1. Techniques of Circuit Analysis
Source Transformations
Thevenin and Norton Equivalents
Maximum Power Transfer
Superposition
Part 6

2. Source Transformations
Replacing a voltage source in series with a resistor by a current source in parallel with the same resistor
Equivalence is achieved if any resistor RL has the same current flow, and thus has the same voltage drop whether connected between nodes a, b in both figures

3. Source Transformations

4. Source Transformations

5. H.W.

6. VTh = vab of original circuit
THEVENIN & NORTON
THEVENIN’S THEOREM:
Thevenin equivalent circuit is an independent voltage source VTH in series with a resistor RTH
This circuit is equivalent to the original circuit, so if we connect the same load across the terminals a, b of each circuit, we get the same voltage and current at the terminals of the load. =
VTh = vab of original circuit

7. First method to find RTH.
THEVENIN & NORTON
If the load resistance is large, we have an open-circuit condition, which is VTH at terminals a, b.
RL Very large
Open Circuit
VTH
Reducing the load resistance to zero gives us a short-circuit condition, which is identical to a short-circuit placed across the terminal a, b
RL is zero
ISC
Short Circuit 1
First method to find RTH.

8. Ex. Find the Thevenin equivalent of the circuit shown.
THEVENIN & NORTON
Ex. Find the Thevenin equivalent of the circuit shown.

9. THEVENIN & NORTON
RTH. IN
Thevenin equivalent
Norton equivalent

10. Second method to find RTH.
THEVENIN & NORTON 2
Second method to find RTH.
Rth can be calculated by deactivating all independent sources and then calculate the resistance seen looking into the network at the designated terminal pair.
A voltage source is deactivated by replacing it with a short circuit.
A current source is deactivated by replacing it with an open circuit.

11. Using source transformation to produce the Thevenin equivalent circuit

12. THEVENIN & NORTON
If a 24Ω resistor is connected across the terminals a, b in both circuits, the voltage across the resistor will be 24V
Prove it please.

13. THEVENIN & NORTON
H.W.

14. Maximum Power Transfer
RL load is connected to the terminal a, b.
Find the value of RL that permits max. power delivery to RL.
To find RL that maximizes the power, we derive p with respect to RL:
The derivative is zero and p is maximized when:

15. Maximum Power Transfer

16. H.W.

17. = + i'1, i'2, i'3 and i'4 i"1, i"2, i"3 and i"4 Superposition
The branch currents i1, i2, i3 and i4
The branch currents resulting from the 120 V voltage source
i'1, i'2, i'3 and i'4
The branch currents resulting from the 12 A current source
i"1, i"2, i"3 and i"4 = +

18. the node-voltage method
Superposition
Please, solve it using
the node-voltage method

19. H.W.