3.2 Analysis with Nodal Equations

In writing nodal equations, we perform the following steps:

1. For a circuit containing N nodes, we choose one of these as a reference node assumed to be zero volts or ground.

2. At each non-reference node we assign node voltages v ₁, v ₂, , v _{n ? 1} where each of these voltages is measured with respect to the chosen reference node, i.e., ground.

3. If the circuit does not contain any voltage sources between nodes, we apply KCL and write a nodal equation for each of the node voltages v ₁, v ₂, , v _{n ? 1}.

4. If the circuit contains a voltage source between two nodes, say nodes j and k denoted as node variables v _j and v _k, we replace the voltage source with a short circuit thus forming a combined node and we write a nodal equation for this common node in terms of both v _j and v _k; then we relate the voltage source to the node variables v _j and v _k.

Example 3.1

Write nodal equations for the circuit shown in Figure 3.1, and solve for the unknowns of these equations using matrix theory, Cramer's rule, or the substitution method. Verify your answers with Excel or MATLAB . Please refer to Appendix A for discussion and examples.

Figure 3.1: Circuit for Example 3.1

Solution:

We observe that there are 4...