SSN COLLEGE OF ENGINEERING, CHENNAI 603 110
DEPARTMENT OF ELECTRICAL & ELECTRONICS
ENGINEERING
LAB INCHRAGES: Mrs.R.Ramaprabha
Mrs.R.Deepalakshmi
131353  MEASUREMENT AND INSTRUMENTATION
LABORATORY
NAME OF THE STUDENT: Mr. /Ms.
REG. NO.:
YEAR/SEM: II/ 3
ACADEMIC YEAR:
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
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 









S. 
Name of the Experiment 
Page 
Marks 
Signature of 

No. 
No 

(10) 
the Staff 













Measurement of Resistance 





1 
Bridge& Kelvinâ€™s Bridge] 


















2 
Measurement of Capacitance [Schering Bridge] 




















Measurement of Inductance [Maxwellâ€™s 





3 



















Measurement of Iron Loss and Permeability of 





4 
Ring Specimen 
[ Maxwellâ€™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: 
4
Expt.No: MEASUREMENT OF RESISTANCE
Date: [USING WHEATSTONEâ€™S BRIDGE]
AIM
To Measure the unknown value of resistance using Wheat stoneâ€™s bridge network, and to study the sensitivity of the bridges.
APPARATUS REQUIRED
Â·Wheatstone bridge trainer
Â·Galvanometer
Â·Unknown resistances
Â·Patching wires.
Â·
Â·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 stoneâ€™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) 





































Model Calculation
RESULT
7
Expt.No: MEASUREMENT OF RESISTANCE
Date: 
[USING KELVINâ€™S BRIDGE] 
AIM
To Measure the unknown value of resistance using Kelvinâ€™s bridge network, and to study the sensitivity of the bridges.
APPARATUS REQUIRED
Â·Kelvinâ€™s bridge trainer
Â·Galvanometer
Â·Unknown resistances
Â·Patching wires.
Â·
Â·DC power supply
FORMULAE
R = P Â´ 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 stoneâ€™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 pointâ€™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 
= 


Â´ Eab 











(P + Q) 









p + q 




And, Eab 
= I R + S + 

Â´ r 
1.1 
















p + q + r 



p 

p + q 


And, Eamc = I R + 




Â´ r 




p + q 

p + q + r 











For zero galvanometer deflection, Ead = Eamc
or
or

P 



p + q 









Â´ r = 





Â´ I R + S + 



P + Q 


p + q + r 

R = 
P 
Â´ S + 
qr 

P 
 
p 








q 


Q 
p + q + r Q 



p 

p + q 


I Â´ R + 




Â´ 




p + q p + q + r 

8
1.2
1.3
1.4
Now if P = p Eqn.1.3 becomes, R = P Â´ 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) 



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
Â·Schering bridge kit
Â·Unknown Capacitances
Â·Patching wires.
Â·
Â·CRO
Â·AC
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 


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 

ÂµF 


(Measured 
(True 





Value) 
Value) 


















































Model Calculation
RESULT:
14
Expt No: 
MEASUREMENT OF INDUCTANCE 
Date: 
[USING MAXWELLâ€™S 
BRIDGE]
AIM
To Measure the unknown value of Inductance using Maxwellâ€™s Inductance Capacitance bridge and to determine the Q factor of the coil
APPARATUS REQUIRED
Â·Maxwellâ€™s
Â·Unknown Inductances
Â·Bridge Oscillator.
Â·Patching wires.
Â·
Â·Loud Speaker.
Â·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
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 
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 Maxwellâ€™s
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 MAXWELLâ€™S BRIDGE] 
AIM:
To measure the iron loss and permeability of the given ring specimen.
APPARATUS REQUIRED
Â·Maxwellâ€™s Bridge Kit
Â·Digital Multimeter
Â·Microphone
Â·Patch Chords
Â·CRO
FORMULAE USED
Unknown inductance Ls = Std.R1 Â´ Std.R3 Â´ C
Unknown resistance Rs = Std.R1 Â´ Std.R3
R2
R2 Standard resistance measured by using multi meter across pot 2.
Iron loss = Il2 Â´ (RS  Rw )
Where Il â€“ current flow to specimen Rs â€“ Specimen resistance Rw â€“ Winding resistance
Permeability m = ls R1 R3C N 2 As
ls â€“ Specimenâ€™s winding length [coil] in meter R1, R3 â€“ Standard Resistances
C â€“ Standard Capacitance N â€“ Number of turns [coil]
A â€“ Area of specimen in M 2
THEORY:
The Maxwellâ€™s Inductance Bridge is most commonly used bridge for
measurement of inductances of Q value less than 10. A typical Maxwellâ€™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
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 Maxwellâ€™s bridge is limited to the measurement of medium Q coils. Hence high Q coils are measured on Hayâ€™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
7.In this condition note down the AC current through ring specimen, POT1 and the source current by using
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 
1 









