Jawaharlal Nehru Engineering College

Laboratory Manual

NETWORK ANALYSIS

For

Second Year Students

Manual made by

Prof. M. A. Mulay Prof. V. J. Lipne Prof. T. A. Mohije

” Author JNEC, Aurangabad

MGM’S

Jawaharlal Nehru Engineering College

N-6, CIDCO, Aurangabad

Department of Electronics

&Telecommunication

Vision of the Departme nt:

To develop GREAT technocrats and to establish centre of excellence in the

field of Electronics and Telecommunications.

Global technocrats with human Values

Research and lifelong learning Attitude,

Excellent ability to tackle challenges

Awareness of the needs of society

Technical expertise

Mission of the Department:

1. To provide good technical education and enhance technical competency by

providing good infrastructure, resources, effective teaching learning process

and competent, caring and committed faculty.

2. To provide various platforms to students for cultivating professional

attitude and ethical values.

3. Creating a strong foundation among students which will enable them

to pursue their career choice.

Jawaharlal Nehru Engineering College

Technical Document

This technical document is a series of Laboratory manuals of Electronics &

Telecommunication and is a certified document of Jawaharlal Nehru Engineering

College. The care has been taken to make the document error free but still if any

error is found kindly bring it to the notice of subject teacher and HOD.

Recommended by,

HOD

Approved by,

Principal

FOREWORD

It is my great pleasure to present this laboratory manual for second year engineering students for the subject of Network Analysis, keeping in view the vast coverage required to visualize the basic concepts of various networks using basic components.

NA 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.

Prof. M. A. Mulay Prof. V. J. Lipne Prof. T. A. Mohije

LABORATORY MANUAL CONTENTS

This manual is intended for the second year students of ECT branches in the subject

of Network Analysis. This manual typically contains practical/Lab Sessions related

to Network Analysis, covering various aspects, related to the subject to enhance

understanding.

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. A. Mulay Prof. V. J. Lipne Prof. T. A. Mohije

SUBJ ECT 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. To design a ∏ attenuator which attenuate given signal to the desired level.

9. To study Transmission Lines Parameters

3. Quiz on the subject.

4. Conduction of Viva-Voce Examination.

5. Evaluation and Marking Systems.

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 the procedure.

3. Check CRO probe before connecting it.

4. Strictly follow 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.

EXPERIMENT NO.1

AIM: - To verify Superposition theorem

APPARATUS: - Breadboard, Resistors(220 Ω ,68 Ω,47 Ω), Milliammeter(0-100

mA), connecting wires, etc.

CIRCUIT DIAGRAMS:-

THEORY:- STATEMENT:- The superposition theorem for electrical network states

that for a linear system the response (voltage or current) in any branch of a bilateral

linear circuit having more than one independent source equals the algebraic sum of

the responses caused by each independent source acting alone, where all the other

independent sources are replaced by their internal impedances

To ascertain the contribution of each individual source, all of the other sources

first must be "turned off" (set to zero) by:

1. Replacing all other independent voltage sources with a short circuit (thereby

eliminating difference of potential i.e. V=0; internal impedance of ideal

voltage source is zero( short circuit).

2. Replacing all other independent current sources with an open circuit (thereby

eliminating current i.e. I=0; internal impedance of ideal current source is

infinite (open circuit).

PROCEDURE:-

1. Connect D. C. power supply across terminals1-1´ and apply voltage of

V1=10 volts and similarly across terminals 2-2´ apply voltage of V2=5 volts.

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

3. Now keeping V1 connected as it is and disconnect V2 from supply

and short circuit terminals 2-2’ that is V2=0 volts.

4. Measure currents flowing through all branches for V1=10 volts using

a milliammeter, say these currents are I1', I2', I3'.

5. Now disconnect V1 from supply and make it short circuit i.e. short circuit terminals 1-1´ that is V1=0 volts and connect supply across terminals 2-2´ say V2=5 volts.

6. Measure current flowing through all branches for V2=5 volts using

a milliammeter, say these currents are I1'', I2'', I3''.

7. For verifying superposition theorem I1= I1'+I1'', I2= I2'+

I2'', I3=I'3+I3''(direction of current depends upon )

8. Calculate theoretical values of currents, these values should

be approximately equal to measured values of currents.

