circuit theory lab manual.pdf

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FUTURE INSTITUTE OF ENGINEERING AND MANAGEMENT ELECTRIC CIRCUIT THEORY LABORATORY LAB MANUAL PAPER CODE : (EE – 391)

List of Experiments Credits:2

1. 2. 3. 4. 5. 6.

7. 8. 9.

Contact:3

Transient response of R-L and R-C network: simulation with PSPICE /Hardware. /Hardware. Transient response of R-L-C series and parallel p arallel circuit: Simulation with PSPICE/ Hardware. Determination of Impedance (Z) and Admittance (Y) parameter of two port network: n etwork: Simulation/Hardware. Simulation/Hardware. Frequency response of LP and HP filters: Simulation / Hardware. Frequency response of BP and BR filters: Simulation /Hardware. /Hardware. Generation of Periodic, Exponential, Sinusoidal, Damped Sinusoidal, Step, Impulse, Ramp signal using MATLAB in both discrete and analog form. Determination of Laplace transform and Inverse Laplace transform using MATLAB. Amplitude and Phase spectrum analysis of different signals using MATLAB. Verification of Network theorem using SPICE.

PAPER CODE: EE-391/EE-2

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List of Experiments Credits:2

1. 2. 3. 4. 5. 6.

7. 8. 9.

Contact:3

Transient response of R-L and R-C network: simulation with PSPICE /Hardware. /Hardware. Transient response of R-L-C series and parallel p arallel circuit: Simulation with PSPICE/ Hardware. Determination of Impedance (Z) and Admittance (Y) parameter of two port network: n etwork: Simulation/Hardware. Simulation/Hardware. Frequency response of LP and HP filters: Simulation / Hardware. Frequency response of BP and BR filters: Simulation /Hardware. /Hardware. Generation of Periodic, Exponential, Sinusoidal, Damped Sinusoidal, Step, Impulse, Ramp signal using MATLAB in both discrete and analog form. Determination of Laplace transform and Inverse Laplace transform using MATLAB. Amplitude and Phase spectrum analysis of different signals using MATLAB. Verification of Network theorem using SPICE.


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EXPERIMENT NO: INTRODUCTION EXP TITLE:

INTRODUCTION OF MATLAB COMMANDS.

M A T L A B is a software package for high performance numerical computation and visualization The full form of MATLAB is Matrix Laboratory. It provides interaction with hundred built in functions for computation, graphics and animation. MATLAB's built in functions provides algebra computation, data analysis, signal processing, optimization, numerical solution, of ordinary differential equations (ODEs), 2-D, 3-D graphics etc. The basic building block of MATLAB is matrix. The fundamental data type is the array, Vectors, scalars, real matrices and complex matrices are automatically handled as special case of the basic data types.

MA TLAB works through three basic windows I . Command Window: This is the main window, It is started with a sign '»' All commands, including those for running user-written programs. are typed in this window. 2. Graphics Window: The output of all graphics commands typed in the command window are flashed to the graphics window or Figure window. 3. Edit Window: Programmer can write. edit. create and save programs 111 1 11 files f iles called 'M-files', 'M-files', in most systems MA TLAB provides its own built in editor BASIC COMPUTATION OF ARITHMETIC, LOGARITHM, TRIGONOMETRIC AND EXPONENTIAL FUNCTION USING MATLAB

1 . Entering and displaying constants and expressions. (i)Y=2^5/(2^5-1); Y=? (ii)X=5; Y=4*X +12/3-100^0.5; Y=?

2 (5 ASSIGNMENT:

Calculate

3

2

−

8

( 2 + 1)

1 5


8

) =?

6

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HANDLING WITH MATRICES

1. Entering a vector and displaying it. X= [1 2 3 4 5]; Y=10+X;

Y =?

2. Entering and displaying matrices (i)A=[1 2;3 4; 5 6]; A=?

(ii)XX=[1;2;3;4]; XX=? (iii)Z=[]; Z=?

(iv)I=eye(4); I=? 3. Creating arrays with a colon. (i)D=1:4 ; D=?

(ii)D=1:0.5:4 ; D=?

length(D)=?

(iii)X=-1:0.5:1; Y=X.*X ; X=?

Y=?


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(iv) Create a vector M with 5 divisions linearly spaced between 0 and10. Use linspace .

4. Note the following functions and special constants from help abs, sin, atan, conj, cosh, exp, log, log10, real, imag, pi, sum, diag. Calculate

3

(i) ln(e ) (ii) log(e) (ii)e


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5. Write the command syntax with its meaning in brief from help. clc, clear, size, quit.

