emi k-notes
DESCRIPTION
k nosTRANSCRIPT
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Contents
Manual for K-Notes ................................................................................. 2
Error Analysis .......................................................................................... 3
Electro-Mechanical Instruments ............................................................. 6
Potentiometer / Null Detector .............................................................. 15
Instrument Transformer ....................................................................... 16
AC Bridges ............................................................................................. 18
Measurement of Resistance ................................................................. 21
Cathode Ray Oscilloscope (CRO) ........................................................... 25
Digital Meters ....................................................................................... 28
Qmeter / Voltage Magnifier ................................................................ 30
2014 Kreatryx. All Rights Reserved.
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Manual for K-Notes
Why K-Notes?
Towards the end of preparation, a student has lost the time to revise all the chapters from his /
her class notes / standard text books. This is the reason why K-Notes is specifically intended for
Quick Revision and should not be considered as comprehensive study material.
What are K-Notes?
A 40 page or less notebook for each subject which contains all concepts covered in GATE
Curriculum in a concise manner to aid a student in final stages of his/her preparation. It is highly
useful for both the students as well as working professionals who are preparing for GATE as it
comes handy while traveling long distances.
When do I start using K-Notes?
It is highly recommended to use K-Notes in the last 2 months before GATE Exam
(November end onwards).
How do I use K-Notes?
Once you finish the entire K-Notes for a particular subject, you should practice the respective
Subject Test / Mixed Question Bag containing questions from all the Chapters to make best use
of it.
2014 Kreatryx. All Rights Reserved.
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Error Analysis
Static characteristics of measuring system
1) Accuracy
Degree of closeness in which a measured value approaches a true value of a quantity under
measurement.
When accuracy is measured in terms of error :
Guaranteed accuracy error (GAE) is measured with respect to full scale deflation.
Limiting error (in terms of measured value)
GAE * Full scale deflectionLE
Measured value
2) Precision
Degree of closeness with which reading in produced again & again for same value of input
quantity.
3) Sensitivity
Change the output quantity per unit change in input quantity.
o
i
qS
q
4) Resolution
Smallest change in input which can be measured by an instrument
5) Threshold
Minimum input required to get measurable output by an instrument
6) Zero Drift
Entire calibration shifts gradually due to permanent set
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7) Span Drift
If there is proportional change in indication all along upward scale is called span drift.
8) Dead zone & Dead time
The range of input for which there is no output this portion is called Dead zone.
To respond the pointer takes a minimum time is called dead time.
TYPES OF ERROR
a) Gross Error : Error due to human negligency, i.e. due to loose connection, reading the value
etc.
b) Systematic error : Errors are common for all observers like instrumental errors,
environmental errors and observational errors.
c) Random errors : Error due to unidentified causes & may be positive or negative.
Absolute Errors :
m rA A A
mA Measured value
rA True value
Relative Errors :
r =
A
T
AbsoluteErrors
Truevalue A
mm rT T
r
AA A A 1
1
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Composite Error :
i) Sum of quantities
1 2
X X X
x x1 x2
ii) Difference of quantities
1 2
X X X
x x1 x2 So for sum & difference absolute errors are added.
iii) Multiplication of quantities
1 2 3
X X X X
31 2
1 2 3
XX XX
X X X X
iv) Division of quantities
1
2
XX
X
1 2
1 2
X XX
X X X
So, for multiplication & division, fractional or relative errors are added.
If m m
1 2
p
3
X XX
X
31 2
1 2 3
XX XXm n p
X X X X
Precision Index
Indicates the precision for a distribution
1h
2
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Probable Error
r = 0.6745
0.4769r
h
Standard deviation of combination of quantities
2 2 2
1 2n1 2
n
2 2 2x x x x
X X X......
X X X
Probable Error
2 2 2
1 2 nn1 2
22 2x x x x
X X Xr r r ...... r
X X X
Electro-Mechanical Instruments 1) Permanent magnet moving Coil (PMMC)
Deflecting Torque
Td = nIAB
Where n = no. of turns
I = current flowing in coil
A = Area of coil
B = magnetic flux density
Deflection G
Ik
G = NBA & K = Spring constant
Eddy current damping & spring control torque in used.
