Department of Electrical Engineering

Course Information
 Text and Reference Books
 Course Outline available on SLATE
 Course Grading
 Quizzes/Homework 20% (Approx. 10 Quizzes)
 Sessional I 15%
 Sessional II 15%
 Final 50%
 Lecture material will be available on SLATE
 Regularly review the lectures discussed in the class

EE220 Instrumentation & Measurement 2

Course Objectives
 Learn to Design and Implement Real-World
Instrumentation and Measurement Systems
 Prior knowledge of Courses required
 Circuit, Electronics, CLD
 Learning Objectives
 Accuracy and Precision of Measuring Instruments
 Minimizing and Measuring Error
 General Purpose and basic measurement systems
 Op-Amps in Instruments and Measurement Systems
 Signal Conditioning
EE220 Instrumentation & Measurement 3
Course Objectives
 Sensors and their interfacing

EE220 Instrumentation & Measurement 4

Definition
 Measurement
 Conversion of a physical quantity or observation to a
domain where a human or computer can determine its
value
 temperature
 Instrumentation
 Devices for converting a physical quantity or observation
to a quantity observable by a human or computer
 thermometer

EE220 Instrumentation & Measurement 5

Applications of I&M
 Monitoring
 Control
 Analysis

EE220 Instrumentation & Measurement 6

Monitoring: Applications of
Instrumentation & Measurement
 Measuring and displaying data in a suitable form to
check the status of a system
 Vehicle Instrument Panel
 ECG

EE220 Instrumentation & Measurement 7

Control: Applications of
Instrumentation & Measurement
 Measuring data and using the data to control the
system
 Cement Plant
 Anti-lock Brake System (ABS)

EE220 Instrumentation & Measurement 8

Analysis: Applications of
Instrumentation & Measurement
 Gathering and analyzing data
 Helps in characterizing, evaluating, predicting and
improving systems
 Climate Prediction
 Oil Exploration

EE220 Instrumentation & Measurement 9

Measurement System
•External excitation
•Sensor
•Amplification
•Converts a physical quantity into electrical signal
•Linearization
Conversion
•May require Signal
external excitation signal
Transducer •Filtering
Element
Conditioning
•Isolation
(Bridge)

•Bridge Circuit

•Remote Location
•Multiplexing
Data Display/ Signal
•Transmission
Recording •Sample
Transmission
and Hold
•Digitize
•Store

EE220 Instrumentation & Measurement 10

Instrument Types and Performance
Characteristics
 Instrument System are divided into different types
based on accuracy, performance and application
 Active and Passive Instruments
 Null-Type and Deflection-Type Instruments
 Analogue and Digital Instruments
 Static and Dynamic Characteristics of Instruments

EE220 Instrumentation & Measurement 11

Active and Passive Instruments
 Active Instrument requires external source of power
(electric, hydraulic, pneumatic)
 The output signal of an Active Instrument is
modulated source of power
 The measurement resolution can be controlled by
controlling the external source
 Example: Petrol Tank level indicator

EE220 Instrumentation & Measurement 12

Fuel Gauge

EE220 Instrumentation & Measurement 13

Active and Passive Instruments
 Passive Instrument requires no external source of
power
 Output signal is the quantity being measured
 Resolution can not be adjusted
 Example: Pressure Gauge

EE220 Instrumentation & Measurement 14

Bourdon Tube Pressure Gauge

EE220 Instrumentation & Measurement 15

Null & Deflection Type Instruments
 Pressure Gauge is a
Deflection Type
Instrument
 Value of quantity
measured displayed in
terms of movement of
pointer
 Accuracy depends upon
Bourdon tube and spring

EE220 Instrumentation & Measurement 1

Null & Deflection Type Instruments
 Calibration of Bourdon
tube and spring is
difficult therefore
Deflection type
instrument is less
accurate
 More convenient to use

EE220 Instrumentation & Measurement 2

Null & Deflection Type Instruments
 Dead Weight Pressure
Gauge is a Null Type
Instrument, works on
the principle that P= F/A
 Weights are put on top of
piston until the
downward force
balances the fluid
pressure

EE220 Instrumentation & Measurement 3

Null & Deflection Type Instruments
 Weights are added until
the piston reaches a
datum level known as
the null point
 Accuracy depends upon
calibration of weights
 Calibration of weights is
easier therefore null type
instruments are more
accurate

EE220 Instrumentation & Measurement 4

Null & Deflection Type Instruments
 Inconvenient to use, for
calibration purposes
only

EE220 Instrumentation & Measurement 5

Analogue and Digital Instruments
 Analogue Instruments
give a continuously
varying output as the
quantity being measured
changes
 Deflection Type
pressure Gauge
 Digital Instruments give
output that varies in
discrete quantities

EE220 Instrumentation & Measurement 6

Static & Dynamic Characteristics
 Static Characteristics deal with steady state or slowly
varying inputs
 Dynamic Characteristics refers to the performance of
the instrument when the input variable is changing
rapidly with time

EE220 Instrumentation & Measurement 7

Static Characteristics
 Characteristics of an instrument at Steady State
 Accuracy
 Precision (Repeatability and Reproducibility)
 Range or Span
 Linearity
 Sensitivity
 Threshold
 Resolution

EE220 Instrumentation & Measurement 8

Accuracy (Measurement
Uncertainty)
 Accuracy of an instrument is a measure of how close
the output reading of an instrument is to the actual
value
 In practice the inaccuracy figure is quoted
 Inaccuracy quoted as percentage of the full scale (f.s.)
reading of an instrument
 Pressure gauge of range 0 – 10 bar has quoted
inaccuracy of ±1.0% f.s.
 Maximum error to be expected in any reading is 0.1 bar

