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NETWORK ANALYSIS (NA)

S.R.C.O.E, LONIKAND PUNE Page

PRACTICAL WORK BOOK

For Academic Session 20_ _

NETWORK ANALYSIS ( 203147 )

2012 pattern

For

S.E. (Electrical Engineering)

Department of Electrical Engineering

(University of Pune)



SHREE RAMCHANDRA COLLEGE OF ENGG. LONIKAND (096)

DEPT. : ELECTRICAL ENGG. NETWORK ANALYSIS ( 203147 ) SEM. : II (SE)

TITLE: INSTRUCTIONS

Do’s and Don’ts in Laboratory (for students):

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 observe the instructions given by the teacher/Lab Instructor.

Guidelines to write your observation book (for students):

1. Experiment Title, Aim, Apparatus, Procedure should be right side.

2. Circuit diagrams, Model graphs, Observations table, Calculations table should be left side.

3. Theoretical and model calculations can be any side as per your convenience.

4. Result and Conclusion should always be at the end.

5. You all are advised to leave sufficient no of pages between experiments for theoretical or

model calculations purpose.

After successful performance of all practical’s following process will be done

Quiz on the subject.

Conduction of Viva-Voce Examination.

Evaluation and Marking Systems





TITLE: LIST OF EXPERIMENTS

Any four experiments from the first five of the following and any four experiments from rest

of the list. (Minimum four experiments should be based on simulation software

PSPICE/MATLAB along with hardware verification)

1. Verification of Superposition theorem in A.C. circuits.

2. Verification of Thevenin’s theorem in A.C. circuits.

3. Verification of Reciprocity theorem in A.C. circuits.

4. Verification of Millmans’ theorem.

5. Verification of Maximum Power Transfer theorem in A.C. circuits.

6. Determination of time response of R-C circuit to a step D.C. voltage input. (Charging and

discharging of a capacitor through a resistor)

7. Determination of time response of R-L circuit to a step D.C. voltage input. (Rise and decay

of current in an inductive circuit)

8. Determination of time response of R-L-C series circuit to a step D.C. voltage input.

9. Determination of parameter of Two Port Network.

10. Determination of Resonance of R-L-C Parallel circuit

11. Determination of Resonance, Bandwidth and Q factor of R-L-C series circuit.





EXPERIMENT NO. : SRCOE/ELECT/NA/01 PAGE:__-__ DATE: EXPERIMENT TITLE: SUPERPOSITION THEOREM

AIM: Verification of Superposition Theorem in A.C. circuits.

APPRATUS:

Sr. No Name of the Equipment Specification Quantity

1 Superposition circuit kit

2 Ammeter

3 Voltmeter

4 Connecting wires

SUPERPOSITION THEOREM STATEMENT

The Superposition Theorem can be used to analyze multi-source AC linear bilateral

networks. It may be stated as follows.

In any multisource (containing initial condition energy sources of emf or current source)

complex network consisting of linear bilateral elements, the responses (loop current or node

voltage) caused by the individual sources of the network may be found by determining the

algebraic sum of the response (current) at that element while considering the effect of

individual source. The other ideal voltage sources are replaced by its internal resistance (or

by a short circuit) and ideal current sources in the network are replaced open circuit across

the terminals. This theorem is valid only for linear systems.

PROOF OF SUPERPOSITION THEOREM:

- Find the current through Z3 by using Superposition Theorem

Z1

1' 2'

21

Z2

Z3 I3 V2V1

Figure No. 1.1

Solution :

Step 1: Considering source V1 acting independently and short-circuiting the other sources

(V2) or replace by internal impedances to measure current through I1’



Z1

1' 2'

21

Z2

V1 Z3 I1'

Figure No. 1.2

I1 is current supplied by V1

I1’ is current through Z3

Step 2: Considering source V2 and short-circuiting the source V1 to measure current through

I2’

Z1

1' 2'

21

Z2

Z3 I2' V2

Figure No. 1.3

I2 is current supplied by V2

I2’ is current through Z3

Step 3: By using superposition theorem current through

I3 is current flowing through load impedance



PROCEDURE:

Superposition Theorem:

1. Connect the circuit as shown in fig (1.1)

2. Set the Variac for rated voltage.

3. Make the supply voltage V2 short-circuited and apply V1 as shown in fig (1.2) and note

down the current through load impedance as .