For pure AC signal, the pointer vibrates around zero position.
It is used to measured DC or average quantity.
It can directly read only up to 50mV or 100mA.
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Enhancement of PMMC
i) Ammeter
For using PMMC as an ammeter with wide range, we connect a small shunt resistance in
parallel to meter.
m
Im
I multiplication factor
Basically, m is ratio of final range (as an ammeter) to initial range of instrument.
m
sh
RR
m 1
; mR = meter resistance
ii) Voltmeter
A series multiples resistance of high magnitude is connected in series with the meter.
M = multiplication factor
m
Vm
V
s mR R m 1
Sensitivity of voltmeter
s mv
fsd
R R1S / V
I V
Application of PMMC
1) Half wave rectifier meter
mavg
II I
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RMS
s m f
2V
R R R
RMS
avg
s m f
0.45VI
R R R
; For Ac input
For DC input
DCavg
s m f
VI
R R R
avg AC DCavgI 0.45 I (Assuming DC RMSV V )
AC DC(Sensitivity) 0.45(Sensitivity)
2) Full wave rectifier meter
RMS
ACf
avgs m
2 2VI
R R 2R
RMS
s m f
0.9V
R R 2R
DCavg DC
s m f
VI
R R 2R
avg DCACavgI 0.9 I (Assuring RMS DCV V )
AC DCSensitivity 0.9 Sensitivity
2) Moving iron meter
Deflecting torque, 2d1 dL
T I2 d
I = current flowing throw the meter
L = Inductance
= deflection
Under steady state
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21 dL
K I2 d
2 I
MI meter measures both ac & dc quantities. In case of AC, It measures RMS value.
1T 2
2
RMS
0
1I i t dt
T
If 0 1 2i t I I sinwt I sin2wt .......
2 2 2RMS 0 1 21
I I I I .......2
Air friction Damping is used
Condition for linearity
dLcons tant
d
MI meter cannot be used beyond 125Hz, as then eddy current error is constant.
3) Elector dynamometer
Deflecting Torque, d 1 2dM
T i id
For DC, 1 2i i I
2ddM
T Id
2 I
For AC, 1 m1i I sin t
2 m2i I sin t
1 2d avg
dMT I I cos
d
Where m11
II
2 & 2
I2I
2
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Applications of dynamometer
1) Ammeter
Fixed coils are connected in series.
1 2I I I
0 (Angel between 1 2I & I )
2d
dMT I
d
At balance, c dT T
2dM
K Id
2 I
It reads both AC & DC & for AC it reads RMS.
2) Voltmeter
sR Series multiplier resistance
2 1
s
VI I
R , 0
cos 1
2
d 2
s
V dMT
dR
At balance, cdT T
2
2s
V dMK
dR
2 V
It reads both AC & DC & for AC it reads RMS.
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3) Wattmeter
Fixed coils carry same current as load & as called as current coils.
Moving coil is connected across voltage and thus current voltage, a high non-inductive
load is connected in series with MC to limit the current.
d 1 2
dMT I I cos
d
avg
s s
PV dM dMI cosR d R d
At balance, d
k T
avg P
Symbol :
Two wattmeter method
1 RY R RY RW V I cos V & I
L LV I cos 30
2 BY B BY BW V I cos V & I
L LV I cos 30
Where LV is line to line voltage
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LI is line current
These expression remain same for -connected load.
1 23P W W
L L3V I cos
2 13Q 3 W W
L L3V I sin
2 1
1 2
3
3
Q 3 W Wtan
P W W
2 11
1 2
3 W Wtan
W W
for lag load
2 11
1 2
3 W Wtan
W W
for lead load
= Remember, In our case 1
W is wattmeter connected to R-phase and 2
W is wattmeter
connected to B-phase.
