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We show that under certain conditions the wave variables ai(t) incident on a frequency independent N-port junction in a passive network satisfy the inner product relation:Â¿Nj = 1 Â¿Nk = 1k Â¿ jÂ¿SijajSikak = 0 i = 1,2..,N where Sij are the scattering parameters of the junction. The conditions are that ai(t) are the result of thermal excitation of the network, or of equivalent white excitation in any lossy parts of the network. A particular case of special applicability is that in which the network is a cascade of transmission lines, and in this case the N-port junction is the 2-port junction of two adjacent lines. Then the relation isÂ¿a1(t)a2(t) Â¿ = 0 The corresponding relationships for discrete time variables and the partial correlation signal processing algorithm may be viewed as particular applications.
Electronic Circuits and Systems, IEE Proceedings G (Volume:133 , Issue: 4 )
Date of Publication: August 1986