4. Make the supply voltageV1 short-circuited and apply V2 as shown in fig (1.3) and note

down the current through load impedance as .

5. Now connect the V1 and V2 source to note down current through load impedance Z3 and

verify that theoretically and practically which proves Superposition theorem.

OBSERVATION TABLE:

Z1= ; Z2= ; Z3=

Sr.

No.

V1 = V; V2 = 0V V2 = V; V1 = 0V V1 = V; V2 =

I1’ (mA) I2’ (mA) I3 = I1’ + I2’ (mA)

Practical Theoretical Practical Theoretical Practical Theoretical

THEORETICAL CALCULATION:

CONCLUSION:

EXERCISE:

1. Prove Superposition theorem to find current through Z3 for the given circuit in figure

no. 1.4 and 1.5 practically and theoretically.

V2

18V

1' 2'

21

I3

Z2

2.2KΩZ1

1KΩ

Z3

10KΩV1

8.48V

V2

10 V

1' 2'

21

I3

Z2

125Z1

125

Z3

300V1

90 V

Figure No. 1.4 Figure No. 1.5





EXPERIMENT NO. : SRCOE/ELECT/NA/02 PAGE:__-__ DATE:__:__:__

EXPERIMENT TITLE: RECIPROCITY THEOREM.

AIM: To study Verification of Reciprocity Theorem in A.C. circuits.

APPRATUS:


1 Experimental kit

2 Variac

3 Connecting wires

4 Ammeter

5 Voltmeter

RECIPROCITY THEOREM STATEMENT

The reciprocity theorem states that in any linear, bilateral network consisting of single source

V1, gives the ratio of voltage V1 introduce in one loop to the current I in other loop is same as

the ratio obtain if the positive of V1 and I are interchanged in the network. The response at

any branch (or) transformation ratio is same even after interchanging the sources is V1 / I1 =

V1 / I2. A network that obeys reciprocity theorem is known as reciprocal network.

Before interchanging the source

Z1

1' 2'

21

Z2

Z3V1 I1

Figure No. 2.1

Apply KVL to loop 1

Apply KVL to loop 2



I1 and I2 will get

Obtain ratio of voltage source V1 in loop 1 and current in loop 2

When is adding in loop 1 and current in loop 2

Step 2: When is adding in loop 2 and find current in loop 1

After interchanging the source

Z1

I2

1' 2'

21

Z2

Z3Vs

A

Figure No. 2.2



Loop 1 abca

Loop2 bcb

Hence, we observe from equation 1 and 2 and current in loop1 . The ratio of

and

is

same.

This proves the reciprocity theorem.

PROCEDURE:

Reciprocity Theorem:

1. Connect the circuit as shown in fig (2.1).

2. Note down the ammeter reading as

3. Now interchange the source and ammeter as in fig (2.2).

4. Note down the ammeter reading as

5. Now verify that

=

theoretically and practically which proves reciprocity theorem.



OBSERVATION TABLE:

Z1= ; Z2= ; Z3=

Sr. No. When V1 is acting in loop 1 and current in

loop 2 (V1= Volts)

When V1 is acting in loop 2 and current in

loop 1(V1= Volts)

Practical values Theoretical values Practical values Theoretical values

(mA)

(Ω) (mA)

(Ω) (mA)

(Ω) (mA)

(Ω)


CONCLUSION:

EXERCISE:

Prove Reciprocity theorem for the given circuit in figure no. 2.3

I2

Z1

125

1' 2'

21

Z2

600

Z3

300Vs A

Figure No. 2.3

I2

Z1

27

1' 2'

21

Z2

27

Z3

56Vs A

Ω Ω

Ω

Figure No. 2.4





EXPERIMENT NO. : SRCOE/ELECT/NA/03 PAGE:__-__ Date :

EXPERIMENT TITLE: THEVENIN’S THEOREM

AIM: To Study Verification of Thevenin’s Theorem in A.C. Circuits.