6. Note the following matrix functions eig, poly, inv, trace, det. With arbitrary nonsingular 3x3 matrices A, B and diagonal -1

-1

matrix L, find L , trace (A), trace(B), eig(L), eig(A LA), poly(L). T

Compare eig(A) and eig(A ).


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7. Note the functions of the linear 2D plot function “ plot” and auxiliary functions “subplot”, “axis”, “grid”, “xlabel”, “ylabel”, “title”. (i)

Try the command sequence x=-pi:pi/300:pi; y=tan(sin(x))-sin(tan(x)). Plot(x,y)

(ii)

Use xlabel, ylabel and title. Change the line type and colour.

(iii)

Toggle the grids on and off.

(iv)

Superimpose 2cos(x) on the graph.

(v)

Crop the graph to view interesting parts of the graph closely.


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……………………………………… Signature of Teacher with date

……………………………………. Signature of student with date Department: Roll No. :


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EXPERIMENT NO. : 01 T I T L E : Transient response in RL & RC networks. OBJECTIVE: To study the transient response of a series RL & RC networks due to continuous pulse excitation. CIRCUIT DIAGRAM:

APPARATUS REQUIRED:

Sl.No .

Name of the apparatus

Specification (Range, Rating, Makers name)

Quantity

1.

CRO

1

2.

Function Generator

1

3.

Decade Resistance Box

2

4.

Decade Inductance Box

1

5.

Decade Capacitance Box

1

6.

CRO Probes

As required

7.

Connecting Wires

As required


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THEORY: SERIES RL NETWORK: A.Charging of Inductor / Decay of Voltage Let ‘i’ be the current flowing through and v L (t) be the instantaneous voltage across the inductor. Applying KVL to the series RL circuit we have

  and L = V   =>V=  � dt + V   =>i =  Ldt � V= R i + L

L

L

L

Taking Laplace on both sides

V = R V (S) + V (S)  �SR  �S V => = [   R ] V ( S ) �S   �  V (S) =>V = � V =>V ( S ) = S R� Taking Inverse Laplace on both sides �  V ( t ) = V�  L

L

L

L

L

L

=> V L ( t ) = V

�

[Where

τ = time constant =

�] 

B. Discharging of Inductor/ Rise in Voltage

  R   R = � dt +  � d t + v  �  R [ � d t = V ( 0 ) ]  R =>0 = V +  � dt + v  R = > - V = � dt + v � Taking Laplace on both sides V R - = [ + 1] V ( S ) S R�S �S V =>- = (S) S �S *V V =>V (S) = S R � 0 = iR + L L

L

L

L

L

-

L

L

L

L

L

L

L

Taking Inverse Laplace on both sides


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�R� =>V (t) = -V �  V L (t) = -V L

SERIES RC NETWORK: A.Charging of Capacitor / Growth of Voltage: V = iR + v c

=>V = RC

 +v 

{i =

c

 

&

q = cv c }

Taking Laplace on both sides

V = RC[Sv ( S ) - v ( 0 ) ] + v ( S )  VRC A V B => = v (S)[RCS + 1] = = +   S SS  RC S S  RC V V = V( -  ) = -  S S RC S S  RC c

-

c

c

c

Taking Inverse Laplace on both sides

�RC)  ( 1- � )

Vc(t) = V(1Vc(t) = Vm



{ (time constant) = RC V m = V}

B.Discharging of Capacitor/ Decay of Voltage

0 = RC

 + v 

c

= 0

Taking Laplace on both sides = > R C [ S V C (S) – V C ( 0 )] + V C (S) = 0 { V C ( 0 - ) = V m = V} =>[RCS + 1]V C (S) = VRC

 ] V (S) = VRC RC V =>V (S) = S RC Taking Inverse Laplace on both sides  V ( t ) = V �  { τ = RC , V = V} =>RC[S +

C

C

c

m

m


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PROCEDURE: 1. Connect the circuit as per the circuit diagram. 2. Switch on the supply. 3. Set the decade resistor and inductor / capacitor box (for RL or RC circuit respectively) to desired values. 4. Apply pulse input by help of function generator and see the output voltage response in CRO. 5. Plot the tr ansient response graph for both charging and discharging inductor / capacitor. 6. Find time constant from the graph and compare with the theoretical value.

OBSERVATION TABLE: A) FOR RL NETWORK:-

R= SL No .