OBSERVATION TABLE:-

V1=10v,V2=5v V1=10v,V2=0v V1=0v, V2=5v Difference

Theoretical Practical Theoretical Practical Theoretical Practical Theoretical Value - practical value

I1= I1= I1'= I1'= I1''= I1''= I1=

I2= I2= I2'= I2'= I2''= I2''= I2=

I3= I3= I3'= I3'= I3''= I3''= I3=

'

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

EXPERIMENT NO.2

AIM: - To verify Thevenin's theorem. APPARATUS: - Breadboard, Resistors(220 Ω ,68 Ω,47 Ω), Milliammeter (0-100

mA), D.C. power supply, connecting wires, etc.

CIRCUIT DIAGRAMS :-

THEOR Y: Statement of Thevenin's Theore m : Any two terminal bilateral linear d.c. circuits can be replaced by an equivalent circuit consisting of a voltage source and a series

resistor.

Formulae : Thevenin's equivalent resistance is given by

Rth= R2 + (R 1 R 3׀׀)

Thevenin's voltage is given by

Load current is given by

PROCEDURE:-

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

2. Connect voltmeter across terminals 2-2' ( as shown in Fig2.4)and measure

voltage on voltmeter. This voltage is known as open circuit voltage or Thevenin's voltage (Vth).

3. Disconnect the applied voltage at terminals 1-1' and voltmeter at terminals 2-2'.

4. Now short terminals 1-1l and connect multimeter across terminals 2-2' (as

shown in Fig2.3). With the help of multimeter measure resistance between terminals 2-2' . This is known as Thevenin's resistance (Rth).

5. Calculate Vth and Rth by theoretical calculations, the theoretical values

and measured values of Vth and Rth should be approximately equal.

6. Draw the Thevenin’s equivalent circuit as shown in Fig.2.2

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

dc voltage(as shown in fig 2.1). 8. Repeat the above procedure for two to three different supply voltages.

OBSERVATION TABLE:-

Difference = ׀Theoretical value

Sr.No Vdc Theoretical values Measured va lues -- practical value ׀

Rth Vth ILRth Vth IL Rth Vth IL

CONCLUSION : - The theoretical values and practical values of Vth and Rth

and IL are approximately equal, hence Thevenin's theorem has been verified.

EXPERIMENT NO. 3

AIM: - To verify Norton’s theorem.

APPARATUS: - Breadboard, milliammeter (0-50mA), D.C. power supply (0-30V), multimeter, resistors (220 Ω ,68 Ω,47 Ω), connecting wires, etc.

CIRCUIT DIAGRAMS :

THEORY: Statement of Norton’s theorem: Any linear electrical network with voltage and current sources and only resistances can be replaced at terminals A-B by an equivalent

current source Isc in parallel connection with an equivalent resistance Rint.

Norton's theorem in DC circuit theory terms, that

This equivalent current Isc is the current obtained at terminals A-B of the

network with terminals A-B short circuited.

This equivalent resistance Rint is the resistance obtained with all its voltage

sources short circuited and all its current sources open circuited.

PROCEDURE:-

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

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

3. Disconnect the applied voltage at terminals 1-1´ and milliammeter at terminals

2-2´ .

4. Short terminals 1-1´ and connect Multimeter (keep it on resistance range) across terminals 2-2´ , and note down the reading , this resistance is known as Req/Rint ernal.

5. Calculate Isc and Req by using formulae, the calculated values and

measured values of Isc and Rth should be approximately equal.

6. Connect RL across terminals 2-2´ and measure IL by milliammeter

for applied D.C. voltage.

7. Repeat the above procedure for two to three different supply voltages.

OBSERVATION TABLE:-

Sr. Difference = ׀Theoretical value

No Vdc Theoretical values Measured values -- practical value ׀

Rint Isc IL Rint Isc IL Rint Isc IL

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

verified.

EXPERIMENT. NO. 4

AIM: - To verify maximum power transfer theorem.

APPARATUS: - Power supply, Breadboard, resistances (2.2kΩ), potentiometer (10kΩ), milliammeter, multimeter, etc.

CIRCUIT DIAGRAMS:

THEORY:- Statement of Maximum Power Transfer Theorem: A resistance load, being connected to a dc network, receives maximum

power when the load resistance is equal to the internal resistance (Thevenin’s equivalent

resistance) of the source network as seen from the load terminals.