APPRATUS:


1 Experimental kit

2 Digital Multimeter

3 Variac/ regulated power supply

4 Connecting wires

5 Ammeter

6 Voltmeter

THEVENIN’S THEOREM OVERVIEW

Thevenin’s Theorem will be examined for the AC case. While the theorem is applicable to

any number of voltage and current sources, this exercise will only examine single source

circuits for the sake of simplicity. The Thevenin’s source voltage and Thevenin’s impedance

will be determined experimentally and compared to theoretically. The Thevenin’s impedance

is found by replacing all sources with their internal impedance and then applying appropriate

series-parallel impedance simplification rules.

THEVENIN’S THEOREM STATEMENT

Thevenin’s Theorem states that any two terminal linear bilateral networks composed of

energy sources, and impedances can be replaced by an equivalent two terminal network

consisting of an independent voltage source Vth in series with an impedance Zth. Where,

thevenin’s voltage Vth is the open circuit voltage between the load terminals and Zth is the

impedance measured between the terminals with all the energy sources replaced by their

internal impedances.

It is a method for reduction of complex circuit into a simple one.

It reduces the need for repeated solution of the same sets of equations.

PROOF OF THEVENIN’S THEOREM:



Z1= R+jxL

ZL =

R-

jxC

1' 2'

21

Z2

= R

+j(xL

-xC

)

V1

Figure No. 3.1

V1 ZL

1' 2'

21

Z1

Z2

ILA

Figure No. 3.2

Z1

1' 2'

21

Z2

V1I1 I2

Z3

Z4

ZL

Step 1: Remove ZL

Z1

1' 2'

21

Z2

V1I1 I2

Figure No. 3.3



Z1

1' 2'

21

Z2

V1I1 I2

Z3

Z4

ZL

Step 2: Find voltage between terminal 2-2’ i.e

Vth

V1

1' 2'

21

Z1

Z2

Figure No. 3.4

Z1

1' 2'

21

Z2

V1I1 I2

Z3

Z4

Vth

Apply KCL for closed loop cabc

Step 3: Find the impedance between terminal 2-2’, Zth



Z1

1' 2'

21

Z2

ZthV1= 0

Figure No. 3.5

Z1

1' 2'

21

Z2

V1=

0V

I1 I2

Z3

Z4

Zth

Step 4: Figure No. 3.2 is replaced and connect ZL

Vth ZL

IL’

1' 2'

21

Zth

A

Figure No. 3.6

By using Thevenin’s theorem current through ZL

PROCEDURE:

THEVENIN’S THEOREM:

1. Connections are made as per the circuit shown in fig (3.2).

2. Set the Variac and apply the voltage to V1 and note down the current IL flowing through

the load.

3. Connect the circuit as shown in fig (3.3 & 3.4) by open circuiting the load resistance.

Apply the voltage and note down the reading of voltmeter as Vth.



4. Connect the circuit as shown in fig (3.5), measure the effective resistance Zth with the help

of a multimeter, by short-circuiting the voltage source.

5. Connect the Thevenin’s equivalent circuit as shown fig (3.6) note down the load current

IL’.

