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Electronic Circuits Analysis L ab Manual Dept of ECE 1 MADANAPALLE INSTITUTE OF TECHNOLOGY & SCIENCE ANGALLU, MADANAPALLE    517325 ELECTRONIC CIRCUITS ANALYSIS LABORATORY MANUAL DEPARTMENT OF ELECTRONICS & COMMUNICATION ENGINEERING JULY   2012 Lab Incharge Head of the Department

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  • Electronic Circuits Analysis Lab Manual

    Dept of ECE 1

    MADANAPALLE INSTITUTE OF TECHNOLOGY & SCIENCE ANGALLU, MADANAPALLE 517325

    ELECTRONIC CIRCUITS ANALYSIS LABORATORY MANUAL

    DEPARTMENT

    OF ELECTRONICS & COMMUNICATION ENGINEERING

    JULY 2012

    Lab Incharge Head of the Department

  • Electronic Circuits Analysis Lab Manual

    Dept of ECE 2

    MADANAPALLE INSTITUTE OF TECHNOLOGY & SCIENCE ANGALLU, MADANAPALLE 517325

    MITS MITS / ECE

    LAB WISE-LABMANAUALS DEPARTMENT : ECE

    ELECTRONIC CIRCUITS LABORATORY MANUAL

    DEPARTMENT OF

    ELECTRONICS & COMMUNICATION ENGINEERING JULY 2012 -2013

  • Electronic Circuits Analysis Lab Manual

    Dept of ECE 3

    INDEX

    S.NO NAME OF THE EXPERIMENT PAGE NO

    SOFT WARE:

    1. COMMON EMITTER AMPLIFIER 4

    2. COMMON SOURCE AMPLIFIER 7

    3. TWO STAGE RC COUPLED AMPLIFIER 10

    4. CURRENT SHUNT FEED BACK AMPLIFIER 14

    5. WIEN BRIDGE OSCILLATOR USING TRANSISTORS 17

    6. RC PHASE SHIFT OSCILLATOR 19

    7. CLASS A AND CLASS AB POWER AMPLIFIERS 22

    8. HIGH FREQUENCY COMMON BASE AMPLIFIER 28

    HARD WARE:

    9. TWO STAGE RC COUPLED AMPLIFER 31

    10. CURRENT SHUNT FEED BACK AMPLIFIER 34

    11. CLASS A AND CLASS AB POWER AMPLIFIERS 37

    12. SINGLE TUNED VOLTAGE AMPLIFIER 41

    13. HARTLEY AND COLPITTS OSCILLATORS 43

    14. MOSFET AMPLIFIER 45

    ADDITIONAL EXPERIMENTS:

    15. SERIES VOLTAGE REGULATOR 48

    16. SHUNTVOLTAGE REGULATOR 50

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    1.COMMON EMITTER AMPLIFIER

    AIM:

    a)To design CE single stage amplifier with potential divider circuit using NPN

    Transistor 2N2923 for the specifications : IC= 3 mA, Vce = 10v, = 190, & IR1 =

    32IB .

    b) To observe dc operating point, frequency response, & C.R.O waveforms using

    MULTISIM software.

    APPARATUS: - Multisim Soft ware.

    DESIGN PROCEDURE:

    Vcc=

    Select Vre Vce

    Select Vre = 5v

    Re=Vre/Ic

    Vrc= Vcc-VCE-VRE

    Rc=VRC/Ic

    IB=Ic/

    IR1=32IB

    IR2=IR1-IB

    VB=VBE+VRE

    R2=VB/IR2

    R1= (VCC-VB)/IR1

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    CIRCUIT DIAGRAM:

    PROCEDURE:-

    1. Rig up the circuit using multisim software and verify the results using DC

    operating point analysis (simulate----analysis ---- DC operating point)

    2. Rig up the circuit using multisim software and verify the results using AC

    analysis (Simulate ---- analysis ----- AC analysis)

    3.Rig up the circuit using multisim software and verify the results using

    oscilloscope

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    EXPECTED WAVEFORMS:

    RESULT:-

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    2.COMMON SOURCE AMPLIFIER

    AIM: a) To design a single stage FET Common Source amplifier with potential

    divider circuit using 2n4861 FET-N channel for the following specifications:

    VDD = 24V,ID = 1ma,VGS=2V,VPMAX =13V,RL=1K. b) To observe dc operating point, frequency response, & C.R.O waveforms.

