MGM’s Jawaharlal Nehru Engineering College, Aurangabad

Laboratory Manual

Network Theory

For

Second Year Students

Manual made by

PROF. M. S. KALE YEAR:-2013-14

© JNEC, Aurangabad

FOREWORD

It is my great pleasure to present this laboratory manual for second year engineering students for the subject of Network Theory, keeping in view the vast coverage required to visualize the basic concepts of various networks using basic components. NT covers designing a network for specific input/output requirements. This being a core subject, it becomes very essential to have clear theoretical and practical designing aspects. This lab manual provides a platform to the students for understanding the basic concepts of network theory. This practical background will help students to gain confidence in qualitative and quantitative approach to electronic networks.

Good Luck for your Enjoyable Laboratory Sessions.

2

LABORATORY MANUAL CONTENTS

This manual is intended for the second year students of engineering branches in the subject of network theory. This manual typically contains practical/Lab Sessions related to Network Theory covering various aspects related the subject to enhance understanding.

In this manual we have made the efforts to cover various experiments on network theory with detailed circuit diagrams, detailed procedure and graphs wherever required.

Students are advised to thoroughly go through this manual rather than only topics mentioned in the syllabus as practical aspects are the key to understanding and conceptual visualization of theoretical aspects covered in the books.

Good Luck for your Enjoyable Laboratory Sessions

PROF. M. S. KALE Author

3

SUBJECT INDEX 1.Do’s and Don’ts

2. Lab exercise:

1. Verification of Superposition Theorem.

2. Verification of Thevenin’s Theorem.

3. Verification of Norton’s theorem.

4. Verification of Maximum power transfer theorem.

5. To plot frequency response of a series resonant circuit.

6. To plot frequency response of a parallel resonant circuit.

7. To measure input impedance and output impedance of a given two port network.

8. Design of a High Pass Filter.

9. Design of a Low Pass Filter.

10. To observe and analyze the waveform across a capacitor of a series RC

circuit exited by a unit step function.

11. To study the behavior of a series R-L-C circuit

3. Quiz on the subject.

4. Conduction of Viva-Voce Examination.

5. Evaluation and Marking Systems.

4

Dos and Don’ts in Laboratory:

1. Do not handle any equipment before reading the instructions/Instruction manuals.

2. Apply proper voltage to the circuit as given in procedure.

3. Check CRO probe before connecting it.

4. Strictly observe the instructions given by the teacher/Lab Instructor.

Instruction for Laboratory Teachers:

1. Submission related to whatever lab work has been completed should be done during the next lab session.

2.

The promptness of submission should be encouraged by way of marking and

evaluation patterns that will benefit the sincere students.

5

EXPERIMENT.NO. 1

AIM: - To verify Superposition theorem.

APPARATUS: - Breadboard, Resistors, Milliammeter, connecting wires, etc.

CIRCUIT DIAGRAM:-

1

R 1 I1

R 2 I2

2

V1

10 VOLTS

R3

I3

V2 15 VOLTS

1 l

2 l

THEORY:

- If network contains two or more than two sources, then principle of superposition theorem is used to simplify network calculations. It may be stated as follows. In a bilateral network if two or more than two energy sources are present, then the current which flows at any point is the vector sum of all currents which would flow at that point if each source was considered separately and all other sources replaced at the time by impedance equal to their internal impedances.

PROCEDURE:-

1. Connect D. C. power supply across terminals 1-1l and apply voltage of say V1=10 volts and similarly across terminals 2-2l apply voltage of say V2=15 volts

2. Measure current flowing through all branches, say these currents are I1, I2, and I3.

3. Now connect only V1=10 volts across terminals1-1l and short circuit terminals 2-2l that is V2=0 volts.

4. Measure currents flowing through all branches for V1=10 volts V2=0 volts using a milliameter, say these currents are I1’, I2’, I3’.

5. Similarly connect only V2 =15 volts across terminals 2-2l and short circuit terminals 1-1l that is V1=0 volts.

6. Measure current flowing through all branches for V1=0 volts and V2=15 volts using a milliameter, say these currents are I1”, I2”, I3”.