6. Thevenin’s theorem can be verified by checking that the currents IL and IL’ are equal.

OBSERVATION TABLE:

Z1= ; Z2= ; Z3= ; Z4= ; ZL=

Vs

Volts

Theoretical values Practical values

IL (mA) Vth (Volts) Zth (Ω) IL’(mA) IL(mA) Vth(Volts) Zth(Ω) IL’(mA)

THEORETICAL CALCULATIONS:

CONCLUSION:

EXERCISE :

1. Find current through 600 ohm by using Thevenin’s theorem shown in fig .

ZL

600

1' 2'

21

Z1

125

Z2

300V1

110

2. Find the current through the 15kΩ resistor (ZL) in the circuit using Thevenin’s th'm.

ZL

15kΩ

Z3

5.1kΩ

1' 2'

21

Z 1

2.2 kΩ

Z2

1kΩV1

110Z 4

10kΩ






EXPERIMENT TITLE: MILLMAN’S THEOREM

AIM: To study Verification of Millman’s Theorem in A.C. circuits.

APPRATUS:


1 Circuit Board



4 Connecting wires

5 Ammeter

6 Voltmeter

MILLMAN’S THEOREM STATEMENT:

If n voltage sources V1, V2, ...,Vn having internal impedances ( or series impedances) Z1,

Z2,... Zn respectively are connected in parallel then these sources may be replaced by a single

voltage source Vm having internal series impedance Zm, where, Vm and Zm are given by

VnV1

Zn

1 ' 2'

21

Z1 Z2 Z3

V2 V3

Figure No. 4.1

Zm

2'

2

Vm

Figure No. 4.2



And

Where, are the admittances

Zm

2 '

2

Figure No. 4.3

Corresponding to the impedances



Z1

V1

Z1I1

Figure No. 4.4

Z2

V2

I2 Z2

Figure No. 4.5

Zn

Vn

In Zn

Figure No. 4.6

In Z1I1 I2 I3 ZnZ2 Z3

Figure No. 4.7



PROCEDURE:

1. Do the connection as per circuit diagram.

2. .

3. .

4. .

5. .

OBSERVATION TABLE:

Sr. No. Practical values (mA) Theoretical values

(mA)


CONCLUSION:

EXERCISE

1. Using Millman’s theorem find the current and voltage in resistor Z4 in the given

network

VnV

51

Z4

5

1 ' 2'

21

Z

5 1 Z

22 Z

103

V

4V2

I3

1A

Figure No.4.8

2. Using Millman’s Theorem find the current through 56 Ω in the given circuit.

Vn

4.42VV2

20 V

Z

27Ω

12

2' 1'

Z

15 Ω3

Z

56ΩZ

10 Ω2

V1

8.84 V

2

Figure No.4.9






EXPERIMENT TITLE: TWO PORT NETWORK PARAMETERS

AIM: To Determine the Parameters of Two Port Network’s.

APPRATUS:


1 Two port network kit



4 Connecting wires

5 Ammeter

6 Voltmeter

THEORY:

A two-port network has two terminals name as 1-1’ to which source is connected (driving

energy/input port) and 2-2’ is connected to load (output port), four variables as shown in

figure. These are the voltages and currents at the input and output ports, namely V1, I1 and

V2, I2. To describe relationship between ports voltages and currents, two linear equations are

required. From this, two are independent and two are dependent variables.

V1 V2

I1

I1 I2

I2

2- port

network

Port 1 Port 2

1'

1 2

2'

Figure No.5.1

We will further see Z-parameter, Y-parameter and ABCD parameter

Z-Parameter: Z parameters are called impedance parameters. The parameters Z22 are defined

only when the current in one of the ports is zero i.e. one of the port is open circuited. Hence,

Z-parameters are open circuited parameters. By expressing V1 and V2 (dependent variables)

in terms of I1 and I2 (independent variables)

In matrix form



From the above equations, either we can find out Z-parameters by input terminals or output

terminals are open circuited (assigning values of the independent variables as zero) called

open circuited impedance (ohms).