    APPARATUS: Multisim soft ware.

    DESIGN PROCEDURE:

    VDSmin = Vpmax + 1 - VGS

    VS=VRD= (VDD - VDS)/2

    RD=RS= VRD/ID

    VG=VR2=VS-VGS

    SELECT R2 = 1M

    R1=(VR1 * R2)/VR2

    CIRCUIT DIAGRAM:

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    PROCEDURE:- 1. Rig up the circuit using multisim software and verify the

    results using DC operating point analysis (simulate----analysis ---- DC operating

    point)

    2. Rig up the circuit using multisim software and verify the results using AC

    analysis (Simulate ---- analysis ----- AC analysis)

    3..Rig up the circuit using multisim software and verify the results using

    Oscilloscope

    EXPECTED WAVEFORMS:

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    RESULT:

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    3.TWO STAGE RC COUPLED AMPLIFIER

    AIM:

    Q1) Design a single stage transistor amplifier with potential divider circuit

    (using an npn si transistors) with following specifications.

    IC=1.6ma,VCE=7.6v,RC=2.2k,VCC=12v, I1=10IB and =54. Verify the DC values (Voltage and current) at various nodes using Multisim software

    DESIGN: IB=IC/ VCC=IC(RC+RE)+VCE ;

    RE=0.516k V2=VBE+ICRE ; V2=

    V2=I1R2 ; R2=V2/(I1=10IB) ;

    I1=VCC/(R1+R2) ; (R1+R2)= ;

    R1=

    PROCEDURE: Rig up the circuit using multisim software and verify the

    results using DC operating point analysis (simulate analysis DC

    operating point)

    Q2) Design a single stage transistor amplifier with potential divider circuit

    (using an npn si transistors) with following specifications.

    IC=2.32ma,VCE=5.7v,RC=2.2k,VCC=12v, I1=10IB and =33. Verify the DC

    values (Voltage and current) at various nodes using Multisim software DESIGN:

    IB=IC/ =

    VCC=IC(RC+RE)+VCE ;

    RE=0.51k V2=VBE+ICRE ;

    V2=I1R2 ; R2=V2/(I1=10IB) ;

    I1=VCC/(R1+R2) ; (R1+R2)=

    PROCEDURE: Rig up the circuit using multisim software and verify the

    results using DC operating point analysis (simulate analysis DC

    operating point)

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    Q3) Cascade above two stages and find overall gain (choose Cc=4.7f,

    Ce=470f, hfe=50) find the frequency response, DC operating points and

    parameter sweep of load resister.

    ANALYSIS:

    Stage-2: AI2= -hfe/(1+hoeRL2) ;

    Ri2 = hie+hreAI2RL2 ; Av2= -AI2*RL2/Ri2 ;

    Stage -1: RL1

    AI1 = Ri1 =

    Av1 = Overall gain Av = Av1*Av2

    Avs = Av*Ri/(Ri+RS) ; Ri =

    CIRCUIT DIAGRAM:

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    PROCEDURE:- 1. Rig up the circuit using multisim software and verify the

    results using DC operating point analysis (simulate----analysis ---- DC operating

    point)

    2. Rig up the circuit using multisim software and verify the results using AC

    analysis (Simulate ---- analysis ----- AC analysis)

    3..Rig up the circuit using multisim software and verify the results using

    Oscilloscope

    EXPECTED WAVEFORMS:

    RESULT:

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    4.CURRENT SHUNT FEEDBACK AMPLIFIER

    AIM: Design current shunt feed back amplifier with a feedback resistance 5K

    using transistor BC 107. Obtain DC operating point and frequency response.

    APPARATUS: Multisim software.

    DESIGN PROCEDURE:

    I R

    I F R E R

    E F E

    I I I I I

    AI IR I C 2 I

    B2 IC1 I

    B1

    S B2 C1 B1 S

    I I

    C2 hFE 50, C1 hFE 50

    IB2

    IB1

    I R

    IC2 R CR1

    C1 C1 I 2

    I R

    IB1 R hie

    S

    AI

    D 1 AI

    AIF

    A

    DI =

    A V I R

    A

    0 O C 2 C2

    VF VS IS RS IF RS

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    Dept of ECE 15

    CIRCUIT DIAGRAM:

    PROCEDURE:- 1. Rig up the circuit using multisim software and verify the

    results using DC operating point analysis (simulate----analysis ---- DC operating

    point)

    2. Rig up the circuit using multisim software and verify the results using AC

    analysis (Simulate ---- analysis ----- AC analysis)

    3..Rig up the circuit using multisim software and verify the results using

    Oscilloscope

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    EXPECTED WAVEFORMS:

    RESULT:

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    5.WIEN BRIDGE OSCILLATOR USING TRANSISTORS

    AIM: To study and calculate frequency of. Wein Bridge Oscillator.

