In the circuit in Figure P3.21, assume the source voltage and source current and all resistances are known.

Question

a. Write the node equations required to determine the node voltages.

b. Write the matrix solution for each node voltage in terms of the known parameters.

Answer 1

Analysis:

a) Specify the nodes (e.g., A on the upper left corner of the circuit in Figure P3.10, and B on the right corner). Choose one node as the reference or ground node. If possible, ground one of the sources in the circuit. Note that this is possible here. When using KCL, assume all unknown current flow out of the node. The direction of the current supplied by the current source is specified and must flow into node A.



Notes:

1. The denominators are the same for both solutions.

2. The main diagonal of a matrix is the one that goes to the right and down.

3. The denominator matrix is the "conductance" matrix and has certain properties:

a) The elements on the main diagonal [i(row) = j(column)] include all the conductance connected to node i=j.

b) The off-diagonal elements are all negative.

c) The off-diagonal elements are all symmetric, i.e., the i j-th element = j i-th element. This is true only because there are no controlled (dependent) sources in this circuit.

d) The off-diagonal elements include all the conductance connected between node i [row] and node j [column].