Z12 I2

Z11

V1

I1

Z22

Z21 I1

I2

V2

Figure No. 5.2

0 .... input impedance

0 .... forward transfer impedance

0 .... reverse transfer impedance

0 .... output impedance

Y-Parameter: These parameters are called admittance parameters. By expressing V1 and V2

(independent variables) in terms of I1 and I2 (dependent variables) given as



From the above equations, we can find out Y-parameters either input or output port are short

circuiting by assigning values of the independent variables as zero. These are called short

circuit admittance parameters (Siemens).

y12 V2

y11

V1

I1

Y21 V1

y22

V2

I2

Figure No. 5.3

0 .... input admittance

ABCD Parameter: These are transmission parameters and are used for analysis of

transmission system where input port is referred as sending end and output port is referred as

receiving end. By expressing V1 and I1 (input port/ dependent variables) in terms of V2 and I2

output port (independent variables).

V1 V2

I1

I1 I2

I2

2- port

network

Port 1 Port 2

1'

1 2

2'

Figure No. 5.3

Considering, the current entering in both the ports and is positive. The indicates that is

leaving the port 2.



ABCD matrix is a transfer matrix of the network. These parameters are measured by open

circuit and short circuit test on the output port (By assigning values of the independent

variables as zero).

A = open circuit voltage gain

B = short circuit transfer parameter

C = open circuit reverse transfer parameter

D = short circuit reverse current gain

PROCEDURE :-

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

.

2. Measure the current I1 by connecting mill ammeter in series with R1 and voltage V2 across

R4 by Multimeter.

3. From these values of V1, V2, I1 and I2 (I2 = 0) find input driving point impedance where V1

= Va. i.e. Z11 = V1 / I1 at I2 = 0 &

Find forward transfer impedance i.e. Z21 = V2 / I2 at I2 = 0.

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

5. Measure the current I2 by connecting milliammeter in series with supply and voltage V1

across R3 by multimeter.

6. From this value of V2, V1, I2 and I1 (I1=0) find output driving point impedance that is Z22 =

V2 / I2 at I1 = 0 & Z12 = V1 / I2 at I1 = 0.

7. Calculate Z-parameters theoretically. These values should be approximately equal to the

practical values of Z-parameters.



OBSERVATION TABLE:

I2 = 0 I1 = 0

Practical values Theoretical values Practical values Theoretical values

V1 V1

V2 V2

I1 I2

Z11 Z12

Z21 Z22

V2 = 0 V1 = 0

I1 I1

I2 I2

V1 V1

Y11 Y11

Y21 Y21


CONCLUSION:

EXERCISE :

1. Find the Z. Y, and ABCD parameter for the given circuit.

'

V2

Z

100

a

1' 2'

21

Z

100

c

Z

50b

V1

I1 I2

Figure No. 5.4

'

Z

2.2kΩ

1' 2'

21

Z

1kΩ

Z560Ω

V1

10 V

I1 I

AA

V2

8 V

Z

560Ω

Z

2.2kΩ

Figure No. 5.5




DEPT. : ELECTRICAL ENGG. NETWORK ANALYSIS ( 203147 ) SEM : II (SE)

EXPERIMENT NO. : SRCOE/ELECT/NA/__ PAGE:__-__ Date :

EXPERIMENT TITLE: RESONANCE OF RLC CIRCUIT

AIM: To Determine Resonance, Resonant frequency, Quality factor and Bandwidth of the

RLC circuit.

APPARATUS:





4 Connecting wires

5 Ammeter

6 Voltmeter

CIRCUIT DIAGRAM :

Vin

R

C

i

Vo

L

Figure No. 6.1

THEORY:

In series RLC circuit Impedance , Current And, Phase angle

Ф= . We know that both and are the function of frequency f. When

f is varied both and get varied.

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 ( = 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 Ф = 0). At this particular resonant frequency, a circuit is in series

resonance. Resonance occurs at that frequency when,

Therefore



BW of series RLC circuit: At series resonance frequency, current is maximum and

impedance is minimum. The power consumption in a circuit is proportional to square of the

current as . Therefore, at series resonance current is maximum and power is also

maximum Pm. The half power occurs at the frequencies for which amplitude of the voltage

across the resistor becomes equal to of the maximum. 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.