EE220 Instrumentation & Measurement 9

Accuracy (Measurement
Uncertainty)
 When instrumentation is reading 1.0 bar the
maximum error which is 0.1 bar gives an error of 10%
 Important Instrument Design Rule
 Instrument Range should be appropriate to the spread
of values to be measured
 Never use an instrument having 0 – 10 bar range to
measure values between 0 and 1 bar

EE220 Instrumentation & Measurement 10

Precision (Repeatability/
Reproducibility)
 Precision of an instrument describes its degree of
freedom from random errors
 If large number of readings are taken of the same
quantity then the spread of readings should be very
small
 A high precision instrument may have low accuracy

EE220 Instrumentation & Measurement 11

Accuracy Vs. Precision

EE220 Instrumentation & Measurement 12

Repeatability vs. Reproducibility
 Repeatability
 Closeness of output readings when same input is
applied repeatability over a short period of time
 With the same measurement conditions
 Same instrument and observer
 Same location
 Same conditions of use maintained throughout

EE220 Instrumentation & Measurement 13

Repeatability vs. Reproducibility
 Reproducibility
 Closeness of output readings for same input when
there are changes in
 Method of measurement
 Observer
 Measuring instrument
 Location
 Conditions of use and time of measurement

EE220 Instrumentation & Measurement 14

Accuracy vs. Repeatability

EE220 Instrumentation & Measurement 15

Range or Span
 Maximum and Minimum values of a quantity that the
instrument is designed to measure

EE220 Instrumentation & Measurement 16

Linearity
 It is desirable that the output reading of an instrument
is linearly proportional to the quantity being measured
 Non-Linearity defined as the maximum deviation of
any of the output readings from the best-fit straight
line output

EE220 Instrumentation & Measurement 17

Linearity
 Non-linearity is expressed as a percentage of full scale
reading

EE220 Instrumentation & Measurement 18

Sensitivity
 It is a measure of the change in instrument output that
occurs when the quantity being measured changes by
a given amount
 Scale Deflection/Value of measurand producing
deflection
 1 V/Ω

EE220 Instrumentation & Measurement 19

Threshold
 The minimum input to an instrument at which the
output is detectable
 Car speedometer typically has a threshold of 15 kmph
 Manufacturers vary in which they specify threshold
 Threshold quoted as an Absolute Value
 Threshold quoted as a percentage of full-scale reading

EE220 Instrumentation & Measurement 20

Resolution
 Resolution is the smallest change in the input which is
detectable by the instrument
 Resolution is specified as an absolute value or as a
percentage of f.s. deflection

EE220 Instrumentation & Measurement 1

Sensitivity to Disturbance
 All calibrations and specifications of an instrument are
only valid under controlled conditions of temperature,
pressure etc.
 Standard ambient conditions are defined in the
instrument specifications
 As variation in ambient conditions occurs certain
static instrument characteristics change
 Instruments are affected in two ways
 Zero Drift or Bias
 Sensitivity Drift
EE220 Instrumentation & Measurement 2
Zero & Sensitivity Drift

EE220 Instrumentation & Measurement 3

Sensitivity to Disturbance
 Spring balance calibrated in an environment at 20 0C
has the following deflection/load characteristics
 Load (kg) 0 1 2 3
 Deflection (mm) 0 20 40 60
 Spring balance is used in an environment at 30 0C. The
deflection/load characteristics are
 Load (kg) 0 1 2 3
 Deflection (mm) 5 27 49 71

EE220 Instrumentation & Measurement 4

Sensitivity to Disturbance
 At 200C the sensitivity = 20 mm/kg
 At 300C the sensitivity = 22 mm/kg
 Zero Drift or Bias = 5 mm
 Sensitivity Drift = 2 mm/kg
 Zero Drift/0C = 5/10 = 0.5 mm/0C
 Sensitivity Drift/0C = 2/10 = 0.2 mm/kg/0C

EE220 Instrumentation & Measurement 5

Hysteresis effect
 Input measured quantity
to the instrument is
steadily increased from a
negative value
 The output reading
varies in the manner
shown in curve A

EE220 Instrumentation & Measurement 6

Hysteresis effect
 Input is then steadily
decreased the output
varies in the manner
shown in curve B
 Non coincidence
between the loading and
unloading curves is
known as hysteresis

EE220 Instrumentation & Measurement 7

Hysteresis effect
 Hysteresis is exhibited
by instruments that
contain springs and
electrical windings
formed around an iron
core

EE220 Instrumentation & Measurement 8

Dynamic Characteristics
 Dynamic Characteristics refers to the performance of
the instrument when the input variable is changing
rapidly with time
 Dynamic Characteristics of a measuring instrument
describe its behavior between the time a measured
quantity changes value and the time when the
instrument output attains a steady value in response
 As with Static Characteristics any values for dynamic
characteristics quoted in instrument data sheets only
apply under specified conditions

EE220 Instrumentation & Measurement 9

Dynamic Characteristics
 Variation in Dynamic Characteristics is expected when
specified conditions change
 Reason for dynamic characteristics is due to presence
of energy storage elements
 Dynamic characteristics are determined by analyzing
the response of the system by applying different type
of signals
 Impulse, step, ramp, sinusoidal etc.

