g1n g21 g22 g2n v2 i2 322

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Unformatted text preview: Fig. 3.2, shown again in Fig. 3.26(a) for convenience. The circuit has two nonreference nodes and the node equations were derived in Section 3.2 as G1 + G2 −G2 −G2 G2 + G 3 v1 I − I2 =1 v2 I2 I2 v2 (3.21) Observe that each of the diagonal terms is the sum of the conductances connected directly to node 1 or 2, while the off-diagonal terms are the negatives of the conductances connected between the nodes. Also, each term on the right-hand side of Eq. (3.21) is the algebraic sum of the currents entering the node. In general, if a circuit with independent current sources has N nonreference nodes, the node-voltage equations can be written in terms of the conductances as v1 i1 G11 G12 . . . G1N G21 G22 . . . G2N v2 i2 (3.22) . . . = . . . . . . . . . . . . . . . GN 1 GN 2 . . . GN N vN iN or simply I1 (3.23) G1 G3 (a) R1 V1 + − R2 R3 i1 i3 + V2 − (b) Figure 3.26 Gv = i G2 v1 (a) The circuit in Fig. 3.2, (b) the circuit in Fig. 3.17. where Gkk = Sum of the conductances connected to node k Gkj =...
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