Bandwidth: The difference between the half power frequency f1 and f2 at which power is

half of its maximum is called bandwidth of the series RLC circuit. Therefore from above figs

Out of two half-power frequencies, the f2 is upper cut off frequency and f1 is lower cut off

frequency. The current in series RLC circuit as

At resonance,

At half power,

Equating eq 1 and 2



From the equation 3 we can find two values of half power frequency which are and

corresponding to f1 and f2

Equation 7 shows that resonant frequency is geometric mean of the two half power frequency

is

Subtracting equation 5 from equation 4 we get,

Quality Factor: It is the ratio of energy stored in the oscillating resonator to the energy

dissipated per cycle by damping processes. It is dimensionless parameter. It determines the



qualitative behaviour of simple damped circuit. The quality factor of RLC series circuit is the

voltage magnification in the circuit at resonance is

Therefore, the quality factor is

It indicates the selectivity or sharpness of the tuning of a series circuit.

It gives correct indication of the selectivity of such series RLC circuit, which are used

in many circuits.

A system with low Q < ½, is said to be overdamped

A system with high Q > ½, is said to be underdamped

A system with intermediate Q = ½ is said to be critically damped

The quality factor increases with decreasing R

The bandwidth decreases with decreasing R

PROCEDURE:

1. Connect function generator to the CRO and set the output voltage 10Vpp at 1kHz. as

shown in circuit diagram.

2. Apply the input voltage to series resonance circuit as shown in fig. and observe output

voltage on CRO.



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). Note the corresponding output voltage.

4. For applied signal frequency measure current with the help of milliammeter.

5. Calculate the gain in dB and theoretical frequency using

6. Plot the graph of frequency v/s Gain, find the frequency on the graph at which gain 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

(Hz)

Output Voltage

(Vo)

Current (mA) Gain(dB) = 20log(Vo/Vin)

10Hz

20

1kHz

100kHz

Nature of Graph

frequency

lo

10/.707BW= f2-f1

f1 f0 f2

Ga

in

Figure No.


CONCLUSION:

Exercise :

L1=10mH C1=0.047microfarad R1= 4.7kohm

L2= 47mH C2=0.1microfarad R2=2.2ohm





EXPERIMENT NO. : SRCOE/ELECT/NA/__ PAGE:__-__ Date : EXPERIMENT TITLE: RESONANCE OF RLC PARALLEL CIRCUIT

AIM: To Determine Resonance of RLC Parallel Circuit.

APPARATUS:





4 Connecting wires

5 Ammeter

6 Voltmeter

CIRCUIT DIAGRAM:

S

V

R L

i

Cic

Figure No. 7.1

THEORY:

A parallel circuit like the one that is illustrated in Fig. No. is said to be under resonance

when the resultant current drawn by it and the line voltage across it’s terminal are in phase.

The frequency at which this happens is known as resonant frequency. Consider a commonly

used tank circuit for easy simplification.

Inductive reactance of the coil

Capacitive reactance of the coil

Impedance of the coil



Ω

Current in an inductive branch

Phase angle between &

Current in the capacitive branch

The resultant is obtained from the phasor addition of and . If F of such a value that =

then, the resultant current I is minimum L= and in phase with the supply

voltage as shown in figure is said to be in response and the frequency at which this happens is

known as resonance frequency.

The expression for the resonant frequency for the circuit under consider

If fr is the resonant frequency then

If R is small then,



Hence, it should be noted that at resonance, the susceptances of both the parallel branches are

equal and net susceptances of the whole circuit is always zero.

Dynamic Impedances :

At resonance, the resultant current is given by

From equation 2

Putting this value in above equation, we get

The term at the denominator in the above equation is known as the equivalent dynamic

impedance of parallel circuit under resonance of obvious corresponding result is minimum.

