15A02307 ELECTRICAL TECHNOLOGY AND BASIC SIMULATION...

15A02307 ELECTRICAL TECHNOLOGY AND BASIC SIMULATION LAB

SIETK , EEE

Expt.

No. Name of the Experiment

PAGE

NO

PART-A

1

Magnetization characteristic of a DC shunt generator. Determination

of critical field resistance and critical speed 2-7

2 Swinburne’s Test on DC shunt machine. Predetermination of Efficiency 8-13

3

Brake Test on D.C. Shunt Motor. Determination of Performance

Curves 14-19

4 OC & SC TESTS ON SINGLE PHASE TRANSFORMER 20-25

5 LOAD TEST ON A SINGLE PHASE TRANSFORMER 26-33

PART-B

Expt.

No. Name of the Experiment

PAGE

NO

1

Generation of Various signals and Sequences (Periodic and Aperiodic),

Such as Unit Impulse, Unit Step, Square, Saw Tooth, Triangular,

Sinusoidal, Ramp, Sinc.

2-7

2

Operations on Signals and Sequences such as Addition, Multiplication,

Scaling, Shifting, Folding, Computation of Energy and Average Power. 8-13

3 Convolution between Signals and Sequences. 14-19

4 Autocorrelation and Cross correlation between Signals and Sequences. 20-25

5

Verification of Linearity and Time Invariance Properties of a Given

Continuous / Discrete System. 26-33


SIETK , EEE

6

Finding the Fourier Transform of a given Signal and plotting its

Magnitude and Phase Spectrum.

7 Waveform Synthesis using Laplace Transform.

8

Generation of Gaussian Noise (Real and Complex), Computation of its

Mean, M.S.Values and its Skew, Kurtosis, and PSD, Probability

Distribution Function.

9 Sampling Theorem Verification.

10

Removal of Noise by Auto Correlation / Cross correlation in a given

signal corrupted by noise.

11 Impulse response of a raised cosine filter.

12 Checking a Random Process for Stationary in Wide Sense.


SIETK , EEE

ELECTRICAL

TECHNOLOGY


SIETK , EEE

CIRCUIT DIAGRAM:

To find Generator Shunt field Resistance Rf:

Fig 1.2


SIETK , EEE

EXPT NO: 1 DATE:

MAGNETIZATION CHARACTERISTICS OF A

DC SHUNT GENERATOR

AIM: To plot the magnetization characteristics of the given DC shunt generator and to

determine its critical field resistance and critical speed.

NAME PLATE DETAILS:

Specifications Motor Generator

Power 2.2 KW 2.2 KW

Voltage 220 V 220 V

Current 12 A 10 A

Speed 1500 Rpm 1500 Rpm

Excitation 220 V,0.95 A 220 V,0.4 A

Winding Shunt Shunt

APPARATUS:

S. No Name of the

apparatus Range Type Quantity

1 Voltmeters (0-250 )V

(0-300)V

MC

MC

1

1

2 Ammeter (0-2)A

(0-5)A

MC

MC

1

1

3 Rheostats 350/1.1A Wire Wound 2

4 SPST switch 1

5 Tachometer 1

6 Resistive Load 5 KW, 230 V 1

6 Connecting probes Required number


SIETK , EEE

MODEL GRAPH:

Fig 1.3

TABULAR COLUMN:

S.No

Increasing

Field

current

IF

Generated

emf (Eg1)

S.No

Decreasing

Field

current

IF

Generated

emf

(Eg2)

Average

Generated

emf

(Eg1 +

Eg2)/2

1 1

2 2

3 3

4 4

5 5

6 6

7 7

8 8

9 9

10 10

11 11

12 12

N = Rated speed of

generator


SIETK , EEE

PRECAUTIONS:

1. Avoid loose connections.

2. Avoid parallax error while taking the readings.

PROCEDURE:

1. Make the connections as per circuit diagram (Fig.1.1).

2. Keep the SPST switch in open position; keep the motor field rheostat at minimum

resistance position and the generator field rheostat at maximum resistance position.

3. Close the DPST switch and start the motor using 3-point starter.

4. Adjust the motor field rheostat till the rated speed of the generator is achieved.

5. Note down the residual voltage (voltmeter reading).

6. Close the SPST switch, decrease the resistance of generator field rheostat in steps till the

generator builds up to 125% of its rated voltage and note down the corresponding values

of generated e.m.f and the shunt field current.

7. Now increase the resistance of generator field rheostat in steps and note down the

generated emf for the same field currents as taken in the step 6.

8. Calculate the average of the generated emf for corresponding field currents obtained in

step 6 & 7.

9. Open the DPST switch and disconnect the circuit.

To calculate Generator Shunt field resistance Rf:

10. Connect the circuit as shown in circuit diagram (Fig.1.2)

11. Keeping the load resistance in off position switch ON 220V DC supply and close the

DPST Switch.

12. By varying the load for different values of current note down the meter readings.

13. Observing the precautions switch OFF the supply.

14. Calculate the Field Resistance in each step and take the average value of it.


SIETK , EEE

To calculate Generator Shunt Field Resistance:

S.No Applied Voltage

V(Volts)

Current I

(Amps)

Field winding resistance

Rf (cold) = I

V

1

2

3

4

Average value of Rf (cold) =

Rf (Hot) = 1.2 X Rf (cold) =


SIETK , EEE

To determine Critical Field Resistance Rc:

15. After plotting the magnetization characteristics draw a tangent line to its initial portion,

which passes through the origin.