Power transfer from a dc source network to a resistive network is maximum when the

internal resistance of the dc source network is equal to the load resistance.

Formulae: Load resistance=RL=VL/IL ;

Power=VL ×IL

PROCEDURE:

1. Make the connections according to circuit diagram.

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

3. Connect variable load/ potentiometer RL across terminals 2-2´ .

4. Vary load resistor RL gradually from minimum value to maximum

value and measure corresponding load current IL .

5. Find load power for each value of RL and IL.

6. Draw the graph of corresponding power v/s load resistances.

7. From the graph note peak power point and correspondingly load

resistance. Verify the same using calculations.

8. Remove the d.c. power supply and short circuit the terminals 1-1´. Remove load resistance connected across terminals 2-2´ and measure the resistance with the help of Multimeter. This resistance is approximately equal to the load resistance .

OBSERVATION TABLE:-

Sr.No. Load voltageVL Load current IL Load resistance=RL Power=VL.IL

PL

RL

CONCLUSION : - The maximum power transfer takes place from the lnetwork to the

load when equivalent resistance of the network between terminals 2-2 is equal to the load resistance.

EXPERIMENT NO 5.

AIM: To plot frequency response of series resonance circuit.

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

CIRCUIT DIAGRAM:

THEORY:- In series resonance circuit

Current I = V/Z

And

Phase angle q= 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= 2pfL) increases linearly and the capacitive reactance (Xc= 1/2pfC) 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 q = 0). At this particular resonant frequency a circuit is in series resonance.

Resonance occurs at that frequency when,

XL=Xc or 2pfL = 1/2pfC

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/o.707 B. W = f2 – f1

f1 fo f2 Freq

Therefore from above fig

Bandwidth =D f = f2- f1 Hz .

And quality factor Q = fr/Df = 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.

OBSERVATION TABLE:

SR.NO Frequency Current (mA) 10Hz 20Hz

1KHz

40kHz

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

EXPERIMENT NO.6

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

APPARATUS:-Breadboard, resistor, capacitor, inductor, function generator, LED. Milliammeter (0-100mA), connecting wires etc.

CIRCUIT DIAGRAM:

THEORY:-

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

If Xc < XL, then Ic >IL & the circuit acts capacitive . 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)

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 (glows or glows very dimly.)

(This is the resonance frequency of the parallel resonance circuit because at parallel resonance , current I through parallel LC circ uit 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

OBSERVATION TABLE:

Sr. No. Input Frequency Output Curre nt

1 10Hz

2 50Hz

: :

: :

: :

6 50KHz

7 100KHz

CONCLUSION:- At resonance the current is minimum because the circuit impedance is maximum.

I

Fr f

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:-

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+ Z12.I2

V2=Z21.I1+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

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.

OBSERVATION TABLE:

When I2=0 When I1=0

Theoretical values Measured values Theoretical values Measured values

V1= V1=

V2= V2=

I1= I2=

Z11

=

Z22

=

Z21= Z12=

CONCLUSION:-Since Z12=Z21 the circuit is reciprocal and since Z11 = Z22 the

circuit is symmetrical.

EXPERIMENT NO.8

AIM: To design an ∏ attenuator which attenuate given signal to the desired level.

APPARATUS : Signal generator(0-1MHz),CRO(0-20MHz),Resistors.

Circuit Diagram:

Theory: What is mean by attenuator?

An attenuator circuit allows a known source of power to be reduced by a predetermined factor usually expressed as decibels. A powerful advantage of an attenuator is since it is made from non- inductive resistors, the attenuator is able to change a source or load, which might be reactive, into one which is precisely known and resistive. This power reduction is achieved by the attenuator without introducing distortion.

Shown in figure 1 is the most common attenuator circuit known as the "pi attenuator network". Below are the formulae for calculating the required resistances R1 and R2. An attenuator may be used in either audio or radio signal circuits.

2. Which are the different types of attenuator? Symmetrical T and ∏ attenuator.

Design: RL=600 Ω, D=10dB, R1=R0(N2

-1)/2N) , R1=853.06Ω, R2=R0/2[(N+1)/ (N-1)] ,

R2=577.78Ω N=antilog (Ddb/20), 2R2=1155.5Ω.

Procedure:

1. Connect the circuit as per circuit diagram.

2. Set input voltage VI=10V using signal generator and vary the frequency from (0-1MHz)

in regular steps.

