SSN COLLEGE OF ENGINEERING, CHENNAI 603 110

DEPARTMENT OF ELECTRICAL & ELECTRONICS

ENGINEERING

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

Mrs.R.Deepalakshm i (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.

No. Name of the Experiment

Page

No

Marks

(10)

Signature of

the Staff

1 Measurement of Resistance [Wheat-stone’s

Bridge& Kelvin’s Bridge]

2 Measurement of Capacitance [Schering Bridge]

3 Measurement of Inductance [Maxwell’s

Inductance-Capacitance Bridge]

4 Measurement of Iron Loss and Permeability of

Ring Specimen [ Maxwell’s Bridge]

5 Calibration of Single Phase Energy Meter

6 Measurement of Three Phase Power & Power

Factor

7 Study of Current Transformer

8 Design of Instrumentation Amplifier

9 Study of LVDT & Pressure transducer

10 Digital to Analog Converter & Analog to Digital

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

2

31

R

RRRX =

Bridge Sensitivity R/R

S B ∆= θ

Where, RX =Unknown value of resistance, R1=Standard resistance R3 &R2=Resistances of ratio arms. θ = Deflection of the galvanometer

R/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

xx RIRI =11 (1)

5

Also [ ]2121 RR

EII

+== (2)

and [ ]33 RR

EII

xx +

== (3)

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

[ ] [ ]321

1

RR

R

RR

R

X

X

+=

+

From which XRRRR 231 =

or 2

31

R

RRRX = (4)

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

Value) Ω Rx (True Value) Ω

Error = Measured-True

%Error

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

SQ

PR ×=

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.

Now, ( ) abad EQP

PE ×

+=

And,

×

+++++= r

rqp

qpSRIEab 1.1

8

And,

×

+++

++= r

rqp

qp

qp

pRIEamc 1.2

For zero galvanometer deflection, Ead = Eamc

or

×

+++

++×=

×

+++++×

+r

rqp

qp

qp

pRIr

rqp

qpSRI

QP

P 1.3

or

−

+++×=

q

p

Q

P

rqp

qrS

Q

PR 1.4

Now if q

p

Q

P = Eqn.1.3 becomes, SQ

PR ×=

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 ratiosq

pand

Q

P.

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

(Measured Value)Ω

Rx (True Value) Ω

Error = Measured-True

%Error

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

32

1 CR

RCx

=

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

132 YZZZ x = or

+

−=− 113

2

11Cj

RCR

C

jR

xx ω

ωω

and expanding

11

−

=−

13

2

3

12

RC

jR

C

CR

C

jR

xx ωω

Equating real terms and the imaginary terms, we find that

3

12

C

CRRX =

2

13

R

RCCx =

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 µF

R1 Ω

R2 Ω

CX nF (Measured

Value)

CX nF (True Value)

% Error

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

4

321 R

RRR =

4321 CRRL =

Q Factor = 441

1 RCR

LQ ω

ω==

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,

[ ] ( )[ ] 3244411 1 RRLCjRLjR =+++ ωω

or 4432324141 RCRRjRRRLjRR ωω +=+

Equating real and imaginary parts, we get

4

321 R

RRR = and 4321 CRRL =

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 Ω L1 = LX mH

(Practical value)

L1 = LX mH (True

value

C4 %Error

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 CRStdRStdLs ××= 31 ..

Unknown resistance 2

31 ..

R

RStdRStdRs

×=

R2 Standard resistance measured by using multi meter across pot 2. Iron loss = ( )wSl RRI −×2

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

Permeability s

s

AN

CRRl2

31=µ

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 M2 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

( ) 3244

411 *

1RR

RCj

RLjR =

++

ωω

4432324141 RCRRjRRRLjRR ωω +=+⇒

Separating into Real and Imaginary terms we have,

43214

321 CRRLand

R

RRR ==

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:

Inductance (Ls) mH Sl No Theoretical

Value Practical

Value

Resistance Rs Ohms

Current I 1 mA

Iron Loss

Permeability

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 Standard wattmeter 300 V; 10A,

UPF

1

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

transformer 230/(0-270 V 1

8 Stop watch

9 Connecting wires

FORMULAE

Energy meter specification = Kwh

rev750

True energy (Pt) = KwhTimePower

10003600××

Measured energy =750

n , n Number of revolutions

% Error = 100×−True

TrueMeasured

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 Sl No

Observed Reading (Watts)

Actual Reading (Watts)

Time for n rev

Seconds

Power Factor

Measured Energy KwH

True Energy KwH

% Error

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

Power factor = cos φ =

+−−

21

211 3PP

PPtancos

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

factor Power factor angle Φ

W1=√3VI Cos (30-Φ)