L= CHARGING

TIME FROM CRO (ms)

DISCHARGING

VL IN VOLT FROM CRO

TIME FROM CRO (ms)

THEORI TICAL TIME CONSTA NT,τ (ms)

VL I N VOLT FROM CRO

TIME CONSTANT FROM GRAPH Chargin g,τc(ms)

Dischar ging, τd (ms)

CALCULATION: CHARGING:For decaying maximum amplitude of voltage = 37% of maximum voltage = τc = Error in time constant, τ DISCHARGING:During rising maximum amplitude of voltage = 63% of maximum voltage = Error in time constant, τ τd =

�

�


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B) FOR RC NETWORK : R = SL No .

C = CHARGING

TIME FROM CRO (ms)

DISCHARGING

VC IN VOLT FROM CRO

TIME FROM CRO (ms)

VC IN VOLT FROM CRO

THEORI TICAL TIME CONST ANT, τ (ms)

TIME CONSTANT FROM GRAPH Chargin g, τ c ( m s )

Dischar ging, τd (ms)

CALCULATION: CHARGING:For charging maximum amplitude of voltage = 63% of maximum voltage = Error in time constant, τ τc = DISCHARGING:For discharging maximum amplitude of voltage = 37% of maximum voltage = Error in time constant, τ τd =

�

�

CONCLUSION:




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EXPERIMENT NO. : 02

Transient response in RLC series & RLC parallel circuit. OBJECTIVE: To study the response of RLC series and RLC parallel circuit due to continuous pulse excitation. RLC SERIES CIRCUIT THEORY:

By applying KVL in the series RLC circuit, Applying KVL,

       

V= iR + L +

Using laplace transformation,

V = R.I (S) + L [SI(S) – I(0 )] +  I(S) S CS  = ( R + SL + ) I(S)   CS V RCS�CS => = I(S) S CS VC = VC  => I(S) = �CSRCS �C S R⁄�S L� V⁄�  = A + B =  � S  L S L� S S S S +

Where

S1, 2 = -

R   R    � � �C


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�  �  R  (a) If (  > , the response is over damped. �R �C (b) If (  = , the response is critically damped. �R �C (c) If (  < , the response is under damped. � �C

=> i(t) = A  + B  The actual response depends on the expression under the radical in equation (*).


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RLC PARALLEL CIRCUIT THEORY :

I0 = IR + IL + IC

V +   ����  � V R �  Taking laplace transform, I = VS +  V(S) + CSV(S) S I R  �S  => = [ + + CS] V(S) SI R�SR �C �CRS =>  = [ S R�SI ⁄C ] V(S) => V(S) =   S  �� S L� A + B => V(S) = S S S S        Where S = RC RC �C => V(t) = A�  + B�    , Under damped. (a) If (  < RC �C   (b) If (  = , Critically damped. RC �C   , Over damped. (c) If (  > RC �C =

1, 2


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voltage

time Under dam ed res onse

voltage

time Critically damped response

voltage

time Over damped response


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Pspice CIRCUIT DIAGRAM: (a) Series RLC Circuit :

(b)

Parallel RLC Circuit :


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SPECIFICATION OF V-PULSE AND I-PULSE:

V-PULSE: DC=1V; AC=0V; V1=0V; V2=1V; TD=.001 µ s; TR=0.001ms; TF=0.001ms; PW=1ms; PER=1.002ms;

I-PULSE : DC=1A; AC=0A; I1=0A; I2=1A; TD=.001 µ s ; TR=0.001ms; TF=0.001ms; PW=1ms; PER=1.002ms;

INITIAL AND CIRCUIT: 

FINAL

VALUE

Pspice schematics: Goto → Analysis → transients →

OF

TIME

AXIS

IN

(i)Print step → 0 µ s ; (ii)Final step → 400 µ s ;


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RLC


OBSERVATION TABLE: RLC SERIES CIRCUIT

SL NO

CONDITION

R L

C

OBSERVATION TIME

1

VOLTAGE

UNDER DAMPED  R 2 1    >   2 L  LC 

2

OVER DAMPED  R 2 1    >   2 L  LC 

3

CRITICALLY DAMPED  R 2 1    =   2 L  LC 


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OBSERVATION TABLE: RLC PARALLEL CIRCUIT

SL NO

CONDITION

R

L

C

OBSERVATION TIME

1

UNDER DAMP

2

OVERDAMP

3

CRITICALLY DAMP


CURRENT



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EXPERIMENT NO. : 03 E X P T I T L E : Determination of impedance and admittance parameters. OBJECTIVES: To s tudy the two port network and determine its impedance and admittance parameters. THEORY: Z-PARAMETER (OPEN PARAMETER) 1 + V1

