Jawaharlal Nehru Engineering College

Jawaharlal Nehru Engineering College Laboratory Manual Network Theory For Second Year Students 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 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 measure input impedance and output impedance of a given two port network. 6. Design of a High Pass Filter. 7. Design of a Low Pass Filter. 8. To observe and analyze the waveform across a capacitor of a series RC circuit exited by a unit step function. 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:- V1 R R 1 1 2 2 I1 I2 R3 I3 V2 10 VOLTS 15 VOLTS l l 2 1 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 1-1 l and apply voltage of say V1=10 volts and similarly across terminals 2-2 l 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 terminals1-1 l and short circuit terminals 2-2 l 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 I 1, I2, I3. 5. Similarly connect only V2 =15 volts across terminals 2-2 l and short circuit terminals 1-1 l 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 I 1 = I 1 + I 1, I 2 = I 2 + I 2, I3=I3 +I3. 8. Calculate theoretical values of currents, these values should be approximately equal to measured values of currents. 6

OBSERVATION TABLE:- V1=10VOLTS V1=10VOLTS V1=0VOLTS V2=15VOLTS V2=0 VOLTS V2=15VOLTS I1= I1 = I1 = I2= I2 = I2 = I3= I3 = I3 = V1 R1 R2 1 2 I1 I2 R3 I3 V2 10V 15V 1 2 V1 R1 R2 1 2 I1 I2 R3 I3 V2 10V 15V 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 R3 RL 1 2 THEORY:- The current flowing through the load impedance R L connected across the terminals 2 & 2 l 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 & 2 l. Its internal impedance is the same as the impedance of the network looking back into the terminals 2 & 2 l, when all sources have been replaced by impedances and sources with output terminals 2 & 2 l. across which load impedance R L is connected. PROCEDURE:- 1. Apply dc voltage across terminals 1-1 l, call this voltage as Vdc. 2. Connect voltmeter across terminals 2-2 l 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 1-1 l and repeat step 2, take two/three readings. 4. Disconnect the applied voltage at terminals 1-1 l and voltmeter at terminals 2-2 l. 5. Now short terminals 1-1 l and connect multimeter across terminals 2-2 l. With the help of multimeter measure resistance between terminals 2-2 l. 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 2-2 l and measure IL for applied dc voltage. 8

OBSERVATION TABLE:- Sr.No. Vdc Measured values Theoretical values Rth Vth I L Rth Vth I L 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 R3 RL 1 2 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 Y AB. The Isc is short circuit current between the network and Y AB is the admittance measured between the terminals, with all energy sources eliminated except their internal impedances. PROCEDURE:- 1. Apply d. c. voltage across terminals 1-1 l called this voltage Vdc. 2. Connect milliammeter across terminals 2-2 l and measure current, this is the short circuit (Isc) current. 3. Vary the d. c. voltage across terminals 1-1 l and repeat step 2, take three readings. 4. Disconnect the applied voltage at terminals 1-1 l and milliammeter at terminals 2-2 l. 5. Short terminals 1-1 l and connect Multimeter (keep it on resistance range) across terminals 2-2 l, 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 2-2 l and measure IL by milliammeter for applied D.C. voltage. 10

OBSERVATION TABLE:- Sr.No. Vdc Measured values Calculated values Isc Req I L Isc Req I L CONCLUSION: - The Calculated values and measured values of Isc, IL, Req are approximately equal; hence Norton s theorem has been verified. 11

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 2 l THEORY:- Maximum power will be delivered by a network to an impedance Z R if the impedance of Z R is the conjugate of the impedance Z l of the network, measured looking back into the terminals of the network. Z l E ZL PROCEDURE:- 1. Make the connections according to circuit diagram. 1. Connect d.c. power supply of say Vdc=20 volts across terminal 1-1 l. 2. Connect variable load RL across terminals 2-2 l. 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 1-1 l. Remove load resistance connected across terminals 2-2 l and measure the resistance with the help of Multimeter. This resistance is approximately equal to the load resistance found in step 6. 12

OBSERVATION TABLE:- Sr.No. Load resistance = Load current I L Power = V L. I L R L =V L /I L CONCLUSION: - The maximum power transfer takes place from the network to the load when equivalent resistance of the network between terminals 2-2 l is equal to the load resistance. IL RL MAX POWER RL 13

EXPERIMENT NO.5 AIM :- To measure input impedance and output impedance of a given two port network APPARATUS :- Breadboard, resistance, multimeter, connecting wires, etc. CIRCUIT DIAGRAM:- 1 I1 R1 R2 2 + V2 V1 R3 R4 _ 1 l 2 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 14

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 Z12 = V1/I2 I1=0 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. 15

EXPERIMENT NO. 6 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 :- C 1uF C 1uF L 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. 16

OBSERVATION:- S.No. Frequency f Vi Vo Gain = 20 log Vo/ Vi FORMULAS Cut- off frequency F c = 1 / 4Π (LC) 1/2 R O = (L / C ) 1/ 2 CONCLUSION:- In this way, we have studied high pass flter. 17

EXPERIMENT NO. 7 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 L2 1uH C1 1uF 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. 18

OBSERVATIONS :- S.No. Frequency f Vi Vo Gain = 20 log Vo/ Vi FORMULAS Cut- off frequency F c = 1 / 2Π (LC) 1/2 R O = (L / C ) 1/ 2 CONCLUSION :- In this way we study Low Pass Filter. 19

EXPERIMENT NO. 8 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() 1 0 t Input Excitation + s + _ vs --1µ Circuit diagram CRO 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 Vc V = Vcc (1 e -t/rc ) t 20

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.

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