7. For verifying superposition theorem I1= I1’+ I1”, I2= I2’+ I2’, I3=I3’+I3”. 8. Calculate theoretical values of currents, these values should be

approximately equal to measured values of currents.

6

V1=10VOLTS V2=15VOLTS

V1=10VOLTS V2=0 VOLTS

V1=0VOLTS V2=15VOLTS

I1= I1’= I1”=

I2= I2’= I2”=

I3= I3’= I3”=

OBSERVATION TABLE:-

1

R1 I1

R2 I2

2

V1

10V

R3

I3 V2

15V

1

2

1

R1 I1

R2 I2

2

V1

10V

R3

I3 V2

15V

1

2

CONCLUSION: - The branch current is the algebraic sum of currents due to individual voltage source when all other voltage sources are short circuited; hence superposition theorem has been verified.

7

EXPERIMENT. NO. 2

AIM: - To verify Thevenin’s theorem.

APPARATUS: - Bread board, resistors, D.C. power supply, multimeter, connecting wires, etc.

CIRCUIT DIAGRAM:-

1

R1

R2

2

1

R3

2

RL

THEORY:- The current flowing through the load impedance RL connected across the terminals 2 & 2l of a network containing impedance & energy sources is the same as it would flow if this load impedance were connected across a simple constant voltage source whose generated emf is an open circuited voltage, measured across the network terminals 2 & 2l. Its internal impedance is the same as the impedance of the network looking back into the terminals 2 & 2l , when all sources have been replaced by impedances and sources with output terminals 2 & 2l. across which load impedance RL

is connected.

PROCEDURE:-

1. Apply dc voltage across terminals 1-1l, call this voltage as Vdc.

2. Connect voltmeter across terminals 2-2l and measure voltage on voltmeter. This voltage is known as open circuit voltage or Thevenin’s voltage (Vth).

3. Vary the dc voltage across terminals 1-1l and repeat step 2, take two/three readings.

4. Disconnect the applied voltage at terminals 1-1l and voltmeter at terminals 2-2l . 5. Now short terminals 1-1l and connect multimeter across terminals 2-2l . With

the help of multimeter measure resistance between terminals 2-2l . This is known as Thevenin’s resistance (Rth).

6. Calculate Vth and Rth by theoretical calculations, the theoretical values and measured values of Vth and Rth should be approximately equal.

7. Connect load resistor RL across terminals 2-2l and measure IL for applied dc voltage.

8

Sr.No. Vdc Measured values Theoretical values

Rth Vth IL Rth Vth IL

OBSERVATION TABLE:-

CONCLUSION: - The theoretical values and measured values of Vth and Rth and IL are approximately equal, hence Thevenin’s theorem has been verified.

9

EXPERIMENT NO. 3

AIM: - To verify Norton’s theorem.

APPARATUS: - Breadboard, milliammeter (0-50mA), D.C. power supply (0-30V), multimeter, resistors, connecting wires, etc.

CIRCUIT DIAGRAM:-

1

R1

R2

2

1

R3

2

RL

THEORY:- Any two terminal linear network, consisting of generators and impedances, can be replaced with an equivalent circuit consisting of a current source Isc in parallel with an admittance YAB . The Isc is short circuit current between the network and YAB is the admittance measured between the terminals, with all energy sources eliminated except their internal impedances.

PROCEDURE:-

1.

Apply d. c. voltage across terminals 1-1l called this voltage Vdc.

2. Connect milliammeter across terminals 2-2l and measure current, this is the short circuit (Isc) current.

3. Vary the d. c. voltage across terminals 1-1l and repeat step 2, take three readings.

4. Disconnect the applied voltage at terminals 1-1l and milliammeter at terminals 2-2l .

5. Short terminals 1-1l and connect Multimeter (keep it on resistance range) across terminals 2-2l , and note down the reading , this resistance is known as Req.

6. Calculate Isc and Req by using formulae, the calculated values and measured values of Isc and Rth should be approximately equal.