    APPARATUS:

    Transistor (BC107) 2no,

    Resistors 10K - 4no,1K - 3no,2.2K, 33K, 6.8K,

    Capacitors - 10 F - 2no, 100uF, 0.01uF 2no, SDC Kit, CRO, Connecting

    wires.

    DESIGN PROCEDURE:

    Formula f =1/2(R1C1R2C2)

    Given R=10k, C=0.01uf

    If R1=R2 ; C1=C2

    fT = 1/ 2RC

    CIRCUITDIAGRAM:

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    PROCEDURE:

    1. Connections are made as per the circuit diagram

    2. Feed the output of the oscillator to a C.R.O by making adjustments in the

    Potentiometer connected in the +ve feedback loop, try to obtain a stable

    sine Wave.

    3. Measure the time period of the waveform obtained on CRO. & calculate

    the Frequency of oscillations.

    4. Repeat the procedure for different values of capacitance.

    MODEL WAVE FORM:

    RESULT:

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    6.RC PHASE SHIFT OSCILLATOR

    AIM: a) Design RC phaseshift oscillator to have resonant frequency of 6KHz.

    Assume R1 = 100k, R2 = 22K, RC = 4 K ,RE =1K & VCC = 12V.

    b) Obtain hfe for the above designed value for AV > - 29, R 2 RC.

    APPARATUS: Multisim software.

    DESIGN PROCEDURE:

    A) Let R = 10K

    Fr = 1 ___________

    2Rc(6+4K) WHERE K=Rc/R

    B)hfe 23= 29/K for sustained oscillations

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    CIRCUIT DIAGRAM:

    VCC

    12V

    VCC

    R1 R3

    100kohm 4kohm

    C2

    10

    C1

    Q2

    4 2N2222A

    10uF

    R2 11 100uF

    22kohm R4

    1kohm

    0

    C6 C5 C4

    7

    9

    R7 R6 R5

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    PROCEDURE: Rig up the circuit using multisim software and verify the results

    using Oscilloscope.

    RESULT:

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    7.CLASS A,AB,B,C POWER AMPLIFIERS AIM :

    To study the operation of Class A, Class AB, Class B, Class C power

    amplifiers.

    APPARATUS: Multisim soft ware.

    CIRCUIT DIAGRAM:

    V2 12V R2 R5

    1kohm 1kohm

    47uFC2

    R3

    XSC1

    Q1

    47uF 30kohm

    G

    R1 PN2369A

    C1 T A B

    100ohm

    V1 R4

    50mV

    100ohm

    35.36mV_rms

    1000Hz

    0Deg

    THEORY:

    The classification of amplifiers is based on the position of the quiescent

    point and extent of the characteristics that is being used to determine the method

    of operation.

    There are 4 classes of operations.They are

    1.Class A 2.Class AB 3.Class B 4.Class C

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    CLASS A:- In class A operation the quiescent point and the input signal are such

    that the current in the output circuit (at the collector) flows for all times. Class A

    amplifier operates essentially over a linear portion of its characteristic there by

    giving rise to minimum of distortion .

    CLASS B:- In class B operation , the quiescent point is at an extreme end of the

    characteristic , so that under quiescent conditions the power drawn from the dc

    power supply is very small .If the input signal is sinusoidal, amplification takes

    place for only half cycle.

    CLASS AB:- A class AB amplifier is the one that operates between the two

    extremes defined for class A and Class B. Hence the output signal exists for

    more than 1800 of the input signal.

    CLASS C :- In class C operation, the quiescent operating point is chosen such

    that output signal (voltage or current)is zero for more than on half of the input

    sinusoidal signal cycle.

    PROCEDURE:

    1. An input sine wave (peak-peak)of 50mV is applied to the circuit.

    2. connect the output to the C.R.O.

