principle of electronics engg
TRANSCRIPT
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EC2002: BASIC ELECTRONICS ENGINEERING LABORATORY
LIST OF EXPERIMENTS:
COMPULSORY EXPERIMENTS:
1. Verification of Forward and Reverse bias characteristics of a PN junction diode.
2. Verification of Zener diode characteristics and calculation of its dynamic resistance.
3. Design of an RC Low Pass filter circuit & RC High Pass filter circuit and observingits response to sinusoidal and square wave inputs
4. Measurement of ripple factor with and without filter for Half wave and Full waverectifier circuits.
5. Observation of output waveforms of Diode Clipper and Clamper Circuits.
6. Obtaining the frequency response of CE transistor amplifier and measurement of itsbandwidth.
7. Measurement of the h-parameters hie and hfe of a CE transistor amplifier.
8. Verification of the transfer characteristics of JFET and measurement of its voltagegain.
9. Obtaining the frequency response and measurement of Bandwidth of an invertingOP-AMP. (Using IC 741).
10.Obtaining the frequency response and measurement of Bandwidth of non invertingOP-AMP. (Using IC 741).
11.Design of an RC Phase Shift Oscillator (Using IC 741 OP AMP) and calculation of itsfrequency of oscillation.
12.Design of a R-2R ladder network for conversion of a 4-bit digital signal to an analogequivalent signal.
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OPTIONAL EXPERIMENTS:
13.Design of a voltage follower (using IC 741 OP-AMP) & plotting of its frequencyresponse.
14.Design of a Differentiator circuit (using IC 741 OP-AMP) and observation of itsoutput waveforms for various input waveforms (Sine wave, Square wave &Triangular wave).
15.Design of an Integrator circuit (using IC 741 OP-AMP) and observation of its outputwaveform for various input waveforms (Sine wave, Square wave & Triangularwave).
16.Measurement of the input impedances for inverting and non-inverting amplifiers withsame voltage gain (using IC 741 OP-AMP).
17.Design of a voltage follower (using IC 741 OP AMP) and plotting of its frequencyresponse curve.
18.Design of an adder circuit and a subtracter circuit (using IC 741 OP-AMP).
19.Measurement of the phase angle between two signals of the same frequency usingCRO.
20.Measurement of unknown frequencies using Lissajous patterns.
21.Obtaining the frequency response of an emitter follower circuit and calculation of itsgain-bandwidth product.
22.Design of a Wein Bridge Oscillator (Using IC 741 OP AMP) and calculation of itsfrequency of oscillation.
23.Design of a Hartley Oscillator and calculation of its frequency of oscillation.
24.Design of Relaxation Oscillator (Using UJT 2N2646) and calculation of its frequencyof oscillation.
25.Design of analog-to-digital Comparator circuit for conversion of an analog signal to8-bit digital signal.
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DEPARTMENT
OF
ELECTRONICS AND COMMUNICATION ENGINEERING
BASIC ELECTRONICS ENGINEERING LABORATORY
LAB INSTRUCTIONS FOR CARRYING OUT PRACTICAL
ON
VERIFICATION OF FORWARD AND REVERSE BIAS
CHARACTERISTICS OF PN JUNCTION DIODE
BIRLA INSTITUTE OF TECHNOLOGYMESRA, RANCHI
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AIM:Verification of forward and reverse bias characteristics of a PN junction diode
APPARATUS:1. Diodes2. Millimeter3. Micro ammeter4. Voltmeter
5. Resistance (220, 560 )
6.power supply7. Connecting wires and breadboard.
THEORY
A p-n junction is formed by combining N-type and P-type semiconductor togetherin very close contact. A p-n junction is formed by combining N- type and P-typesemiconductor together in very close contact. At the junction of a p-type and an n-typesemiconductor there forms a region called the depletion region, which have beendepleted of the mobile charges. Since the electrons or holes have left the depletion region,due to diffusion in the process of formation of p-n junction, this depletion region iselectrically charged. The p-type depletion regions are negatively charged (due touncompensated acceptor ions) and n-type depletion regions are positively charged (due touncompensated donor ions). The potential difference exists across the depletion regionknown as contact potential.
The act of applying a voltage across a p-n junction is known as biasing. There aretwo ways in which a p-n junction can be biased. One is known as forward biasing. Theother is known as reverse biasing.
In forward biasing, the positive terminal of the battery is connected to the p-sideand negative terminal of the battery is connected to n- side of the diode. In this set up theconduction across p-n junction takes place due to the migration of the majority chargecarriers. This means electrons migrate from n- side to p- side and the holes migrate fromp- side to n- side. In forward biasing the size of the depletion layer becomes smaller andthe resistance of the p-n junction diode becomes low.
In reverse biasing, the positive terminal of the battery is connected to n- side andthe negative terminal of the battery is connected to p- side of the p-n junction. In thearrangement, the size of the depletion region becomes large and the resistance of thediode becomes high.
The graph of voltage applied across the diode (V) versus the current (I) flowingthru it is called its V-I characteristic. A typical V-I characteristic of a p-n junction diodeis as shown.
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IF (mA)Forward Bias
VR VBVF
Breakdown Region 0.7V
Reverse Bias
IR (A)
Procedure:
1. Connect the circuit as shown in figure 1.2. Bring the variable voltage of the DC source to zero. The current through
milliammeter should also be zero.3. Increase the variable voltage of the DC source slowly and in steps. Corresponding
to each setting, note down the voltmeter and milliammeter readings.4. Do not exceed the current beyond the current rating of the diode. This completesthe observation for V-I characteristics of the forward biased diode
5. Plot Current (I) Voltage (V) by choosing proper scales6. Make the connections as shown in figure 2.7. Repeat the steps 2 and 3. This completes observation for V-I characteristics of
reverse biased diode.8. Plot Current (I) Voltage (V) by choosing proper scales
0-10 VVF
R=100
+
IF- 0 10 mA
Fig.1. Circuit for forward biasing of the diode
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DEPARTMENT
OF
ELECTRONICS AND COMMUNICATION ENGINEERING
BASIC ELECTRONICS ENGINEERING LABORATORY
LAB INSTRUCTIONS FOR CARRYING OUT PRACTICAL
ON
VERIFICATION OF ZENER DIODE CHARACTERISTICS ANDCALCULATION OF ITS DYNAMIC RESISTANCE.
BIRLA INSTITUTE OF TECHNOLOGY
MESRA, RANCHI
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AIM: Verification of Zener diode characteristics and calculation of its dynamicresistance.
APPARATUS:1. Power supply.2. DC voltmeter.3. DC ammeter.
COMPONENTS:1. Resistors 470, 1.5K, 2.2K, 3.3K, 5.6K, 12K.2. Zener EC 3Z 12A.
THEORY:
If the reverse voltage across a Zener diode reaches a level called breakdownvoltage, it starts conducting heavily. Before this reverse voltage is reached it does not
conduct, however a small reverse current does flow (few A).
To prevent high current through the Zener (for it may be damaged), a seriesresistor is included. After breakdown the voltage across the zener remains constant evenif the input voltage varies or the load current changes.
PROCEDURE:
A.For Characteristic of Zener diode and measuring the Breakdown Voltage:
1. Connect the circuit as shown. Fix the load resistance to 2.2 K2. Vary V and note the values of I1, I2 and Vi and Vdc.3. Tabulate the readings in table given below:4. Draw V-I characteristics for the zener.5. Find out the Breakdown Voltage (Vz) of the Zener diode
Vi (volts) Ii (mA) Iz (mA) Vdc (volts)
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B. For Study Voltage regulation Characteristic of Zener diode:
1. Keep Vi > Vz (fixed)2. Vary load (By connecting different load resistances) and measure I1 , Iz and
Vdc.3. Tabulate the readings in table given below:
RL (k) I1 (mA) Iz (mA) Vdc (volts)
1.5
2.2
3.3
5.6
12
RESULT:
PRECAUTIONS:
D1
5 VVin
(0-30V)
R1
470ohm00.000 A
+ -
00.000 A+
-
R2
1.5kohm
R3
2.2kohm
R4
3.3kohm
R5
12kohm
R6
5.6kohm 00.000 V+
-
Fig. CIRCUIT DIAGRAM TO STUDY ZENER DIODE CHARACTERISTICS
Iz
Ii
Vz
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DEPARTMENT
OF
ELECTRONICS AND COMMUNICATION ENGINEERING
BASIC ELECTRONICS ENGINEERING LABORATORY
LAB INSTRUCTIONS FOR CARRYING OUT PRACTICAL
ON
DESIGN OF AN RC LOW PASS FILTER & HIHG PASS FILTER CIRCUIT
& OBSERVING ITS RESPONSE TO SINUSOIDAL AND SQUARE WAVE
INPUTS.
BIRLA INSTITUTE OF TECHNOLOGY
MESRA, RANCHI
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AIM: Design of an RC Low Pass filter circuit & High Pass Filter and observing its
response to sinusoidal and square wave inputs.
APPARATUS:1. Function Generator2. AC Millivoltmeter3. CRO4. Breadboard
COMPONENTS:
1. Resistor
2. Wish board3. Connecting wires4. Capacitor
THEORY:
Low Pass Filter:Passive RC circuit acts as Low Pass filter if output is taken across capacitor. It also
acts as integrator for high time constant.
For sinusoidal signal voltage Gain is given by
0
1
1
f
fjA+
=
Where f0 is critical frequency given by
RCf
2
10 =
For square wave input it acts as integrator if time constant RC is high withrespect to swing time of input wave and under this condition output voltage is given byapproximately
dtVCR
V i=1
0
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High Pass Filter:
Passive RC circuit acts as High Pass filter if output is taken across resistor. It alsoacts as differentiator for low time constant.
For sinusoidal signal voltage Gain is given by
f
fjA
01
1
=
Where f0 is critical frequency given by
RC
f2
10 =
For square wave input it acts as differentiator if time constant RC is small withrespect to swing time of input wave and under this condition output voltage is given byapproximately
dt
dVCRV i=0
PROCEDURE:
Low Pass Filter:1. Connect the circuit as shown in the circuit diagram.2. Apply ac sinusoidal input voltage of 25 milivolt from function generator.3. Connect ac Millivoltmeter across capacitor4. Vary frequency of ac input and measure output voltage.5. Instead of sinusoidal signal apply square wave input and study output
waveform by CRO.
High Pass Filter:
6. Connect the circuit as shown in the circuit diagram.7. Apply ac sinusoidal input voltage of 25 milivolt from function generator.8. Connect ac Millivoltmeter across resister9. Vary frequency of ac input and measure output voltage.
10. Instead of sinusoidal signal apply square wave input and study outputwaveform by CRO.
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OBSERVATIONS:
Input voltage=1 mV
RESULT
PRECAUTION:
1. The breadboard should be handled carefully.
2. The base portions of wires and connection shouldnt touch during the experiment,as it would result distortion at output.
Sl. No. Frequency(Hz)
Measured O/PVoltageIn mV
Voltage Gain20 log10(|Vout/Vin|)
TheoreticalVoltage
Gain
1 50
2 70
3 90
4 100
5 200
6
7
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R1
10kOhm_5%C1
1.6nF
Fig Circuit for Low pass Filter
R1
10.0kOhm_1%
C1
1.6nF
Fig Circuit for HIGH PASS Filter
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DEPARTMENT
OF
ELECTRONICS AND COMMUNICATION ENGINEERING
BASIC ELECTRONICS ENGINEERING LABORATORY
LAB INSTRUCTIONS FOR CARRYING OUT PRACTICAL
ON
MEASUREMENT OF RIPPLE FACTOR WITH AND WITHOUT FILTER FORHALF WAVE AND FULL WAVE RECTIFIER CIRCUITS
BIRLA INSTITUTE OF TECHNOLOGY
MESRA, RANCHI
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AIM: Measurement of ripple factor with and without filter for half wave and full waverectifier Circuits
APPARATUS:1. CRO.2. DC voltmeter.3. AC voltmeter.4. Half wave and Full wave Rectifier circuits5. Circuit board.
THEORY:
Half-Wave rectifier rectifies the positive half cycles of the ac input. Full-Wave rectifier
rectifies both the positive and negative half cycles of the ac input.
Ripple factor (r) = rms value of the ac component / dc value of the rectifier wave.i.e. r = Vrms/Vdc
PROCEDURE:1. Connect a dc voltmeter, an ac voltmeter and a CRO across the output.2. Connect the circuit as a half wave rectifier (by close K3 and open K1, K2 and
K4) and measure the dc and ac voltages with and without filter in each type3. Plug in the input.4. Measure Vrms, Vdc and observe waveform on CRO.
5. Tabulate the readings.6. Calculate r from the readings.7. Calculate r theoretically.
8. Connect the circuit as C-filter, L-filter, LC-filter and -filter (By Closingsuitable key K2, K3 and K4.) and note the readings of dc voltmeter and acvoltmeter in each case. Tabulate the readings.
9. Now connect the circuit as a center tapped full wave rectifier (by close K1, K3and open K2 and K4) and measure the dc and ac voltages with and withoutfilter (By Closing suitable key K2, K3 and K4.) in each type.
10.Calculate r from measured value and theoretically.
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T1
D1
D2
R1
1kohmC1
1uF
C2
1uF
L1
1mH
k1
k3
k2 k4
Vin
230V,50C/S
Vout
Fig. CIRCUIT DIAGRAM OF A HALF WAVE AND FULL WAVE RECTIFIER
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DEPARTMENT
OF
ELECTRONICS AND COMMUNICATION ENGINEERING
BASIC ELECTRONICS ENGINEERING LABORATORY
LAB INSTRUCTIONS FOR CARRYING OUT PRACTICAL
ON
OBSERVATION OF OUTPUT WAVEFORMS OF DIODE
CLIPPER AND CLAMPER CIRCUITS
BIRLA INSTITUTE OF TECHNOLOGY
MESRA, RANCHI
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AIM: Observation of output waveforms of Diode Clippers and Clampers Circuits
APPARATUS REQUIRED:
1. Wish board2. D.C. Power Supply3. Function Generator Or Trainer Kit (Microlab-II)4. C.R.O
CIRCUIT COMPONENTS:
1. Diode (IN 4007)
2. Capacitors3. Resistors
THEORY
PROCEDURE:
1. Connect the circuit as shown in the circuit diagram-1.2. Connect the C.R.O. probe across the output terminal and ground.
3. Observe the output waveform.4. Trace the waveform on the tracing paper.5. Measure the Amplitude of Sine wave and clipping/clamping Voltage.6. Repeat the above procedure for circuit diagram- 2,3,4,5 and 6.
RESULT:
PRECAUTIONS:
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R
1.2kohm
-
---
---
+
-
Vo
R2
1.2kohm
Vo
C21uF
---
---
+
-
Vo
---
---
+
-1N4001
1N4001
1N4001
Fig. (a) Fig. (b)
Fig. (f)
---
---
+
-
Vo
R4
1.2kohm
1N4001
Fig. (c)
---
---
Vo
R1
1.2kohm
+
-
1N4001
Fig. (d)
C11uF ---
---
+
-
Vo1N4001
Fig. (e)
DIODE CLIPPER AND CLAMPER CIRCUITS
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DEPARTMENT
OFELECTRONICS AND COMMUNICATION ENGINEERING
BASIC ELECTRONICS ENGINEERING LABORATORY
LAB INSTRUCTIONS FOR CARRYING OUT PRACTICAL
ON
OBTAINING THE FREQUENCY RESPONSE OF CE
TRANSISTOR AMPLIFIER AND MEASUREMENT OF ITS
BANDWIDTH
BIRLA INSTITUTE OF TECHNOLOGY
MESRA, RANCHI
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R1
1kohm
R2
8.2kohm
R3
1.5kohm
R4
1kohm
R5
470ohm
R61kohm
C1
50uF
C2
50uF
C3
250uF
Vin
Q1
V2
12V
Vout
Fig. CIRCUIT DIAGRAM OF COMMON EMITTER AMPLIFIER
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DEPARTMENT
OF
ELECTRONICS AND COMMUNICATION ENGINEERING
BASIC ELECTRONICS ENGINEERING LABORATORY
LAB INSTRUCTIONS FOR CARRYING OUT PRACTICAL
ON
MEASUREMENT OF THE h-PARAMETERS, hie AND hfe
OF A TRANSISTOR
BIRLA INSTITUTE OF TECHNOLOGYMESRA, RANCHI
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AIM: Measurement of the h-Parameters hie and hfe of a CE transistor amplifier
APPARATUS:1. Function generator.2. VTVM/AC Mill voltmeter3. DC milliammeter.4. Dual DC Power Supply
THEORY:
hie =Vbe/ Ib = Input impedance in CE configuration.hfe =Ic / Ib = Forward current gain in CE configuration
PROCEDURE:
1. Connect the circuit as shown in fig.2. Apply Vin as 25mV and 1KHz from function generator.3. Fix collector voltage Vcc at 6 V.4. Vary ICQ by varying VEE .5. Measure Vbe, Vce and Vcr for various collector currents (IC).6. Tabulate the readings and calculate hie and hfe.7. Plot hie vs. ICQ and hfe vs. ICQ.
OBSERVATIONS:
ICQ(mA)
Vbe(mV )
Vce(mv)
Vcr(mV)
Ib= (Vin-Vbe)/10K
(A)
Ic
= (Vce Vcr)/ 10(mA)
Hie=Vbe/Ib
(K)
Hfe=Ic/Ib
1.0
2.0
3.0
4.0
5.0
RESULT:
PRECAUTIONS:
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Vin
25mV Vcc
6V0-3V
10kohm
100kohm
1mH
R3
10ohm
50uF
50uFSK100
00.000 A+
-
Icq
Fig. CIRCUIT DIAGRAM TO MEASURE h-PARAMETER
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DEPARTMENT
OFELECTRONICS AND COMMUNICATION ENGINEERING
BASIC ELECTRONICS ENGINEERING LABORATORY
LAB INSTRUCTIONS FOR CARRYING OUT PRACTICAL
ON
VERIFICATION OF THE TRANSFER CHARACTERISTICS OF JFETAND MEASUREMENT OF ITS VOLTAGE GAIN
BIRLA INSTITUTE OF TECHNOLOGY
MESRA, RANCHI
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AIM: Verification of the transfer characteristics of JFET and measurement of its voltagegain.
EQUIPMENTS/APPARATUSREQUIRED:1. Bread board,2. Transistor3. Power Supply4. Milliammeter5.Electronic Multimeter.
THEORY: A field effect transistor is a three-terminal unipolar device. Its inputimpedance is very high. A field effect transistor can be either a JFET orMOSFET. A JFET, MOSFET both can be either have N-channel or P-channel. An N-channel JFET has an N-type Semiconductor bar, the twoends of which make the drain and source terminals. On the other two sidesof this N-type Semiconductor bar, two P type regions are made. TheseP-regions form gates. Usually, these two Gates are connected together toform a single gate. The gate is given a negative bias with respect to thesource. The drain is given positive potential with respect to the source. Incase of a P-channel JFET, the terminals of all the batteries are reversed.
FORMULAE USED:1. Amplification factor = VDS/VGSID=constant2. Tran conductance gm= ID/VGS|VDS=constant
3. Drain Resistance rd = VDS/Id |VGS=constant
4. = rd * gm
PROCEDURE:(a)To plot the output characteristics
1. Assemble the circuit as shown in fig.2. First, fix VGS at some value say 0 V. Increase the drain voltage VDS slowly
in steps say (0-10 V). Note drain current ID for each step.3. Now, change VGS to another value and repeat the above for VGS=1V to
3V.4. Plot the drain characteristics (graph between ID and VDS for fixed value of
VGS).
(b)To plot the transfer characteristics1. Adjust VDS to any value say 2V and keep it constant throughout the
observations.2. Vary VGS in small steps and note ID for each value.3. Plot the Transfer characteristics (graph between ID and VGS for fixed value
of VDD).
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The values given below are typical for an ordinary 741, better versions (moreexpensive) may give better results...Typical values of Basic Parameters:
Rail voltages : +/- 15V dc (+/- 5V min, +/- 18V max)Input impedance: Around 2MegOhms
Low Frequency voltage gain: approx 200,000
Input bias current: 80nA
Slew rate: 0.5V per microsecond
Maximum output current: 20mA
Recommended output load: not less than 2kilOhms
Note that, due to the frequency compensation, the 741's voltage gain falls rapidly withincreasing signal frequency. Typically down to 1000 at 1kHz, 100 at 10kHz, and unity atabout 1MHz. To make this easy to remember we can say that the 741 has a gain-bandwidth productof around one million (i.e. 1 MHz as the units of frequency are Hz).
THEORY:
PROCEDURE:
1. Connect the circuit as shown in the circuit diagram.2. Keep Rf = 470K ,R1=47K3. Keep Vin = 100mV (fixed) each time.4. Vary the frequency from 20Hz to 200KHz and note down the output reading
at each time keeping Vin =100mV (fixed) and tabulate the readings in toobservation table.
5. Replace R1=4.7K and repeat the procedure as above (Vin=10mV).6. Plot Gain against frequency on semilogrethmic graph sheet.7. Find 3dB point frequencies and Bandwidth.
