1. Lesson 19: AC Source Transformation and Nodal Analysis

2. Learning Objectives
Construct equivalent circuits by converting an AC voltage source and a resistor to an AC current source and a resistor.
Apply Nodal Analysis to an AC Circuit.

3. DC Source Transformation
DC Source transformation is the process of replacing a voltage source (vs) in series with a resistor (R) by a current source (is) in parallel with a resistor (R), or vice versa.

4. AC Source Transformation
A voltage source with impedance (Z) in series is the same as a current source with an impedance (Z) in parallel and vice versa.

5. Example Problem 1 Convert the voltage source to a current source:
Use the same rules as you would with a DC source conversion only this time you are calculating your source conversion with complex numbers and ‘moving’ the impedance. 9Ω
40Ω

6. Example Problem 2
Convert the current source to a voltage source:

7. Example Problem 3
Using source transformations, determine the voltage drop VR across the 3 ohm resistor. 2Ω 5Ω

8. Example Problem 4
Using source transformations, determine the voltage drop Vab across the 10 ohm resistor and IR through resistor.
24Ω
12Ω
24Ω
12Ω
10Ω

9. AC Nodal Analysis General Approach (similar to the DC approach):
The fundamental steps are the following:
Determine the number of nodes within the network.
Pick a reference node and label each remaining node with a subscripted value of voltage: Va, Vb, and so on.
Apply Kirchhoff’s current law at each node except the reference.
Assume that all unknown currents leave the node for each application of Kirchhoff’s current law.
Solve the resulting equations for the nodal voltages.

10. Example Problem 5 Determine the voltage Vb in the circuit below:
Determine the number of nodes within the network. a b c
Pick a reference node and label each remaining node with a subscripted value of voltage: Va, Vb, and so on.
NOTE: In this problem, we are not considering the node between L1 and R1 to be useful so we can ignore it. In addition, it is appropriate to say there is no node between L1 and R1 because they are considered part of one branch of the circuit.
Apply Kirchhoff’s current law at each node except the reference.
Assume that all unknown currents leave the node for each application of Kirchhoff’s current law. d
Solve the resulting equations for the nodal voltages.
Use solver:

11. QUESTIONS?