Electronics measurements and instrumentation basics

EC410501
Electronic Measurements and Instruments
Department of Electronics and Communication Engineering
Indus Institute ofTechnology andEngineering
Indus University

 Units
 Standards
 Accuracy, precision, resolution
 Notations
 Electronic measurements
R.N.Mutagi EMI June 2016 2

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

 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

 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

 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

 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

 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

 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

 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

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

 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)

 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

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

Values Scientific
notation
Engineering
notation
Metrix prefix
notation
45 000 000 Hz
0. 000 0047 F
120 000 000 Ω
3 000W
0.01V
0.00001 H
0.000 0012A
0.000 056V
0.000 000 000 07W

 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

Not Precise,
NotAccurate
Not Precise
Accurate
Precise
NotAccurate
Precise
Accurate

 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

 Gross errors
 Humanerrors
 Systematic errors
 Instrumenterrors
 Environmental errors
 Observational errors
 Random errors

 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%

 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)

 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
4 6R.N.Mutagi EMI June52016 24

E V1 V2
 (V1  V1)  (V2  V2 )
 (V1 V2 )  (V1  V2 )
E  V1V2
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

EI
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)

 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

 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

 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
d
n
d 
 d
2
i
2
n3
2 2
2
2
1  d ..... d
 

Electric
Input
parameter
Signal
conditioner
Analog/Dig
Converter
Signal
processor
Display
unit
Non-
electric
Input
parameter
Signal
conditioner
A/D
Converter
Signal
processor
Display
unit
Trans
ducer

Electronics measurements and instrumentation basics

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