CIRCUIT I2

I1 TWO PORT NETWORK

─

/IMPEDANCE 2 + V2

─ 2′

1′

In case of two port network, the input and output voltages V 1 & V 2 can he expressed in terms of input and output currents I 1 & 1 2 respectively as [V]=[Z][I] where Z is the impedance matrix. This is represented as: Where,

Z1 1 =

V 1 I 1

V 1 = Z 11 I 1 + Z 12 I 2 V 2 = Z 21 I 1 + Z 22 I 2

when output terminal (2-2’) is open (i.e. I 2 =0) =

input driving point impedance. Z21=

V 2 I 1

when output terminal (2-2’) is open (i.e. I 2 =0)= reverse

transfer impedance. Z22 =

V 2 I 2

when input terminal (I-I’) is open (i.e. 11 =0)=output

driving point impedance. Z12=

V 1 I 2

when output terminal (I-I’) is open (i.e. I 1 =0) = forward

transfer impedance. Z 1 1 , Z 1 2 , Z 2 2 , Z 2 1 are also called impedance parameters or open circuit parameters If Z1 2 = Z 2 1 then the network satisfies the principle of reciprocity or the network is reciprocal .


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Y-PARAMETER PARAMETER) 1 + V1

(SHORT

CIRCUIT I2

I1

2 + V2

TWO PORT NETWORK

─

/ADMITTANCE

─ 2′

1′

In case of two port network, the input and output currents I 1 & I 2 can he expressed in terms of input and output voltages V 1 & V 2 respectively as [I]=[Y][V] where Y is the admittance matrix. This is represented as: Where,

Y11=

I 1 V 1

I 1 = Y 11V 1 + Y 12V 2 I 2 = Y 21V 1 + Y 22V 2

when output terminal (2-2’) is shorted (i.e.

V 2 =0)=input driving point admittance Y21=

I 2 V 1

when output terminal (2-2’) is open (i.e. V2 =0)= reverse

transfer admittance. Y22 =

I 2 V 2

when input terminal (I-I’) is shorted (i.e. V1 =0)=output

driving point admittance. Y12=

I 1 V 2

when output terminal (I-I’) is open (i.e. V1 =0) = forward

transfer admittance i.e. Y 1 1 , Y 1 2 , Y 2 2 , Y 2 1 are also called admittance parameters or short circuit parameters If Y 1 2 = Y 2 1 then the network satisfies the principle of reciprocity or the network is reciprocal.

GENERAL PROCEDURE:

● Write down the program in PSPICE AD AD text file. ● Save the file file with .cir extension extension name in circuit file. ● Then run and see the output from the output file and different reading to calculate the parameters.


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take


ASSIGNMENT:

Find the Z parameters and Y parameters of the circuit above. Given parameters: V 1 = V2= Z1= Z2= Z3= Z4= Z5= For Z parameters: Set-I: Circuit Diagram:

Pspice Program :

Output File:


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Interpretation:

Set-II: Circuit Diagram:

Pspice Program :

Output File:

Interpretation:


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EXPERIMENTAL DATA FOR Z-PARAMETERS

V1

V2

I1 0

I2

0 CALCULATION:

Z11= Z21=

V 1 I 1 V 2 I 1

Z12=

=

(when I 2 =0)

=

(when I 2 =0)

V 1 I 2

Z22 =

=

V 2 I 2

(when I 1 =0)

=

(when I 1 =0)

THEORETICAL VERIFICATION:

Z 1 1 =Z 1 +Z 3 Z 1 2 =Z 2 1 =Z 3 Z 2 2 =Z 2 +Z 3


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For Y parameters: Set-I: Circuit Diagram:

Pspice Program :

Output File:

Interpretation:

Set-II: Circuit Diagram:


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Pspice Program :

Output File:

Interpretation:

EXPERIMENTAL DATA

V1

FOR

Y-PARAMETERS

V2

I1

I2

0 0


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CALCULATION:

Y11= Y21=

I 1 V 1 I 2 V 1

Y22 = Y12=

I 2 V 2

I 1 V 2

=

(when V 2 =0)

=

(when V 2 =0) =

(when V 1 =0)

=

(when V 1 =0)

THEORETICAL VERIFICATION:

                      DISCUSSION:




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EXPEERIMENT NO: 04 TITLE:

Frequency responses of low pass & high pass filter.