Purely resistive as the parallel circuit under resonance offer’s maximum impedance to current

of one particular circuit may be used in ratio or electric circuits to filter out or rejected the

circuit of the desired frequency.

Q-factor of parallel circuit:

Parallel resonance is often refers to as current resonance because even through very little

current is known from supply by the parallel circuit under resonance.

Now from equation 5 the line current drawn from the supply at resonance it given by

The current in the inductive branch is given by

The ratio of current circulating between the two parallel branches to the line current drawn

from the supply is called current magnification. Therefore, from the above equation we have,



Alternatively,

It is the same as that for series resonance circuit

OBSERVATION TABLE:

Sr. No. Parameter Value

1. Resonant frequency (fr)

2. Quality factor

Nature of graph:

ФL

Ic s

inФ

L

CONCLUSION:

EXERCISE:





EXPERIMENT NO. : SRCOE/ELECT/NA/__ PAGE:__-__ Date : EXPERIMENT TITLE: TIME RESPONSE OF RL SERIES CIRCUIT

AIM: Determination of Time Response of series RL circuit to step DC input voltage (rise

and decay of current in an inductive circuit)

EQUIPMENTS REQUIRED:

1. MATLAB SOFTWARE

CIRCUIT DIAGRAM:

S

V

R

Li

Figure No. .1

THEORY

Consider a RL series circuit shown in figure .1 with S is closed at t=0. Kirchoff’s law gives

the differential equation for the circuit

Taking Laplace transform

The initial condition specified by the last equation is as the inductance is unfluxed,

=0 thus above equation is as

Where and are unknown coefficients. As the first step, simplify the equation by putting

all terms over a common denominator.

Equating coefficients to obtain set of linear algebraic equations



From the above equations we get the ,

] , t

The final solution gives a transform into the sum of reversed separate parts is known as

loading of partial fraction expansion.

PROGRAM :

V = 100;

R =.0100;

L=0.10

Lamda =L/R;

Im = V/R;

t=0:01:100

i=Im*(1-exp(-t / lamda)); % rise in current

iL = Im*exp(-t / lamda ); % decay in current

plot (t,i,t,iL);

xlabel(‘time(t) in sec’);

ylabel(‘current in ampere’);

title(determination of time response of RL circuit for step D.C. voltage ( rise and decay of

current in an inductive circuit’).

Nature of graph:



PROCEDURE :

1. Connect the circuit as shown in figure no.

CONCLUSION :




DEPT. : ELECTRICAL ENGG. NETWORK ANALYSIS ( 203147 ) SEM : II (SE)

EXPERIMENT NO. : SRCOE/ELECT/NA/0 PAGE:__-__ Date : EXPERIMENT TITLE: TIME RESPONSE OF RC SERIES CIRCUIT

AIM: Determination of Time Response of RC circuit to step DC input voltage (charging and

discharging of Capacitor).


1. MATLAB SOFTWARE

CIRCUIT DAIGRAM:

S

V

R

C

i

Figure No. .1

THEORY:



PROGRAM:

V = 100;

R = 100000;

C = 100E-6;

Lamda =R*C;

t=0:.1:100

Vc = V*(1-exp(-t / lamda));

Vr = V*exp(-t / lamda );

plot (t, Vc, t, Vr);

xlabel(‘time(t) in sec’);

ylabel(‘voltage in Volts’);

title(‘determination of time response of RC circuit for step D.C. voltage’)





EXPERIMENT NO. : SRCOE/ELECT/NA/__ PAGE:__-__ Date :

EXPERIMENT TITLE: TIME RESPONSE OF RLC SERIES CIRCUIT.

AIM: Determination of Time Response of series RLC circuit to step DC voltage.


1. MATLAB SOFTWARE

CIRCUIT DIAGRAM:

V

R

L

C

Figure No .1

THEORY:

Taking Laplace transform

Multiply by s/L to num and den,

Nature of graph

CONCLUSION :

network analysis (na) - sres, pune · network analysis (na) ... verification of superposition...

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