18233_eel1166_ck1

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FACULTY OF ENGINEERING

LAB SHEET

CIRCUIT THEORY

EEL1166

TRIMESTER 1 (2015/2016)

CK1-Thevenin’s Theorem and Superposition Theorem CK2-AC Circuits

*Note: Students are advised to read through this lab sheet before doing experiment. Your performance, teamwork effort, and learning attitude will count towards the marks. Marking

scheme is given at the end of the labsheet.

Experiment CK1: Thevenin’s Theorem and Superposition Theorem

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1! "#$ective

!o verif" the !hevenin#s theorem b" using circuit theor" experiment board. !o verif" Superposition theorem.

2! %ntroduction

!hevenin#s !heorem is a ver" useful and fre$uentl" used theorem in circuit anal"sis.!o verif" !hevenin#s !heorem, consider a load resistor % & 'or load impedance (&) that isconnected to a black box+ as shown in igure -. !he black box can contain an"combination of the circuit elements. !hevenin#s !heorem states that insofar as the loadresistor % & 'or load impedance (&) is concerned, the black box can be represented b" aseries combination of an ideal voltage source, !/, and a resistor, % !/ 'or impedance (!/).!/ is known as the !hevenin e$uivalent voltage source. 0ts value can be found b"

measuring the open1circuit voltage between terminals 2 and Y when the resistor % & isremoved. % !/ is called the !hevenin e$uivalent resistance and (!/ is called the !hevenine$uivalent impedance. 3" measuring the short1circuit current 0S4 flowing through a wirethat connects 2 to Y, the value of % !/ 'or (!/) can be calculated as the ratio of !/ over 0S4.

5hen calculating the !hevenin e$uivalent impedance, the phasor values are to be used.

!he series combination of !/ and % !/ 'or (!/) is the e$uivalent circuit of the black box. 3" e$uivalent, it means the voltage across and current through an" circuit element thatis connected between terminals 2 and Y of the black box will be the same as the case whenthat circuit element is connected in series with % !/ 'or (!/) and !/. !he theorem is valid

provided that the circuit inside the black box+ is linear. !he load resistor % & 'or load

impedance (&) however, ma" not be linear.

Black

box

VOC

=VTH I

SC

=VTH

/RTH

!

RTH

VTH

RL

"

Y

Black

box

"

Y

Black

box

"

Y

RL

"

Y

igure -: !hevenin e$uivalent circuit

6nother important theorem for circuit anal"sis is the Superposition !heorem. or a&inear circuit, the total effect of several causes acting simultaneousl" is e$ual to the sum of the effects of individual causes acting one at a time. or example, consider the circuit inigure 7. !he current 0x can be found b" calculating the current 0- due to the 8 voltage

source alone, and the current 07 due to the 76 current source alone, and then taking the sumof 0- and 07. or a more complicated circuit, the effect of each individual source can be

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determined one at a time b" turning off all the other sources. 6 voltage source is turned off b" replacing it b" a short circuit, while a current source is turned off b" replacing it b" anopen1circuit.

2 #

!

$ Ω

% V

!% V 2 #

Ix

I1

I2

6 Ω

$ Ω $ Ω

6 Ω 6 Ω

68.9:

80-

=

+

= ( ) .;6769:

:07

=

+

=

-.-60007-x

=+=

igure 7: 0llustration of Superposition !heorem

'! Apparatus (or the experiments

4ircuit !heor"+ experiment board<4 =ower Suppl"<ual1trace >scilloscope

unction ?enerator <igital Multimeter 4onnecting wires

)! *rocedures

)1 +eri(ication o( Thevenin’s Theorem

-. 4onstruct the circuit shown in igure 8'a) b" connecting !7 to !8, !9 to !@, !-9 to!-@, !- to !-A, !; to !--, and !-7 to !-8 on the experimental board using

connection wires. Set the <4 =ower Suppl" to 8B connect the positive terminal to =-,and the negative terminal to =7.,Be care(u& hen insertin. and removin. connections (rom the #oard /o not

dama.e the #oard Avoid usin. unnecessari&0 &on. ires that ma0 introduce noiseinto the circuit

7

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R2

22 k Ω

R%

22 k Ω

R$

22 k Ω

T&

T1%

%V

R1

11 k Ω T&

T1%

VTH

(a) (b)

VL

igure 8: !hevenin e$uivalent circuit

7. Csing a voltmeterDmultimeter, measure the voltage & between !; and !-8. !his is theoutput voltage across the resistor % '4onsider % as the load resistor % &).

