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Electronics measurements and instrumentation basics
1. EC410501
Electronic Measurements and Instruments
Department of Electronics and Communication Engineering
Indus Institute ofTechnology andEngineering
Indus University
2. Units
Standards
Accuracy, precision, resolution
Notations
Electronic measurements
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3. PhysicalUnits
Length (Meter: centimeter, kilometer) l m
Mass (Gram: milligram, kilogram) m gm
Time (Second: hour, day, year) t s
Temperature (degree Kelvin) T K
Luminous intensity (Candela) Cd
Electrical Units
Electric charge (Coulomb) q C
Electric current (Ampere) I A
Electromotive force (Volt) v V
Capacitance (Farad) C f
Inductance (Henry) L H
Resistance (Ohms) R ῼ
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4. Meter (m): Length = 1650 763 times the λ of radiation
corresponding to transition between 2p10 and 5 d5 of
krypton-86 atom
Kilogram (kg): Mass = the mass of international
prototype of mass of 1 kg
Second (s): Duration of 9,192,631770 times
corresponding to the transition between two hyperfine
states of the ground level of Cesium -133 atom.
Ampere ( A): Constant current maintained in 2 straight
parallel conductors of infinite length and negligible
circular cross section and placed 1 m apart in vacuum,
would produce between them a force of 2x 10-7
Newtons/meter length
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5. Kelvin (K): Unit of thermodynamic temperature is the
fraction 1/273.16 of thermodynamic temperature of the
triple point of water.
Candela (cd): Unit of intensity. One cd is the luminous
intensity, in the perpendicular direction, of a surface at
1/600000 m2 of a blackbody at the temperature of
freezing platinum under a pressure of 101,325
newtons/m2
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6. Kelvin Scale (K)
Starts at absolute zero
(-273.150C)
Celsius scale (oC)
Range of temp between
freezing point and
boiling point divided in
100 divisions
Fahrenheit scale (oF)
Freezing point is 32oF
to and boiling point is
212oF
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7. Newton (N): Unit ofForce
1 N is a force that gives a mass of 1 kg an acceleration of1
meter per sec persec
Force = mass x acceleration, F =ma
Joule (J): Unit ofWork
1 joule is the amount of work done when a force of 1 Nacts
through a distance of 1 m
Work = Force x distance, W =F.d
Watts (W): Unit ofPower
1W is the power developed when 1 joule of work is donein
1 second
Power = work/ time, P =W /t
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8. Ampere (A): Unit of electric current
It is the constant current which
when flowing in each of two
infinitely long parallel conductors 1
meter apart, exerts a force of 2 x
10-7 Newtons per meter of lengthof
each conductor
Coulomb (C): Unit of electric charge
When a current of 1 A flows 1
coulomb of charge passes a given
point in a conductor
Ampere = coulomb / second
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9. Volt (V): Unit of emf and potential difference
It is the potential difference between two points on a
conductor carrying a constant current of 1 Awhen power
dissipated between these points is 1Watt
Ohm (Ω): Unit of resistance
It is the resistance that permits the flow of 1 A current
through it when a potential difference of 1 V isapplied
across it
Siemens (G): Unit of conductance
It is the reciprocal of resistance
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10. Henry (H): Unit of Inductance
It is the inductance in which 1Volt emf is induced by a
current changing at 1A/s
Farad (F): Unit of Capacitance
It is the capacitance that contains a charge of 1 coulomb
when the potential difference across it is 1 V
Weber (Wb): Unit of Magnetic Flux
It is the magnetic flux, which linking a single-turn coil,
produces 1 V emf when flux is reduced to 0 at a constant
rate in 1 s.
Tesla (T): Unit of Magnetic Flux Density
It is the flux density of 1 Wb/m2
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11. Standard of measurement is a physical representation of a unit of
measurement
International standards
Defined by international agreement, maintained by
International Bureau of weight and measures in Paris
Primary standards
Maintained at National Bureau of Standards. Used for calibration
and verification of secondary standards
Secondary standards
Used by measurement and calibration laboratories in industry
Working standards
Principle tools in measurements laboratories
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14. Logarithmic notation often used in expressing measured
results
Ex. Gain = output power / input power
Gain-dB = 10 log (output power / input power)
dB is dimensionless
Then what are dBm, dBW, dBHz, dBi ?
