Diakoptics and Networks by H.H. Happ (Eds.)

By H.H. Happ (Eds.)

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Both concepts will be further illustrated in this chapter in conjunction with a n interconnected network example. The major aim of this chapter is to transform the currents and voltages of the primitive network t o those of another network specified by the transformation tensor and vice versa and finally t o transform the primitive network itself. A new network called a n orthogonal network is shown to result. The equations transforming the currents and voltages in the primitive t o those in the orthogonal network and vice versa are tabulated.

46) is thus 3, and the number of independent meshes according to Eq. 47) is also 3. According to the definition of M , three closed paths are selected so that each branch is traced out by at least one closed-path contour. The contours are shown i n Fig. 7. labeled c l , c2, c3, where c stands for closed path. The junction pairs selected are also shown in Fig. 7. 7. 0 . Veblen, op. cii. 23 5. Topological Concepts in an Unexcited (Dead) Network been selected all have a node in common (node 4). This case will later be called the " node-to-datum " case and really represents a special case.

9) A requirement imposed upon the transformation is that the power input o r the power dissipated, a linear form as Eq. 10) V,, and V,, are row vectors as was indicated in the last chapter; when the voltages and currents are expressed in terms of phasors, the products of I t is shown in Chapter IV that this assumption is valid. 17 4. 11) The star indicates the cotijugate. The transformation law for voltages now follows from the procedure illustrated in Eqs. 35): Substituting Eq. 6) into Eq. 13) If Eq.

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