EE220 Instrumentation & Measurement 10

Dynamic Characteristics
 Dynamic performance of an instrument is expressed
by a differential equation relating the input and output
quantities
d n qo d n1qo dqo
 Output an n  an1 n1  ...  a1  a0 q0
dt dt dt
d m qi d m1qi dqi
 Input bm m  bm1 m1  ...  b1  b0 qi
dt dt dt

EE220 Instrumentation & Measurement 11

Dynamic Characteristics
 Transfer function G(s)

xo ( s) an s n  an 1s n1...  a1s  a0

 G( s)  
xi ( s) bm s m  bm1s m1...  b1s  b0

 n is called the order of the system

 Commonly available sensors characteristics can be
approximated as zero-th order, first order or second
order

EE220 Instrumentation & Measurement 12

Zero Order Instrument
 If all the coefficients are zero other than ao
 a0 qo  b0 qi
 qo  b0 qi / a0  kqi
 k is a constant known as instrument sensitivity
 Potentiometer is a zero order instrument
 Output voltage changes instantaneously as the slider is
moved

EE220 Instrumentation & Measurement 13

Potentiometer
 Sensors using
Potentiometric principle
has no storage elements
 Output voltage eo can be
related with input
displacement xi
 eo (t ) xt  Exi (t )

eo (t ) E
  = constant
xi (t ) xt

EE220 Instrumentation & Measurement 14

First Order Instrument
 If all the coefficients are zero other than ao and a1
dqo
 a1  a0 qo  b0 qi
dt
b0 qi / a0
 qo 
1  (a1 / a0 ) D
 K= b0/a0 is a constant known as instrument sensitivity
 τ= a1/a0 is the time constant of the system
 q  Kqi
o
1  D
EE220 Instrumentation & Measurement 15
First Order Instrument
 Thermometer and Thermocouple are examples of first
order instruments
 Output of Thermometer and Thermocouple in
response to a step change in input varies with time in
an exponential manner
 τ time constant of the step response is the time taken
for the output quantity to reach 63% of its final value

EE220 Instrumentation & Measurement 16

Thermocouple
eo ( s) Kv
 
T f ( s) 1  s

 Kv steady state voltage

sensitivity of
Thermocouple V/C0

EE220 Instrumentation & Measurement 17

Thermocouple
mC
 
hA

 ‘m’ mass of the junction

 ‘C’ Specific Heat
 ‘h’ heat transfer co-
efficient
 ‘A’ surface area of hot
junction

EE220 Instrumentation & Measurement 18

Example: First Order Instrument
 Weather balloon has temperature and altitude
measuring instruments and can transmit data to
ground
 Balloon initially at ground with instrument reading in
steady state
 Altitude measuring instrument is zero-order
 Temperature measuring instrument is first-order
 Time Constant = 15 sec
 Temperature on ground is T0 = 100 C
 Temperature Tx at altitude of x meter is Tx = T0 – 0.01x

EE220 Instrumentation & Measurement 1

Example: First Order Instrument
 Balloon is released at time zero
 Balloon rises upwards at velocity of 5 meters/sec
 Plot temperature readings transmitted to ground at
intervals of 10 sec for first 50 sec of flight
 Plot error in temperature reading

EE220 Instrumentation & Measurement 2

Example: First Order Instrument
Tx T0  0.01x 10  0.01x
 Tr   
1  D 1  D 1  15D
10  0.05t Tr 10  0.05t
 x = 5t Tr  DTr  
1  15D  
T
 Natural Response DTr  r  0

 Assuming Tn  Ke st
t

 Solving Tn  Ke 15

EE220 Instrumentation & Measurement 3

Example: First Order Instrument
Tf 10  0.05t
 Forced Response DTf  
 

 Solving T f  10  0.05(t  15)

t

 Tr  Ke 15
 10  0.05(t  15)
 At t =0 Tr = 10
 10  K  10  0.05(0 15)
 K = - 0.75

EE220 Instrumentation & Measurement 4

Example: First Order Instrument
t

 Tr  0.75e 15
 10  0.05(t  15)
Time Altitude Temp Temp Error
(Actual) (Read)

0 0 10 10 0
10 50 9.5 9.86 0.36
20 100 9 9.55 0.55
30 150 8.5 9.15 0.65
40 200 8 8.70 0.7
50 250 7.5 8.22 0.72

EE220 Instrumentation & Measurement 5

Example: First Order Instrument
 What temperature does the balloon transmit at 5000
meters?
 At 5000 m
 t = 1000 sec
t

 Tr  0.75e 15
 10  0.05(t  15)  39.25

EE220 Instrumentation & Measurement 6

Second Order Instrument
 If all the coefficients are zero other than ao, a1 and a2
d 2 qo dqo
 a2 2  a1  a0 qo  b0 qi
dt dt
b0 qi
 qo 
a0  a1D  a2 D 2

 Accelerometers (Seismic sensors) are examples of

second order instruments
 Output of second order instrument in response to a
step change in input varies with time in a sinusoidal
(damped, over damped, under damped) manner
EE220 Instrumentation & Measurement 7
Seismic Sensor
 Used for vibration and
acceleration
measurement of
foundations
xo ( s) Ms 2
 
xi ( s) Ms 2  Bs  K

 ‘M’ mass of seismic body

 ‘B’ Damping Constant
 ‘K’ Spring Constant

EE220 Instrumentation & Measurement 8

Step Response Performance
 Peak Overshoot (Mp)
 Maximum value minus
the steady state value,
normally expressed in
terms of percentage
 Settling Time (ts)
 Time taken to attain the
response within ±2% of
the steady state value

EE220 Instrumentation & Measurement 9

Step Response Performance
 Rise Time (tr)
 Time required for the
response to rise from
10% to 90% of its final
value

EE220 Instrumentation & Measurement 10

Errors
 Errors are of two main types
 Errors introduced during the measurement process
 Systematic Errors
 Random Errors
 Errors introduced due to adding of noise during
transfer of signal from point of measurement to some
other point

