317 shown again in fig 326b for convenience the

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Unformatted text preview: Gj k = Negative of the sum of the conductances directly connecting nodes k and j , k = j vk = Unknown voltage at node k ik = Sum of all independent current sources directly connected to node k , with currents entering the node treated as positive G is called the conductance matrix, v is the output vector; and i is the input vector. Equation (3.22) can be solved to obtain the unknown node voltages. Keep in mind that this is valid for circuits with only independent current sources and linear resistors. Similarly, we can obtain mesh-current equations by inspection when a linear resistive circuit has only independent voltage sources. Consider the circuit in Fig. 3.17, shown again in Fig. 3.26(b) for convenience. The circuit has two nonreference nodes and the node equations were derived in Section 3.4 as | v v R1 + R3 −R3 | −R3 R2 + R 3 e-Text Main Menu i1 v1 = i2 −v2 | Textbook Table of Contents | (3.24) Problem Solving Workbook Contents 96 PART 1 DC Circuits We notice that each of the diagonal terms is the sum of the resistances in the related mesh, while each of the off-diagonal terms is the negative of the resistance common to meshes 1 and 2. Each term on the right-hand side of Eq. (3.24) is the algebraic sum taken clockwise of all independent voltage sources in the related mesh. In general, if the c...
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This note was uploaded on 07/16/2012 for the course KA KA 2000 taught by Professor Bkav during the Spring '12 term at Cambridge.

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