3. Note down the corresponding output voltage.

4. Plot the graph: output voltage Vs frequencies.

Observations:

SR.NO

Frequency

Voltage

Attenuation

Theoretical

Attenuation

Practical

Attenuation

Difference

01 10Hz

02 20Hz

03 1KHz

04 1MHz

Result: Attenuation Theoretical: Attenuation Practical:

Conclusion:

EXPERIMENT NO. 9

Aim:- To study Transmission Lines Types and Parameters

Theory:-

Introduction

A transmission line is used for the transmission of electrical power from generating substation to

the various distribution units. It transmits the wave of voltage and current from one end to

another. The transmission line is made up of a conductor having a uniform cross-section along

the line. Air act as an insulating or dielectric medium between the conductors.

For safety purpose, the distance between the line and ground is much more. The electrical

tower is used for supporting the conductors of the transmission line. Tower are made up of steel

for providing high strength to the conductor. For transmitting high voltage, over long distance

high voltage direct current is used in the transmission line.

Different types of transmission lines

Parameters of transmission line

The performance of transmission line depends on the parameters of the line. The transmission

line has mainly four parameters, resistance, inductance, capacitance and shunt conductance.

These parameters are uniformly distributed along the line. Hence, it is also called the distributed

parameter of the transmission line.

The inductance and resistance form series impedance whereas the capacitance and conductance

form the shunt admittance. Some critical parameters of transmission line are explained below

in detail

Line inductance – The current flow in the transmission line induces the magnetic flux.When

the current in the transmission line changes, the magnetic flux also varies due to which emf

induces in the circuit. The magnitude of inducing emf depends on the rate of change of flux.

Emf produces in the transmission line resist the flow of current in the conductor, and this

parameter is known as the inductance of the line.

Line capacitance – In the transmission lines, air acts as a dielectric medium. This dielectric

medium constitutes the capacitor between the conductors, which store the electrical energy, or

increase the capacitance of the line. The capacitance of the conductor is defined as the present

of charge per unit of potential difference.

Capacitance is negligible in short transmission lines whereas in long transmission; it is the most

important parameter. It affects the efficiency, voltage regulation, power factor and stability of

the system.

Shunt conductance – Air act as a dielectric medium between the conductors. When the

alternating voltage applies in a conductor, some current flow in the dielectric medium because

of dielectric imperfections. Such current is called leakage current. Leakage current depends on

the atmospheric condition and pollution like moisture and surface deposits.

Shunt conductance is defined as the flow of leakage current between the conductors. It is

distributed uniformly along the whole length of the line. The symbol Y represented it, and it

is measured in Siemens.

Performance of transmission lines

The term performance includes the calculation of sending end voltage, sending end current,

sending end power factor, power loss in the lines, efficiency of transmission, regulation and

limits of power flows during steady state and transient conditions. Performance calculations are

helpful in system planning. Some critical parameters are explained below

Voltage regulation – Voltage regulation is defined as the change in the magnitude of the

voltage between the sending and receiving ends of the transmission line.

The efficiency of trans mission lines – Efficiency of the transmission lines is defined as the

ratio of the input power to the output power.

Conclusion:

3. Quiz

1. State the function of resistor, capacitor and inductor in a circuit?

2. What are the Kirchhoff’s laws?

3. What is mesh analysis or loop analysis?

4. What is node or junction analysis?

5. What is mean by network and what are different types of networks?

6. Explain the term magnetic coupling?

7. State the meaning of resonance in LC circuit?

8. What is the impedance of series LC circuit?

9. State the condition for resonance in a series LC circuit?

10. What are the characteristics of series LC circuit at resonance?

11. Explain the relationship between the Q factor and bandwidth?

12. What are the different characteristics of LC parallel circuit at resonance?

13. List a few applications of series and parallel LC circuit?

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

15. What are the different types of symmetrical and asymmetrical attenuator?

16. What is minimum loss attenuator?

17. What is balanced and unbalanced attenuator? Where balanced attenuator is required?

18. What is mean by equalizers? What are the types of equalizers?

19. What is inverse impedance?

20. What are the different parameters of linear time invariant two port network?

21. What is linear graph?

22. What are the properties of trees?

23.Which are the different types of transmission lines ?

24. What are various parameters of transmission lines?

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 co-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. 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 that right students who are really putting up lot of hard wo rk 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.