    3. varying R3 value, observe and record the output waveforms for different

    classes of operation.

    4. Also observe the Vi & Vo waveforms using parameter sweep for different

    classes of operation.

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    OBSERVATIONS:

    CLASS A:

    CLASS AB :

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    CLASS B :

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    CLASS C :

    RESULT :

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    8.HIGH FREQUENCY COMMON BASE AMPLIFIER

    AIM - Design a common Base high frequency amplifier with a over all gain of 30

    and Lower cut off frequency of 130 Hz and Higher cut frequency 10 MHz .

    Transistor Specifications: hib = 22.6, hfb = -0.98, hrb = 2.910-4 ,

    hob = 0.49 s, IC =

    1.35ma = -IE, VCE = 5.85V, VEB = 0.6V, VCB = 5.25V. Verify the DC values (Voltage and current) at various nodes using Multisim software

    APPARATUS: Multisim software.

    DESIGN PROCEDURE:

    1. DESIGN OF BIASING CIRCUIT :

    VBE = 0.6V, VCE = 5.85V, IC = 1.35mA = -IE

    VCB = 5.25V

    Find the value of Re :

    KVL to Input:

    Find the value of RC :

    KVL to Output :

    Vcc ICRC - VCB = 0

    RC =

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    Dept of ECE 29

    2.DESIGN OF AMPLIFIER CIRCUIT :

    1.To find Cb

    Assume Rs = 100 Calculate the value of Cb

    f L= 1

    _____________

    2(Rs + Ri)Cb

    2. To calculate RL Av = - hfb RL/Ri

    Overall gain = Avs = Av * Ri/(Ri+Rs) For the above circuit Ri1=Ri = hib

    Avs = - hib * RL1/(Ri+Rs) ;

    RL1= RL// Rc

    3. To Calculate Shunt Capacitance Csh

    fh = 1

    2RL C sh

    The Internal junction capacitance Cbc 3pf

    Csh = Cbc + Csh

  • Electronic Circuits Analysis Lab Manual

    Dept of ECE 30

    CIRCUIT DIAGRAM :

    XSC1

    G

    A B T

    Rs Cb 10uF BC107BP 10uF Cb1

    10 11 12 3

    100ohm Q1 Rc 8 Re V1

    5kohm

    R5

    Csh

    1kohm

    10mV 15kohm 2pF 7.07mV_rms 7 VEE 12V

    6

    1000Hz 2V 0Deg VCC

    0

    PROCEDURE: 1.Rig up the circuit using multisim software and verify the results using DC operating point analysis (Simulate ------Analysis------ DC operating point)

    2. Rig up the circuit using multisim software and verify the results using AC

    analysis (Simulate--- Analysis--- AC analysis)

    RESULTS:

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    Dept of ECE 31

    9.TWO STAGE RC COUPLED AMPLIFIER

    AIM: 1. To study the Two-stage RC coupled amplifier.

    2. To measure the voltage gain of the amplifier at 1KHz.

    3. To obtain the frequency response characteristic and the band width of the

    amplifier.

    EQUIPMENT: Two stage RC coupled amplifier, trainer.

    1. Signal Generator.

    2. C.R.O

    3. Connecting patch cords.

    CIRCUIT DIAGRAM:

    VCC

    12V

    R1 RC

    R6

    R3 2.2kohm

    33kohm 2.2kohm

    CC 15kohm C2

    C1 Q1 10uF Q2 10uF

    RG BC107BP BC107BP

    15kohm 10uF

    C3 OUTPUT

    INPUT V CE 10uF VO

    50mV R2 RE 10uF R4 R5

    5.1kohm 510ohm 2.7kohm 1kohm

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    PROCEDURE: 1.Switch ON the power supply.

    2. Connect the signal generator with sine wave output 50mV p-p at the

    input terminals.

    3. Connect the C.R.O at output terminals of the module.

    4. Measure the voltage at the second stage of amplifier.

    5. Now vary the input frequency from 10Hz to 1MHz in steps,and for every

    value of input frequency note the output voltage keeping the input

    amplitude at constant value.

    6. Calculate the gain magnitude of the amplifier using the formula

    Gain = Vo/Vi

    Gain in dB= 20 log (Vo / Vi )

    7. Plot a graph of frequency versus gain (dB) of the amplifier. Sample

    frequency response graph is as shown in fig. Below.

