Download 1.5 Series-Parallel Network, Source Transformation

Chapter 1:
Introduction and DC Circuit
AZRALMUKMIN BIN AZMI
Chapter 1.5:
Series-Parallel Network, Source
Transformation, Thevenin’s Theorem
AZRALMUKMIN BIN AZMI
Series-Parallel Network

Series-parallel networks are networks that contain both
series and parallel circuit configuration.

General approach to circuit analysis:
- Reduce and return approach
- Block diagram approach
Series-Parallel Network (Cont…)

Reduce and return approach
Series-Parallel Network (Cont…)

Reduce and return approach
Series-Parallel Network (Cont…)

Find I3:
Series-Parallel Network (Cont…)

Find I4, Is and V2:
Series-Parallel Network (Cont…)

Block diagram approach
Series-Parallel Network (Cont…)

Find all current and voltage:
Series-Parallel Network (Cont…)

Find all current and voltage:
Series-Parallel Network (Cont…)

Find V1, V3, Vab and IS:
Series-Parallel Network (Cont…)

Find V1, V2 and I:
Series-Parallel Network (Cont…)

Find Va, Vb, Vc, Vac, Vbc, I2 and IS3:
Source Transformation

In reality, all sources (voltage or current source) have
some internal resistance.
Voltage source
Current source
Source Transformation (Cont…)

Source conversion:
Source Transformation (Cont…)

Find:
- IL
- Convert to a current source
and calculate IL
Source Transformation (Cont…)

Find I2:
Thevenin’s Theorem

Any two terminal can be replaced by an equivalent circuit
consisting of a voltage source (VTH) and a series resistor
(RTH).
Thevenin’s Theorem (Cont…)

Used to:
- Analyze networks and sources that are not in parallel and
series.
- Reduce the number of components required to establish
the same characteristics at the output terminals.
Thevenin’s Theorem (Cont…)

Procedure to determine RTH and VTH:
Thevenin’s Theorem (Cont…)

Preliminary:
1. Remove that portion of the network across which
Thevenin's equivalent circuit is to be found. In figure,
required RL is temporarily removed from network.
2. Mark the terminals of remaining two terminal network.
Thevenin’s Theorem (Cont…)

RTH:
3. Calculate RTH by setting all source to zero
(Voltage = short circuit and Current = open circuit)
4. Finding the resultant resistance between the two
marked terminals.
RTH  R1 // R2
R1 R2

R1  R2
(3)(6)

 2
3 6
Thevenin’s Theorem (Cont…)

ETH:
5. Calculate VTH by first returning all sources to their
original position and finding the open circuit voltage
between the marked terminals.
ETH
R2

E1
R1  R2
6

(9)
3 6
 6V
Thevenin’s Theorem (Cont…)

Conclusion:
6. Draw the Thevenin’s equivalent circuit.
Thevenin’s Theorem (Cont…)

Conclusion (Cont…):
7. If required reconnect the portion which had been
removed previously.
Thevenin’s Theorem (Cont…)

Find Thevenin's equivalent circuit for the network in the
shaded area:
Thevenin’s Theorem (Cont…)

Find Thevenin's equivalent circuit for the network in the
shaded area:
Thevenin’s Theorem (Cont…)

Find Thevenin's equivalent circuit for the network in the
shaded area: