ECT1012 Circuit Theory and Field Theory - Faculty of Engineering

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Oct 7, 2013 (3 years and 10 months ago)

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FACULTY OF ENGINEERING




LAB SHEET





CIRCUIT THEORY


ECT
1016


TRIMESTER 1 (201
3
/20
1
4
)





CK1
-
Thevenin’s Theorem and Superposition Theorem

CK2
-
AC Circuits



*Note: Students are advised to read through this lab sheet before doing experiment. Your
per
formance, teamwork effort, and learning attitude will count towards the marks. Marking
scheme is given at the end.









1

Experiment CK1: Thevenin’s Theorem and Superposition Theorem



1.0
Objective




To verify the Thevenin’s theorem

by using circuit theory e
xperiment board
.



To verify Superposition
t
heorem.



2.0 Introduction



Thevenin’s
T
heorem is a very useful and frequently used theorem in circuit
analysis.
To verify Thevenin’s
T
heorem, c
onsider a load resistor R
L

(or load impedance Z
L
)
that is connected t
o a “black box” as shown in Figure 1. The black box
can contain
any
combination of
the
circuit elements. Thevenin’s
T
heorem states that insofar as the load
resistor R
L

(or load impedance Z
L
) is concerned, the black box can be represented by a
series combin
ation of an ideal voltage source, V
TH
, and a resistor, R
TH

(or impedance Z
TH
).
V
TH

is known as the Thevenin equivalent voltage source. Its value can be found by
measuring the open
-
circuit voltage between terminals X and Y when the resistor R
L

is
removed. R
TH

is called the Thevenin equivalent resistance

and
Z
TH
is called the Thevenin
equivalent impedance
.

By measuring the short
-
circuit current I
SC

flowing through a wire
that connects X to Y, the value of R
TH

(or Z
TH
) can be calculated as the ratio of V
TH

ove
r
I
SC.
W
hen calculating the Thevenin equivalent impedance, the p
hasor values are to be used
.




The series combination of V
TH

and R
TH

(or Z
TH
) is the equivalent circuit of the
black box. By equivalent, it means the voltage across and current through any c
ircuit
element that is connected between terminals X and Y of the black box will be the same as
the case when that circuit element is connected in series with R
TH

(or Z
TH
) and V
TH
. The
theorem is valid provided that the circuit inside the “black box” is li
near. The load resistor
R
L

(or load impedance Z
L
) however, may not be linear.




Figure 1: The
venin equivalent circuit




Another important theorem for circuit analysis is the Superposition
T
heorem. For a
linear circuit
, the tot
al effect of several causes acting simultaneously is equal to the sum of

2

the effects of individual causes acting one at a time. For example, consider the circuit in
Figure 2. The current I
x

can be found by calculating the current I
1

due to the 3V voltage
s
ource alone, and the current I
2

due to the 2A current source alone, and then taking the sum
of I
1

and I
2
. For a more complicated circuit, the effect of each individual source can be
determined one at a time by turning off all the other sources.
A
voltage s
ource is turned off
by replacing it by a short circuit, while a current source is turned off by replacing it by an
open
-
circuit.










Figure 2: Illust
rati
on of Superposition Theorem



3.0

Apparatus

for the experiments


“Circuit Theory” experiment board

DC Power Supply

Dual
-
trace Oscilloscope

Function Generator

Digital Multimeter

Connecting wires



4.0
Procedures


4.1
Verification of Thevenin’s Theorem


1.

Construct the ci
rcuit shown in Figure 3(a) by connecting T2 to T3, T6 to T7, T16 to
T17, T14 to T15, T8 to T11, and T12 to T13 on the experimental board

using
connection wires
. Set the DC Power Supply to 3V, connect the positive terminal to P1,
and the negative terminal t
o P2.

(Be careful when inserting and removing connections from the board. Do not
damage the board. Avoid using unnecessarily long wires that may introduce noise
into the circuit.)



3


Figure 3: Thevenin equivalent circuit


2.

Using
a
voltmeter/
multimeter, measure the voltage V
L

between T8 and T13. This is the
output voltage across the resistor R4 (Consider R4 as the load resistor R
L
)
.


3.

Remove the co
nnections of T8
-
T11 and T12
-
T13.


4.

Measure the voltage between T8 and T13. This open
-
ci
rcuit voltage is the Thevenin
equivalent voltage V
TH
.


5.

Set the multimeter to function as a milli
-
ammeter. Connect the meter between T8 and
T13. The milli
-
ammeter acts as a short
-
circuit from T8 to T13 and measure the short
-
circuit current I
SC

at the same t
ime.


6.

Calculate the Thevenin equivalent resistance R
TH

= V
TH
/I
SC
. Is the value equal to

11 k

?



7.

Set the DC Power Supply to a value equal to V
TH
. Remove the connections of T16
-
T17
and T14
-
T15.


8.

Construct the circuit shown in Figure 3(b) by connectin
g T2 to T4 and T5 to T7.


9.

Set the multimeter to function as a voltmeter. Measure the voltage between T8 and
T13. Is the reading equal to V
TH
?


10.
Use the multimeter as a milli
-
ammeter. Measure the short
-
circuit current from T8 to
T13. Is the value equal to I
S
C

measured in step
5
?


11.
Connect T8 to T11 and T12 to T13. Measure the voltage across T8 and T13. Is the
reading equal to that measured in step 2?




4.2
Verification of Superposition Theorem


1.

Remove all the wires from the experiment board.


2.

Set both CH1 and CH2

of the oscilloscope to DC coupling (AC/GND/DC switch in the
DC position). Set the vertical sensitivity to 2 V/div for both CH1 and CH2.

(Make sure the INTENSITY of the displayed waveforms is not too high, which
can burn the screen material of the oscillos
cope)
.


4

3.

Set “VERT MODE” to “DUAL”, “SOURCE” to “CH1”, “COUPLING” to “AUTO”.


4.

Set the function generator for a 10 kHz sine wave, with 2V amplitude (4V peak to
peak). Check the waveform using the oscilloscope.

(Never short circuit the output, which may burn t
he output
stage of the function
generator
)
.


5.

Connect the sine wave signal to terminals P5
-

P6 (grounded at P6).


6.

Set the DC Power Supply to 3V; connect the positive terminal to P1, and the negative
terminal to P2.


7.

Construct the circuit shown in Figure 4.


8.

Connect a probe from CH1 of the oscilloscope to P3
-

P6 (grounded at P6).


9.

Connect the second probe from CH2 to P4
-

P6 (grounded at P6).



Figure 4: Experimental set
-
up for
verifying Superposition
T
heorem



10.
Sketch the wavef
orms displayed on the oscilloscope and label the traces (CH1 and
CH2).


11.
Remove the DC Power
s
upply connections from P1 and P2.


12.
Short
-
circuit T1 to T18 with a wire. The circuit should look like that shown in Figure
5(a).



13.
Sketch the waveforms displayed on

the oscilloscope and label the traces (CH1 and
CH2).


14.
Remove the Function
g
enerator connections from P5 and P6.


15.
Remove the short
-
circuit at T1
-

T18
, and do s
hort
-
circuit T12 to T13 with a wire.


P1

P2


5

16.
Connect the DC Power
s
upply positive terminal to P1, and t
he negative terminal to P2.
The circuit should look like that shown in Figure 5(b).


17.
Measure the voltage at P3, and the voltage at P4, using the oscilloscope. Sketch the
oscilloscope display and label the traces (CH1 and CH2).





