symmetric_juncti

symmetric_juncti - Junction elements in network models....

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Junction elements in network models. Classify by number of ports and examine the possible structures that result. Using only one-port elements, no more than two elements can be assembled. Combining two two-ports yields another two-port. At most two one-port elements could be connected. Thus three-port junction elements are necessary . They are also sufficient insofar as junctions with more than three ports may be constructed from assemblages of three-ports. An assembly of two three-port elements yields a four-port element. Using two- and three-port junctions, an arbitrary number of one-port (or n-port) elements may be assembled into a system. Three-port junction elements A junction structure or junction element is treated as a system with certain special properties which are derived from energetic considerations. Mod. Sim. Dyn. Sys. page 1 Neville Hogan
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An ideal junction structure is power-continuous : power is transmitted instantaneously without storing or dissipating energy. instantaneous power out equals instantaneous power in. Power flow in and out of a three-port may be characterized by six real-valued wave-scattering variables u 1 , u 2 , u 3 , define the input power flow v 1 , v 2 , v 3 , define the output power flow Using vector notation: u = u 1 u 2 u 3 (A.1) v = v 1 v 2 v 3 (A.2) The input and output power flows are the square of the length of these vectors, their inner products. P in = i=1 3 u i 2 = u t u (A.3) P out = i=1 3 v i 2 = v t v (A.4) Mod. Sim. Dyn. Sys. page 2 Neville Hogan
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Constitutive equations of the junction structure may be written in vector form as an algebraic relation between input and output scattering variables. v
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symmetric_juncti - Junction elements in network models....

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