    OBSERVATION:

    Vi = 50mV(p-p)

    Frequency

    VO

    Gain =20 log

    (Vo/Vi)dB

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    FREQUENCY RESPONSE:

    0.707 VO/VI

    Gain VO/VI

    FL FH Frequency

    RESULT:

    The gain of the amplifier at 1 KHz is ------

    The BW of the amplifier is -------

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    Dept of ECE 34

    10.CURRENT SHUNT FEEDBACK AMPLIFIER

    AIM: 1. To study the current shunt feedback amplifier 2. To measure the voltage gain of the amplifier at 1KHz.

    3. To obtain the frequency response characteristic and the band width

    of the amplifier. EQUIPMENT:

    Current shunt feed back amplifier trainer.

    4. Signal Generator.

    5. C.R.O

    6. Connecting patch cords.

    CIRCUIT DIAGRAM:

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    PROCEDURE: 1. Switch ON the power supply.

    2. Connect the signal generator with sine wave output 50mV p-p at the

    input terminals.

    3. Connect the C.R.O at output terminals of the module.

    4. Measure the voltage at the second stage of amplifier.

    5. Now vary the input frequency from 10Hz to 1MHz in steps, and for

    each value of input frequency note the output voltage keeping the

    input amplitude at constant value.

    6. Calculate the gain magnitude of the amplifier using the formula

    Gain = Vo/Vi

    Gain in dB= 20 log (Vo / Vi )

    7. Plot a graph of frequency versus gain (dB) of the amplifier. Sample

    frequency response graph is as shown in fig. Below.

    OBSERVATIONS :

    Vi = 50mV(p-p)

    Frequency VO Gain =20 log (Vo/Vi)dB

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    Dept of ECE 36

    FREQUENCY RESPONSE:

    RESULT: The gain of the amplifier at 1 KHz is ------

    The BW of the amplifier is -------

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    Dept of ECE 37

    11.CLASS A/B/C/AB POWER AMPLIFIER

    AIM: To study the operation of Class A, Class B, Class AB and Class C power

    amplifiers.

    EQUIPMENT: 1.Class/A/B/C/AB amplifier trainer

    2.Function generator.

    3.C.R.O

    4. Connecting patch cords.

    CIRCUIT DIAGRAM:

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    PROCEDURE:

    1.Connect the circuit as shown in the circuit diagram, and get the circuit

    verified by your Instructor.

    2. Connect the signal generator with sine wave at 1KHz and keep the

    amplitude at .5V (peak-to-peak)

    3. Connect the C.R.O across the output terminals.

    4. Now switch ON the trainer and see that the supply LED glows.

    5. Keep the potentiometer at minimum position, observe and record

    the waveform from the C.R.O.

    6. Slowly varying the potentiometer, observe the outputs for the

    Class A/B/AB/C amplifiers as shown in fig.

    CLASS A:

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    CLASS B:

    CLASS AB:

  • Electronic Circuits Analysis Lab Manual

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    CLASS C :

    RESULT:

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    12.SINGLE TUNED VOLTAGE AMPLIFIER

    AIM: 1.To calculate the resonant frequency of tank circuit.

    2. To plot the frequency response of the tuned amplifier.

    EQUIPMENT: 1. Tuned voltage amplifier trainer.

    2. Function generator.

    3. C.R.O.

    4. Connecting patch cords.

    CIRCUIT DIAGRAM:

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    PROCEDURE:

    1.Connect the circuit as shown in fig and get the circuit verified by

    your Instructor.

    2. Connect the signal generator with sine wave at the input and

    keep the amplitude to minimum position, and connect a C.R.O at

    output terminals of the circuit.

    3. Apply the amplitude between 1.6v to 4.4v to get the distortion

    less output sine wave.

    4. Now, vary the input frequency in steps and observe and record

    The output voltage.

    5. Calculate the gain of the tuned RF amplifier using the formula

    Gain = out put voltage/ input voltage.

    6. plot a graph with input frequency versus gain (in dBs)

    Gain (in dBs) = 20 log (Vo/Vi) Graph :-

    Gain

    Frequency

    RESULT:

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    13.HARTLEY AND COLPITTS OSCILLATORS

    AIM: To design Hartley and Colpitts Oscillators to have resonant frequency of 1KHz.