EE220 Instrumentation & Measurement 11

Systematic Errors
 Errors in the output readings of measurement system
that are consistently on one side of the correct reading
 Either all errors are positive or negative
 Major sources of systematic errors are
 System disturbance during measurement is a common
source of Systematic Error
 System disturbance due to Environmental Changes
(offset and sensitivity error)
 Wear in instrument components
 Connecting leads

EE220 Instrumentation & Measurement 12

System Disturbance during
measurements
 A beaker containing hot water
 The temperature of the hot water is to be measured
using a thermometer
 Thermometer at room temperature is inserted in hot
water
 Heat transfer takes place between hot water and room
temperature thermometer
 Heat transfer lowers the temperature of the water
 Although the affect is negligible, whoever
measurement disturbs the system
EE220 Instrumentation & Measurement 13
System Disturbance during
measurements
 Measuring the flow rate
inside a fluid carrying
pipe using an Orifice
plate
 Measurement procedure
causes a permanent
pressure loss in the
flowing fluid

EE220 Instrumentation & Measurement 14

Measurement in electrical circuits
 Voltage across Rx is Vx
 A voltmeter having a series resistance Rs is connected
across Rx to measure the voltage
 Voltage measured is not equal to Vx
 Rs is connected in parallel with Rx reducing the
effective resistance and reducing the voltage Vx
 Rs should be very large to minimize the disturbance of
the electrical system

EE220 Instrumentation & Measurement 15

System Disturbance during
measurements
 Process of measurement disturbs the system being
measured
 Magnitude of disturbance varies from one system to
the other and is affected by type of instrument used for
measurement

EE220 Instrumentation & Measurement 16

Random Errors
 Caused by unpredictable variations in the
measurement system
 Positive and negative errors occur in approximately
equal number for a series of measurement made of the
same constant quantity
 Random errors can be eliminated by calculating the
average of a number of repeated measurements,
provided the measured quantity remains constant
during the process of taking repeated measurement

EE220 Instrumentation & Measurement 1

Statistical Analysis: Mean &
Median
 Average value of a set of measurements of a constant
quantity can be expressed as either the mean or
median value
x1  x2  ..xn
 Mean xmean 
n
 Median is the middle value when the measurements in
the data set are written down in ascending order of
magnitude
 For a set of n measurements x1, x2, … xn
 Median xmedian  xn1 / 2

EE220 Instrumentation & Measurement 2

Statistical Analysis: Mean &
Median
 As the number of measurements increases, the
difference between mean and median values becomes
very small

EE220 Instrumentation & Measurement 3

Statistical Analysis
 Measurements A
 398, 420, 394, 416, 404, 408, 400, 420, 396, 413, 430
 Mean = 409 Median = 408 Spread = 36

 Measurements B
 409, 406, 402, 407, 405, 404, 407, 404, 407, 407, 408
 Mean = 406 Median = 407 Spread = 7
 Measurement B more reliable as spread is small

EE220 Instrumentation & Measurement 4

Statistical Analysis: Standard
Deviation
 Spread of measurement on the basis of min and max
range is not a good way of examining how the
measurement values are distributed about the mean
value
 A better method is to calculate variance or standard
deviation
 Deviation di  xi  xmean
d12  d 22  ...d n2
 Variance V 
n d12  d 22  ...d n2
 Standard Deviation   V 
n

EE220 Instrumentation & Measurement 5

Statistical Analysis: Standard
Deviation
 Mean (µ) of A = 409
 Standard Deviation (σ) of A = 11.7
 Mean (µ) of B = 406
 Standard Deviation (σ) of B = 2.05
A 398 420 394 416 404 408 400 420 396 413 430
Dev -11 11 -15 7 -5 -1 -9 11 -13 4 21
Dev2 121 121 225 49 25 1 81 121 169 16 441

B 409 406 402 407 405 404 407 404 407 407 408
Dev 3 0 -4 1 -1 -2 1 -2 1 1 2
Dev2 9 0 16 1 1 4 1 4 1 1 4

EE220 Instrumentation & Measurement 6

Statistical Analysis: Standard
Deviation
 Mean (µ) of C = 406.5 Median = 406
 Standard Deviation (σ) of C = 1.92

C 409 406 402 407 405 404 407 404 407 407 408
Dev 2.5 -0.5 -4.5 0.5 -1.5 -2.5 0.5 -2.5 0.5 0.5 1.5
Dev2 6.25 0.25 20.25 0.25 2.25 6.25 0.25 6.25 0.25 0.25 2.25

C 406 410 406 405 408 406 409 406 405 409 406
Dev -0.5 3.5 -0.5 -1.5 1.5 -0.5 2.5 -0.5 -1.5 2.5 -0.5
Dev2 0.25 12.25 0.25 2.25 2.25 0.25 6.25 0.25 2.25 6.25 0.25

EE220 Instrumentation & Measurement 7

Statistical Analysis
 Random errors can be reduced by taking the average of
a number of measurements
 The mean is close to true value if infinite number of
measurements are considered
 Since finite number of measurements are taken,
therefore the average will have some error
 Error is quantified as the Standard error of the mean 

EE220 Instrumentation & Measurement 8

Graphical Data Analysis: Histogram
 Histogram shows the
distribution of data
 Total area of the
histogram is equal to the
number of data

EE220 Instrumentation & Measurement 9

Graphical Data Analysis: Histogram
 For measurement of
error it is more useful to
draw a histogram of the
deviations of the
measurement from the
mean value
 Symmetry about the zero
deviation value shows
graphically that the
measurement data only
has random errors
EE220 Instrumentation & Measurement 10
Graphical Data Analysis: Histogram
 Y-axis is the frequency of
each occurrence of each
deviation value F(D)
 X-axis is the magnitude
of deviation D
 Height of the frequency
distribution curve is
normalized such that the
area under the curve is
unity