OBJECTIVES: To study the first order low pass and high pass filter. To implement graphs showing frequency response of low pass and high pass filter and calculate the cut off frequency from the experiment observation. THEORY: Filter: Filter is a frequency selector network which passes a range of signals and attenuates other signal. The basic electrical filters are of two forms as regards the component constituting them. They are: (i) Active Filters and (ii) Passive Filters. Active filters use active elements like Operational Amplifiers addition to passive elements like resistor, inductor, and capacitor. Passive filters only use passive circuit elements like resistor, inductor, and capacitor. Both passive and active filters may be classified as:(i) Low Pass Filters (ii) High Pass Filters (iii) Band Pass Filters and (iii) Band Stop Filters. LOW PASS FILTER THEORY: Low pass filter passes the low frequency of signals below the cut off frequency and rejects other signals.Fig. below shows a first order low-pass Butterworth filter that uses an RC network for filtering. Here Opamp is used in the non-inverting configuration. According to the voltage divider rule, the voltage at the noninverting terminal (across capacitor C) is,


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V 1 =

V 1 =

− jX C

R − − jX C

vin where − jX C =

1 j 2π fC

v in

1 + j 2π RC

And the output voltage, V O = (1 +

Or,

V O

RF R1

)V 1 A F

=

1 + j ( f / f C )

V in

A F = 1+R F /R 1 = pass band gain f= frequency of the input signal f C = cut-off frequency =

1 2π RC

CIRCUIT DIAGRAM: Rf 1k

+15V V1 2

R1 1K

─ 7

Gain

741 1K

3

R C

+

0.1µF

4

AF -15V RL

Pass band

Stop band

0.707 AF

vsin 0

f C

freq.

Frequency Response of Low Pass Filter 1 OREDR LOW PASS FILTER

Cut off frequency:

The frequency above which there will be no output sign al corresponding to input signal, whatever be the magnitude of the input signal, is called the cut-off frequency.


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It is given by, f C =

1 2π RC

The signals having a frequency range of 0 – f C will be faithfully reproduced with a constant gain. The output corresponding signal above cut-off frequency (f C ) is zero, i.e. they are rejected HIGH PASS FILTER High pass filter passes the frequency of signals above the cut off frequency and rejects other signals For the high pass filter frequencies after the cut-off frequency is passed. This circuit passes high frequencies and rejects the low frequencies. The output voltage is, V O = (1 + V O V in

RF

)

j 2π RC

V in R1 1 + j 2π RC

 j ( f / f C )   1 + j ( f / f C ) 

= AF 

CIRCUIT DIAGRAM: Rf 1k

+15V R1

2

1K

─ 7 741

3

+

6

VOUT gain

4 -15V

AF

RL

Stop band

1K

R

Pass band

0.707 AF

0

f C

freq.

Frequency Response of High Pass Filter 1ST OREDR HIGH PASS FILTER


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Procedure: a)

b)

Low Pass (LP) Filter: i. Draw the circuit using PSPICE as per Figure. From the g e t new part of draw menu bring all the elements and join them. i i. Select the value of resistance (R) a nd capacitance (C). iii. Set the value of Vsin. i v. From the set up menu go to AC Sweep , give the start frequency, end frequency. v. Simulate the circuit. vi. Observe gain (out put / input voltage). vii. Note frequency & gain on Table. High Pass (HP) Filter: i. Draw the circuit as per Figure-3b. ii. Repeat the above procedure

EXPERIMENTAL DATA:

CAPACITOR = RESISTANCE = CAPACITOR = RESISTANCE = OBSERVATION TABLE: FREQUE NCY

1 V IN (V)

ST

ORDER LPF VOUT VOLTAGE (V) GAIN

FOR LPF FOR HPF

ST

1 ORDER HPF FREQUE V O U T VOLTAGE NCY (V) GAIN


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ACTIV E 1 FILTER

ORDER

MEASURED FROM GRAPH

CALCULATED f =

1 RC 2π

LPF(CUT OFF FREQUENCY) HPF(CUT OFF FREQUENCY)

DISCUSSION: •

The LPF has constant gain A f from 0Hz to cut off frequency. At cut off frequency gain is 0.707 A f and after cut off

•

frequency gain decreases at a constant rate with increase in frequency. The HPF has constant gain A f from cut off frequency to highest frequency. At cut off frequency gain is 0.707 A f and

•

before cut off frequency, gain increases at a constant rate with increase in frequency from zero to maximum value. The amplitude of the input signal should be such that the gain value can be easily plotted w.r.t frequency.




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EXPERIMENT NO : 05 EXP. TITLE:

Frequency responses of band pass & band reject pass filter.

