In this method, we set up and solve a system of equations in which the unknowns are the voltages at the principal nodes of the circuit. From these nodal voltages the currents in the various branches of the circuit are easily determined. The steps in the nodal analysis method are:
For example, for the node to the right KCL yields the equation:
Ia + Ib + Ic = 0
Express the current in each branch in terms of the nodal voltages at each end of the branch using Ohm’s Law (I = V / R). Here are some examples:The result, after simplification, is a system of m linear equations in the m unknown nodal voltages (where m is one less than the number of nodes; m = n - 1). The equations are of this form:
where G11, G12, . . . , Gmm and I1, I2, . . . , Im are constants.
Alternatively, the system of equations can be gotten (already in simplified form) by using the inspection method.
Use nodal analysis to find the voltage at each node of this circuit.
We will number the nodes as shown to the right.
node 1 and the second equation results from KCL applied at node 3. Collecting terms this becomes:
This form for the system of equations could have been gotten immediately by using the inspection method.
Use nodal analysis to find the voltage at each node of this circuit.
Use nodal analysis to find the voltage at each node of this circuit.
Written by Eric Hiob, Tuesday, December 31, 1996