8. %emove the connections of !;1!-- and !-71!-8.

. Measure the voltage between !; and !-8. !his open1circuit voltage is the !hevenine$uivalent voltage !/.

A. Set the multimeter to function as a milli1ammeter. 4onnect the meter between !; and!-8. !he milli1ammeter acts as a short1circuit from !; to !-8 and measure the short1circuit current 0S4 at the same time.

9. 4alculate the !hevenin e$uivalent resistance % !/ E !/D0S4. 0s the value e$ual to --

k ΩF

@. Set the <4 =ower Suppl" to a value e$ual to !/. %emove the connections of !-91!-@

and !-1!-A.

;. 4onstruct the circuit shown in igure 8'b) b" connecting !7 to ! and !A to !@.

G. Set the multimeter to function as a voltmeter. Measure the voltage between !; and !-8.0s the reading e$ual to !/F

-. Cse the multimeter as a milli1ammeter. Measure the short1circuit current from !; to!-8. 0s the value e$ual to 0S4 measured in Step AF

--. 4onnect !; to !-- and !-7 to !-8. Measure the voltage across !; and !-8. 0s the

reading e$ual to that measured in Step 7F

)2 +eri(ication o( Superposition Theorem

-. %emove all the wires from the experiment board.

7. Set both 4/- and 4/7 of the oscilloscope to <4 coupling '64D?N<D<4 switch in the<4 position). Set the vertical sensitivit" to 7 Ddiv for both 4/- and 4/7.,a3e sure the %4TE4S%T5 o( the disp&a0ed ave(orms is not too hi.h6 hich can#urn the screen materia& o( the osci&&oscope

8. Set H%! M><H+ to <C6&+, S>C%4H+ to 4/-+, 4>C=&0N?+ to 6C!>+.

8

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. Set the function generator for a - k/I sine wave, with 7 amplitude ' peak to peak). 4heck the waveform using the oscilloscope.,4ever short circuit the output6 hich ma0 #urn the output sta.e o( the (unction.enerator

A. 4onnect the sine wave signal to terminals =A 1 =9 'grounded at =9).

9. Set the <4 =ower Suppl" to 8B connect the positive terminal to =-, and the negativeterminal to =7.

@. 4onstruct the circuit shown in igure .

;. 4onnect a probe from 4/- of the oscilloscope to =8 1 =9 'grounded at =9).

G. 4onnect the second probe from 4/7 to = 1 =9 'grounded at =9).

R%

22 k Ω

R$

22 k Ω

'% '$

%V

R1

11 k Ω

('6 '5!

CH1 CH2

C1

01 µ *

2 +,- ω .

igure : Hxperimental set1up for verif"ing Superposition !heorem

-. Sketch the waveforms displa"ed on the oscilloscope and label the traces '4/- and4/7).

--. %emove the <4 =ower suppl" connections from =- and =7.

-7. Short1circuit !- to !-; with a wire. !he circuit should look like that shown inigure A'a).

-8. Sketch the waveforms displa"ed on the oscilloscope and label the traces '4/- and4/7).

-. %emove the unction generator connections from =A and =9.

-A. %emove the short1circuit at !- 1 !-;, and do short1circuit !-7 to !-8 with a wire.

-9. 4onnect the <4 =ower suppl" positive terminal to =-, and the negative terminal to=7. !he circuit should look like that shown in igure A'b).

-@. Measure the voltage at =8, and the voltage at =, using the oscilloscope. Sketch theoscilloscope displa" and label the traces '4/- and 4/7).