7. Connect RL across terminals 2-2l and measure IL by milliammeter for applied D.C. voltage.

10

Sr.No. Vdc Measured values Isc Req IL

Calculated values Isc Req IL

OBSERVATION TABLE:-

CONCLUSION: - The Calculated values and measured values of Isc, IL, Req are approximately equal; hence Norton’s theorem has been verified.

11

2

EXPERIMENT. NO. 4

AIM: - To verify maximum power transfer theorem.

APPARATUS: - Breadboard, resistance, potentiometer, milliammeter, multimeter, etc.

CIRCUIT DIAGRAM:-

1

R1 R2 2 +

mA _ _

Vdc

R3

+

V

RL

_

1 l

THEORY:-

l

Maximum power will be delivered by a network to an impedance ZR if the impedance of ZR is the conjugate of the impedance Z measured looking back into the terminals of the network.

Zl

ZL E

PROCEDURE:- 1. Make the connections according to circuit diagram.

l of the network,

1. Connect d.c. power supply of say Vdc=20 volts across terminal 1-1l .

2. Connect variable load RL across terminals 2-2l . 3. Vary RL gradually from minimum value and measure corresponding load current

IL . 4. Find load power for each value of RL and IL. 5. Draw the graph of power v/s load resistances. 6. From the graph note peak power point and correspondingly load resistance.

Verify the same using calculations. 7. Remove the d.c.power supply and short circuit the terminals 1-1l. Remove load

resistance connected across terminals 2-2l and measure the resistance with the help of Multimeter. This resistance is approximately equal to the load resistance found in step 6.

12

Sr.No. Load resistance = RL=VL/IL

Load current IL Power = VL . IL

OBSERVATION TABLE:-

CONCLUSION: - The maximum power transfer takes place from the network to the load when equivalent resistance of the network between terminals 2-2l is equal to the load resistance.

IL

RL

RL

MAX POWER

13

EXPERIMENT NO 5.

AIM: To plot frequency response of series resonance circuit.

APPARATUS: Breadboard, Resistance, Inductance, capacitor, function generator, millimeter (A.C), connecting wires etc.

CIRCUIT DIAGRAM:

R

L

C

Vs

Fun Gen

MA

THEORY:-

In series RLC circuit

Impedance Z =

R2 + (XL –Xc) 2

Current I = V/Z And, Phase angle θ = tan-1 (XL-Xc)/R

If the frequency of the signal fed to such a series circuit is increased from minimum , the inductive reactance (XL= 2πfl) increases linearly and the capacitive reactance (Xc= 1/2πfc) decreases exponentially.

At resonant frequency fr , - Net reactance , X=0 (i.e., XL=Xc) - Impedance of the circuit is minimum , purely resistive and is equal to R - Current I through the circuit is maximum and equal to V/R - Circuit current , I is in phase with the applied voltage V (i.e. phase angle θ = 0). At this particular resonant frequency a circuit is in series resonance. Resonance occurs at that frequency when, XL=Xc or 2πfL = 1/2πfc Therefore fr = 1/2πΓLC

14

BW of series RLC circuit : For frequency above and below resonant frequency fr, f1 and f2 are frequencies at which the circuit current is 0.707 times the maximum current , Imax or the 3dB points.

current

Io

Io/.707

Β. W= f2 – f1

f1

fo

f2

Freq

Therefore from above figs

Bandwidth = ∆f = f2-f1 Hz .

And quality factor Q = fr/∆f = fr/f2-f1

PROCEDURE:

1. Connect function generator and milliammeter as shown in circuit diagram.

2. Set the function generator output voltage to say Vs=10 Volts. 3. Increase the function generator output signal frequency from minimum say 10 Hz

to a maximum signal frequency of 100KHz in decade steps(10,20,30…..100,200,…..1000,2000…..10k,20k…….100kHz).

4. For applied signal frequency measure current with the help of milliammeter. 5. Calculate theoretical frequency using fr =1/2π√LC 6. Plot the graph of frequency v/s current, find the frequency on the graph at which

current is maximum, this frequency is known as Resonant frequency and this should be approximately to the theoretical frequency calculated in step 5.