EE220 Instrumentation & Measurement 11

Graphical Data Analysis: PDF
 Curve is known as
Probability Curve
 Height F(D) at any
particular deviation
magnitude D is known
as Probability Density
Function (PDF)

EE220 Instrumentation & Measurement 12

Graphical Data Analysis: PDF
 Area under curve is unity


 F ( D)dD  1


EE220 Instrumentation & Measurement 13

Graphical Data Analysis: PDF
 Probability that the error in any one measurement lies
between two levels D1 and D2 can be calculated
D2
 P( D1  D  D2)  F ( D)dD
 D1

 Probability of observing an error less than or equal to

DO is the Cumulative Distribution Function (CDF)
calculated as
D0

P( D  D0)   F ( D)dD


EE220 Instrumentation & Measurement 14

Gaussian Distribution
 Measurement sets that only contain random errors
confirm to a distribution with a particular shape that is
called Gaussian
 Alternate names for Gaussian distribution are Normal,
Bell Shaped
 Gaussian function is defined as
1 [  ( x  m ) 2 / 2 2 ]
F ( x)  e
 2
 m is the mean value of the date set x

EE220 Instrumentation & Measurement 15

Graphical Data Analysis: PDF
 Probability that the error in any one measurement in a
Gaussian data set lies between two levels D1 and D2
can be calculatedD 2
1
 P( D1  D  D2)   e (  D 2 / 2 2 )
dD
D1 2

 Substituting z = D/σ changes the distribution curve

into a new Gaussian distribution that has standard
deviation σ = 1 and mean µ = 0
z2
 1
P( D1  D  D2)  P( z1  z  z 2)   e (  z 2 / 2)
dz
z1  2

EE220 Instrumentation & Measurement 16

Gaussian Distribution

 Distribution with mean µ = 0 and variance σ2 = 1 is

called the Standard Gaussian Curve
EE220 Instrumentation & Measurement 17
Standard Gaussian Tables
 See table
 How many measurements in a data set subject to
random errors lie outside deviation boundaries of +σ
and –σ
 Mathematically expressed as P(E < -σ or E > +σ)
 = P(E < -σ) + P(E > +σ)
 E = –σ, z = -1 From table P(E < -σ) = 0.1587
 E = σ, z = 1 From table P(E > σ) = 1 – 0.8413 = 0.1587
 = 0.1587 + 0.1587 = 0.3174 = 32%

EE220 Instrumentation & Measurement 18

Standard Error of the mean

EE220 Instrumentation & Measurement 19

Standard Error of the mean
 Some error remains between the set of measurements
and the true value
 The error between the mean of a finite data set and the
true measurement value is defined as the standard
error of the mean 
   / n
  reduces to zero as the measurements in the data set
expand

EE220 Instrumentation & Measurement 1

Standard Error of the mean
 Measurement value obtained from a set of n
measurements can be expressed as x = xmean ± 
 For measurement C
 n = 22, σ = 1.92,  = 0.4
 Measurement is expressed as
 406.5 ± 0.4 (68% confidence limit) 0r
 406.5 ± 0.8 (95% confidence limit)

EE220 Instrumentation & Measurement 2

Estimation of random error in a
single measurement
 In many situations where measurements are subject to
random errors, it is not practical to take repeated
measurements and find the average value
 Averaging process becomes invalid if the measured
quantity does not remain at a constant value
 If one measurement can be made, some means of
estimating the likely magnitude of error in it is
required
 The normal approach to this is to calculate the error
within 95% confidence limits (±1.96σ)
EE220 Instrumentation & Measurement 3
Estimation of random error in a
single measurement
 Maintain the measured quantity at a constant value
whilst a number of measurements are taken in order to
create a reference measurement set from which σ can
be calculated
 Subsequently, the maximum likely deviation in a
single measurement can be expressed as
 Deviation = ±1.96σ
 Maximum likely error in a single measurement is
Error = ±(1.96σ + )

EE220 Instrumentation & Measurement 4

Example
 A standard mass is measured 30 times with the same
instrument to create a reference data set
 Calculated values of  and σ are  = 0.08 and σ = 0.43
 The instrument is then used to measure an unknown
mass and the reading is 105.6 kg
 How should the mass value be expressed?
 1.96σ +  = 0.92
 Mass value = 105.6 ± 0.9 kg

EE220 Instrumentation & Measurement 5

Distribution of Manufacturing
tolerances
 Manufacturing processes are subject to random
variations caused by factors that are similar to those
that cause random errors in measurements
 Random variations in manufacturing are known as
tolerances
 Tolerances fit a Gaussian distribution

EE220 Instrumentation & Measurement 6

Distribution of Manufacturing
tolerances
 An integrated circuit chip contains 10 5 transistors
 Transistors have a mean current gain of 20 and a
standard deviation of 2
 Calculate the number of transistors with a current gain
between 19.8 and 20.2
 P(X < 20.2) = P(z < 0.1) = 0.5398
 P(X > 19.8) = P(z > -0.1) = 1 – P(z < 0.1) = 0.4602
 P(X < 20.2) - P(X > 19.8) = 0.5398 – 0.4602 = 0.0796
 Transistors in the range 19.8 and 20.2 = .0796 x 10 5 =
7960
EE220 Instrumentation & Measurement 7
Distribution of Manufacturing
tolerances
 Calculate the number of transistors with a current gain
greater than 17
 P(X > 17) = P(z > -1.5) = 1 – P(z < 1.5) = 0.9332
 93.32% transistors having gain > 17 = 93320

EE220 Instrumentation & Measurement 8

Combined effect of Systematic and
Random errors
 If systematic error is ±x
 If random error is ±y
 Maximum error is e  x 2  y 2

EE220 Instrumentation & Measurement 9

Aggregation of errors from separate
measurement system components
 Measurement system often consists of several separate
components, each is subject to errors
 How the errors associated with each component
combine together?

