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Node Voltage Method:

The node voltage method can also be used with networks containing complex impedances and excited by sinusoidal voltage sources. In general, in an N node network, we can choose any node as the reference or datum node In many circuits, this reference is most conveniently chosen as the common terminal or ground terminal. Then it is possible to write (N – 1) nodal equations using KCL. We shall illustrate nodal analysis with the following example.

Consider the circuit shown in Fig.7.5.

Node Voltage Method

Let us take a and b as nodes, and c as reference node. Va is the voltage between nodes a and c. Vb is the voltage between nodes b and c. Applying Kirchhoff’s current law at each node, the unknowns Va and Vb are obtained.

In Fig. 7.6, node a is redrawn with all its branches, assuming that all currents are leaving the node a.

Node Voltage Method

In Fig. 7.6, the sum of the currents leaving node a is zero.

where

Substituting I1,I2 and I3 in Eq. 1, we get

Similarly, in Fig. 7.7, node b is redrawn with all its branches, assuming that all currents are leaving the node b.

In Fig. 7.7, the sum of the currents leaving the node b is zero.

Node Voltage Method

where

Substituting I3,I4 and I5 in Eq. 7.26

Node Voltage Methodwe get

Rearranging Eqs 7.25 and 7.27, we get

Node Voltage Method

Node Voltage Method

From Eqs 7.28 and 7.29, we can find the unknown voltages Va and Vb.