Upload
sarah-azlina
View
305
Download
8
Embed Size (px)
Citation preview
7/28/2019 Chapter 4 - Circuit Theorems
1/26
Chapter 4
Circuit Theorems
EEE3103 Circuits and Signals
PowerPointSlides
by Alex Chan
7/28/2019 Chapter 4 - Circuit Theorems
2/26
2 I-Station Solutions Sdn BhdLast Updated:
Chapter Outline
4.1 Superposition
4.2 Source Transformation
4.3 Thevenins Theorem
4.4 Nortons Theorem4.5 Maximum Power Transfer
17/07/2013
7/28/2019 Chapter 4 - Circuit Theorems
3/26
3 I-Station Solutions Sdn BhdLast Updated:
4.1 Superposition Theorem
Superposition is another approach introduced to determine
the value of a specific variable (voltage or current) if the
circuit has two or more independent sources.
Definition:
Superposition states that the voltage across (or current
through) an element in a linear circuit is the algebraic sum
of the voltage across (or currents through) that element due
to EACH independent source acting alone.
17/07/2013
7/28/2019 Chapter 4 - Circuit Theorems
4/26
4 I-Station Solutions Sdn BhdLast Updated:
4.1 Superposition Theorem
The principle of superposition helps us to analyze a linear
circuit with more than one independent source by
calculating the contribution of each independent source
separately and then adding them up.
Example:
We consider the effects of 8A and 20V one by one, then
add the two effects together
for final v0.
17/07/2013
7/28/2019 Chapter 4 - Circuit Theorems
5/26
5 I-Station Solutions Sdn BhdLast Updated:
4.1 Superposition Theorem
Steps to apply superposition theorem:
1. Turn off all independent sources except one source.
Find the output (voltage or current) due to that active
source using nodal or mesh analysis.
2. Repeat step 1 for each of the other independent
sources.
3. Find the total contribution by adding algebraically all the
contributions due to the independent sources.
17/07/2013
7/28/2019 Chapter 4 - Circuit Theorems
6/26
6 I-Station Solutions Sdn BhdLast Updated:
4.1 Superposition Theorem
Two things to keep in mind:
1. When we say turn off all other independent sources:
Independent voltage sources are replaced by 0 V
(short-circuit) and Independent current sources are replaced by 0 A
(open-circuit).
2. Dependent sources are left intact because they are
controlled by circuit variables.
PP 4.3 4.5
17/07/2013
7/28/2019 Chapter 4 - Circuit Theorems
7/267 I-Station Solutions Sdn BhdLast Updated:
4.2 Source Transformation
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.
17/07/2013
s sv i Rs
s
vi
R
7/28/2019 Chapter 4 - Circuit Theorems
8/268 I-Station Solutions Sdn BhdLast Updated:
4.2 Source Transformation
Independent Source Transform
17/07/2013
7/28/2019 Chapter 4 - Circuit Theorems
9/269 I-Station Solutions Sdn BhdLast Updated:
4.2 Source Transformation
Dependent Source Transform
17/07/2013
7/28/2019 Chapter 4 - Circuit Theorems
10/2610 I-Station Solutions Sdn BhdLast Updated:
4.2 Source Transformation
Two things to keep in mind:
1. During transformation, the arrow of current source is
directed toward the positive terminal of voltage source.
2. Not possible when: R = 0 for voltage source.
R = for current source.
PP 4.6 4.7
17/07/2013
7/28/2019 Chapter 4 - Circuit Theorems
11/2611 I-Station Solutions Sdn BhdLast Updated:
4.3 Thevenins Theorem
In practice the load usually varies, while the source is
fixed eg. Fixed household outlet terminal and different
electrical appliances which constitute variable loads.
Each time the load is changed, the entire circuit has to
be analyzed all over again.
To avoid this problem, Thevenins theorem provides a
technique by which the fixed part of the circuit is
replaced with an equivalent circuit.
17/07/2013
7/28/2019 Chapter 4 - Circuit Theorems
12/2612 I-Station Solutions Sdn BhdLast Updated:
4.3 Thevenins Theorem
Thevenins theorem states that a linear two-terminal circuit
can be replaced by an equivalent circuit consisting of a
voltage source VTh in series with resistor RTh.
