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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
G1 + G2
G2 + G 3 v1
I − I2
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
G11 G12 . . . G1N G21 G22 . . . G2N v2 i2 (3.22)
. . = . .
. . . .
GN 1 GN 2 . . . GN N
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
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- Spring '12