16. Calculate the slope of this tangent line, which gives the critical field resistance (Rc) at the

rated speed of the generator.

To determine Critical Speed Nc:

17. Draw the designed field resistance line (Rf)

18. Draw a line parallel to y-axis, which cuts the Rf line and Rc line with in the linear portion

of the magnetization characteristics.

19. Take the generated emf values corresponding to points of intersection of the line.

20. Calculate the critical speed using the formula. rated

1

C NE

E2N

SAMPLE CALCULATIONS:

From Graph

1) Critical field resistance, f

2c

I

ER

2) Critical speed, rated

1

C NE

E2N

=

RESULT:


SIETK , EEE

CIRCUIT DIAGRAMS:

Fig 2.1

To find Armature Resistance Ra:

Fig 2.2


SIETK , EEE

EXPT NO: 2 DATE:

SWINBURNE’S TEST ON A DC SHUNT MACHINE

AIM: To conduct the Swinburne’s test on the given DC shunt machine and to pre-determine its

efficiency at various loads when it runs as (a) motor (b) generator.

NAME PLATE DETAILS:

Specifications Motor

Power 3.5 KW

Voltage 220 V

Current 18.5 A

Speed 1500 Rpm

Excitation 220V / 0.9A

APPARATUS REQUIRED:

S. No Name of the


1 Voltmeters (0-300 )V

(0-50)V

MC

MC

1

1

2 Ammeters (0-2) A

(0-5)A

MC

MC

1

1

3 Rheostat 350/1.1A Wire wound 1

4 Tachometer 1

5 Connecting probes Required number

PRECAUTIONS:




SIETK , EEE

TABULAR COLUMN:

S.No

No-Load

Current

IL0

(Amp)

Field

Current

Ish

(Amp)

Terminal

Voltage

VL

(volt)

No-Load

Armature

Current

Iao =ILo- Ish

(Amp)

Armature

Cu loss

Iao2Ra(cold)

(watt)

No-load

Input

VL x ILo

(Watt)

Constant

Losses(WC) =

Input – Cu.

Loss

(Watt)

1

When the machine runs as a Motor:

S.No

Load

current

IL

(Amp)

Field

Current

If

(Amp)

Armature

current

Ia = IL- Ish

(Amp)

Armature

Cu loss

Ia2Ra(hot)

(watt)

Total

losses

WC+

Ia2Ra2

(watt)

Input

=

VL x

IL

(watt)

Output

=

Input –

losses

(watt)

=

100Input

Output

(%)

1

2

3

4

5

6

When the machine runs as a Generator:

S.No

Load

current

IL

(Amp)

Field

Current

If

(Amp)

Armature

current

Ia = IL+

Ish

(Amp)

Armature

Cu loss

Ia2Ra(hot)

(watt)

Total

losses

WC+

Ia2Ra2

(watt)

Output

=

VL x IL

(watt)

Input

=outp

ut

+losses

(watt)

=

100Input

Output

(%)

1

2

3

4

5

6


SIETK , EEE

PROCEDURE:

1. Make the connections as per the circuit diagram (Fig 2.1).

2. Initially close the SPST switch.

3. Close the DPST switch and start the motor using the 3-point starter.

4. Set the motor speed to its rated value by adjusting the field rheostat .

5. Note down the no load motor current ILo, shunt field current Ish and terminal voltage (VL).

6. Open the DPST switch and disconnect the circuit.

To calculate Armature Resistance:

7. Connect the circuit as shown in circuit diagram (Fig 2.2)

8. Keeping the load resistance in off position switch ON 220V DC supply and close the DPST

Switch.

9. By varying the load for different values of current note down the meter readings.

10. Observing the precautions switch OFF the supply.

11. Calculate the Armature Resistance in each step and take the average value of it.


When the machine runs as a Motor:

To find Constant losses:

Terminal voltage (VL) =

No load current (ILO) =

Field current Ish =

No-Load armature current, Iao =ILO- Ish =

Armature resistance Ra(cold) =

No-load Armature Cu loss, Iao2Ra(cold ) =

No-load Input (PO) = VL x ILo =

Constant losses (WC) = PO – No-load Armature Cu loss =


SIETK , EEE

To calculate Armature Resistance Ra:

S.No

Applied

Voltage

V(Volt)

Current

I

(Amp)

Armature resistance

Ra= I

V

1

2

3

4

Average value of Ra (cold) =

Ra(hot) = 1.2 x Ra (cold) =

EXPECTED GRAPH:


SIETK , EEE

To determine Motor Efficiency:

Input voltage (VL) =

Load current (IL) =

Field current (If) =

Armature current (Ia=IL - If) =

Armature resistance Ra(hot) =

Armature copper loss=Ia2Ra(hot) =

Input = VLIL =

Total Losses = WC + Armature copper loss =

Output= Input –losses =

% Efficiency = 100Input

Output =

To determine Generator Efficiency:

Input voltage (VL) =

Load current (IL) =

Field current (If) =

Armature current (Ia=IL - If) =

Armature resistance Ra(hot) =

Armature copper loss=Ia2Ra(hot) =

Output = VLIL =

Total Losses = WC + Armature copper loss =

Input= Output + losses=

% Efficiency = 100Input

Output =

RESULT:


SIETK , EEE

CIRCUIT DIAGRAM:

Fig.3.1

MODEL GRAPH:

Fig 3.2


SIETK , EEE

EXPT NO: 3 DATE:

BRAKE TEST ON DC SHUNT MOTOR

AIM: To obtain the performance curves of the DC shunt motor by conducting brake test.