= If one of the wattmeter indicates negative sign, then pf < 0.5
Errors in wattmeter
a) Due to potential coil connection
2
T
cLr
I r% * 100
P
LI = load current
Cr = CC Resistance
TP = True Power
2
T
rs
V% *100
R P
V = voltage across PC
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sR = Series multiplier resistance
TP = True Power
b) Due to self inductance of PC
If PC has finite inductance
p p sZ R R jwLp
p sR R p sZ R jwLp
r% tan tan *100
= load pf angle
p1
s
Ltan
R
4) Energy meter
Energy = Power * Time
T
VIcos tW * kwhr
1000 3600
TW = True energy
It is based on principle of induction.
It is an integrating type instrument.
mt
W VIsin * kwhr3600
Where mW = measured Energy
= angle between potential coil voltage & flux produced by it.
= load pf angle
Error = m TW W
Energy constant = No.ofRe voluations N
kwhr P.t
Measured Energy = mTotalno.ofrevolutions
KW
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True Energy =
TVIcos t
* kw.hr1000 3600
W
Error = m TrT
W W% *100
W
Creeping Error in energy meter
If friction is over compensated by placing shading loop nearer to PC, then disc starts rotating
slow with only PC excited without connecting any load is creeping.
Otherwise if over voltage is applied on pressure coil then also creeping may happen due to
stray magnetic fields.
To remove creeping holes are kept on either side of disc diametrically opposite & the torque
experienced by both holes is opposite & they stop creeping.
% creeping error = TotalNo.ofRew / kwhr due to creeping
*100TotalNo.ofRew / kwhr due to load
Thermal Instruments
These instruments work on the principle of heating and are called as Thermal Instruments.
These are used for high frequency measurements.
They can measure both AC & DC.
In case of AC, they measure RMS value.
Electrostatic voltmeter
Deflecting torque, 2d
1 dcT V
2 d
At Balance,
cdT T
21 dc
V k2 d
2 V
Condition for linearity
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15
dc
constantd
For increasing the range, we connect another capacitor in series
To increase the range from mV to V
m
s
CC
m 1 ;
m
Vm
V
Potentiometer / Null Detector wI = working current
B
wh
VI
R l.r _____________(1)
Switch at (A)
If gI 0
s w 1V I l r
sw1
VI
l r _____________(2)
Switch at (B)
2x wV I l r
xw
2
VI
l r ________(3)
s x
1 2
V V
l r l r
2x s1
lV V
l
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r = resistance of slide wire (/ m)
l = Total length of slide wire (m)
1l = length at which standard cell ( sV ) is balanced
2l = length at which test voltage ( xV ) is balanced
Measuring a low resistance
R
s
VR S
V
Instrument Transformer Current transformer
Equivalent circuit
Turns Ratio = Nominal Ratio 2
1
Nn
N
1 l s
l s
X Xtan
R R
R = Actual Ratio
s
I cos I sinn
I
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Errors in current transformer
1) Ratio Error :
Current ratio p
s
I
I is not equal to turns ratio due to no-load component of current.
r
K R% *100
R
K = n = Nominal Ratio
R = Actual Ratio
2) Phase Angel Ratio :
Ideally, Phase difference between p sI & I should be 0180 but due to no-load component of
current, it deviates from that value.
Phase angle error =
s
I cos I sin 180*
nI degrees
Phase angle between primary & secondary currents
= 180 degrees
Potential Transformer
Equivalent circuit
Turns Ratio = n = 2
1
N
N
Actual Transformation Ratio = R = P
S
V
V
SP P P P
S
I1R n R cos X sin I R I X
V n , Where
1 XtanR
Phases angle error
SP P P P
s
IX cos R sin I X I R
nnV
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AC Bridges
AC Bridges
Balance condition : DI 0
41 2 3Z Z Z Z
41 2 3Z Z Z Z
41 2 3
432 3
1 24
Z ZZ
Z
Quality Factor & dissipation factor
Quality Factor (Q) Dissipation Factor
(D)
1 wLQ
R
RD
wL
2 RQ
wL
wLD
R
3 1Q
wCR
D =wcR
4 Q = wcR 1D
wCR
Measurement of Inductance
(i) Maxwells Inductance Bridge
Here, we try to measure 1
R & 1
L
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2 31
4
R RR
R
2 31
4
L LL
R
(ii) Maxwells Inductance Capacitance Bridge
2 31
4
R RR
R
41 2 3L R R C
This bridge is only suitable for coils where 1 < Q < 10
Q = Quality Factor
(iii) Hays Bridge
Used for coils having high Q value
2 24 42 3
1 2
R R R CR
11
Q
42 31 2
R R CL
11
Q
4 4
1Q
R C
(iv) Andersons Bridge
This Bridge is used for low Q coils.