EE220 Instrumentation & Measurement 10

Error in a sum
 Two outputs y and z of separate system components
are to be added together
 Smax = (y + ay)+(z + bz)
 Smin = (y - ay)+(z - bz)
 S = y + z ±(ay + bz) not convenient
 e ay 2  bz 2
 S = y + z ±e
 S = (y + z)(1 ± f) where f = e/(y + z)

EE220 Instrumentation & Measurement 11

Error in a sum: Example
 A circuit requirement of 550 Ω resistance is satisfied
by connecting together two resistors of 220 Ω and
330 Ω in series
 Each resistance has tolerance of 2%
 e  0.02 x220  0.02 x330 = 7.93
2 2

 f = 7.93/550 = 0.0144
 S = 550 ± 7.93 Ω
 S = 550(1 ± 0.0144) = 550 Ω ± 1.4%

EE220 Instrumentation & Measurement 12

Error in a difference
 S = y - z ±e
 S = (y - z)(1 ± f) where f = e/(y - z)
 Fluid flow rate is calculated from the difference in
pressure measured on both sides of an orifice plate
 If pressure measurements are 10 bar and 9.5 bar and
error in the pressure measuring instrument is ±0.1%
 e  0.001x102  0.001x9.52 = 0.0138
 f = 0.0138/0.5 = 0.0276

EE220 Instrumentation & Measurement 13

Error in a product
 Two outputs y and z of separate system components
are multiplied together
 Pmax = (y + ay)(z + bz) = yz + ayz + ybz + aybz
 Pmin = (y - ay)(z - bz) = yz – ayz – ybz + aybz
 For an output error of 1% to 2%, term aybz is negligible
 Pmax = yz(1 + a + b)
 Pmin = yz(1 – a – b)
 P = yz ± yz(a + b)
 e  a 2  b 2 calculated in terms of fractional error

EE220 Instrumentation & Measurement 14

Error in a quotient
 Output y is divided by output z
 Qmax = (y + ay)/(z - bz) = yz(1 + a + b)/z2
 Qmin = (y - ay)/(z + bz) = yz(1 – a – b)/z2
 For an output error of 1% to 2%, term aybz, a2 and b2
are negligible
 Q = y/z ± y/z(a + b)
 e  a 2  b 2 calculated in terms of fractional error

EE220 Instrumentation & Measurement 15

Measurement Noise
 Errors are created in measurement systems when
electrical signals from sensors and transducers are
corrupted by induced noise
 Noises is added during transmission of measurement
signals to remote points
 Aim when designing measurement systems is to
reduce noise voltage levels
 Filters have to be employed to remove the remaining
noise

EE220 Instrumentation & Measurement 1

Measurement Noise
 Vs 
 Signal to Noise ratio = 20 log10  
 Vs is the mean signal voltage  Vn 

 Vn is the mean noise voltage

 For a.c. noise voltages the rms value is used as a mean
 External sources of electrical include
 Fluorescent light
 Motors
 Ignition systems/switching
 Computers, monitors, printers
 Radio/Radar transmitters/Cell phones
EE220 Instrumentation & Measurement 2
Measurement of Voltage (AC)
 The Moving coil meter can not measure AC
 A rectifier circuit is connected between the AC and
moving coil to measure AC
 The RMS value is measured
T
1
 
2
 VRMS V (t ) dt
T 0

 VRMS = 0.707VP

EE220 Instrumentation & Measurement 3

Measurement of Voltage (AC)
 VRMS is equivalent to DC voltage which produces the
same amount of heating in a resistive load
2VP
 VAV   0.637VP


EE220 Instrumentation & Measurement 4

Noise: Inductive Coupling
 Primary mechanism by which noise is induced
 Significant mutual inductance M exists between
nearby signal carrying and mains cable
 A noise signal of several mV is generated Vn = MI
 Where I is rate of change of current in the mains
circuit

EE220 Instrumentation & Measurement 5

Noise: Capacitive Coupling
 Electrostatic coupling can occur between the signal
carrying conductor and nearby main carrying
conductor
 Coupling Capacitance C1 and C2 exists between main
conductor and signal carrying conductors
 Coupling Capacitance C3 and C4 exists between signal
wires and earth

EE220 Instrumentation & Measurement 6

Noise: Capacitive Coupling
 If signal carrying conductor is parallel to mains then
C1 = C2 and C3 = C4 consequently noise signal is zero

EE220 Instrumentation & Measurement 7

Noise due to Multiple Earths
 Ideally, measurement signal circuits are isolated from
earth
 Practically, leakage paths exist between measurement
circuit signal wires and earth at the sensor end and the
measuring instrument end
 Does not cause problem if earth potential is same at
both ends
 Other equipment carrying large current connected to
earth, creates potential differences
 Series Mode noise is added
EE220 Instrumentation & Measurement 8
Noise in the form of voltage
transient
 Large changes of power consumption occur in electric
supply system when electrical motors and other
equipment are switched on/off
 Causes voltage transients in instruments connected to
same power supply

EE220 Instrumentation & Measurement 9

Noise due to Thermoelectric
Potential
 Whenever two different metals are connected together
a thermoelectric potential is generated according to
the temperature of the joint
 Thermocouples operate on the same principle

EE220 Instrumentation & Measurement 10

Techniques for reducing
measurement noise
 Location and design of signal cables
 Earthing
 Shielding
 Other techniques

EE220 Instrumentation & Measurement 11

Location and design of signal
cables
 Mutual inductance and capacitance between signal
wires and other cables are inversely proportional to the
square of the distance between the wires and the cable
 Noise can be minimized by positioning the signal
wires away from noise sources
 Minimum separation of 0.3 m is essential
 Separation of 1 m is preferable

EE220 Instrumentation & Measurement 12

Location and design of signal
cables
 Noise due to inductive coupling can be substantially
reduced by twisting the cable along its length
 Identical voltages are induced in the two signal pairs

EE220 Instrumentation & Measurement 13

Earthing
 Noise due to multiple earths can be avoided by good
earthing practices
 Keep earths for signal wires and earths for high current
equipment entirely separate
 Recommended practice is to install four completely
isolated earth circuits
 Power earth
 Logic Earth
 Analog Earth
 Safety Earth
EE220 Instrumentation & Measurement 14
Shielding
 Signal wire is enclosed in
an earthed, metal shield
that is itself isolated
electrically from the
signal wire
 The shield should be
earthed at only one
point, preferably the
signal source end

EE220 Instrumentation & Measurement 15

Shielding
 A shield consisting of
braided metal eliminates
85% of noise due to
capacitive coupling
 A lapped metal foil
shield eliminates noise
almost entirely

EE220 Instrumentation & Measurement 16

DC and AC Deflection Meter
Movements
 Deflection Meters
measure dc/ac quantities
 Most common dc meter
movement is the
d’Arsonval design
 A current carrying coil
placed in a magnetic
field deflects
Chapter 3 dc and ac Deflection Meter
Movements
Elements of Electronic Instrumentation
and Measurement
EE220 Instrumentation & Measurement 1
DC and AC Deflection Meter
Movements
 T = BANI
 T = Torque
 B = Flux density
 A = Area of coil
 N = turns of coil
 I = current in the coil
 θk = BANI
 θ = angle of twist
 k = torsion constant

EE220 Instrumentation & Measurement 2

DC and AC Deflection Meter
Movements
 θ/I = BAN/k
 Current sensitivity of
meter

EE220 Instrumentation & Measurement 3

Measurement of Current (DC)
 Connect meter in series with the load through which
current is measured
 Meter should have a full-scale current IFS rating
greater than the maximum current expected
 Meter should have an internal resistor RS lower ( < 1:
10) than the circuit in which it is used
 Resistance connected in shunt to obtain higher current
measuring scales
Rm
 I s  I FS
Rm  RS

EE220 Instrumentation & Measurement 4

Measurement of Current (DC)
 0 to 50 µA DC meter movement
 Coil resistance Rm = 1250 Ω
 Full scale current to be measured = 500 µA
 RS = ?
Rm 1250
 I s  I FS (500  50)  500
Rm  RS 1250  RS

 RS = 139 Ω

EE220 Instrumentation & Measurement 5

Measurement of Voltage (DC)
 Voltage can be measured by connecting a ‘Multiplier’
resistor RM in series with the meter movement
 Connect meter in parallel with the load across which
voltage is measured
 Meter should have a full-scale voltage rating greater
than the maximum voltage expected
 Meter should have an internal resistor which is very
high (> 100: 1) than the circuit resistance
Rm VM V
 VM  V I 
Rm  RM Rm Rm  RM

EE220 Instrumentation & Measurement 6

Measurement of Voltage (DC)
 0 to 100 µA DC meter movement
 Coil resistance Rm = 500 Ω
 Full scale voltage to be measured = 10 V
 RM = ?
V 4 10
 I 10 
Rm  RM 500  RM

 RM = 99500 Ω

EE220 Instrumentation & Measurement 7

Voltmeter Sensitivity Ф
 Sensitivity Ф of a voltmeter is specified in terms of
ohms/volts
 Sensitivity is dependant upon full-scale current range of
the dc meter movement
Full-Scale Meter Current Sensitivity Ф
1 mA 1000 Ω/V
100 µA 10 kΩ/V
50 µA 20 kΩ/V
20 µA 50 kΩ/V
10 µA 100 kΩ/V

EE220 Instrumentation & Measurement 8

Bridge Circuits
 Sensor outputs in the form of voltage signals can be
measured using voltage measuring instruments
 Sensors outputs which are not in the form of voltage
signals have to be converted into an appropriate form
by a variable conversion element in the measurement
system
 Sensor outputs can be translational displacement,
changes in resistance, inductance, capacitance,
frequency, phase

EE220 Instrumentation & Measurement 1

Bridge Circuits
 Bridge circuits are commonly used as variable
conversion element which produce a voltage output
signal
 Provide an accurate method of measuring resistance,
inductance, capacitance
 Excitation of Bridge circuit is by dc voltage for
resistance measurement
 Excitation of Bridge circuit is by ac voltage for
measurement of inductance and capacitance

EE220 Instrumentation & Measurement 2

Bridge Circuits
 Null type and deflection type Bridges exist
 Null type are used for calibration purposes
 Deflection type are used for closed-loop automatic
control schemes

EE220 Instrumentation & Measurement 3

Null-Type dc Bridge (Wheatstone
Bridge)
 Ru unknown resistor
 Rv variable resistor
 R2 = R3 fixed resistor
 DC excitation voltage Vi
applied across Nodes AC
 High sensitivity
Galvanometer connected
across BD