NAME PLATE DETAILS:

Specification Motor

Power 3.5 KW

Voltage 220 V

Current 18.5 A

Speed 1500 Rpm

Excitation 220 V, 0.95A

Winding Shunt

EQUIPMENT REQUIRED:

S.No Name of the


1 Voltmeter (0-300 )V MC 1

2 Ammeter (0-20) A MC 1

3 Rheostat 350/1.1A Wire Wound 1

4 Tachometer 1

5 Connecting

probes

Required

number

PRECAUTIONS:



3. Before starting the motor, ensure that brake drum is filled with water and it is free

from mechanical load.


SIETK , EEE

TABULAR COLUMN:

Radius of the brake drum(r) =

S.

No

Input

voltage

(Volt)

Current

(I)

(Amp)

Spring

balance

S=

S1~

S2

kg

Speed

(N)

rpm

Torque

(T)

rS9.81

N-m

Output

60

NT2π

(Watt)

Input

V I

(Watt)

%

Efficiency

Input

Output

*100

S1

( kg )

S2

( kg )

1

2

3

4

5

6

7

8

SAMPLE CALCULATIOS:

Input voltage (V) =

Line Current (I) =

Spring balance reading (S1) =

Spring balance reading (S2) =

Radius of the brake drum(r) =

Torque (T)= rSS )~(81.9 21 =

Speed of the motor (N) =

Output power =60

NT2π=

Input power = IV =

%Efficiency = 100Input

Output =


SIETK , EEE

PROCEDURE:

1. Make the connections as per the circuit diagram.

2. Initially keep the field rheostat in minimum resistance position and keep the SPST switch in closed

position.

3. Close the DPST switch and start the motor with the help of 3-point starter.

4. Open the SPST switch and gradually apply the load on the motor up to the rated value and note

down corresponding supply voltage, line current, speed and spring readings.

5. Gradually reduce the load to zero, and then open the DPST switch to disconnect the circuit.

RESULT:


SIETK , EEE

CIRCUIT DIAGRAM :-


SIETK , EEE

EXPT NO: 4 DATE:

OC & SC TESTS ON SINGLE PHASE TRANSFORMER

AIM: -

1. To determine the efficiency and regulation of the given single phase transformer by

conducting open circuit and short circuit test on the given single phase transformer.

2. To determine the equivalent circuit of a given single phase transformer.

NAME PLATE DETAILS:-

S.NO SPECIFICATION RANGE

1 Transformer Rating 2 KVA

2 LV Side Voltage 115 V

3 HV Side Voltage 230 V

4 LV Side Current 17.39 A

5 HV Side Current 8.69 A

6 Frequency 50 HZ

APPARATUS REQUIRED:-

S.No. NAME OF THE APPARATUS RANGE TYPE QUANTITY

1. Auto traonsformer (1 ) 230/(0-270)V 1

2. Ammeter (0-2)A

(0-10)A MI

1

1

3. Voltmeter (0-150)V

(0-75)V MI

1

1

4. Wattmeter 150V,2A,LPF

75V,10A,UPF

DYNAMO

METER

1

1

5. Connecting wires 1 set

PROCEDURE:-

OPEN CIRCUIT TEST:

1. Connections are made as per the circuit diagram.

2. Close the DPST switch after the verification of connections.

3. Gradually increase the input voltage to the single – phase transformer by using auto

transformer to get the rated secondary voltage of single – phase transformer.


SIETK , EEE

TABULAR COLUMN:-

OPEN CIRCUIT:

S. No

Open circuit

voltage in Volts

(V0)

Open circuit

Current in

Amps

(I0)

Watt meter

reading in

watts

Observed

Multiplication

Factor

Total power

in Watts

(Wo)

SHORT CIRCUIT:

S.No

Short circuit

voltage in Volts

(VSc)

Short circuit

Current in

Amps

(ISc)

Watt meter

reading in

watts

Observed

Multiplication

Factor

Total power

in Watts

(WSC)

CALCULATION OF EFFICIENCY:

S.NO POWER

FACTOR

PERCENTAGE EFFICIENCY

¼ LOAD ½ LOAD ¾ LOAD FULL LOAD

1 0.2

2 0.4

3 0.6

4 0.8

5 1


SIETK , EEE

4. Note down the corresponding readings of all the meters connected in the circuit.

5. Now open the DPST switch after gradually reducing the auto transformer’s secondary

voltage to a minimum value.

SHORT CIRCUIT TEST:

1. Connections are made as per the circuit diagram.

2. Close the DPST switch after the verification of connections.

3. Gradually increase the input voltage to the single – phase transformer by using auro

transformer to ger the rated secondary current of single – phase transfomer.

4. Note down the corresponding readings of all the meters connected in the circuit.

5. Now open the DPST switch after gradually reducing the auto transformer’s secondary

voltage to a minimum value.

PRECAUTION:-

1. DPST switch should be kept open.

2. The Auto Transformer should be kept in Minimum Position.


SIETK , EEE

CALCULATION OF REGULATION:

S.