'1

'2

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(a) (b)

R%

22 k Ω

R$

22 k Ω

'% '$

R1

11 k Ω

('6 '5!

CH1 CH2

C1

01 µ *

R%

22 k Ω

R$

22 k Ω

'% '$

%V

R1

11 k Ω

'6 '5

CH1 CH2

C1

01 µ *

igure A: 6nal"sis using Superposition !heorem

7! 8esu&ts

71 +eri(ication o( Thevenin’s theorem

'a) %esults based on the measurements on the circuit in igure 8'a)

Before removing the load resistor R4:

A

'1

'2

'1

'2

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oltage across the load resistor, & E JJJJJJJJ

After removing load resistor R4:

>pen circuit voltage, !/, between !; and !-8 E JJJJJJJJ

Short circuit current, 0S4, from !; to !-8 E JJJJJJJJ

!hevenin e$uivalent resistance % !/ E !/D0S4 E JJJJJJJJ

'b) %esults based on the measurements on the circuit in igure 8'b)

Before connecting the load resistor R4:

>pen circuit voltage between !; and !-8 E JJJJJJJJ

Short circuit current from !; to !-8 E JJJJJJJJ

After connecting the load resistor R4:

oltage across the load resistor E JJJJJJJJ

'c) !heoretical anal"sis of the circuit in igure 8'a)!heoretical calculation of the !hevenin e$uivalent voltage:

!heoretical calculation of the !hevenin e$uivalent resistance:

<raw the !hevenin e$uivalent circuit. 6ssume that now "ou have a load resistor % & of --kK connected between the terminals of "our !hevenin e$uivalent circuit. 4alculate thevoltage across the load resistor.

72 +eri(ication o( Superposition Theorem

'a) %esults based on the measurements on the circuit in igure Sketch the waveforms at 4/- and 4/7.

9

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'b) %esults based on the measurements on the circuit in igure A'a)Sketch the waveforms at 4/- and 4/7.

5rite a mathematical expression for each of these waveforms. or a sinusoidal voltagewaveform with Iero mean value, find the peak value m and the period of the waveform !

'in seconds). !he angular fre$uenc" ω 'in rad s1-) can be calculated using ω E 7πD!. !he

mathematical expression is then E m sin ωt.

or voltage on 4/-, peak value E JJJJJJJJ

period of waveform E JJJJJJJJ

@

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angular fre$uenc" of waveform E JJJJJJJJ

4/-a E JJJJJJJJJJJJJJJJ

or voltage on 4/7, peak value E JJJJJJJJ

period of waveform E JJJJJJJJ

angular fre$uenc" of waveform E JJJJJJJJ

4/7a E JJJJJJJJJJJJJJJJ

'c) %esults based on the measurements on the circuit in igure A'b)Sketch the waveforms at 4/- and 4/7.

5rite a mathematical expression for each of these waveforms. or a constant waveform, themathematical expression is Lust e$ual to the value of the waveform.

4/-b E JJJJJJJJJJJJJJJJ

4/7b E JJJJJJJJJJJJJJJJ

'd) !heoretical anal"sis using Superposition !heorem

Csing Superposition !heorem, add the waveforms in parts 'b) and 'c) to obtain the totalwaveform caused b" the two sources 'one ac source and one dc source).

4/-,total E JJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJ

4/7,total E JJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJ

;

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4ompare the graphs in part 'd) with the graphs in part 'a).

9uestions and discussion:-1 5hat is Superposition theoremF

71 /ow do "ou appl" the superposition of independent sourcesF

81 /ow do "ou deactivate the voltage and the current sources to do superpositionF

1 Mention in details the three steps to construct a !hevenin e$uivalent circuit.

A1 State briefl" what "ou have learned from this experiment.

G

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ar3in. Scheme

La#,7

AssessmentComponents

/etai&s

/ands1>n Hfforts'7O)

!he hands1on capabilit" of the students and their effortsduring the lab sessions will be assessed.

&ab %eport '8O) Hach student will have to submit hisDher lab discussionsheet and recorded experimental data on the same da" of

performing the lab experiments.

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