2 31 1
4
R RR r
R
3 41 2 2 34
CRL R R r R R
R
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(v) Owens Bridge
431
2
R CR
C
2 41 3L R R C
Measurement Of Capacitance
De-Sautys Bridge
31 2 2 14
Rr R r R
R
42
31
RC C
R
D = dissipation factor
= 1 1
C r
1r = internal resistance of
1C
Schering Bridge
431
2
R CR
C
4 21
3
R CC
R
dissipation factor = D = 4 4C R
Measurement of frequency
Wien Bridge Oscillator
Balancing Condition
3 1 2
4 2 1
R R C
R R C
Frequency of Osculation
1 2 1 2
1f
2 R R C C
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Measurement of Resistance
Classification of Resistance
1) Low Resistance : R 1 , Motor and Generator
2) Medium Resistance : 1 < R < 100k , Electronic equipment
3) High Resistance : R > 100 k, winding insulation of electrical motor
DC Bridges
Medium Resistance Measurement
1. Wheatstone Bridge
Finding Theremin Equivalent
th
ggth
VI
R R
Th
P RV V
P Q R S
Th
PQ RSR
P Q R S
For Balance Condition
gI 0
Th
V 0
PS = RQ
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Sensitivities
1) Current sensitivity , i
g
SI
mm/mA
= deflection of Galvan meter in mm
2) Voltage sensitivity,
Th
SV
mm/V
3) Bridge Sensitivity , B
SR /R
mm
ThB
vV SSR / R
B
vV.SSSR 2
S R
For Maximum Sensitivity
SRS R = 1
B, maxvV.SS
4
2. Carey foster slide wire Bridge
r = slide wire resistance in m
.
for case (1).
At balance
1
1
R rP
Q S L r
.(1)
For case (2)
R & S is reversed
2
2
S rP
Q R L r
..(2)
From (1) & (2)
1 2
1 2
R r S r
S L r R L r
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3. Voltmeter Ammeter Method
a) Ammeter near the load
vm X AA
VR R R
I
vV = voltage across voltmeter
A
I = Ammeter current
XR = Test resistance, AR = Animator resistance
% error = m T A
xT
R R R100 100%
R R
b) Voltmeter near the load
X
v Xm
vA
VVR
I I I
vXm
X v vX
X X
R R1R
I I R R
V V
% error = m X
X
R R100%
R
If a vXR R R , voltmeter is connected near the load
a vXR R R , ammeter is connected near the load
4. Ohmmeter
a) Series Type
when XR 0
m FSDI I = Full scale deflection
when XR
mI 0 = zero deflection
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for Half scale deflection
mshseX h
msh
R .RR R R
R R
b) Shunt Type
S
R = current limiting resistor
If X
R 0
mI 0 = zero deflection
If xR
m FSDI I = Full scale deflection
For Half scale Deflection
m S
x hm S
R RR R
R R
Measurement of Low Resistance
Kelvins Double Bridge Method
Unknown resistance
qr pP P
R SQ p q r Q q
P, Q = outer ratio arms
p, q = inner ratio arms
S = standard resistance
r = lead resistance
R = Test resistance
High Resistance Measurement
Loss of charge Method
tRc
eCV t V
10
C
0.4343tR
VC log
V
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t = time in (seconds)
V = source voltage
CV = Capacitor voltage
Cathode Ray Oscilloscope (CRO)
The velocity of e is changed by changing the pre-accelerating & accelerating anode
potential
KE =PE
2
a1
mv qV2
a2qV
m
Deflection sensitivity
D = deflection height on screen
d = distance between plates
d = length of vertical deflecting plates
L = distance between centre of plate & screen
aV = anode potential
yV = Vertical plate Potential
yd
a
L VVD
mm2dV
deflection sensitivity
d
y a
LD VSmmV 2dV
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Lissajous Pattern
If both horizontal & vertical deflection plates of CRT is applied with the sinusoidal signal,
the wave form pattern appearing on screen is called Lissajous Pattern.