N

O

POWER

FACTOR

PERCENTAGE EFFICIENCY

REGULATION AT ¼

LOAD

REGULATION AT ½

LOAD

REGULATION AT

¾ LOAD

REGULATION AT

FULL LOAD

LAGGING LEADING LAGGING LEADING LAGGING LEADING LAGGING LEADING

1 0.2

2 0.4

3 0.6

4 0.8

5 1

EQUIVALENT CIRCUIT:-

Model Graph:

Z1

R01

X0

X01

R0

V1

I1

IN

IM

Out put power in Watts

% Regulation

Power Factor

Lagging

Leading

UPF


SIETK , EEE

Formulae:

1. Transformation ratio (K) = Vs/Vp =

2. W0 = V0* I0* cos 0 =

3. Iw =I0* cos 0 =

4. Iµ =I0* sin 0 =

5. cos 0 = W0/V0*I0 =

6. sin0 =√(1-cos2 0 =

7. R0=V1/Iw =

8. X0=V1 / Iµ =

9. Ro1 = Wsc/ (Isc)2 in Ohms=

10. X01 = √(Zo1)2 – (R01)

2 in Ohms=

11. Z01 = vsc/ISC(Primary) in Ohms=

12. R02 = K2 . R01 in Ohms=

13. X02 = K2 . X01 in Ohms=

14. Z02 = K2 . Z01 in Ohms=

15. Copper loss = Is2 . R2 Watts=

16. Total loss = Core loss + X2 * Copper loss =

17. Output power = X * Vs * Is * Cos =

18. Input power = Output power + Total losses =

19. % Efficiency = ( Output power / Input power)* 100 =

20. % Regulation at UPF = [(Is * R02) / Vs (rated)] *100 =

21. % Regulation at lagging PF = [ X * Is * (R02 * Cos + X02 Sin) / Vs] * 100

22. % Regulation at leading PF = [X * Is * (R02 * Cos - X02 Sin) / Vs] * 100

RESULT:


SIETK , EEE

CIRCUIT DIAGRAM:-

EXPECTED GRAPH:-


SIETK , EEE

EXPT NO: 5 DATE:

LOAD TEST ON A SINGLE PHASE TRANSFORMER

AIM:-

To determine the efficiency and voltage regulation of a given transformer by conducting

load test on it, using resistive load.

NAME PLATE DETAILS:-

PARAMETER PRIMARY SECONDARY

Power 2 KVA 2 KVA

Voltage 115 V 230 V

Current 17.39 A 8.69 A

APPARATUS REQUIRED:-

EQUIPMENT RANGE TYPE QUANTITY

Ammeter 0 –20 A MI 2 NO’s

Voltmeter 0-300 V MI 1 NO

Voltmeter 0-150 V MI 1 NO

Wattmeters 300 V,20A, UPF DYNAMOMETER 1 NO

Resistive load 5 KW, 20 A --- 1 NO

PROCEDURE:-

1. Connect the circuit as per the diagram and with the load switched off, apply rated voltage to

the primary of the transformer.

2. Note down the readings of the Wattmeter, voltmeter on the secondary side (0V2) in the table

for zero load current.

3. Switch on the load and increase the load in steps and at each step, record the voltage,V2, the

load current, I2 and the input power, Wi in the table.


SIETK , EEE

TABULAR COLUMN:-

S.NO

Primary

Voltage

V1(volts)

Primary

Current

I1(Amps)

Input

Power

W1(watts)

Secondary

Voltage

V2(volts)

Secondary

Current

I2(Amps)

O/P Power

=

V2I2(Watts)

%Efficiency

= (Output /

Input)100

%Regulation =

[(0V2-V2) / V2] 100

1

2

3

4

5

6

7

8

9

10


SIETK , EEE

4. For each set of readings, calculate output powerW0 and hence efficiency and voltage

regulation.

5. Plot the graphs, load versus efficiency and load versus voltage regulation.

6. Find the maximum efficiency of the given transformer and voltage regulation of the

transformer at its full load.

PRECAUTIONS:

1. Care is taken such that there are no loose connections.

2. Readings are noted down without parallax error.


1. Primary Voltage V1 =

2. Primary Current I1 =

3. Input Power W1 =

4. Secondary Voltage V2 =

5. Secondary Current I2 =

6. Output Power = W2 = V2*I2 =

7. % Efficiency = (Output Power / Input Power) * 100

= (W2 / W1) * 100 =

RESULT:


SIETK , EEE

BASIC

SIMULATION


SIETK , EEE

EXPT NO: 1 DATE:

GENERATION OF SIGNALS & SEQUENCES

1. GENERATION OF DISCRETE SIGNALS

AIM: To write a “MATLAB” Program to generate discrete time signals and analog time

signals like unit impulse, unit step, unit ramp, sawtooth, exponential signal and sinusoidal

signals.

SOFTWARE REQURIED :

ATLAB R2006 b (7.3 Versions)

PROCEDURE:

• Open MATLAB

• Open new M-file

• Type the program

• Save in current directory

• Compile and Run the program

• For the output see command windowFigure window

PROGRAM:

clc;

clear all;

close all;

n=-10:1:10;

L=length(n);

for i=1:L

if n(i)==0

x1(i)=1;

else

x1(i)=0;

end;


SIETK , EEE

OUTPUT:


SIETK , EEE

if n(i)>=0

x2(i)=1;

x3(i)=n(i);

else

x2(i)=0;

x3(i)=0;

end;

end;

% to generate exponential sequence

a=0.85;

x4=a.^n;

% to generate sinusoidal sequence

f=0.1;

x5=sin(2*pi*f*n);

figure;

subplot(3,2,1);

stem(n,x1);

xlabel('time n ---->');

ylabel('amplitude---->');

title('Unit step signal');

subplot(3,2,2);

stem(n,x2);xlabel('time n ---->');


title('Unit impluse signal')

subplot(3,2,3);

stem(n,x3);



title('Unit remp signal');

subplot(3,2,4);

stem(n,x4);xlabel('time n ---->');


SIETK , EEE


SIETK , EEE


title('exponential signal');

subplot(3,2,[5,6]);

stem(n,x5);



title('sinusoidal signal');

RESULT:

Thus the Generation of discrete time signals like unit impulse, unit step, unit ramp,

exponential signal and sinusoidal signals was successfully Completed.