17/07/2013
7/28/2019 Chapter 4 - Circuit Theorems
13/2613 I-Station Solutions Sdn BhdLast Updated:
4.3 Thevenins Theorem
Definitions:
VTh = open-circuit voltage at the terminals.
RTh = input or equivalent resistance at the terminals when
the independent sources are turned off.
ie.
Voltage sources = 0 V (short circuit) Current sources = 0 A (open circuit)
17/07/2013
7/28/2019 Chapter 4 - Circuit Theorems
14/2614 I-Station Solutions Sdn BhdLast Updated:
4.3 Thevenins Theorem
How to find VTh:
Find the voltage across point a and b using any methodin previous chapters (by taking out the load from the
circuit).
17/07/2013
7/28/2019 Chapter 4 - Circuit Theorems
15/2615 I-Station Solutions Sdn BhdLast Updated:
4.3 Thevenins Theorem
How to find RTh:
Case 1: No dependent sources in the circuit
1. Turn off all independent sources.
2. Find RThby finding the equivalent resistance at point a
and b.
17/07/2013
7/28/2019 Chapter 4 - Circuit Theorems
16/2616 I-Station Solutions Sdn BhdLast Updated:
4.3 Thevenins Theorem
Case 2: Circuit has dependent sources.
1. Turn off all independent sources.
2. Leave dependent sources intact.
3. Apply voltage source vo across a and b then find
=0
0
OR apply current source i0 and find =0
0
.
17/07/2013
7/28/2019 Chapter 4 - Circuit Theorems
17/26
7/28/2019 Chapter 4 - Circuit Theorems
18/2618 I-Station Solutions Sdn BhdLast Updated:
4.3 Thevenins Theorem
Consider a linear circuit terminated by load RL.
Current IL through the load and voltage VL across the load
is given by:
PP 4.8 4.10
17/07/2013
Th
L
ThL
VI
R R
L
L L L Th
ThL
RV R I V
R R
7/28/2019 Chapter 4 - Circuit Theorems
19/2619 I-Station Solutions Sdn BhdLast Updated:
4.4 Nortons Theorem
Nortons theorem states that a linear two-terminal circuit
can be replaced by an equivalent circuit consisting of a
current source IN in parallel with resistor RN.
17/07/2013
7/28/2019 Chapter 4 - Circuit Theorems
20/2620 I-Station Solutions Sdn BhdLast Updated:
4.4 Nortons Theorem
Definitions:
IN = short-circuit current through the terminals.
RN = input or equivalent resistance at the terminals when
the independent sources are turned off.
ie.
Voltage sources = 0 V (short circuit) Current sources = 0 A (open circuit)
17/07/2013
7/28/2019 Chapter 4 - Circuit Theorems
21/2621 I-Station Solutions Sdn BhdLast Updated:
4.4 Nortons Theorem
Relation between Nortons and Thevenins Theorem
The Thevenins and Norton equivalent circuits are related
by a source transformation.
In source transformation, the resistor does not change.
Thus:
=
17/07/2013
7/28/2019 Chapter 4 - Circuit Theorems
22/2622 I-Station Solutions Sdn BhdLast Updated:
4.4 Nortons Theorem
How to find IN:
1. The short-circuit current flowing
from terminal a to b is IN.
Since the resistors, = :
2. Dependent and independent sources are treated the
same way as in Thevenins Theorem.
PP 4.11 4.12
17/07/2013
Th
N
Th
V
I R
7/28/2019 Chapter 4 - Circuit Theorems
23/26
7/28/2019 Chapter 4 - Circuit Theorems
24/26
24 I-Station Solutions Sdn BhdLast Updated:
4.5 Maximum Power Transfer
By varying the load resistance RL, the power delivered will
also vary, as per the graph.
17/07/2013
7/28/2019 Chapter 4 - Circuit Theorems
25/26
7/28/2019 Chapter 4 - Circuit Theorems
26/26
References
Alexander & Sadiku, Fundamentals of Electrical Circuits,
4th Edition, McGraw-Hill Company.