15

SR.NO Frequency Current (mA) 10Hz

20Hz 1KHz 100kHz

OBSERVATION TABLE:

CONCLUSION: At resonance the current is maximum because the circuit impedance is minimum and is equal to the value of resistance.

16

EXPERIMENT NO.6

AIM:-To plot frequency response of parallel resonant circuit.

APPARATUS:-Bread board, resistor, capacitor, inductor, function generator, LED. milliammeter, connecting wires etc.

CIRCUIT DIAGRAM:-

Ic

I

S

mA 0-30mA

IL

0.1µ

Ic L1 1uH

90 90 IL

Vs

THEORY:-

The circuit having an inductor & capacitor connected in parallel is called parallel resonant circuit

If Xc < XL, then Ic >IL & the circuit acts capacitively . If XL < Xc , then IL >Ic & the circuit acts inductively. If XL = Xc, then IL =Ic & hence the circuit acts as a pure resistor .

In parallel resonant circuit at resonance condition 1. Phase difference between the circuit current and the applied voltage is zero 2. Maximum impedance 3. Minimum line current .

As in series resonance , all resonance circuit have the property of discriminating between the frequency at resonance frequency (fr) and these not at resonance . this property of the resonant circuit is expressed in terms of it’s bandwidth (BW)

17

PROCEDURE :- 1. Make the connections on breadboard according to circuit diagram. 2. Knowing the values of L and C calculate and record the resonance frequency of

parallel resonance circuit. 3. Set the output of function generator to 4 Vrms and frequency to 1khz .Record

the current I through the circuit 4. Increase the frequency gradually and record the resonance frequency Fr at

which the circuit current becomes minimum (that is LED does not glows or glows very dimly.) (This is the resonance frequency of the parallel resonance circuit because at

parallel resonance , current I through parallel LC circuit will be minimum)

5. Compare & record the difference in the resonance frequency calculated at step 2 & that measured in step4

6. Vary the input frequency in steps of 500 Hz around the resonance frequency & in each step record the value of circuit current.

7. From the recorded readings of current in step 6 plot a graph of frequency versus current & mark the resonance frequency.

8. Mark the -3 dB points on the plotted graph. Find bandwidth (B W) & quality factor Q

CONCLUSION:-LED will glow at all frequencies other than at resonant frequency that is circuit impedance is maximum & circuit current is minimum at resonant condition.

I

Fr

f

18

2

EXPERIMENT NO.7

AIM :- To measure input impedance and output impedance of a given two port network

APPARATUS :- Breadboard , resistance , multimeter , connecting wires, etc.

CIRCUIT DIAGRAM:-

V1

1

+

_

I1

R1

R3

R2

R4

2

V2

1 l

l

THEORY:- In two port network port variables are port currents and port voltages. To describe relationship between ports voltages and currents , two linear equations are required. In the two port network , there are four variables . These are the voltages and currents at the input and output ports , namely V1 , I1 and V2 , I2. From this two are independent and two are dependent variables.

By expressing V1 and V2 in terms of I1 and I2

V1=Z11.I1+ Z22.I2 V2=Z21.I2+Z22.I2

From these equations we can find out all Z parameters.

PROCEDURE :-

1. Connect dc power supply Va =5V at port 1-1’ and keep output port open circuited i.e. I2=0.

2. Measure the current I1 by connecting milliammeter in series with R1. 3. Measure voltage V2 across R4 by Multimeter. 4. From these values of V1, V2, I1 and I2 (I2=0) find input driving point

impedance where V1=Va.

i.e. Z11 = V1/I1 I2=0

& Find forward transfer impedance i.e. Z21 = V2/I1

I2=0

19

5. Connect dc power supply Vb= 5v at port 2-2’ and keep input port open circuited i.e. I1=0.

6. Measure the current I2 by connecting milliammeter in series with supply . 7. Measure the voltage V1 across R3 by multimeter . 8. From this value of V2 , V1 , I2 and I1( I1=0) find output driving point impedance

that is

Z22 = V2/I2 I1=0

&

Z12 = V1/I2

I1=0

9. Calculate z-parameters theoretically. These values should be approximately equal to the practical values of z-parameters.