    APPARATUS:

    BJT(BC107),Resistors(2.2k,100k,10k,1k),

    Capacitors(10f,100f,0.33 f), Decade inductance box ,RPS.

    EQUIPMENT: 1. SDC kit.

    2. Function generator.

    3. C.R.O.

    DESIGN PROCEDURE:

    Hartley Oscillator

    F = 1 / (2LeqC) Where Leq=L1+L2

    Colpitts Oscillator

    F = 1 / (2LCeq) Where Ceq= (c1*c2) / (c1+c2)

    CIRCUIT DIAGRAMS: HARTLEY OSCILLATOR:

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    COLPITTS OSCILLATOR:

    EXPECTED WAVEFORM:

    RESULT:

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    14.COMMON SOURCE FET AMPLIFIER

    AIM: 1. To obtain the frequency response of the common source FET Amplifier

    2. To find the Bandwidth.

    APPRATUS:

    N-channel FET (BFW11),Resistors (6.8K, 1M, 1.5K),Capacitors (0.1F, 47F)

    Regulated power Supply (0-30V), Function generator, CRO,CRO probes,Bread board,

    Connecting wires

    CIRCUIT DIAGRAM:

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    PROCEDURE:

    1. Connections are made as per the circuit diagram.

    2. A signal of 1 KHz frequency and 50mV peak-to-peak is applied at the

    Input of amplifier.

    3. Output is taken at drain and gain is calculated by using the expression,

    Av=V0/Vi

    4. Voltage gain in dB is calculated by using the expression,

    Av=20log 10(V0/Vi)

    5. Repeat the above steps for various input voltages.

    6. Plot Av vs. Frequency

    7. The Bandwidth of the amplifier is calculated from the graph using the

    Expression,

    Bandwidth BW=f2-f1

    Where f1 is lower 3 dB frequency, f2 is upper 3 dB frequency

    OBSERVATIONS:

    S.NO INPUT

    VOLTAGE(Vi)

    OUTPUT

    VOLTAGE(V0)

    VOLTAGE GAIN

    Av= (V0/Vi)

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    MODEL GRAPH:

    .

    RESULT:

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    15.SERIES VOLTAGE REGULATOR

    AIM : To study and design a Series voltage regulator and to observe the load

    regulation feature. EQUIPMENT :

    1. Series voltage regulated power supply trainer.

    2. Multimeter.

    3. Patch chords

    CIRCUIT DIAGRAM:

    3055 + -

    560E

    IL

    Rs + -

    IR +

    500E

    Un Regulated

    - IZ

    VO

    Input

    VZ=12V

    50%

    PROCEDURE:

    1. Switch ON the power supply.

    2. Observe the Unregulated voltage at the output of rectifier.

    3. Connect this voltage to the input of series voltage regulator circuit.

    4. Keep the load resistance 1K at constant.

    5. Observe the output voltage VO = VZ-VBE

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    6. And also observe the voltage across RS,and values of IR,IL and IZ.

    7. Compare the practical values with theoretical values.

    8. By changing the load resistance, observe the output voltage and various

    currents.

    OBSERVATIONS:

    RL VO IR IZ IL

    LOAD REGULATION :

    VO

    RL

    RESULT:

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    16.SHUNT VOLTAGE REGULATOR

    AIM : To study and design a Shunt Regulator and to observe the load

    regulation feature.

    EQUIPMENT :

    1. Shunt regulated power supply trainer.

    2. Multimeter.

    3. Patch chords.

    CIRCUIT DIAGRAM:

    RS

    + - + -

    220E

    +

    IL

    Un Regulated 8.2V IC 1K

    In put

    -

    RL VO

    50%

    3055

    PROCEDURE:

    1. Switch On the main power supply.

    2. Observe the unregulated voltage at the output of rectifier.

    3. Connect this voltage to the input of shunt Regulator circuit

    4 .Keep the load resistance 1K constant. 5. Observe the output voltage across the load resistor V0 =VZ + VBE

  • Electronic Circuits Analysis Lab Manual

    Dept of ECE 51

    6. Also observe IL, IS & IC.

    7. Compare the practical values with theoretical values.

    8. By changing the load resistance, observe the output voltage and

    various currents.

    OBSERVATIONS:

    RL VO IS IC IL

    LOAD REGULATION:

    VO

    RL

    RESULT: