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SSN COLLEGE OF ENGINEERING, CHENNAI 603 110

DEPARTMENT OF ELECTRICAL & ELECTRONICS

ENGINEERING

LAB INCHRAGES: Mrs.R.Ramaprabha (Sec-A)

Mrs.R.Deepalakshmi (Sec-B)

131353 - MEASUREMENT AND INSTRUMENTATION

LABORATORY

NAME OF THE STUDENT: Mr. /Ms.

REG. NO.:

YEAR/SEM: II/ 3

ACADEMIC YEAR: 2011-2012

2

SYLLABUS

131353 - Measurements and Instrumentation Laboratory

P = 45 Total = 45

AIM

The aim of this lab is to fortify the students with an adequate work experience in the measurement of different quantities and also the expertise in handling the instruments involved.

OBJECTIVE

To train the students in the measurement of displacement, resistance, inductance, torque and angle etc., and to give exposure to AC, DC bridges and transient measurement.

LIST OF EXPERIMENTS

1.Study of displacement and pressure transducers

2.AC bridges.

3.DC bridges.

4.Instrumentation amplifiers.

5.A/D and D/A converters.

6.Study of transients.

7.Calibration of single-phase energy meter.

8.Calibration of current transformer.

9.Measurement of three phase power and power factor.

10.Measurement of iron loss.

 

 

 

 

 

 

3

 

 

CONTENTS

 

 

 

Name: ---------------------------

Reg No:: ---------------------------

Batch No: :--------------

 

 

 

 

 

 

 

S.

Name of the Experiment

Page

Marks

Signature of

No.

No

 

(10)

the Staff

 

 

 

 

 

 

 

 

 

 

Measurement of Resistance [Wheat-stone’s

 

 

 

 

1

Bridge& Kelvin’s Bridge]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2

Measurement of Capacitance [Schering Bridge]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Measurement of Inductance [Maxwell’s

 

 

 

 

3

Inductance-Capacitance Bridge]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Measurement of Iron Loss and Permeability of

 

 

 

 

4

Ring Specimen

[ Maxwell’s Bridge]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5

Calibration of Single Phase Energy Meter

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Measurement of Three Phase Power & Power

 

 

 

 

6

 

Factor

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

7

Study of Current Transformer

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

8

Design of Instrumentation Amplifier

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

9

Study of LVDT & Pressure transducer

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Digital to Analog Converter & Analog to Digital

 

 

 

 

10

Converter

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

11

Study of transients

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

TOTAL MARKS: -------/10

4

Expt.No: MEASUREMENT OF RESISTANCE

Date: [USING WHEATSTONE’S BRIDGE]

AIM

To Measure the unknown value of resistance using Wheat stone’s bridge network, and to study the sensitivity of the bridges.

APPARATUS REQUIRED

·Wheatstone bridge trainer

·Galvanometer

·Unknown resistances

·Patching wires.

·Multi-meter

·DC power supply

FORMULAE

RX

=

R1 R3

 

 

 

 

 

 

R2

 

Bridge Sensitivity S B

=

 

q

DR / R

 

 

 

 

Where, RX =Unknown value of resistance, R1=Standard resistance

R3 &R2=Resistances of ratio arms. q = Deflection of the galvanometer

DR / R = Fractional change in unknown resistance

THEORY:

A very important device used in the measurement of medium resistances is the Wheat stone’s bridge. It has four resistive arms, together with 1 kHz oscillator. The output of 1 kHz oscillator is given to the bridge circuit through an isolation transformer. Suppose a galvanometer is connected across the points B & D, the bridge is set to be balanced if the potential difference across the galvanometer is 0 Volts, so that there is no current through galvanometer. This condition occurs when the voltage from point B to point A equals the voltage from point D to point A or by referring to the other terminal when the voltage from point B to point C equals the voltage from

Point D to point C. Hence, the bridge is balanced when

 

I1 R1 = I x Rx

(1)

5

Also I1

= I 2

=

 

 

E

(2)

 

[R1 + R2 ]

 

and I x

= I3

=

 

 

 

E

(3)

 

 

 

 

 

[Rx

+ R3 ]

Combining the equations1, 2 & 3 and simplifying, we obtain

 

 

R1

 

=

 

 

 

RX

 

 

 

 

 

 

[R1 + R2 ]

[RX + R3 ]

 

 

From which R1 R3

= R2 RX

 

or RX

=

R1 R3

 

 

 

 

 

(4)

R2

 

 

 

 

 

 

 

 

 

 

 

 

 

PROCEDURE

1.Switch ON the trainer and check the power supply to be +15 V.

2.Patch the circuit as shown in wiring diagram.

3.Connect the unknown resistance in the arm marked RX .

4.Observe the sine wave at the secondary of the isolation transformer on an oscilloscope.

5.Select some values of R2 & R3 .

6.Adjust R1 for balance and then at balance, measure the value of R1.

7.Calculate the value of unknown resistance as per the formula.

Circuit Diagram

6

Wiring Diagram

Tabulation

S.No.

Rx (Measured

Rx (True

Error =

%Error

 

Value)

Value)

Measured-True

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Model Calculation

RESULT

7

Expt.No: MEASUREMENT OF RESISTANCE

Date:

[USING KELVIN’S BRIDGE]

AIM

To Measure the unknown value of resistance using Kelvin’s bridge network, and to study the sensitivity of the bridges.

APPARATUS REQUIRED

·Kelvin’s bridge trainer

·Galvanometer

·Unknown resistances

·Patching wires.

·Multi-meter

·DC power supply

FORMULAE

R = P ´ S

Q

Where, R =Unknown value of resistance,

S=Standard resistance

P &Q=Resistances of ratio arms

THEORY:

Kelvin Bridge is a modification of Wheat stone’s bridge and provides increased accuracy in measurement of low resistance. Kelvin double bridge incorporates two sets of ratio arms and the use of four terminal resistors for the low resistance arms. Consider the circuit shown in Fig (2). The first of ratio arms is P and Q. The second set of ratio arms, p and q is used to connect the galvanometer to a point c at the appropriate potential between point’s m and n to eliminate the effect of connecting lead of resistance r between the known resistance R and the standard resistance S. The ratio p/q is made equal to P/Q. Under balanced condition, there is current through the galvanometer, which means that the voltage drop between a and d,

Ead is equal to the voltage drop Eamc between a & c.

 

 

 

P

 

 

 

 

Now, Ead

=

 

 

´ Eab

 

 

 

 

 

 

 

 

 

(P + Q)

 

 

 

 

 

 

 

 

p + q

 

 

 

And, Eab

= I R + S +

 

´ r

1.1

 

 

 

 

 

 

 

 

 

 

 

 

 

p + q + r

 

 

 

p

 

p + q

 

 

And, Eamc = I R +

 

 

 

 

´ r

 

 

 

p + q

 

p + q + r

 

 

 

 

 

 

 

 

 

 

For zero galvanometer deflection, Ead = Eamc

or

or

 

P

 

 

 

p + q

 

 

 

 

 

 

 

 

 

´ r =

 

 

 

 

´ I R + S +

 

 

P + Q

 

 

p + q + r

 

R =

P

´ S +

qr

 

P

-

p

 

 

 

 

 

 

q

 

Q

p + q + r Q

 

 

 

p

 

p + q

 

 

I ´ R +

 

 

 

 

´

 

 

 

p + q p + q + r

 

8

1.2

1.3

1.4

Now if P = p Eqn.1.3 becomes, R = P ´ S

Q q Q

Eqn. (1.4) is the usual working for the Kelvin Bridge. It indicates that the resistance of connecting lead, r has no effect on the measurement, provided that the two sets of ratio arms have equal ratios. Eqn. (1.3) is useful, however, as it shows the error that is introduced in case the ratios are not exactly equal. It indicates that it is desirable to keep r as small as possible in order to minimize the errors in case there is difference

between ratios P and p .

Q q

PROCEDURE:

1.Study the front panel configuration given an the front panel of the trainer.

2.Energize the trainer and check the power supply to be +5V.

3.Connect externally a galvanometer Q as indicated on the trainer.

4.Connect the unknown resistance RX as marked on the trainer.

5.Select the values of P & Q such that P/Q =p/q =0.01.

6.Adjust S for balance and then at balance, measure the value of S.

7.Calculate the value of unknown resistance as per the formula.

Circuit Diagram

9

Wiring Diagram

Tabulation

S.No.

Rx

Rx (True

Error =

%Error

 

(Measured

Value)

Measured-True

 

 

Value)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Model Calculation

RESULT

10

Expt No:

MEASUREMENT OF CAPACITANCE

Date:

[USING SCHERING BRIDGE]

AIM

To measure the unknown value of Capacitance using Schering bridge and to find the dissipation factor.

APPARATUS REQUIRED

·Schering bridge kit

·Unknown Capacitances

·Patching wires.

·Multi-meter

·CRO

·AC Source-1 KHz Oscillator

FORMULAE

C = R1 C x 3

R2

Where, CX =Unknown value of resistance,

R1=Resistance of arm 1.

R2=Resistance of arm 2

C3 =Standard capacitor.

THEORY

The balance conditions require that the sum of the phase angles of arms 1 and 4 equals the sum of the phase angles of arms 2 and 3.Since the standard capacitor is in the arm 3, the sum of the phase angles of arm 2 and arm 3 will be 0o+90o= 90o.In order to obtain the 90o. phase angle needed for balance, the sum of the angles of arm 1 and 4 must equal 90o.Since in general measurement work the unknown will have a phase angle smaller than 90o.It is necessary toj give arm 1 a small capacitive angle by connecting capacitor C1 in parallel with resistor R1.A small capacitive angle is very easy to obtain, requiring a small capacitor across resistor R1. The balance equations are derived in the usual manner, and by substituting the corresponding impedance and admittance values in the equation, we obtain

Z x = Z2 Z3Y1 or

 

j

 

-1

 

1

 

Rx -

= R2

 

+ jwC1

wCx

 

 

 

wC3 R1

 

and expanding

11

 

j

 

R2C1

 

 

jR2

 

Rx -

=

 

-

 

wCx

 

 

 

 

C3

wC3 R1

Equating real terms and the imaginary terms, we find that

RX

=

R2C1

Cx

=

C3 R1

 

C3

R2

 

 

 

 

As can be seen from the circuit diagram of fig. the two variables chosen for the balance adjustment are capacitor C1 and resistor R2.There seems to be nothing unusual about the balance equations or the choice of variables components, but consider for a moment how the quality of a capacitor is defined.

PROCEDURE

1.Switch ON the trainer and check the power supply to be +15 V.

2.Patch the circuit as shown in wiring diagram.

3.Connect the unknown capacitance in the arm marked CX .

4.Observe the sine wave at the secondary of the isolation transformer on an oscilloscope.

5.Select some value of R2.

6.Connect the oscilloscope between the ground and the output point.

7.Vary R1 from the minimum position in a clockwise direction. If the selection of R2 is correct the balance or null point can be observed on the oscilloscope i.e. the amplitude of the output waveform comes to a minimum for a particular value of R1 and then again increases by varying R1 in the same clockwise direction. If that not the case, select another value of R2.

8.Vary the capacitor C1 for fine balance adjustment.

9.The null condition can also be observed by using loudspeaker. Connect the output of the bridge to the input of the detector. The loudspeaker is connected at the output of the detector. Adjust R1 and proper selection of R2 for a minimum sound in the loudspeaker.

10.The process of manipulation of this resistance is typical of the general balancing procedure for bridges and is said to cause convergence of the balance point.

11.Finally calculate the value of the unknown capacitance using the equation by substituting the measured value of R1 at the balance point.

12

Circuit Diagram

Wiring Diagram

13

Phasor Diagram

Tabulation

S.No.

C3

R1

R2

CX nF

CX nF

% Error

 

µF

 

 

(Measured

(True

 

 

 

 

 

Value)

Value)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Model Calculation

RESULT:

14

Expt No:

MEASUREMENT OF INDUCTANCE

Date:

[USING MAXWELL’S INDUCTANCE-CAPACITANCE

BRIDGE]

AIM

To Measure the unknown value of Inductance using Maxwell’s Inductance- Capacitance bridge and to determine the Q factor of the coil

APPARATUS REQUIRED

·Maxwell’s Inductance-Capacitance bridge kit

·Unknown Inductances

·Bridge Oscillator.

·Patching wires.

·Multi-meter

·Loud Speaker.

·CRO

FORMULAE

R1 = R2 R3

R4

L1 = R2 R3C4

Q Factor = Q = wL1 = wC4 R4

R1

L1 =Self inductance to be measured,

R1 =resistance of self inductor L1,

R2, R3,R4 =known non-inductive resistance, and C4 =fixed standard capacitor.

THEORY

In this bridge an inductance is measured by comparison with a standard

variable capacitance.

Let

L1 =Self inductance to be measured,

 

R1 =resistance of self inductor L1,

 

R2, R3,R4 =known non-inductive resistance,

and

C4 =fixed standard capacitor.

Writing the balance equations,

[R1 + jwL1 ][R4 + (1+ jwC4 L4 )]= R2 R3 or R1R4 + jwL1R4 = R2 R3 + jwR2 R3C4 R4

Equating real and imaginary parts, we get

R1 = R2 R3 and L1 = R2 R3C4

R4

15

Thus we have two variables R4 and C4 which appear in one of the balance equations

and hence the two equations are independent.

PROCEDURE

1.Lab Maxwell’s Inductance-Capacitance bridge consists of built-in +15 V power supply, 1kHz oscillator & the detector.

2.Patch the circuit as shown in wiring diagram.

3.Switch on the training board and check the power supply and oscillator output. Connect oscilloscope output to AF input of bridge circuit.

4.Vary R from the minimum position in a clockwise direction to obtain balance condition. Output should be connected to oscilloscope to observe convergence and to get precise balance.

5.The null condition can be observed by using loudspeaker. Connect the output of the bridge to the input of the detector. The loudspeaker is connected at the output of the detector. While adjusting R &C the sound in the loudspeaker should decrease to minimum and then increase. Similarly in the oscilloscope the output of the bridge comes to a minimum and then increases. The point of balance is indicated by flat waveform.

6.For further fine balance vary C4 which will compensate for negative component of the inductor because every inductor has some resistance.

7.Finally calculate the value of the self inductance of the coil in terms of standard capacitor can be calculated using the equation

Circuit Diagram

16

Phasor diagram:

Wiring Diagram

Tabulation

S.No.

R4in

L1 = LX

L1 = LX

C4

%Error

 

 

mH

mH (True

 

 

 

 

(Practical

value

 

 

 

 

value)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

17

Model Calculation

RESULT:

18

Expt No:

MEASUREMENT OF IRON LOSS AND

Date:

PERMEABILITY [USING MAXWELL’S BRIDGE]

AIM:

To measure the iron loss and permeability of the given ring specimen.

APPARATUS REQUIRED

·Maxwell’s Bridge Kit

·Digital Multimeter

·Microphone

·Patch Chords

·CRO

FORMULAE USED

Unknown inductance Ls = Std.R1 ´ Std.R3 ´ C

Unknown resistance Rs = Std.R1 ´ Std.R3

R2

R2 Standard resistance measured by using multi meter across pot 2.

Iron loss = Il2 ´ (RS - Rw )

Where Il – current flow to specimen Rs – Specimen resistance Rw – Winding resistance

Permeability m = ls R1 R3C N 2 As

ls – Specimen’s winding length [coil] in meter R1, R3 – Standard Resistances

C – Standard Capacitance N – Number of turns [coil]

A – Area of specimen in M 2

THEORY:

The Maxwell’s Inductance Bridge is most commonly used bridge for

measurement of inductances of Q value less than 10. A typical Maxwell’s bridge

consists of an inductance measured in comparison with a capacitance in laboratory

operations. The input of the bridge is given through a standard 1 KHz oscillator which

produces a 1 KHz sine wave at constant amplitude.

Let L1 be the unknown inductance

R1 be the resistance of inductor

19

R1, R3 & R4 be the known non-inductive resistances.

L4 be the variable standard capacitor

At balanced condition

 

 

R4

 

 

(R1

+ jwL1 )

 

 

 

= R2 * R3

 

+ jwC4 R4

 

1

 

 

R1 R4 + jwL1 R4 = R2 R3 + jwR2 R3C4 R4

Separating into Real and Imaginary terms we have,

R =

R2 R3

and L = R R C

 

 

4

1

R4

1

2

3

 

 

 

 

 

The Maxwell’s bridge is limited to the measurement of medium Q coils. Hence high Q coils are measured on Hay’s bridge. The main advantage of the bridge is that if we choose R4 and C4 as variable elements and also the frequency does not appear in any of the equations. In a ring specimen the iron loss meant for the power loss due to magnetization loss. The power loss in the specimen includes both copper and iron loss. Permeability of the ring specimen is dependent on the length of the winding number of turns, area of the specimen and the arm parameters. Normally these values are given by specimen manufacturers.

PROCEDURE:

1.Connections are made as per the diagram.

2.Connect the ring specimen to the bridge arm, for which measurement to be made.

3.Keep the POT 2 in maximum position and switch on the unit.

4.The output can be detected by microphone or CRO.

5.For detecting the output by CRO, vary the POT1 from lower to higher value. At one stage the output goes to minimum value.

6.Now note down the resistance of POT1 by using multi-meter.

7.In this condition note down the AC current through ring specimen, POT1 and the source current by using milli-ammeter.

8.Apply these values in to an approximated formula and find out the iron loss and permeability of the given ring specimen.

9.Repeat the same procedure for different ring specimen.

20

Wiring Diagram

TABULATION:

Sl

Inductance (Ls) mH

Resistance Rs

Current I1

Iron

Permeability

 

 

No

Theoretical

Practical

Ohms

mA

Loss

 

 

Value

Value

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

21

MODEL CALCULATION

RESULT:

Specimen 1 Specimen 2 Specimen 3

Iron Loss

Permeability

22

Expt No:

CALIBRATION OF SINGLE PHASE ENERGY METER

Date:

(Phantom Loading)

AIM

To calibrate the given single phase energy meter at unity and other power factors and to draw the calibration curve..

APPARATUS REQUIRED

S.No

Apparatus Name

Type

Range

Qty

 

 

 

 

 

1

Single phase energy meter

Induction type

 

1

 

 

 

 

 

 

 

2

 

 

300 V; 10A,

1

Standard wattmeter

 

 

 

 

UPF

 

 

 

 

 

 

 

 

 

 

3

Voltmeter

MI

(0-300) V

1

 

 

 

 

 

 

 

4

Ammeter

MI

(0-10) A

1

 

 

 

 

 

 

 

5

Lamp Load

 

230 V, 5 Kw

1

 

 

 

 

 

 

 

 

6

Phase Shifting transformer

 

 

1

 

 

 

 

 

7.

Single phase auto

 

 

1

transformer

 

230/(0-270 V

 

 

 

 

 

 

 

 

 

 

 

 

8

Stop watch

 

 

 

 

 

 

 

 

9

Connecting wires

 

 

 

 

 

 

 

 

FORMULAE

Energy meter specification = 750 rev

Kwh

True energy (Pt) = Power ´Time Kwh

3600´1000

Measured energy = n , n Number of revolutions

750

% Error = Measured - True ´100 True

THEORY

The energy meter is an integrated type of instrument where the speed of rotation of the aluminum disc is directly proportional to power consumed and the number of revolution per minute is proportional to the energy consumed by the load. The ratings associated with the energy meter are

1.Voltage rating

23

2.Current rating

3.Frequency rating

4.Meter constants

The driving system of the meter provides the rotational torque for the moving system, which in turn activates the energy registration system for reading purposes. The energy meter is operated on induction principle, in which the eddy current induced in the aluminum disc interacts with the main field and creates the driving torque.

This system employs phantom loading. Here, the phase shifting transformer to supply the voltage of varying power factor to the potential coil of energy meter. The system phase supply is used to supply current of energy required value to the current coil of energy meter. Thus energy meter is tested under various power factor loads without applying any actual load. This is called phantom loading.

PROCEDURE

1.Give the connections as per the circuit diagram.

2.Switch on the three phase supply through phase shifting transformer. Also switch on the single phase supply through autotransformer. The autotransformer should be kept in minimum position before switching on.

3.Set the 5A current in ammeter with the help of auto transformer.

4.Now note down the voltage, current and power from the respective meters. Also note the time required for the disc to rotate hundred times.

5.Repeat step 3 for various power factors The power factor is set with the help of phase shifting transformer.

6.Tabulate the readings and do the necessary calculations.

24

Circuit Diagram

Tabulation

 

Wattmeter Power

Time for

 

Measured

True

 

Sl

Observed

Actual

Power

%

n rev

Energy

Energy

No

Reading

Reading

Factor

Error

Seconds

KwH

KwH

 

(Watts)

(Watts)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Model Calculation

RESULT:

25

Expt No:

MEASUREMENT OF THREE PHASE POWER & POWER

Date:

FACTOR

AIM

 

To measure the three phase power and power factor using two wattmeter method given load. Also to draw the phasor diagrams

APPARATUS REQUIRED

S.No

Apparatus Name

Type

Range

Qty

 

 

 

 

 

1

Voltmeter

MI

(0-600)V

1

 

 

 

 

 

2

Ammeter

MI

(0-10)A

1

 

 

 

 

 

3

wattmeter

 

600V,10A,UPF

2

 

 

 

 

 

4

Three phase resistive load

 

 

1

 

 

 

 

 

5

Three phase inductive load

 

 

1

 

 

 

 

 

6

Three phase capacitive load

 

 

1

 

 

 

 

 

7

Connecting wires

 

 

 

 

 

 

 

 

FORMULAE

 

-1

 

 

P1

- P2

 

 

Power factor = cos f = cos tan

 

 

 

 

 

 

 

 

3

P1

+ P2

 

 

 

 

 

 

THEORY

Power Measurement

There are different methods to measure three-phase power. They are one wattmeter method, two-wattmeter method, three-wattmeter method & also using three-phase wattmeter. Reactive power can be measured by using varmeter (volt ampere reactive meter).

PROCEDURE

1.Give the connections as per circuit diagram.

2.Switch on the three-phase supply. Also Switch on the resistive load.

3.Note down the wattmeter reading and voltmeter and ammeter reading for a particular load.

4.Repeat the same procedure for different loads.( RL, L alone ,C alone and RC )

5.Tabulate the readings and calculate the real power and reactive power.

6.Calculate power factor also draw the phasor diagrams for all cases.

26

Circuit Diagram:

Connection Diagram :

Case:1 Normal Connection

Case:2 Connection for watt meters if one of the wattmeter reads negative

27

Phasor Diagram:

Reference Table:

S.No

Load

Power

Power

W1=v3VI

W2=vVI

Active

Reactive

Tan

 

 

factor

factor

Cos (30-

Cos

Power

Power

F

 

 

 

angle

F)

(30+F)

(P)

(Q) v3

 

 

 

 

F

 

 

W1+

(W1-

 

 

 

 

 

 

 

W2

W2)

 

1

R

1

0

(3/2) VI

(3/2) VI

3VI

0

0

 

alone

 

 

 

 

 

 

 

2

RL

0.5

60

(3/2) VI

0

(3/2)

(3v3/2)

v3

 

 

Lag

 

 

 

VI

VI

 

3

L

0.5

90

(v3/2) VI

(-v3/2)

0

3VI

8

 

alone

Lag

 

 

VI

 

 

 

4

C

0.5

-90

(-v3/2) VI

(v3/2)

0

-3VI

-8

 

alone

lead

 

 

VI

 

 

 

5

RC

0.5

-60

0

(3/2) VI

(3/2)

(-3v3/2)

-v3

 

 

lead

 

 

 

VI

VI

 

V-Phase to neutral voltage: I- Current per phase

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

28

TABULATION:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

M.F=

 

M.F=

 

S.No

Load

Voltage

 

Current

 

 

W1

 

W2

 

 

 

(V) in

 

(I) in

 

Observed

 

Actual

Observed

 

Actual

 

 

 

 

Volts

 

amps

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1

R alone

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2

RL

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3

L alone

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4

C alone

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5

RC

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Real

 

Reactive

 

 

Power Factor

 

 

 

 

 

 

 

 

 

 

Power

 

 

angle,

 

 

 

W1

 

W2

 

Power

 

Power

 

 

 

S.No

Load

 

 

 

factor

 

-1

 

 

P1 - P2

(Watts)

Watts)

(P)in

 

(Q) in

 

tan

3

 

 

 

 

P + P

 

 

 

 

 

F=

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CosF

 

 

 

 

 

1 2

 

 

 

 

 

 

 

 

 

Watts

 

vars

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(degrees)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1

R

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

alone

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2

RL

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3

L

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

alone

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4

C

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

alone

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5

RC

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

RESULT:

29

Exp No:

Date:

STUDY OF CURRENT TRANSFORMER ERRORS

AIM

To study the working of current transformer and also to calculate the various

errors.

APPARATUS REQUIRED

S.No

Apparatus Name

Type

Range

Qty

 

 

 

 

 

 

Current

 

 

2

1

Transformer

 

 

 

 

 

 

 

 

2

Single Phase auto

 

230/(0-270)V,8

1

transformer

 

A

 

 

 

 

 

 

 

 

 

3

Ammeter

MI

(0-10) A

1

 

 

 

 

 

 

 

4

Ammeter

MI

(0-5)A

1

 

 

 

 

 

 

 

5

Wattmeter(W1)

 

300V,5A,LPF

1

 

 

 

 

 

 

 

 

6

Wattmeter(W2)

 

300V,2.5A,LPF

1

 

 

 

 

 

 

 

 

7

Phase shifting Transformer

 

 

1

 

 

 

 

 

8

Single Phase transformer

LV, HC

 

1

 

 

 

 

 

9

Burden

 

 

 

 

 

 

 

 

10

Connecting wires

 

 

 

 

 

 

 

 

FORMULA:

 

 

 

Ratio error:

 

 

 

R

W1P

 

 

 

X

= -------------

 

 

 

W1P –W 2P

Phase Angle error:

W2Q

30

θ

= -------------

+ θ

 

X

S

W1P –W 2P

PRECAUTIONS:

1.The Primaries of 2 CT’s should be correctly connected.

2.The Secondaries of 2 CT’s should be correctly connected.

3.The Secondary of CT should never be opened when primary is energized.

THEORY

The current transformer is used with it’s primary winding connected in series with line carrying the current to be measured and, therefore, the secondary current is dependent upon the load connected to the system and is not determined by the load (burden) connected on the secondary winding of the current transformer. The primary winding consists of very few turns, and, therefore there is no appreciable voltage drop across it. The secondary winding of the current transformer has large number of turns, the exact number being determined by the turns ratio. The ammeter or wattmeter current coil is connected directly across secondary winding terminals. Thus a current transformer operates its secondary winding nearly under short circuit conditions. One of the secondary winding is earthed so as to protect the equipment and personnel in the vicinity in the event of insulation breakdown in the current transformer.

The various ratios of instrument transformers are:

Transformation ratio: It is the ratio of magnitude of the primary phasor to the secondary.

Nominal ration: It is the ratio of rated primary winding current (or voltage) to the secondary winding current (or voltage).

Turns ratio: It is the ratio of number of turns on secondary winding to the number of turns on primary winding.

Errors in Current Transformer: The value of transformation (actual ratio) is not equal to turns ratio. Also the value is not constant and it depends upon magnetizing and loss components of the exciting current, the secondary winding load current and its power factor. This means that the secondary winding current is not a constant fraction of the primary winding current. In power measurements, owing to use of C.T two types of errors are introduced; namely ratio error and phase angle error.

31

Ratio error is defined as no min al ratio - actual ratio ´100

 

 

actual ratio

 

Phase angle error is defined as

180

I m Cos d - I e Sin d

 

 

 

 

 

 

p

nls

 

 

 

 

Silsbee’s Method:

It is a Comparison method which is used to calculate ratio error and phase angle error by using two current transformers. The ratio error and phase angle error of test transformer X are determined in terms of that of a standard transformer S having the same nominal ratio. Two transformers are connected with their primaries in series. An adjustable burden is put in the secondary circuit of transformer under test. An ammeter is included in the secondary circuit of standard transformer so that current may be set to desired value.

The Current coil of wattmeter W1 is connected to carry secondary current of standard transformer. The Current coil of wattmeter W2 carries a current ∆I which is the difference between the secondary current of the standard and test transformers. The voltage coils of the wattmeter’s are supplied in parallel from a phase shifting transformer at a constant voltage V.

(1) Phase angle of voltage is so adjusted that wattmeter W reads zero 1

Voltage V is in quadrature with current Iss. 1

Reading of wattmeter W1, W1q=Vq Iss Cos 90 =0

Reading of wattmeter W2, W2q= Vq X Component of current ∆I in phase with Vq.

Vq=vq Isx Sin (θx-θs)

θx- Phase angle of CT under test.

θs-Phase angle of standard CT.

(2)The Phase of voltage V is shifted through 90 so that it occupies a position Vp and is in phase with Iss.

Reading of wattmeter W1, W1p=Vp Iss Cos θ =Vp Iss

Reading of wattmeter W2, W2p= Vp X Component of current ∆I in phase with Vp.

= Vp X ∆Ip= Vp[ Iss- Isx Cos (θx-θs)]

32

If V is kept same for both sets of readings.

V=Vp-Vq

 

 

W q=V Isx Sin (θx-θs)

 

 

2

 

 

W p=V Iss

 

 

1

 

 

W p= V [ Iss- Isx Cos (θx-θs)]= V I - V I

Cos(θx-θs)

2

ss

sx

+ W1p-V Isx Cos (θx-θs)=1p-V Isx

V Isx=W1p-W2p

Actual ratio of transformer under test, Rx= Ip/ Isx

Actual ratio of standard transformer , Rs= Ip/Iss

Rx

 

Iss

V Iss

W1p

------

=

-----

= ------

= ---------

Rs

 

Isx

VIsx

W1p-W2p

Rx

 

1

 

W2p

-----

= --------------

 

= 1+

----------

Rs

1- ( W2p/W1p)

W1p

Rx = Rs {1+(W2p/W1p)}

 

 

 

 

W 2q

 

Sin (θx-θs)= -------

 

 

 

 

 

V Isx

 

 

 

 

VIss-W2p

W1p-W2p

Cos (θx-θs) = ----------------

 

= ------------------

 

 

 

VIsx

V Isx

 

 

 

W2q

 

tan (θx-θs) =

-----------

 

 

 

 

W1p-W2p

 

 

 

W2q

 

(θx-θs) =

-----------

+ θs ; radian

 

 

W1p-W2p

 

33

=(W2q/ W1p) + θs, radian ( as W2p is very small.)

PROCEDURE:

1.Give the connections as per the circuit diagram.

2.Switch on the supply through phase shifting transformer. also switch on the supply through single phase autotransformer( also through q single phase transformer which provides low voltage and high current to the primaries of CT’s)

3.The single phase autotransformer should be kept in minimum position before switching on.

4.Now adjust the single phase autotransformer to set a desired primary current for both CT”s.

5.Adjust the phase shifting transformer until the wattmeter W1 reads maximum (which corresponds to UPF). Note down this value as W1p also note down the reading of W2 as W2p.

6.Adjust the phase shifting transformer until the wattmeter W1 reads zero( which corresponds to ZPF). Note down this value as W1q also note down the reading of W2 as W2q.

7.Repeat steps 4 to 6 for different values of primary current as well as for different values of burden.

8.Tabulate the readings. And calculate ratio and phase angle errors.

9.Draw the graph between burden Vs ratio and phase angle error.

34

Circuit Diagram

35

Model Graph:

[Ratio error Vs Burden] [Phase angle error Vs burden]

TABULATION

S.No

Primary

Burden

 

 

UPF

 

LPF

 

Ratio

Phase

 

current

 

 

 

 

 

 

 

 

 

error

angle

 

W1p

 

W2p

W1q=0

W2q

 

 

 

 

(M.F=

)

(M.F= )

 

(M.F= )

 

 

error

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Obs

 

Act

Obs

Act

 

Obs

Act

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1

 

0.33

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2

 

0.66

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3

 

1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4

 

1.33

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5

 

1.66

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6

 

2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

7

 

0.33

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

8

 

0.66

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

9

 

1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

10

 

1.33

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

11

 

1.66

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

12

 

2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

MODEL CALCULATION:

RESULT

36

Expt No:

Date:

DESIGN & TESTING OF INSTRUMENTATION AMPLIFIER

AIM

To design and test an Instrumentation amplifier.

APPARATUS REQUIRED

1.Op-Amp IC 741 2.Resistors 3.AFO

4.C.R.O.

5.Decade Resistance Box

6.Bread board

7.Dual RPS 8.Connecting wires

FORMULA

 

 

2R

 

R f

Vo

= 1+

2

 

 

 

 

 

(V2 -V1 )

 

 

R R1

DESIGN

V

= ---------- V.

1

= R = 10 K .

R

4

f

R

= 33 K .

1

= 0, A = -16

Let V

2

 

V

 

A =

0

= - 1+

V1

 

 

 

R = ----------

 

 

K .

2

 

 

 

2R

R f

= -16

2

 

 

R

R1

 

 

37

THEORY

An Instrumentation amplifier is used for high gain accuracy, high CMRR,

high gain stability with low temperature co efficient, low dc offset & low output impedance. A high resistance buffer is used preceding each input to avoid loading. The

Op-Amps A1 & A2 have zero differential input voltage. For V

= V ,i.e. in common

1

2

mode condition, the voltage across R is zero. As no current flows through R & R ‘ , the

non-inverting amplifier A1 acts as a voltage follower. So its output V

‘ = V .Simillarly

A

acts as voltage follower with output V

‘ = V . If V

 

2

2

 

≠ V , Current flows in R & R’

2

 

’-V

’) > (V

1

1

1

2

 

,(V

 

-V ) .This circuit has differential gain & CMRR more than the single

 

2

1

2

1

 

 

 

 

Op-Amp circuit. The output voltage is

 

 

 

 

 

 

2R

 

R f

Vo

= 1+

2

 

 

 

 

 

(V2 -V1 )

 

 

R R1

The difference gain can be varied using a variable resistance R.

PROCEDURE

1.Give the connections as per circuit diagram.

2.Set the input Voltage at a particular value.

3.Vary the frequency & note down the corresponding output on CRO.

4.Tabulate the readings & Draw the Graph.

Circuit Diagram

38

Model Graph

Tabulation

 

 

Vin = -------

volts,R = ---------

 

S.No. Frequency (Hz) Vo (volts) Gain dB

39

f = 1 KHz

S.No.

R

Vo in volts

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

RESULT

40

Expt No:

Date:

STUDY OF PRESSURE TRANSDUCER

AIM

To measure the Pressure using Pressure transducer.

APPARATUS REQUIRED

·Power Supply

·Pressure measurement trainer kit

·Display unit

·Connecting Chords.

THEORY

Pressure is basically a physical parameter encountered in many fields. It is defined as the force acting per unit area measured at a given point or over a surface. Most pressure measuring devices use elastic members for sensing pressure at the primary stage. These elastic members are of many types and convert the pressure into mechanical displacement which is later converted into an electrical form using a secondary transducer.

The principle of working of these devices can be explained as: the fluid or gas whose pressure is to be measured is made to press the pressure sensitive element and since the element is an elastic member, it deflects causing a mechanical displacement. This displacement is proportional to the pressure applied. This displacement is then measured with the electrical transducers. The output of the electrical transducer is proportional to the displacement and hence to the applied pressure. The commonly used pressure sensitive devices are Diaphragms, capsule, Bourdon tube & Bellows. The commonly used electrical transducer is Strain gauge whose resistance is varied with the input displacement caused by pressure sensitive elements. Four strain gauge elements are interconnected to form a Wheat stone’s bridge. The imbalance of the bridge is a measure of applied pressure on the elastic membrane.

PROCEDURE

1.Swiitch ON the instrument by rocker switch at the front panel.

2.Allow the instrument in ON position for 10 minutes for “initial warm up”

41

3.Adjust the potentiometer in the front panel till the display reads “000”

4.Apply pressure on the sensor using the loading arrangement provided.

