By H.H. Happ (Eds.)
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Additional resources for Diakoptics and Networks
5 is explicitly shown and represented by current source 1'. i' is a response quantity as i n the case of Fig. 4, and can therefore not be as easily shown as 1'. Its actual sources are a combination of current and voltage sources such as I ' , e l , and similar sources associated with the The three syiiibols in Fig. 2 . 3 , a rectangle for current source, a circle for voltage source, and that indicated for the impedance elenienl will be used throughout the book. 15 3. 2 . 3 . 4. 5 other branches in the network, and finally additional voltage and current sources applied across the extremities of more than a single branch.
Veblen, 0. " Amer. Math. , Providence, Rhode Island, 1931. 22 11. 6. a linear graph according to Veblen’s’ definition. The branches in the actual network consist of branches like those in Fig. 5, but they are not represented in Fig. 6. The network has six branches ( B = 6), and four nodes or junctions ( N = 4); since all branches are interconnected, S = 1. The number of independent junction pairs according to Eq. 46) is thus 3, and the number of independent meshes according to Eq. 47) is also 3.
6). 1' was designated as the component current vector due to external current sources, and ib as the component current vector that results due to all other sources. From this definition, the equations expressing the components of J b in terms of their open- and closed-path current vectors follow from Eq. 5) From Eq. 6) The inverse of Eq. 6), assuming that the inverse of Cps exists, is Eq. 9) b A partitioning again appears as in Cbs, but this time dividing the rows of Arb into rows belonging to the open paths and rows belonging to the closed paths.