Remember
log(1/x) = - log(x)
log(xy) = y.log(x)
log(x.y) = log(x) + log(y)
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15. Scientific notation
Very small and large numbers are expressed as a
number multiplied by 10 raised to a power
Ex. 1400 = 1.4 x 103, 0.0047 = 4.7 x 10-3
Engineering notation
The power of 10 is a multiple of 3
Ex. 140000 = 140 x 103, 14x108 = 1.4x109
0.00047 = 47x 10-6
Metric prefix notation
Symbols of metric prefix are employed
Ex.140 kΩ, 4.2 GHz, 0.47µF, 2.7 nH
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16. Values Scientific notation Prefix Symbol
1 000 000 000 000 1012 tera T
1 000 000 000 109 giga G
1 000 000 106 mega M
1 000 103 kilo K
100 102 hecto h
10 10 deca da
0.1 10-1 deci d
0.01 10-2 centi c
0.001 10-3 milli m
0.000 001 10-6 micro µ
0.000 000 001 10-9 nano n
0.000 000 000 001 10-12 pico p
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18. Accuracy: Closeness of the measured value to the actual
value
Precision: A measure of the reproducibility of
measurement
Sensitivity: Ratio of the output response of instrument to
the input change
Resolution: Smallest change in the input to which the
instrument responds
Error: Deviation from the true (expected) value of
measured parameter
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20. Error is the degree to which a measurement
conforms to the expected or true value
Errors are due to measuring instruments (causing
the change in the value of the parameter being
measured) or due to persons carrying out the
measurements (human errors)
Errors may be expressed as absolute or percentage
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22. The output voltage of a 5 V DC supply is measured as 4.9 V.
Find (1) Absolute error (2) Percent error (3) Relativeaccuracy
and (4) Percent accuracy
Solution:
(1) Absolute error = 5 – 4.9 = 0.1V
(2) Percent error = [(5- 4.9)/5]100 = (0.1/5)100 = 2 %
(3) Relative accuracy = 1 – 0.02 = 0.98
(4) Percent accuracy = 0.98 x100 = 98%
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23. A production batch of resistors of 4.7 kΩ has measured
values ranging from 4.935 kΩ and 4.465 kΩ at 25 0C.
The temperature coefficient of the resistors is 5 ppm/0C
Find: (i) Maximum absolute error, (ii) Maximum relative
error, (iii) Resistor tolerance (iv) Max resistance of a
resistor at 800C (pg 19)
Answers:
(i) maximum absolute error = + 235 Ω
(ii) maximum relative error = + 5%
(iii) tolerance = + 5%
(iv)
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24. Indicates the precision of measurement
A voltmeter with 4 significant figure display has a
precision of 0.001 V
Result Range of Actual value
5 m 4.5 m – 5.5 m
5.0 m 4.95 m – 5.05m
5.00m 4.995m – 5.005 m
5.000 m 4.9995 m – 5.0005 m
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25. E V1 V2
(V1 V1) (V2 V2 )
(V1 V2 ) (V1 V2 )
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E V1V2
Error in the sum of quantities
equal the sum of absolute errors
(V1 V1) (V2 V2 )
(V1 V2 ) (V1 V2 )
Error in the difference of quantities
equal the sum of absolute errors
26. EI
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Percentage error in P is
% error in P %error in I %error in E
I E
I
E
100%
I. E
100% P
E.I
E.I E.I I.E
Percentage error in the product
or quotient of quantities equals
the sum of percentage errors
P EI (E E)(I I)
E.I E.I I.E E.I
( E.I is verysmall)
27. When measurements are repeated the results can be
different each time due to errors
To estimate the deviation from true value and
correctness of the measured value statistical methods
are adopted
Statistical parameters used are
Arithmetic mean
Deviation from the mean
Average deviation
Standard deviation
Variance
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28. If x1, x2, x3, …., xn are the readings from n
measurements the arithmetic mean is obtained as
x
x1 x2 x3 ..... xn
n
Deviation of a reading is the departure of the measured
value from the arithmetic mean
di xi x
Deviation can be positive or negative
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29. Average deviation D is the arithmetic mean of the absolute
values of the deviations of each of the n measurements. The
algebraic sum of deviations is always zero.
It indicates the precision of the measuring instrument
Standard deviation σ is the RMS value of the deviation
Variance σ2 is the mean square deviation
d
n
D
1 2 3d
d d ..... dn
n
n
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d
n
d
d
2
i
2
n3
2 2
2
2
1 d ..... d