Node Current Analysis

1.

Select a reference node. Label each node except the reference with a letter, except:

(a)

If one end of a voltage source is connected to ground, label the other end of the voltage source with the actual voltage (v_S2 below).

(b)

If there is a voltage source not connected to ground, label the - end with a letter (v_A below), and label the + end with the voltage at the - end plus the voltage of the source ( v_A + v_S1 below).

2.

For each node except the reference node and nodes connected to voltage sources write KCL in the form

$$\sum i_{OUT} = 0$$

where i_OUT is written in terms of node voltages (e.g., $(v_A - v_{S2}) \times G_4$ for R₄ below).

The nodal equation for node B below is

$$\{v_B - (v_A + v_{S1})\} G_2 + (v_B - v_{S2}) G_3 - i_{S3} = 0$$

or

-v_A G₂ + v_B (G₂ + G₃) = i_S3 + v_S1 G₂ + v_S2 G₃

(a)

For nodes of the form of 1(a) there is no need to write KCL since the voltage is already known.

(b)

For nodes of the form 1(b) write one KCL for both ends of the voltage source. For example:

The nodal equation for v_S1 is

v_A G₅ + (v_A - v_S2)G₄ + (v_A + v_S1) G₁ + (v_A + v_S1 - v_B) G₂ = 0

or

v_A (G₁ + G₂ + G₄ + G₅) - v_B G₂ = v_S2 G₄ - v_S1 (G₁ + G₂)

3.

Solve the equations.