4 
Ammeter 
MI 
1 









5 
Lamp Load 

230 V, 5 Kw 
1 









6 
Phase Shifting transformer 


1 





7. 
Single phase auto 


1 
transformer 
















8 
Stop watch 








9 
Connecting wires 








FORMULAE
Energy meter specification = 750 rev
Kwh
True energy (Pt) = Power Â´Time Kwh
3600Â´1000
Measured energy = n , n Number of revolutions
750
% Error = Measured  True Â´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 
1 






2 
Ammeter 
MI 
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



P1 
 P2 




Power factor = cos f = cos tan 










3 
P1 
+ P2 







THEORY
Power Measurement
There are different methods to measure
PROCEDURE
1.Give the connections as per circuit diagram.
2.Switch on the
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 
0 
3VI 
8 


alone 
Lag 


VI 



4 
C 
0.5 
(v3/2) 
0 


alone 
lead 


VI 



5 
RC 
0.5 
0 
(3/2) VI 
(3/2) 



lead 



VI 
VI 





















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 



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 

1 

transformer 

A 











3 
Ammeter 
MI 
1 









4 
Ammeter 
MI 
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
Phase Angle error:
W2Q
30
Î¸ 
= 
+ Î¸ 

X 
S 
W1P
PRECAUTIONS:
1.The Primaries of 2 CTâ€™s should be correctly connected.
2.The Secondaries of 2 CTâ€™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 itâ€™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 Â´100


actual ratio 


Phase angle error is defined as 
180 
I m Cos d  I e Sin d 








p 
nls 





Silsbeeâ€™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 âˆ†I which is the difference between the secondary current of the standard and test transformers. The voltage coils of the wattmeterâ€™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 âˆ†I in phase with Vq.
Vq=vq Isx Sin
Î¸x Phase angle of CT under test.
(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 Î¸ =Vp Iss
Reading of wattmeter W2, W2p= Vp X Component of current âˆ†I in phase with Vp.
= Vp X âˆ†Ip= Vp[ Iss Isx Cos
32
If V is kept same for both sets of readings.



W q=V Isx Sin 


2 


W p=V Iss 


1 


W p= V [ Iss Isx Cos 

2 
ss 
sx 
+
V
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 

Rx 

1 

W2p 
= 

= 1+ 

Rs 
1 ( W2p/W1p) 
W1p 

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





W 2q 

Sin 






V Isx 





Cos 

= 




VIsx 
V Isx 



W2q 

tan 









W2q 


+ Î¸s ; radian 




33
=(W2q/ W1p) + Î¸s, 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 CTâ€™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 CTâ€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
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 



R R1 
DESIGN
V 
= 
1 
= R = 10 K . 
R 

4 
f 
R 
= 33 K . 
1 
= 0, A = 

Let V 

2 

V 


A = 
0 
=  1+ 

V1 





R = 


K . 

2 



2R 
R f 
= 

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
= V ,i.e. in common 

1 
2 
mode condition, the voltage across R is zero. As no current flows through R & R â€˜ , the
â€˜ = V .Simillarly 

A 
acts as voltage follower with output V 
â€˜ = V . If V 

2 
2 


â‰ V , Current flows in R & Râ€™ 

2 

â€™) > (V 
1 
1 
1 
2 


,(V 



2 
1 
2 
1 










2R 

R f 

Vo 
= 1+ 
2 





(V2 



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
Â·Power Supply
Â·Pressure measurement trainer kit
Â·Display unit
Â·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 stoneâ€™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 â€œinitial warm upâ€
41
3.Adjust the potentiometer in the front panel till the display reads â€œ000â€
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
Â·Power Supply
Â·LVDT trainer kit
Â·Display unit
Â·Connecting Chords.
Â·
FORMULAE
Error = Actual micrometer reading â€“ 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 
(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
CRO
FORMULA USED:
x=Decimal value
THEORY:
In electronics, a digital
The DAC fundamentally converts
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
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.
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
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 â€œEâ€ (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 



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
CRO
FORMULA USED:
Vs=4.99V
THEORY
An
A Successive
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
Because the approximations are successive, conversion takes one
53
A
*Use a clocked counter driving a DAC and then use the comparator to preserve the counterâ€™s value.
*Calibrate the timed ramp.
A very simple
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
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 
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
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 





























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 










i(t )= 

 




e 



























R 


RC 












The voltages across R and C are 

vR = Ri(t )= 







q 
0 










E 
 








C 





























vR = E 
= E(1  
q0 







C 

If the initial charge q0 is zero 

E 

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 