OBJECTIVES:

To study the first order band pass and band reject filter To implement graphs showing frequency response of band pass and band reject filter and calculate the lower cut off frequency and higher cut off frequency from the experimental observation. THEORY: Band Pass Filter:

Band pass filter passes a band of frequency of signals between the lower and higher cut off frequency and rejects other signals A simple BP filter can be constructed by cascading an LP filter and a HP filter as shown in the figure. There is a pass band, with a lower cut off frequency, f L and upper cut-off frequency at f H . I n the pass band, the circuit behaves like a voltage divider gain AF

0.707 AF

Stop band

Pass band f L

f H

freq

Frequency response of band pass filter


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CIRCUIT DIAGRAM OF BAND PASS FILTER: Rf

Rf

10k +15V

10k

+15V

2

10K

R1 10K

C

R1

2

─ 7

7

─

6

741 + 0.1 F 3

6

741 1K

3

10k

4

C

-15V

+

VOUT

4 -15V

0.01µF

Band Reject Filter:

Band reject filter attenuates a band of frequency of signals between the higher and lower cut off frequency and passes other signals The band reject filter is also called band stop or band elimination filter

gain AF

0.707 AF

Pass band

Stop Pass band band f L f O f H

freq

Frequency response of band reject filter


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CIRCUIT DIAGRAM OF BAND REJECT (ELIMINATION) FILTER: Rf 10k

10K

+15V R1

2

10K

─ 7 741

C2 0.01 F 3

+

10K

6

2

4 -15V

10K

10k R3

R2

3

─ 741 +

10K Ro 10k

Rf 10k

+15V R1

2

10K

─ 7 741

10K

3

R1

+

4 -15V

C1

1

6

0.1µF

OREDR BAND REJECT FILTER


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VOUT


OBSERVATION TABLE:

FREQUE NCY

BAND PASS FILTER V IN VOUT VOLTAGE (V) (V) GAIN

ACTIVE FILTER

MEASURED FROM GRAPH

BAND REJECT FILTER FREQUE V O U T VOLTAGE NCY (V) GAIN

CALCULATED CUT OFF FREQUENCY

BAND PASS FILTER

f L =

•

LOWER CUT OFF FREQUENCY • HIGHER CUT OFF FREQUENCY • BANDWIDTH


FORMULAE CUT OFF FREQUENCY

f U =

1 R1C 1 2π

1 2π R 2 C 2

BW = f U − f L

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BAND REJECT FILTER

f L = f U =

•

LOWER CUT OFF FREQUENCY • HIGHER CUT OFF FREQUENCY • BANDWIDTH

1 2π R1C 1 1 2π R 2 C 2

BW = f U − f L

DISCUSSION: •

•

•

The BPF has a pass band frequency between the higher cutoff frequency and the lower cut-off frequency. The band reject filter has attenuation band between the higher cut-off frequency and the lower cut-off frequency. In BPF the frequency response curve increases to the maximum and then decreases and in case of BRF the frequency response curve decreases from the maximum and then increases to the maximum value.




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EXPERIMENT NO : 06 E X P T I T L E : Generation of periodic exponential damped sinusoidal step impulse signals using MATLAB in analog and discrete form. MATLAB COMMANDS plot(x,y): Plots vector y verses vector x stem(n,y) : Plot the discrete signal Examples: • Plot the straight line using plot command y=mx+c, where m=0.5, c=-2 and the x coordinates are x=0,1.5,3,4.5.

m=0.5; c=-2; x=[0 1.5 3 4.5]; y=m*x+c; plot(x,y) •

Generate a damped sinusoidal Signal in analog and discrete form. x=0:.1:5; y=sin(x.^2).*exp(-x); plot(x,y) stem(x,y)

•

Generate unit step function in analog and discrete form. t=0:.01:2; y=stepfun(t,0); plot(t,y) axis([0 2 0 2]); t=0:.1:2; y=stepfun(t,0); stem(t,y)


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PROCEDURE ● Open the MATLAB Command Window by clicking on the MATLAB icon. ● Write down the progrm on edit window and save it. ● Run the file and see the output ASSIGNMENTS

1.

Create a vector t with 10 elements 0 to 1and Plot the signals a) x=t.sin(t) b) y=sin(t.^2)./(t.^2)

2. Write necessary commands for generating a single pulse of width 2sec and magnitude 3V.


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3.

Generate a ramp signal of θ =30 ° ;

30 0

3. Generate an exponential function y = e − at and plot the signal in analog and discrete form.


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5.

Generate a gate function.

6.

