By H.H. Happ (Eds.)
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The material of this chapter will be limited to one current per contour. The next chapter will consider two currents per contour. The open-path currents that are imposed upon the contours represent currents from external current sources. Since the currents in the primitive network due to external current sources have been denoted by I b, the openpath current sources will also be denoted by I , but with an index o to denote the open paths. The open-path currents are thus denoted by I " . In the particular case of the network in Fig.
Open- and closed-path current and voltage contours-not node-to-datum case. cate that the open-path contours pertain to both currents and voltages, the currents and voltages have been written alongside the contours (I1,El ; I , , E, ; 13, E 3 ) . The closed-path contours have been analogously identified (icl, E c l ;ic2,E,, ; ic3,Ec3). The extremities of the voltage and current contours are illustrated in Figs. 4. These latter voltages and currents are junction-pairs voltages and 46 111. The Orthogonal Network currents, from our definition previously given, and can be considered to be superimposed upon the junction pairs.
6) into Eq. 13) If Eq. 14) When all transformation matrices are assumed real, Eq. 14) then becomes Notice that Eq. 15) also follows from Eq. 10). The inverse of Eq. 15) follows from Eq. 16) The invariance relationship in Eq. 1 1) can readily be proved by substituting Eqs. 15) into Eq. 17) where t indicates the transpose From Eq. 13) On substituting Eq. 13) into Eq. 18), we obtain V,bJb*on the right-hand side of the equation also, thus proving Eq. 11). 18 11. Transformation Equations and Topological Concepts We could also prove Eq.