W2=√VI Cos (30+Φ)

Active Power (P) W1+ W2

Reactive Power (Q) √3 (W1-W2)

Tan Φ

1 R alone

1 0 (3/2) VI (3/2) VI 3VI 0 0

2 RL 0.5 Lag

60 (3/2) VI 0 (3/2) VI

(3√3/2) VI

√3

3 L alone

0.5 Lag

90 (√3/2) VI (-√3/2) VI

0 3VI ∞

4 C alone

0.5 lead

-90 (-√3/2) VI (√3/2) VI

0 -3VI -∞

5 RC 0.5 lead

-60 0 (3/2) VI (3/2) VI

(-3√3/2) VI

-√3

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

28

TABULATION: M.F= M.F=

W1 W2 S.No Load

Voltage (V) in Volts

Current (I) in amps Observed Actual Observed Actual

1 R alone 2 RL 3 L alone 4 C alone 5 RC

S.No Load W1

(Watts)

W2

Watts)

Real

Power

(P)in

Watts

Reactive

Power

(Q) in

vars

Power

factor

CosΦ

Power Factor

angle,

Φ=

+−−

21

211

PP

PP3tan

(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

1

Current

Transformer

2

2 Single Phase auto

transformer

230/(0-270)V,8

A

1

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:

W1P

RX = -------------

W1P –W2P

Phase Angle error:

W2Q

30

θX = ------------- + θS

W1P –W2P

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 100×−ratioactual

ratioactualratioalminno

Phase angle error is defined as

−

s

em

nl

SinICosI δδπ

180

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 W1 reads zero

Voltage V1 is in quadrature with current Iss.

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

W2q=V Isx Sin (θx-θs)

W1p=V Iss

W2p= V [ Iss- Isx Cos (θx-θs)]= V I

ss- V I

sx Cos(θx-θs)

+ 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

UPF LPF

W1p

(M.F= )

W2p

(M.F= )

W1q=0 W2q

(M.F= )

S.No Primary

current

Burden

Obs Act Obs Act Obs Act

Ratio

error

Phase

angle

error

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 AMPLIFI ER

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

( )121

221

VVR

R

R

RV f

o −

+=

DESIGN

V1 = ---------- V.

R4 = R

f = 10 KΩ.

R1 = 33 KΩ.

Let V2 = 0, A = -16

162

11

2

1

0 −=

+−==R

R

R

R

V

VA f

R2 = ----------KΩ.

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 V1

= V2

,i.e. in common

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 V2 ‘ = V

2.Simillarly

A2 acts as voltage follower with output V

1 ‘ = V

1. If V

1≠ V

2 , Current flows in R & R’

,(V2’ -V

1’ ) > (V

2-V

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

Op-Amp circuit. The output voltage is

( )121

221

VVR

R

R

RV f

o −

+=

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 = --------- Ω

S.No.

Frequency (Hz)

Vo (volts)

Gain dB

39

f = 1 KHz

S.No.

R Ω

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

in kg/cm2

Indicator Reading

Kg/Cm2

Error=Actual

pressure-

Indicator reading

% Error

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 reading.

% 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

micrometer

reading(mm)

[B]

Indicator

Reading(mm) [C]

Error

[B –C]

mm

%Error

(B-

C)/C*100

Output

Voltage

(in mV)

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

Binary

Input Data in

Hex

Output Voltage

(Observed)

Output Voltage

(Calculated)

Input Data In

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

SW1 SW2 SW3 CHANNEL

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

in Volts Output data in binary Output Output data in Hex

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 0q . At t=0, the switch K is closed, causing a voltage E to be applied to

the circuit,

57

The KVL equation for the circuit is

( ) ( ) ( )∫+=t

dttiC

tRitUE0

1

Taking Laplace transform on both sides

where ( ) ( ) 0

01 0 qdttii == ∫

∞−

−

Then ( )

+=−Cs

RsICs

q

s

E 10

or

( )

+

−=

+

−=

RCsR

C

qE

CsRs

C

qE

sI11

00

Taking inverse Laplace transform

( ) RC/teRC

q

R

Eti −

−= 0

The voltages across R and C are

( ) RC/tR e

C

qEtRiv −

−== 0

( ) RC/tRC/tRR e

C

qeEVEv −− +−=−= 01

If the initial charge 0q is zero

( ) RC/teR

Eti −

=

The above equation shows that the charging current decays from its initial value

R

E

to zero in RC circuit. MODEL CALCULATION : R = 220 ohms: C = 1uF RESULT