Generate the following function. 10

10

2

4

0

2

10

0

2

Fig.1


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4 Fig.2

10





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EXPERIMENT NO : 07 EXP TITLE:

Determination of Laplace transform and Inverse Laplace Transform using MATLAB. Laplace Transform laplace(F) is the Laplace transform of the scalar function F with default independent variable t. The default return is a function of S. To determine the Laplace transform of a given function f(t), we first multiply f(t) by e − st , s being a complex numbers s= σ +j ω , t h e n integrate this product w.r.t time with limits as zero to infinity. ∞

Laplace transform of f(t)=F(S)= ∫ f (t )e − st dt 0

Example :

syms a w t; laplace(a*cos(w*t)) result: a*s/(s^2+w^2) Inverse Laplace Transform F = ilaplace(L) is the inverse Laplace transform of the scalar sym L with default independent variable s. The default return is a function of t. Example: syms s ; ilaplace(1/(s-1))

Result: exp(t) PROCEDURE

● ● ●

Open the MATLAB Command Window by clicking on the MATLAB icon. Write down the program on edit window and save it. Run the file and see the output PAPER CODE: EE-391/EE-2

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ASSIGNMENT-I

Find out the Laplace transform of the following functions; compare with theoretical values. 1.

  ��  2   

2.

 

3.

  


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4.

5.

    2  



ASSIGNMENT-II Find out the Inverse Laplace transform of the following functions and compare with theoretical values.

1.

1   


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2. 1   

3.

4.

3 /   2

      


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5.

  

DISCUSSION:




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EXPERIMENT NO : 08 EXP TITLE:

Amplitude and phase spectrum analysis of different signals.

OBJECTIVE: To study the amplitude and phase spectrum analysis of different signals. THEORY: Discrete Fourier transform (DFT) is a powerful computation tool j ω which allow us to evaluate the Fourier Transform X(e ).A waveform can be represented by a finite length sequence x[n], where 0 ≤ n ≤ N-1; N=period for such a finite length sequence j ω x[n]. Its discrete fourier transform X(e ) is obtained by uniformly j ω sampling X(e ) on the ω axis between 0 ≤ ω ≤ 2 π a t ω k =2 π / N

j ω

So, X[k] = X(e ) while ω =2 π k/N N − 1

X [ k ] =

∑ X [ n ] e

− j 2 π kn / N

0

X[k] is the DFT of the sequence x[n]. The inverse DFT is given by

X [ n ] =

1 N

N − 1

∑

X [ k ]e

j 2 π kn / N

k = 0

DFT using MATLAB fft(X,M) → computes M point DFT of a se quence X[n] of length N. To ensure correct values M must be greater than or equal to N. PROCEDURE

● ● ●

Open the MATLAB Command Window by clicking on the MATLAB icon. Write down the progrm on edit window and save it. Run the file and see the output


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Example:

Find the magnitude and phase spectrum of the following waveform.

2 E 0

5

10 n

n=0:1:10; n1=length(n); M=16; u=[2*ones(1,(n1-5)),-2*zeros(1,(n1-6))]; U=fft(u,M); t=0:n1-1; subplot(511);stem(t,u); title('the original time domain sequence'); xlabel('time'); ylabel('amplitude'); k=0:1:M-1; subplot(513);stem(k,abs(U)); title('magnitude of the DFT samples'); xlabel('frequency index k'); ylabel('magnitude'); subplot(515);stem(k,angle(U)); title('magnitude of the DFT samples'); xlabel('frequency index k'); ylabel('phase');


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ASSIGNMENTS

Find the magnitude and phase spectrum of the following waveform. i) ii)

5V E 0

3V E 5 n

0


5

n

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EXPERIMENT NO: 09 EXP TITLE:

Verification of Network Theorems in SPICE

OBJECTIVE : To study To study To study To study

the the the the

Superposition theorem. Thevenin’s theorem. Norton’s theorem. Millman’s theorem.

GENERAL PROCEDURE:

• • • •

Open PSpice A/D Demo. Create a new text file. Write the program based on the assignment. Save the program in circuit file with .cir extension.

PROGRAM

1. 2.

3. 4. 5. 6.

Title is written in the first line of the program. Describe the individual elements with the nodes • For energy sources mention the nature of the source (ac or dc). • Give the magnitude of the element. Put the above mentioned characteristics in respective columns. Describe each element of the circuit in this manner. .probe .end

OUTPUT • Go to view • Next see the output file PLOT • Go to trace • Next go to Add trace and see the different plot. Finally compare the results with theoretical values.


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SUPERPOSITION THEOREM THEORY: STATEMENT: In a linear bilateral network containing two or more independent sources, the voltage across or current through any branch is the algebraic sum of individual voltages or currents produced by each independent source acting separately with all the independent sources set equal to zero.