5.The instrument reads the pressure coming on the sensor and displays through LED.

6.6. The readings can be tabulated and % error of the instrument can be calculated.

Block diagram

42

43

Tabulation

S.No.

Actual pressure

Indicator Reading

Error=Actual

% Error

 

in kg/cm2

Kg/Cm2

pressure-

 

 

 

 

Indicator reading

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

MODEL CALCULATION:

RESULT

.

44

Expt No:

STUDY OF LVDT

Date:

AIM

To measure the displacement using LVDT (Linear Variable Differential Transformer).

APPARATUS REQUIRED

·Power Supply

·LVDT trainer kit

·Display unit

·Connecting Chords.

·Multi-meter

FORMULAE

Error = Actual micrometer reading – Indicated read ing. % Error = (Error / True value) * 100

THEORY

The Linear Variable Differential Transformer is the most widely used inductive transducer. The arrangement is such that it has a primary coil, two secondary coils and a rod shaped magnetic core at the center. The magnetic core is made of Nickel alloy and is slotted. The displacement to be measured is applied to the arm attached to the core. When the core is placed symmetrically with respect to the two secondary coils , equal voltage is induced in the two coils. When these voltages are in phase opposition, the resultant becomes zero. This is called null position of the core. When the core moves from its null position due to the displacement of the object linked mechanically to it, the voltage induced in the secondary coil toward with the core has moved, increases, simultaneously reducing the voltage in the other secondary winding. The difference of the two voltages induced in the secondary appears across the output terminals of the transducer giving a measure of the displacement.

45

PROCEDURE

1.Connect the power supply chord at the rear panel to the 230 V, 50Hz supply. Switch on the instrument by pressing down the toggle switch. The display glows to indicate the instrument is ON.

2.Allow the instrument in ON position for 10 minutes for initial warm up.

3.Rotate the core of the micrometer in steps of 1 of 2 mm and tabulate the readings. The micrometer will show the exact displacement given to the LVDT core and display will read the displacement sensed by the LVDT. Tabulate the readings and plot the graph as Actual Vs Indicated reading.

Basic Schematic Diagram

46

Model Graph

47

Tabulation

S.No.

Actual

Indicator

Error

%Error

Output

 

micrometer

Reading(mm) [C]

[B –C]

(B-

Voltage

 

reading(mm)

 

mm

C)/C*100

(in mV)

 

[B]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

RESULT

48

Expt No:

Date:

(a)DIGITAL TO ANALOG CONVERTER

AIM

To obtain the corresponding analog output for a given digital input, to generate different waveforms and to study the linearity of digital to analog converter.

APPRATUS REQUIRED:

Digital to Analog Converter Kit

Patching Wires

Multi-meter

CRO

FORMULA USED:

Vout=Vref[(2x-255)/256]

x=Decimal value

THEORY:

In electronics, a digital –to-analog converter (DAC or D-to-A) is a device which is used for converting (usually binary) code to an analog signal (current, voltage or electric charge).

The DAC fundamentally converts finite-precision numbers (usually fixed-point binary numbers) into a physical quantity, usually an electrical voltage. Normally the output voltage is a linear function of the input number. Usually these numbers are updated at uniform sampling intervals and can be thought of as numbers obtained from a sampling process.

These numbers are written to the DAC, sometimes along with a clock signal that causes each number to be latched in sequence, at which time the DAC output voltage changes rapidly from the previous value to the value represented by the currently latched number.

The effect of this is that the output voltage is held in time at the current value until the next input number is latched resulting in a piecewise constant output. This is equivalently a zero-order hold operation and has an effect on the frequency response of the reconstructed signal.

49

The most common types of electronic DACs are:

Binary Weighted DAC:

It contains one resistor or current source for each bit of the DAC connected to a summing point. These precise voltages and currents sum to the correct output value. This is one of the fastest conversion methods but suffers from poor accuracy because of the high precision required for each individual voltage or current. Such high precision resistors and current sources are expensive, so this type of converter is usually limited to 8- bit resolution or less.

R-2R ladder DAC:

It is a binary weighted DAC that uses a repeating cascaded structure of resistor values R and 2R.This improves the precision due to the relative ease of producing equal valued matched resistors ( or current sources). However, wide converters perform slowly due to increasingly large RC-constants for each added R-2R link.

PROCEDURE:

1.Switch on the power supply.

2.The jumpers J9 through J!6 should be in S/W (right) position.

3.The switches SW1 throughSW8 are placed appropriately to represent the desired digital input of00h through FFh.

4.Draw the graph between digital word and analog output.

5.The Output voltage can be observed using a CRO at the terminal pin P2.

WAVEFORM GENERATION: 1. Switch on the power supply.

2. The jumpers J9 through J16 should be in “E” (Left) position.

3. The position of the jumpers for different waveform is selected from the table below.

Waveform

Position of J4

Position of J5

 

 

 

Sine wave

High

High

 

 

 

Triangular wave

Low

High

 

 

 

Square wave

Low

Low

 

 

 

Saw-tooth wave

High

Low

 

 

 

4. The output voltage can be observed using a CRO at the terminal pin P2.5.The amplitude and frequency of the output waveform can be varied by using potentiometer PT1 and PT2 respectively.

50

 

 

 

 

51

.TABULATION:

 

 

 

 

 

 

 

 

 

Input Data In

Input Data in

Output Voltage

Output Voltage

Input Data In

Binary

Hex

(Observed)

(Calculated)

Decimal

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

MODEL GRAPH:

RESULT

52

Expt No.

Date:

(b). ANALOG TO DIGITAL CONVERTER

AIM:

To obtain the digital output for the given analog input, to calculate its input voltage and to study the linearity of the analog to digital converter.

APPRATUS REQUIRED:

Analog to digital converter kit

Patching wires

Multi-meter

CRO

FORMULA USED:

Vin=Vr(b1*2-1+b2*2-2+b3*2-3+…..+bn*2-n)

Vs=4.99V

THEORY

An analog-to-digital converter (ADC, A/D or A to D) is an electronic integrated circuit, which converts continuous signals to discrete digital numbers. Typically, an ADC is an electronic device that converts an input analog voltage (or current) to a digital number.

