Bounding of Signal Levels at Terminations of a Multiconductor Transmission-Line Network

摘要

Starting from the norm concept for vectors and matrices, this report addresses the problem of bounding signal levels at terminations of a multiconductor transmission-line network. The overall network equation is formulated in terms of the combined voltage supervector (a special combination of the voltage and current vectors). Utilizing the scattering and propagation supermatrices for the waves on the transmission-line network and the combined voltage supervector for sources, the BLT equation is used to express the combined voltage supervectors and the voltage and current supervectors at the junctions. The upper and lower bounds for the combined voltage supervector, voltage supervector and current supervector are obtained in terms of the norms of the propagation and scattering supermatrices and the normo f the combined voltage source supervector. Various properties of the propagation and scattering supermatrices are discussed for two cases, namely a uniform section of a multiconductor transmission line and a multiconductor transmission line with a branch. The expersions for upper and lower bounds for combined voltage supervectors and voltage and current supervectors are derived. Various forms of vectors, matrices, supervectors, and supermatrices are also discussed. (Author)