R1

A

R2 I

V1

V2

R3 B

R2

R1

R2

R1

I2

I1 V1

R3

R3

STEP-1

STEP-2

Current through resistor R 3 , I=I 1 +I 2


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V2


ASSIGNMENT: R1

R2

R3

A I

V1

R4

V2

R5

B

Using superposition theorem, find the current I through the resistance R 5 or in the branch AB. Case I:

V 1 acting alone

Circuit Diagram:

Pspice Program:


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Output:

Interpretation:

Case II: V 2 acting alone Circuit Diagram:

Pspice Program:


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Output:

Interpretation:

Case III: Both V 1 , V 2 acting simultaneously Circuit Diagram:

Pspice Program:


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Output:

Interpretation:

THEVENIN’S THEOREM THEORY : STATEMENT : In any linear active two terminal network containing resistance and voltage sources and or current sources can be replaced by a single voltage source V t h in series with a single resistance R t h . The Thevenin’s equivalent voltage V t h is the open circuit voltage at the network terminals, and the Thevenin’s resistance R t h is the resistance between the network terminals when all the sources are replaced with their internal resistances.

For finding current through the branch AB of the following circuit, one has to remove that particular branch first, the n calculate thevenin voltage V t h and thevenin resistance R t h . Lastly connect the branch and calculate the current.


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FUTURE INSTITUTE OF ENGINEERING AND MANAGEMENT ELECTRIC CIRCUIT THEORY LABORATORY LAB MANUAL PAPER CODE : (EE – 391) R2

R1

A I V1

R3

RL

B R2

R1

R2

R1

A

A V1

Vth

R3

R3

Rth B

B Rth

STEP-1

STEP-2 I RL

Vth

STEP-3

ASSIGNMENT: R1

R2

R3

A I

V1

R4

V2

R5

B

Using thevenin’s theorem, find the current I through the resistance R 5 or in the branch AB. PAPER CODE: EE-391/EE-2

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Set I: Finding V t h Circuit Diagram:

Pspice Program:

Output:

Interpretation:


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Set II: Finding R t h Circuit Diagram:

Pspice Program:

Output:

Interpretation:


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Set III: Finding current through R 5 Circuit Diagram:

Pspice Program:

Output:

Interpretation:


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NORTON’S THEOREM THEORY: STATEMENT: In any linear active two terminal network containing resistance and voltage sources and or current sources can be replaced by a single current source I N in parallel with a single resistance R N . The Norton’s equivalent current I N is the short circuit current through the network terminals, and the Norton’s resistance R N is the resistance between the network terminals when all the sources are replaced with their internal resistances. R2

R1

A I

V1

R1

RL

R3

R1 B

R2

R2

IN V1

A V2

R3

R3

RN B

STEP-2

STEP-1

I IN

RL

RN

STEP-3


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ASSIGNMENT: R1

R2

R3

A I

V1

R4

V2

R5

B

Using Norton’s theorem, find the current I through the resistance R 5 or in the branch AB. Set I: Finding Norton current I N Circuit Diagram:

Pspice Program:

Output:


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Interpretation:

Set II: Finding R N Circuit Diagram:

Pspice Program:

Output:


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Interpretation:

Set III: Finding current through R 5 Circuit Diagram:

Pspice Program:

Output:

Interpretation:


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MILLMAN’S THEOREM THEORY : STATEMENT : Consider N voltage sources V 1 , V 2 , ………….., V N in series with N resistors R 1 , R 2 , ……….., R N .Then according to Millman’s theorem we can replace all the voltage sources and resistances between terminals AB by a single voltage source V in series with a single resistance R, where

V=(V 1 G 1 + V2 G2 + V 3 G 3 +……………… G 3 +……….+ G N ) and

V N G N )/(

G1+

G2+

R=1/( G 1 + G 2 + G 3 +……….+ G N ) A A R

R1

R2

R3

RN ……………………

I

V V1

V2

V3

VN

B

B

ASSIGNMENT: CIRCUIT DIAGRAM: R1 V1

R2

A

RL

V2 B

Applying Millman’s theorem, find the current in the branch AB or through the resistance RL. PAPER CODE: EE-391/EE-2

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Set I: Finding equivalent voltage Circuit Diagram:

Pspice Program:

Output:

Interpretation:

Set II: Finding equivalent resistance Circuit Diagram:


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Pspice Program:

Output:

Interpretation:

Set III: Finding current through R L Circuit Diagram:

Pspice Program:


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Output:

Interpretation:




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circuit theory lab manual.pdf

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