A Successive –approximation ADC uses a comparator to reject ranges of voltages, eventually settling on a final voltage range. Successive approximation works by constantly comparing the input voltage to the output of an internal digital to analog converter (DAC, fed by the current value of the approximation) until the best approximation is achieved.

At each step in the progress, a binary value of the approximation is stored in a successive approximation register (SAR).

The SAR uses a reference voltage (which is the largest signal the ADC is to convert) for Comparisons. The analog value is rounded to the nearest binary value below, meaning this converter type is mid-rise.

Because the approximations are successive, conversion takes one clock-cycle for each bit of resolution is desired. The clock frequency must be equal to the sampling frequency multiplied by the bits of resolution desired.

53

A ramp-compare ADC (also called integrating, dual-slope or multi-slope ADC) produces a saw-tooth signal that ramps up, then quickly falls to zero. When the ramp starts, a timer starts counting. When the ramp voltage matches the input, a comparator fires, and the timer’s value is recorded. Timed ramp converters require the least number of transistors. The ramp time is sensitive to temperature because the circuit generating the ramp is often just some simple oscillator. There are two solutions:

*Use a clocked counter driving a DAC and then use the comparator to preserve the counter’s value.

*Calibrate the timed ramp.

A very simple (non-linear) ramp converter can be implemented with a micro-controller and one resistor and capacitor.

A/D converters are used virtually everywhere where an analog signal has to be processed, stored, or transported in digital form. Fast video ADCs are used in TV tuner cards. Very fast ADCs are needed in digital oscilloscopes.

PROCEDURE:

1.The power supply is switched on.

2.The variable terminal of the potentiometer is given to the analog input channel2.

3.The following table shows that the switches SW1 through SW3 position and the corresponding channel section.

4.The start of conversion (SOC) button is pressed once to start the conversion from analog signal to digital form. The LED L9 glows on pressing start of conversion button.

5.The Address Latch Enable (ALE) button is also pressed once, so as to enable the digital data to be sent to the output.

 

SWITCHES

 

CHANNEL

 

 

 

 

SW1

SW2

 

SW3

 

 

 

 

 

 

0

0

 

0

CH0

 

 

 

 

 

0

0

 

1

CH1

 

 

 

 

 

0

1

 

0

CH2

 

 

 

 

 

0

1

 

1

CH3

 

 

 

 

 

1

0

 

0

CH4

 

 

 

 

 

1

0

 

1

CH5

 

 

 

 

 

1

1

 

0

CH6

 

 

 

 

 

1

1

 

1

CH7

 

 

 

 

 

54

LINEARITY OF DAC:

1.The power supply is switched on.

2.The channel 3 is selected.

3.The analog input voltage is fed to the channel 3 by connecting variable terminal in the potentiometer.

4.The digital data corresponding to analog input is displayed on the LED and the digital data value is noted.

5.Now the potentiometer is varied and the analog input is measured using CRO>

6.Now the position of the potentiometer, the corresponding digital data is noted.

7.Graph is drawn between the analog input values and the corresponding digital data displayed on the LED.

CIRCUIT DIAGRAM:

55

TABULATION

Input data

Output data in binary Output data in Hex

in Volts

RESULT:

56

Exp No:

Date:

STUDY OF TRANSIENTS

AIM

1.To study the transient response of RC circuit for Step input and to draw the response.

2.To study the transient response of RC circuit for the following inputs using Psim/Matlab-Simulink/Pspice.

a.Pulse excitation

b.Sinusoidal excitation v(t) = 100 sin 40 t

3.Derive the expression for part 2

APPRATUS REQUIRED:

Sl.No

APPRATUS

RANGE

QTY

1

Regulated power supply

(0-30) V

1

2

Resistor

220 ohms

1

3

Capacitor

1uF

1

4.

SPST switch

 

1

5.

Connecting wires

 

Reqd

6.

CRO

 

1

THEORY

Any switching operation within a network causes transient conditions in the network. This switching operation may be a change in applied voltages or a change in one or more elements of the network. During the transient period, the mathematical expressions for currents and voltages contain certain terms other than the steady state terms. These additional terms known as transient terms are damped out by certain damping factors.

STEP RESPONSE OF R-C CIRCUIT:

The Figure shows a capacitor and a resistor connected in series. The capacitor has an initial charge q0 . At t=0, the switch K is closed, causing a voltage E to be applied to the circuit,

The KVL equation for the circuit is

t

E U (t )= Ri(t )+ 1 i(t)dt C 0

Taking Laplace transform on both sides

 

 

 

 

 

 

 

 

 

 

 

 

 

0

 

 

 

 

 

 

 

 

 

 

 

 

where i -1 (0)= i(t )dt = q0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

-Â¥

 

 

 

 

 

 

 

 

 

 

 

 

Then

E

-

q0

= I (s) R +

 

1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

s

 

Cs

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Cs

 

 

 

or

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

E -

q0

 

 

 

 

 

 

E -

q0

 

 

 

I (s)=

 

 

 

C

 

 

 

=

C

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1

 

 

 

 

 

 

1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

s R +

 

 

 

 

 

 

 

R s

+

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Cs

 

 

 

 

 

 

RC

Taking inverse Laplace transform

E

 

 

 

q

0

 

 

-t / RC

 

 

 

 

 

 

 

i(t )=

 

-

 

 

 

 

e

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

R

 

 

RC

 

 

 

 

 

 

 

 

 

 

 

The voltages across R and C are

vR = Ri(t )=

 

 

 

 

 

 

 

q

0

 

 

 

 

 

 

 

 

 

E

-

 

 

 

e-t / RC

 

 

 

 

C

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

vR = E -VR

= E(1 - e-t / RC )+

q0

e-t / RC

 

 

 

 

 

C

If the initial charge q0 is zero

E

-t / RC

i(t ) =

 

e

 

 

 

 

R

 

 

 

The above equation shows that the charging current decays from its initial value to zero in RC circuit.

MODEL CALCULATION:

R = 220 ohms: C = 1uF

RESULT

57

 

E

 

 

 

 

 

 

 

 

R