CONCLUSION:-Since Z12=Z21 the circuit is reciprocal and since Z11 = Z22 the circuit is not symmetrical.

20

EXPERIMENT NO. 8

AIM

:- To study high pass filter.

APPARTUS

:-Signal Generator, CRO(dual trace), Connecting Wires

THEORY :- An electric wave filter or simply filter is one electric network which passes or allowed unattenuated transmission of electric signal within certain frequency range & stops transmission of electric signal outside this range.

PARAMETERS OF HIGH PASS FILTER:- 1. What is Characteristic impedance. 2. What is pass band. 3. What is stop band. 4. What is cut-off frequency.

CIRCUIT DIAGRAM :-

PROCEDURE:

C

1uF

L

1uH

C

1uF

Connect function generator as shown in circuit diagram. Set the function generator output voltage to say Vs=10 Volts. Increase the function generator output signal frequency from minimum say 10 Hz to a maximum signal frequency of 1MHz in decade steps(10,20,30…..100,200,…..1000,2000…..10k,20k…….). For applied signal frequency measure voltage. Calculate gain for the frequency . Plot the graph of frequency v/s gain. Find cutoff freq and Ro.

21

S.No. Frequency f Vi Vo Gain = 20 log Vo/ Vi

OBSERVATION:-

FORMULAS Cut- off frequency Fc = 1 / 4Π (LC)1/2

RO = (L / C )1/ 2

CONCLUSION:-

In this way , we have studied high pass flter.

22

EXPERIMENT NO. 9

AIM

:- To study Low pass filter.

APPARTUS :-Signal Generator, CRO(dual trace), Connecting Wires THEORY :- An electric wave filter or simply filter is one electric network which passes or allowed attenuated transmission of electric signal within certain frequency range & stops transmission of electric signal outside this range. PARAMETERS OF LOW PASS FILTER:- 1. What is Characteristic impedance. 2. What is pass band. 3. What is stop band. 4. What is cut-off frequency.

CIRCUIT DIAGRAM :-

L1 1uH

C1 1uF

L2 1uH

PROCEDURE

:-

Connect function generator as shown in circuit diagram. Set the function generator output voltage to say Vs=10 Volts. Increase the function generator output signal frequency from minimum say 10 Hz to a maximum signal frequency of 1MHz in decade steps(10,20,30…..100,200,…..1000,2000…..10k,20k…….). For applied signal frequency measure voltage. Calculate gain for the frequency . Plot the graph of frequency v/s gain. Find cutoff freq and Ro.

23

S.No. Frequency f Vi Vo Gain = 20 log Vo/ Vi

OBSERVATIONS :-

FORMULAS Cut- off frequency Fc = 1 / 2Π (LC)1/2

RO = (L / C )1/ 2

CONCLUSION :- In this way we study Low Pass Filter.

24

s

EXPERIMENT NO. 10

AIM: - To observe and analyze the waveform across capacitor of a series RC circuit excited by a unit step function.

APPARATUS: - Function generator, CRO, breadboard, resistor, capacitor and connecting wires.

CIRCUIT DIAGRAM:-

V( ) t

+

s

+

1 _

v - 1µ - CRO

0

Input Excitation

t

Circuit diagram

THEORY:- The basic switching equation that applies any RC circuit is:

V = vi + (vf – vi )(1 – e-t/RC)

Where V = instantaneous capacitor voltage

vi = initial capacitor voltage (i.e. = 0) vf = target capacitor voltage (i.e.= vcc) t = charging time

RC = time constant.

Therefore V = Vcc (1 – e-t/RC)

Vc

t

25

PROCEDURE:- 1. Connect the setup as shown in diagram . 2. Calculate the RC time constant α (Z=RC) of the circuit and record it . 3. Set the function generator at pulse of Vp-p and pulse tme tp= 1ms 4. For the circuit setup calculate and record the voltage across capacitor on CRO

CONCLUSION :- If we excite the capacitor by unit step function capacitor will charge for period Γ=RC time constant of the ckt.