Figure 5: Analy
sis using Superposition Theorem































P1

P2

P1

P2


6

5.0
Results


5.1
Verification of Thevenin’s
t
heorem


(a) Results based on the measurements on the circuit in Figure 3(a)

Before removing the load resistor R4:

Voltage across the lo
ad resistor, V
L

= ________


After removing load resistor R4:

Open circuit voltage, V
TH
, between T8 and T13 = ________

Short circuit current, I
SC
, from T8 to T13 = ________

Thevenin equivalent resistance R
TH

= V
TH
/I
SC

= ________


(b) Results based on the me
asurements on the circuit in Figure 3(b)

Before connecting the load resistor R4:

Open circuit voltage between T8 and T13 = ________

Short circuit current from T8 to T13 = ________


After connecting the load resistor R4:

Voltage across the load resistor = _
_______


(c) Theoretical analysis of the circuit in Figure 3(a)

Theoretical calculation of the Thevenin equivalent voltage:





Theoretical calculation of the Thevenin equivalent resistance:






Draw the Thevenin equivalent circuit. Assume that now you ha
ve a load resistor R
L

of 11
k
Ω

connected between the terminals of your Thevenin equivalent circuit. Calculate the
voltage across the load resistor.







7

5.2
Verification of Superposition Theorem


(a) Results based on the measurements on the circuit in Figure 4

Sketch the waveforms CH1 and

CH2.




(b) Results based on the measurements on the circuit in Figure 5(a)

Sketch the waveforms CH1 and CH2.





8

Write a mathematical expression for each of these waveforms. For a sinusoidal voltage
wa
veform with zero mean value, find the peak value V
m

and the period of the waveform T
(in seconds). The angular frequency


(in rad s
-
1
) can be calculated using


= 2

/T. The
mathematical expression is then V = V
m

sin

t.


For voltage on CH1,

peak value =
________




period of waveform = ________




angular frequency of waveform = ________



V
CH1a

= ________________


For voltage on CH2,

peak value = ________




period of waveform = ________




angular frequency of waveform = ________

V
CH2a

= ______________
__



(c) Results based on the measurements on the circuit in Figure 5(b)

Sketch the waveforms CH1 and CH2.



Write a mathematical expression for each of these waveforms. For a constant waveform,
the mathematical expression is jus
t equal to the value of the waveform.


V
CH1b

= ________________

V
CH2b

= ________________


9

(d) Theoretical analysis using Superposition Theorem


Using Superposition Theorem, add the waveforms in parts (b) and (c) to obtain the total
waveform caused by the tw
o sources (one ac source and one dc source).


V
CH1,total

= ________________________________


V
CH2,total

= ________________________________



Compare the graphs in part (d) with the graphs in part (a).



Q
uestions and discussion:

1
-

What is Superposition theorem?

…………………………………………………………………………………

…………………………………………………………………………………

…………………………………………………………………………………

…………………………………………………………………………………


2
-

How do you apply the superposition of independent sources?

…………………………………………………………………………………

…………
………………………………………………………………………

…………………………………………………………………………………

…………………………………………………………………………………


3
-

How do you deactivate the voltage and the current sources to do superposition?

……………………………………………………………………………………

…………………………………………………………………………………

…………………………………………………
………………………………

…………………………………………………………………………………


10

4
-

Mention in details the three steps to construct a Thevenin equivalent circuit.

…………………………………………………………………………………

…………………………………………………………………………………

…………………………………………………………………………………

…………………………………………………………………………………

…………
………………………………………………………………………


5
-

State briefly what you have learned from this experiment.

…………………………………………………………………………………

…………………………………………………………………………………

…………………………………………………………………………………

…………………………………………………………………………………

…………………………………………………………………………………






Mark
ing Scheme



Lab
(
5
%)

Assessment
Components

Details

Hands
-
On & Efforts
(
2
%)

The hands
-
on capability of the students and their efforts
during the lab sessions will be assessed.

Lab Report

(
3
%)

Each student will have to submit his/her lab discussion
she
et and recorded experimental data on the same day of
performing the lab experiments.