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By H.H. Happ (Eds.)

ISBN-10: 0123241502

ISBN-13: 9780123241504

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Example text

32 111. The Orthogonal Network The orthogonal network will be shown to be different from the interconnected network but electrically equivalent to it. 3. Transformation of Currents Currents will be superimposed upon the contours selected in Figs. 10 of Chapter 11. We will thus have currents flowing along the open paths which will be called open-path currents, and currents flowing along the closed paths which will be called closed-path currents. The open- and closedpath currents can also be called lamellar and solenoidal currents, respectively.

27) Premultiplying both sides of Eq. 27) by C t and substituting Eq. 32) 20 11. Transformation Equations and Topological Concepts Substituting Eq. 6) into Eq. 33) The basic form of Eq. 34) We have previously described the primitive network designated by the index b. We can likewise also describe the network designated by the index s, but must postpone any such description until more information pertaining to reference frame s is known. The current vector in one reference frame can be related to the voltage vector in a second reference frame.

15) is Eq. 56) We can summarize our work on voltages as follows. The transformation equations of the voltages Vb followed from power invariance. The two constituent sets of voltages in V, namely Eb and eb also transform to voltages E, and e,. Note that Kirchhoff’s voltage law has not been invoked in the derivation of the transformation equations. Instead, through power invariance the transformation equations of voltage were derived ; the voltage equations obtained obey Kirchhoff’s voltage law and properly reflect the constraints of the network.

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

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