Note: Try totake the readinguntil gain will drop from its constant gain upto thevalue, which is approximately equal to the gain value for first reading
OBSERVATIONS:
SL. No. Frequency
(Hz)
Vin
(mv)
Vout
(mv)
Gain Av=Vout/Vin Gain
[20 log10 Vout/Vin)]
(dB)
12
3
4
5
RESULT:
PRECAUTIONS:
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U1
741
3
2
4
7
6
51
Vin
R1
4.7kohmVout
+10V
-10V
10mV
Rf 470kohm
Fig. CIRCUIT DIAGRAM OF AN INVERTING AMPLIFIE
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DEPARTMENT
OF
ELECTRONICS AND COMMUNICATION ENGINEERING
BASIC ELECTRONICS ENGINEERING LABORATORY
LAB INSTRUCTIONS FOR CARRYING OUT PRACTICAL
ON
OBTAINING THE FREQUENCY RESPONSE AND MEASUREMENT OF
BANDWIDTH OF A NON- INVERTING OP-AMP (USING IC 741)
BIRLA INSTITUTE OF TECHNOLOGY
MESRA, RANCHI
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U1
741
3
2
4
7
6
51
V1
R1
47kohm
Vout
+10V
-10V
100mV
Rf
470kohm
Fig. CIRCUIT DIAGRAM OF A NON-INVERTINGN CIRCUIT
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DEPARTMENT
OF
ELECTRONICS AND COMMUNICATION ENGINEERING
BASIC ELECTRONICS ENGINEERING LABORATORY
LAB INSTRUCTIONS FOR CARRYING OUT PRACTICAL
ON
DESIGN OF AN RC PHASE SHIFT OSCILLATOR (USING IC 741 OP AMP) ANDCALCULATION OF ITS FREQUENCY OF OSCILLATION.
BIRLA INSTITUTE OF TECHNOLOGY
MESRA RANCHI
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different versions, which work better than others in some respect. Each has a slightlydifferent part number, but it generally has 741 in it somewhere!
The values given below are typical for an ordinary 741, better versions (moreexpensive) may give better results...Typical values of Basic Parameters:
Rail voltages : +/- 15V dc (+/- 5V min, +/- 18V max)
Input impedance: Around 2MegOhms
Low Frequency voltage gain: approx 200,000
Input bias current: 80nA
Slew rate: 0.5V per microsecond
Maximum output current: 20mA
Recommended output load: not less than 2kilOhms
Note that, due to the frequency compensation, the 741's voltage gain falls rapidly with
increasing signal frequency. Typically down to 1000 at 1kHz, 100 at 10kHz, and unity atabout 1MHz. To make this easy to remember we can say that the 741 has a gain-bandwidth productof around one million (i.e. 1 MHz as the units of frequency are Hz).
THEORY:The RC phase shift oscillator consists of an op-amp as amplifier and 3 RC
cascade networks as the feedback circuit. The op-amp is used in the inverting mode, sooutput signal will be 180 out of phase. The feedback RC network provides the exactly180 phase shift. So the total phase shift is 0.
The gain of the amplifier is also kept large to produce oscillation.
The frequency of oscillation is given byF= 0.065/RC.
PROCEDURE:
1. Connect the circuit as shown in the circuit 1.2. Observe the sinusoidal output on CRO.3. Measure the time period of the sinusoidal wave and calculate its frequency.4. Compare the measured frequency with
F= 0.065/RC.
RESULT:
PRECAUTION:
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DEPARTMENT
OF
ELECTRONICS AND COMMUNICATION ENGINEERING
BASIC ELECTRONICS ENGINEERING LABORATORY
LAB INSTRUCTIONS FOR CARRYING OUT PRACTICAL
ON
DESIGN OF A R-2R LADDER NETWORK FOR CONVERSION OF A 4-BIT
DIGITAL SIGNAL TO AN ANALOG EQUIVALENT SIGNAL.
BIRLA INSTITUTE OF TECHNOLOGY
MESRA, RANCHI
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10kohm
20kohmU1
741
3
2
4
7
6
51
5V
10kohm 10kohm
20kohm 20kohm 20kohm
20kohm
20kohm
10kohm
Vout
R R R RF
2R 2R 2R 2R 2R
RL
-15v
+15v
Fig. R-2R Ladder Network