SIETK , EEE


SIETK , EEE

2. GENERATION OF CONTINUOUS SIGNALS

PROGRAM:

clc;

Clear all;

Close all;

t=-10:0.01:10;

L=length(t);

for i=1:L

%to generate unit Step and ramp function

if t(i)<0

x1(i)=0;

x2(i)=0;

else

x1(i)=1;

x2(i)=t(i);

end;

end;

%to generate sinusoidal function

f=0.1;

x3=sin(2*pi*f*t);

%to generate Triangular and Sawtooth waveforms

x4=sawtooth(t,0.5);

x5=sawtooth(t);

%to generate sinc function

x6=sinc(t);

figure;

subplot(2,3,1);

plot(t,x1);

xlabel('t--->');ylabel('amp--->');

title('unit step');


SIETK , EEE

OUTPUT:


SIETK , EEE

subplot(2,3,2);

plot(t,x2);


title('unit ramp');

subplot(2,3,3);

plot(t,x3);


title('sinusoidal');

subplot(2,3,4);

plot(t,x4);


title('triangular');

subplot(2,3,5);

plot(t,x5);


title('sawtooth');

subplot(2,3,6);

plot(t,x6);


title('sinc function');

RESULT:

Thus the Generation of continuous time signals like unit step, sawtooth, triangular,

sinusoidal, ramp and sinc functions are successfully completed.


SIETK , EEE


SIETK , EEE

EXPT NO: 2 DATE:

OPERATIONS ON SIGNALS AND SEQUENCES

AIM: To perform various operations on signals such as addition, multiplication,

scaling, shifting and folding, computation of energy and avg power using MATLAB

program.

SOFTWARE REQURIED : MATLAB R2006 b (7.3 Versions)

PROCEDURE:

• Open MATLAB

• Open new M-file





PROGRAM: clc,

close all;

clear all;

t=0:0.001:1;

L=length(t);

f1=1;

f2=3;

x1=sin(2*pi*f1*t);

x2=sin(2*pi*f2*t);

figure;

subplot(3,2,1);

plot(t,x1,'b',t,x2,'r');


SIETK , EEE

OUTPUT:


SIETK , EEE

title('the signals x1(t) and x2(t)');

x3=x1+x2;

subplot(3,2,2);

plot(t,x3);

title('the sum of x1(t) and x2(t)');

x4=x1.*x2;

subplot(3,2,3);

plot(t,x4);

title('the multiplication of x1(t) and x2(t)');

t=-1:0.001:0;

x5=sin(2*pi*f1*(-t));

x6=sin(2*pi*f2*(-t));

subplot(3,2,4);

plot(t,x5,'b',t,x6,'r');

title('the folding of x1(t)and x2(t)');

x7=[zeros(1,200),x2(1:(L-200))];

subplot(3,2,5);

plot(t,x7);

title('the shifting of x1(t)and x2(t)');

x8=x2.^2;

subplot(3,2,6);

plot(t,x8);

title('the squaring of x1(t)and x2(t)');

RESULT:

Thus the MATLAB Program to perform some operations on signals was completed

successfully.


SIETK , EEE


SIETK , EEE

EXPT NO: 3 DATE:

CONVOLUTION OF TWO SEQUENCES

AIM: To write a MATLAB program to find the convolution of two sequences.

SOFTWARE REQURIED :

MATLAB R2006 b (7.3 Versions)

PROCEDURE:

• Open MATLAB

• Open new M-file





PROGRAM:

clc;

clear all;

close all;

n=0:8;

x1=1;

x2=0;

y1=x1.*(n>=0 & n<=2)+x2.*(n>=2 & n<=8);

subplot(2,2,1);

stem(n,y1);

axis([0 8 0 1.5]);



title('the sequence y1[n]')

y2=x1.*(n>=0 & n<=4)+x2.*(n>=4 & n<=8);

subplot(2,2,2);


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OUTPUT:


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stem(n,y2);

axis([0 8 0 1.5]);



title('the sequence y2[n]')

y=conv(y1,y2);

L=length(y);

n=0:L-1;

subplot(2,2,[3,4]);

stem(n,y);

axis([0 10 0 4]);



title('the convolution sequence of y1[n]&y2[n]');

RESULT:

Thus the MATLAB Program to finding the convolution of two sequences is completed

successfully.


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OUTPUT:


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EXPT NO: 4 DATE:

AUTO-CORRELATION & CROSS-CORRELATION

BETWEEN SIGNALS

AIM: To write a matlab program to compute autocorrelation and cross correlation

between signals.

SOFTWARE REQURIED :


PROCEDURE:

• Open MATLAB

• Open new M-file





PROGRAM: clc; clear all; close all;

t=0:0.01:1;

f1=3;

x1=sin(2*pi*f1*t);

figure;

subplot(2,1,1);

plot(t,x1);

title('sine wave');

xlabel('time ---->');


grid;

[rxx lag1]=xcorr(x1);


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OUTPUT:


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subplot(2,1,2);

plot(lag1,rxx);

grid;

title('auto-correlation function of sine wave');

figure;

subplot(2,2,1);

plot(t,x1);

title('sine wave x1');

xlabel('time ---->');


grid;

f2=2;

x2=sin(2*pi*f2*t);

subplot(2,2,2);

plot(t,x2);

title('sine wave x2');

xlabel('time ---->');,ylabel('amplitude---->');

grid;

[cxx lag2]=xcorr(x1,x2);

subplot(2,2,[3,4]);

plot(lag2,cxx);

grid;

title('cross-correlation function of sine wave');

RESULT:

Thus the MATLAB Program of computing auto correlation and cross correlation

between signals was completed successfully.


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EXPT NO: 5 DATE:

LINEAR SYSTEM OR NON-LINEAR SYSTEM

AIM: To write a matlab program to verify the given system is linear or non-linear.

SOFTWARE REQURIED :


PROCEDURE:

• Open MATLAB

• Open new M-file





PROGRAM: clc; clear all; close all;

x1=input('enter the x1[n] sequence='); % [0 2 4 6]

x2=input('enter the x2[n] sequence='); % [3 5 -2 -5]

if length(x1)~=length(x2)

disp(' length of x2 must be equal to the length of x1');

return;

end;

h=input('enter the h[n] sequence=');% [-1 0 -3 -1 2 1]

a=input('enter the constant a= '); % 2

b=input('enter the constant b= '); % 3

y01=conv(a*x1,h);

y02=conv(b*x2,h);

y1=y01+y02;

x=a*x1+b*x2;


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OUTPUT:


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y2=conv(x,h);

L=length(x1)+length(h)-1;

n=0:L-1;

subplot(2,1,1);

stem(n,y1);

label('n --->'); label('amp ---->');

title('sum of the individual response');

subplot(2,1,2);

stem(n,y2);

xlabel('n --->'); ylabel('amp ---->');

title('total response');

if y1==y2

disp('the system is a Linear system');

else

disp('the system is a non-linear system');

end;

INPUT SEQUENCE:

Enter the x1[n] sequence= [0 2 4 6]

Enter the x2[n] sequence= [3 5 -2 -5]

Enter the h[n] sequence= [-1 0 -3 -1 2 1]

Enter the constant a= 2 & enter the constant b= 3

The system is a linear system

RESULT: Thus the MATLAB Program of verifying the system is linear or non linear by

using matlab has performed.


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OUTPUT:


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TIME-INVARIANT OR TIME-VARIANT SYSTEM

AIM: To write a matlab program to verify the given system is Time –invariant or Time–

variant.

SOFTWARE REQURIED :


PROCEDURE:

• Open MATLAB

• Open new M-file





PROGRAM:

clc; clear all; close all;

x=input('enter the sequence x[n]='); %[0 2 3 1 -2 7 3]

h=input('enter the sequence h[n]='); %[4 -5 -11 -3 7 2 6 8 -15]

d=input('enter the positive number for delay d='); % 5

xdn=[zeros(1,d),x]; % delayed input

yn=conv(xdn,h); % output for delayed input

y=conv(x,h); % actual output

ydn=[zeros(1,d),y]; % delayed output

figure;

subplot(2,1,1);

stem(0:length(x)-1,x);

xlabel('n ---->'),ylabel('amp --->');

title('the sequence x[n] ');

subplot(2,1,2);

stem(0:length(xdn)-1,xdn);


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OUTPUT:


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title('the delayed sequence of x[n] ');

figure;

subplot(2,1,1);

stem(0:length(yn)-1,yn);


title('the response of the system to the delayed sequence of x[n] ');

subplot(2,1,2);

stem(0:length(ydn)-1,ydn);


title('the delayed output sequence ');

if yn==ydn

disp('the given system is a Time-invarient system');

else

disp('the given system is a Time-varient system');

end;

INPUT SEQUENCE: Enter the sequence x[n] = [0 2 3 1 -2 7 3]

Enter the sequence h[n] = [4 -5 -11 -3 7 2 6 8 -15]

Enter the positive number for delay d=5

The given system is a Time-invariant system

RESULT:

Thus the MATLAB Program of verifying the system is Time –invariant or Time–variant

System by using matlab has performed.


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SIETK , EEE

EXPT NO: 6 DATE:

FOURIER TRANSFORMS AND INVERSE FOURIER

TRANSFORMS AIM: To find Fourier transform and inverse Fourier transforms of given functions.

SOFTWARE REQURIED :


PROCEDURE:

• Open MATLAB

• Open new M-file





PROGRAM:

To find Fourier transform


syms t s;syms w real;

syms A real;syms o real;syms b float;

f=dirac(t);

F=fourier(f);

disp('the fourier transform of dirac(t) =');

disp(F);

f1=A*heaviside(t);

F1=fourier(f1);

disp('the fourier transform of A =');

disp(F1);

f2=A*exp(-t)*heaviside(t);

F2=fourier(f2);


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OUTPUT:

the fourier transform of dirac(t) =1

the fourier transform of A =A*(pi*dirac(w)-i/w)

the fourier transform of exp(-t) =

A/(1+i*w)

the fourier transform of A*t*exp(-b*t)*u(t) =

A/(b+i*w)^2

the fourier transform of sin(o*t) =

i*pi*(dirac(w+o)-dirac(w-o))

the inverse fourier transform of A*pi*(dirac(w-o)+dirac(w+o)=

A*cos(o*t)

the inverse fourier transform of A*pi*(dirac(w-o)+dirac(w+o)/i=

A*sin(o*t)

the inverse fourier transform of A/(1+jw)=

A*exp(-t)*heaviside(t)

the inverse fourier transform of (3*i*w+14)/((i*w)^2+7*i*w+12)=

heaviside(t)*(-2*exp(-4*t)+5*exp(-3*t))


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disp('the fourier transform of exp(-t) =');

disp(F2);

f3=A*t*exp(-b*t)*heaviside(t);

F3=fourier(f3);

disp('the fourier transform of A*t*exp(-b*t)*u(t) =');

disp(F3);

f4=sin(o*t);

F4=fourier(f4);

disp('the fourier transform of sin(o*t) =');

disp(F4);

To find inverse Fourier transforms of Given functions.

F1=A*pi*(dirac(w-o)+dirac(w+o));

f1=ifourier(F1,t);

disp('the inverse fourier transform of A*pi*(dirac(w-o)+dirac(w+o)=');

disp(f1);

F2=A*pi*(dirac(w-o)-dirac(w+o))/i;

f2=ifourier(F2,t);

disp('the inverse fourier transform of A*pi*(dirac(w-o)+dirac(w+o)/i=');

disp(f2);

F3=A/(1+i*w);

f3=ifourier(F3,t);

disp('the inverse fourier transform of A/(1+jw)=');

disp(f3);

F4=(3*i*w+14)/((i*w)^2+7*i*w+12);

f4=ifourier(F4,t);

disp('the inverse fourier transform of (3*i*w+14)/((i*w)^2+7*i*w+12)=');

disp(f4);

RESULT: Thus the MATLAB program to find fouries transform and inverse fouries

transform of given functions is successfully completed.


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MAGNITUDE AND PHASE SPECTRUM OF FOURIER TRANSFORMS

AIM: To find Fourier transform of the given signal and to plot its magnitude and

phase spectrum.

SOFTWARE REQURIED :


PROCEDURE:

• Open MATLAB

• Open new M-file





PROGRAM:


syms t s ;

syms w float;

f=3*exp(-t)*heaviside(t); % given function

F=fourier(f); % to find Fourier Transform

disp('the fourier transform of 3*exp(-t)*u(t) =');

disp(F); % to display the result in the command window

w=-2*pi:pi/50:2*pi;

F1=subs(F,w); % substitute w in F function

Fmag=abs(F1); % to find magnitude

Fphas=angle(F1); % to find phase

subplot(2,1,1);

plot(w,Fmag);

xlabel('w ---->');


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OUTPUT:

The fourier transform of 3*exp (-t)*u (t) = 3/(1+i*w)


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ylabel('Magnitude --->');

title('Magnitude spectrum');

grid;

subplot(2,1,2);

plot(w,Fphas);

xlabel('w ---->');

ylabel('Phase in radians--->');

title('Phase spectrum');

grid;

RESULT: Thus the MATLAB program to find fouries transform and ploting magnitude

and Phase spectrums is successfully completed.


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OUTPUT:


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EXPT NO: 7 DATE:

LAPLACE TRANSFORM

AIM: MATLAB program to plot the given waveform using waveform synthesis using

Laplace transform.

SOFTWARE REQURIED :


PROCEDURE:

• Open MATLAB Software

• Open new M-file



• Run the program


PROGRAM:

clc;

close all;

syms s;

F =(1/(s^2))*(1-exp(-s)-(1/2)*exp(-3*s)+(1/2)*exp(-5*s));

f=ilaplace(F);

pretty(simplify(f))

ezplot(f,[0,5]);

grid;

RESULT: Thus the MATLAB program the given waveform is plotted by using wave

form synthesis is successfully completed.


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SIETK , EEE

EXPT NO: 8 DATE:

GAUSSIAN NOISE

AIM: To generate a Gaussian noise and to compute its Mean, Mean Square Value,

Skew, Kurtosis, PSD, Probability Distribution function.

SOFTWARE REQURIED :


PROCEDURE:


• Open new M-file



• Run the program


PROGRAM:


t=-10:0.01:10;

L=length(t);

n=randn(1,L);

subplot(2,1,1);

plot(t,n);

xlabel('t --->'),ylabel('amp ---->');

title('normal randon function');

nmean=mean(n);

disp('mean=');disp(nmean);

nmeansquare=sum(n.^2)/length(n);

disp('mean square=');disp(nmeansquare);

nstd=std(n);

disp('std=');disp(nstd);


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OUTPUT:

Mean= 9.2676e-004

Mean square= 0.9775

STD= 0.9889

Var= 0.9780

Skew= -0.0091

Kurt= 2.9520


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nvar=var(n);

disp('var=');disp(nvar);

nskew=skewness(n);

disp('skew=');disp(nskew);

nkurt=kurtosis(n);

disp('kurt=');disp(nkurt);

p=normpdf(n,nmean,nstd);

subplot(2,1,2);

stem(n,p)

RESULTS: Thus To generate Gaussian noise and to compute its Mean, Mean Square Value,

Skew, Kurtosis, PSD, Probability Distribution function is performed.


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EXPT NO: 9 DATE:

SAMPLING THEOREM

AIM: To generate a MATLAB Program to verify sampling theorem.

SOFTWARE REQURIED :


PROCEDURE:


• Open new M-file



• Run the program


PROGRAM:

clc;

close all;

clear all;

f1=3;

f2=23;

t=-0.4:0.0001:0.4;

x=cos(2*pi*f1*t)+cos(2*pi*f2*t);

figure(1);

plot(t,x,'-.r');

xlabel('time-----');

ylabel('amp---');

title('The original signal');

%case 1: (fs<2fm)

fs1=1.4*f2;

ts1=1/fs1;


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OUTPUT:


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n1=-0.4:ts1:0.4;

xs1=cos(2*pi*f1*n1)+cos(2*pi*f2*n1);

figure(2);

stem(n1,xs1);

hold on;

plot(t,x,'-.r');

hold off;

legend('fs<2fm');

%case 2: (fs=2fm)

fs2=2*f2;

ts2=1/fs2;

n2=-0.4:ts2:0.4;


figure(3);

stem(n2,xs2);

hold on;

plot(t,x,'-.r');

hold off;

legend('fs=2fm');

%case 3: (fs>2fm)

fs3=7*f2;

ts3=1/fs3;

n3=-0.4:ts3:0.4;


figure(4);

stem(n3,xs3);

hold on;

plot(t,x,'-.r');

hold off;

legend('fs>2fm');


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RESULTS:

Thus the MATLAB program to verify Sampling theorem is performed.


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SIETK , EEE

EXPT NO: 10 DATE:

REMOVAL OF NOISE BYAUTO-CORRELATION/CROSS-

CORRELATION

AIM: To write a program to detect the periodic signal by Noise using Auto correlation

and Cross Correlation method.

SOFTWARE REQURIED :


PROCEDURE:


• Open new M-file



• Run the program

• For the output see command windowFigure window.

PROGRAM:

clc;

clear all;

close all;

t=0:0.01:10;

s=cos(2*pi*3*t)+sin(2*pi*5*t); % periodic signal

figure;

subplot(2,1,1);

plot(t,s);

axis([0 10 -2 2]);

xlabel(' t ---->'),ylabel(' amp ----> ');

title('the periodic signal');

L=length(t);


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OUTPUT:


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n=randn(1,L); % noise signal

subplot(2,1,2);

plot(t,n);


title('the noise signal');

L=length(t);

f=s+n; % received signal

figure;

subplot(2,1,1);

plot(t,f);


title('the received signal');

rxx=xcorr(f,s,200);

subplot(2,1,2);

plot(rxx);

title('the Correlator output');

RESULTS: Thus the MATLAB Program to detect the periodic signal masked by noise

using Auto Correlation &Cross Correlation method is performed.


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OUTPUT: enter Fd the sampling frequency of digital i/p signal:1

The ratio Fs/Fd must be a positive integer greater than 1

enter Fs the sampling frequency for the filter:4

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

-120

-100

-80

-60

-40

-20

0

20

Magnitude

(

dB)

Magnitude Response (dB)

Normalized Frequency (.. rad/sample)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

-1200

-1000

-800

-600

-400

-200

0

Phase

(

degrees)

Phase Response


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EXPT NO: 11 DATE:

IMPULSE RESPONSE OF RAISED COSINE FILTER

AIM: To Design an FIR Raised Cosine Filter and to plot its Magnitude, Phase and

Impulse responses using MATLAB.

SOFTWARE REQURIED :


PROCEDURE:


• Open new M-file



• Run the program


PROGRAM:

Fd=input('enter Fd the sampling frequency of digital i/p signal:');

disp('The ratio Fs/Fd must be a positive integer greater than 1');

% Define filter-related parameters.

Fs=input('enter Fs the sampling frequency for the filter:');

filtorder = 40; % Filter order

delay = filtorder/(Fs*2); % Group delay (# of input samples)

rolloff = 0.25; % Rolloff factor of filter

rcfilter = rcosine(Fd,Fs,'fir',rolloff,delay);

H=tf(rcfilter)

% Plot impulse response.

%figure; impz(rcfilter,1)

fvtool(rcfilter)


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Normalized Frequency (.. rad/sample)

Impulse Response

Amplitude

1.2

1

0.8

0.6

0.4

0.2

0

-0.2

0 5 1015 20253035 40

Samples


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RESULT: The Impulse Response of a Raised Cosine Filter was plotted using fvtool in

MATLAB.


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SIETK , EEE

EXPT NO: 12 DATE:

WSS OF A RANDOM PROCESS

AIM: To generate a Random process and to check for its Wide Sense Stationary using

MATLAB

SOFTWARE REQURIED :-


PROCEDURE:


• Open new M-file



• Run the program


PROGRAM:

clc;

clear all;

close all;

syms pi a wo t t1 t2 theta

l=input('Enter the lower limit');

u=input('Enter the upper limit');

x=input('Enter the PDF');

f=a*cos((wo*t)+theta);

f1=f*x;

y1=int(f1,theta,l,u);

disp('The Expectation is:');

disp(y1);

f2=a*cos((wo*t1)+theta);


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OUTPUT:

Enter the lower limit0

Enter the upper limit2*pi

Enter the PDF1/(2*pi)

The Expectation is: 0

The AutoCorrelation is:

1/2*a^2*(cos(wo*t1)*cos(wo*t2)+sin(wo*t1)*sin(wo*t2))


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f3=a*cos((wo*t2)+theta);

f4=f2*f3*x;

y2=int(f4,theta,l,u);

disp('The AutoCorrelation is:');

disp(y2);

Manual Calculation

1) Consider the random process X(t)=Acos(.0t+T) Where “T” is real-valued random

variable and is uniformly distributed over [0, p]. Check if the process is wide sense

stationary.

2) Consider the random process X(t)=A cos(.0t+T) Where “T” is real-valued random

variable and is uniformly distributed over [0, 2p]. Check if the process is wide sense

stationary.

RESULT: Thus the given random processes are identified whether they are WSS or

not through calculating the mean and autocorrelation functions manually and verified

these results through MATLAB simulation.

15A02307 ELECTRICAL TECHNOLOGY AND BASIC SIMULATION...

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