Case 1: Both signals have same frequency
x m xV V sin w t
y m yV V sin w t
x y mV V V
x yw w w
= variable
S.No Lissayous Pattern
1
0 or 360
2
0 90
Or
270 360
3
90 or 270
4
90 270
Or
180 270
5
180
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Finding
1) Lissajous Pattern in Ist & IIIrd Quadrant
1 11 1
2 2
X Ysin sin
X Y
for anti-clockwise orientation phase difference = (360 - )
for clockwise orientation, phase difference =
2) Lissajous Pattern in IInd & IVth Quadrant
2
1 1X
180 sinX
2
1 1Y
180 sinY
for clockwise orientation, phase difference =
for anti-clockwise orientation = 360
Case 2
x yw w
x m xV V sinw t
y m yV V sinw t
y y
x x
w f Number of horizental tangencies
w f Number of vertical tangencies
y
x
f 42
f 2
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Digital Meters
Type of converter Maximum Conversion Time
1) Dual slope ADC n 12 Clocks
2) Successive Approximation Register (ADC) n Clocks
3) Counter ADC n2 Clocks
4) Flash ADC 1 Clock
Dual slope A/D Converter
aV = analog input
RV = Reference input
Ra 2 11
VV T T
T
1n
CLKT 2 T
Maximum conversion time = n 1
CLK2 T
Successive Approximation Register
Suppose = REF aV 1 V
and aV = 12V
3D 2D 1D 0D
10 5 2.5 1.25
1
T 1 0 0 0 10V < 12V
2T 1 1 0 0 15V > 12 V
3T 1 0 1 0 12.5 > 12 V
4T 1 0 0 1 11.25 < 12 V
In first clock cycle, MSB is set to get voltage corresponding to the digital o/p
If 0
V < aV , then in next cycle next bit is set else,
If 0
V > aV , MSB is reset & next bit is set
We continue the same process till we reach LSB.
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Specifications of Digital Voltmeter
1) Resolution
The smallest value of input that can be measured by digital meter is called resolution.
n
1R
10
n = No. of full Digits (0, 1,.., 9)
2) Sensitivity
S = Resolution x Range
3) Over Ranging
The extra 12
digit is called over-ranging
If n = 3, we can measure from 0 999
Resolution , 3
1R 0.001
10
if 1n 32
digit, 12
digit can be 0 & 1.
we can measure from 0 1999
Resolution, 1
R 0.0052000
if 34
digit is there than MSB can be 0 3.
4) Total Error
Error = (% error in reading) x reading + (NO. of counts) Full Scale
Range of meter
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Qmeter / Voltage Magnifier
If works on the principal of series resonance.
At series resonance
L C
X X
V
IR
CCV IX
LCX X
V VR R
C
V = V. Q
CV Q
Practical Q-meter
Also includes series resistance of source (oscillator)
True T
wLQ
R
Measured Q,
Tm
sh shsh
QwL wLQ
R RR RR 1 1
R R
msh
T
RQ Q 1
R
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Measurement of unknown capacitance
Test capacitance is connected at 43T & T .
Circuit is resonated at C = 1
C
fr= T1
1
2 2 C C (1)
TC = Test Capacitance
TC is removed & circuit is resonated at C = 2C
fr =
2
1
2 LC (2)
from (1) & (2)
T 2 1C C C
Measurement of self-capacitance
Resonance is achieved at C = 1
C
1
1 d
1f
2 L C C
At C = 2
C , resonance is achieved at 2
fr
2
2 d
1f
2 L C C
= n f1,
21 2
d 2
C n CC
n 1
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