis of all networks, lossless networks have received particular study. Much of the theory holds for very general networks, but when the network is described by ordinary differential equations (KTHAT IS, FINITE, LUMPED NETWORKS) then it is possible to describe the network by an equivalent in terms of time-invariant resistors, inductors and capacitors and time-varying transformers and gyrators. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 28, 1963
- Accession Number
- AD0424272
Entities
People
- D. A. Spaulding
- R. W. Newcomb
Organizations
- Stanford University