26

Sl Vs W I VRµ VL Vc IVR cos θ=W/(VS.I)

θ from meter reading

Θ from phasor diagram

EXPERIMENT NO. 10

SERIES RLC Circuit

AIM: To study the behavior of a series R-L-C circuit.

PROCEDURE :

1. Connect the circuit as shown in the diagram. 2. Adjust the rheostat for maximum resistance and the auto transformer to the

position of zero-output voltage and switch on the supply. 3. Adjust the voltage across the circuit to about 70 V and note I, Vs, VL, Vc, VR and

W. 4. Adjust the rheostat for several settings and repeat step 3. 5. Adjust the rheostat to the maximum setting and change the capacitance to 140 µF

and repeat step 4. 6. Compare the values of phase angle as obtained from the meter readings and from

the phasor diagrams. (From the phasor diagrams compute cos θ and θ as given in the last two columns of the table). Draw phasor diagrams showing VR, VL, VC, Vs, & I for different sets of readings.

OBSERVATION:

TABLE- 1 Study of series R- L-C circuit

DISCUSSION:

1. Do you expect θ to be a constant? Is it so as per your experiment? Why? 2. Is IVR equal to W? Compare the difference of wattmeter reading W with IV cos θ

for a few readings and give your comments. 3. Discuss the phenomenon of series resonance in an electrical circuit. 4. Is it possible to have a voltage drop across the energy storage element greater than

the supply?

Questions for Quiz on NT.

1. 2. 3. 4. 5. 6. 7. 8. 9.

10. 11. 12. 13.

State the function of resistor, capacitor and inductor in a circuit? What are the Kirchhoff’s laws? What is mesh analysis or loop analysis? What is node or junction analysis? What is mean by network and what are different types of networks? Explain the term magnetic coupling? State the meaning of resonance in LC circuit? What is the impedance of series LC circuit? State the condition for resonance in a series LC circuit?

What are the characteristics of series LC circuit at resonance? Explain the relationship between the Q factor and bandwidth? What are the different characteristics of LC parallel circuit at resonance? List a few applications of series and parallel LC circuit?

14. What is mean by attenuator? What are the basic requirements of attenuator?

15. 16. 17.

18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30.

What are the different types of symmetrical and asymmetrical attenuator? What is minimum loss attenuator? What is balanced and unbalanced attenuator? Where balanced attenuator is required? What is mean by equalizers? What are the types of equalizers? What is inverse impedance? What are the different parameters of linear time invariant two port network? What is linear graph? What are the properties of trees? What is incidence matrix, cutset matrix and tieset matrix? What are the Laplace transform and sin (ωt) and cos (ωt) ? What is gate function, draw it? State the basic principle of superposition theorem? What are the steps to convert any network into its thevenin’s equivalent? Convert the following network into Norton’s equivalent circuit? What is maximum power transfer theorem? When a linear network is said to be reciprocal or bilateral?

29

4. Conduction of Viva-Voce Examinations:

Teacher should conduct oral exams of the students with full preparation. Normally, the objective questions with guess are to be avoided. To make it meaningful, the questions should be such that depth of the students in the subject is tested. Oral examinations are to be conducted in cordial environment amongst the teachers taking the examination. Teachers taking such examinations should not have ill thoughts about each other and courtesies should be offered to each other in case of difference of opinion, which should be critically suppressed in front of the students.

5. Evaluation and marking system:

Basic honesty in the evaluation and marking system is absolutely essential and in the process impartial nature of the evaluator is required in the examination system to become. It is a wrong approach or concept to award the students by way of easy marking to get cheap popularity among the students, which they do not deserve. It is a primary responsibility of the teacher to see that right students who are really putting up lot of hard work with right kind of intelligence are correctly awarded.

The marking patterns should be justifiable to the students without any ambiguity and teacher should see that students are faced with just circumstances.

30