EE220 Instrumentation & Measurement 4

Null-Type dc Bridge (Wheatstone
Bridge)
 Current through Ru, Rv, R3
and R2 is I1, I2, I3 and I4
 High impedance
Galvanometer connected
draws negligible current
 I1 = I3 and I2 = I4
 Vi = I1Ru + I3R3 = I1(Ru + R3)
 Vi = I2Rv + I4R2 = I2(Rv + R2)

EE220 Instrumentation & Measurement 5

Null-Type dc Bridge (Wheatstone
Bridge)
 VAD = ViRu/(Ru + R3)
 VAB = ViRv/(Rv + R2)
 At null point VO = 0
 VAB = VAD
 ViRv/(Rv + R2) = ViRu/(Ru + R3)
 R2/Rv = R3/Ru
 Ru = Rv(R3/R2)

EE220 Instrumentation & Measurement 6

Deflection-Type dc Bridge
(Wheatstone Bridge)
 Variable resistor replaced
by fixed resistance R1
 Ru unknown resistor
 R1 = nominal value of Ru
 R2 = R3 fixed resistor
 DC excitation voltage Vi
applied across Nodes AC
 High sensitivity
Galvanometer connected
across BD
EE220 Instrumentation & Measurement 7
Deflection-Type dc Bridge
(Wheatstone Bridge)
 As Ru changes VO
changes
 Relationship between Ru
and VO must be
calculated
 VO = VAD – VAB
  Ru R1 
VO  Vi   
 Ru  R3 R1  R2 
 VO varies in a non-linear
way with Ru
EE220 Instrumentation & Measurement 8
Deflection-Type dc Bridge: Example
 Pressure transducer is designed to measure pressures
in the range 0 – 10 bar
 Pressure transducer consists of diaphragm with a
strain gauge cemented to it to detect diaphragm
deflection
 Nominal resistance of strain gauge is 120 Ω
 Three arms of Wheatstone bride have resistances of
120 Ω each
 Maximum strain gauge current is 30 mA to limit
heating effect
EE220 Instrumentation & Measurement 9
Deflection-Type dc Bridge: Example
 What is the maximum dc
excitation voltage?
 Vi = I(Ru + R3)
 Vi = 0.03(120 + 120)
 Vi = 7.2 V

EE220 Instrumentation & Measurement 10

Deflection-Type dc Bridge: Example
 Sensitivity of the strain
gauge is 338 mΩ/bar
 Calculate the bridge
output voltage when
measuring a pressure of
10 bar
 Resistance of strain
gauge changes by 3.38 Ω
when pressure of 10 bar
is applied

EE220 Instrumentation & Measurement 11

Deflection-Type dc Bridge: Example
 Nominal resistance of
strain gauge increases to
123.38 Ω
 V  V  Ru  R1 
i 
 Ru  R3 R1  R2 
O

 V  7.2 123.38  120 

O  
 243.38 240 
 49.9 mV

EE220 Instrumentation & Measurement 12

Deflection-Type dc Bridge: Example
 Change in VO for Ru = 121 Ru
Deflection (mV)
R2 = R3 = 120 Ω
Deflection (mV)
R2 = R3 = 1200 Ω

Ω to 119 Ω by 0.5 Ω when

1 118.9 -16.58 -16.38
2 119 -15.06 -14.89

R2 = R3 = 120 Ω
3 119.1 -13.55 -13.40
4 119.2 -12.04 -11.91
5 119.3 -10.53 -10.42

 7.46, 7.48, 7.52, 7.54

6 119.4 -9.02 -8.93
7 119.5 -7.52 -7.44
8 119.6 -6.01 -5.95

 Linearity can be 9
10
119.7
119.8
-4.51
-3.00
-4.46
-2.98

improved if R2 and R3 are 11

12
119.9
120
-1.50
0.00
-1.49
0.00
13 120.1 1.50 1.49
made 10 times R1 and Ru 14 120.2 3.00 2.97
15 120.3 4.49 4.46
16 120.4 5.99 5.95
17 120.5 7.48 7.44
18 120.6 8.98 8.92
19 120.7 10.47 10.41
20 120.8 11.96 11.89
21 120.9 13.45 13.38
22 121 14.94 14.86
23 121.1 16.42 16.35
24 121.2 17.91 17.84
EE220 Instrumentation & Measurement 13
Deflection-Type dc Bridge: Example
 Change in VO for Rx = 121 Ru
Deflection (mV)
R2 = R3 = 120 Ω
Deflection (mV)
R2 = R3 = 1200 Ω

Ω to 119 Ω by 0.5 Ω when

1 118.9 -16.58 -16.38
2 119 -15.06 -14.89

R2 = R3 = 1200 Ω
3 119.1 -13.55 -13.40
4 119.2 -12.04 -11.91
5 119.3 -10.53 -10.42

 7.42, 7.44, 7.44, 7.45

6 119.4 -9.02 -8.93
7 119.5 -7.52 -7.44
8 119.6 -6.01 -5.95

 Increasing R2 and R3 9
10
119.7
119.8
-4.51
-3.00
-4.46
-2.98

requires excitation 11
12
119.9
120
-1.50
0.00
-1.49
0.00
13 120.1 1.50 1.49
voltage to be increased 14 120.2 3.00 2.97
15 120.3 4.49 4.46
16 120.4 5.99 5.95
17 120.5 7.48 7.44
18 120.6 8.98 8.92
19 120.7 10.47 10.41
20 120.8 11.96 11.89
21 120.9 13.45 13.38
22 121 14.94 14.86
23 121.1 16.42 16.35
24 121.2 17.91 17.84
EE220 Instrumentation & Measurement 14
Current drawn by measuring
instrument is not negligible
 Thevenin’s Resistance
across DB
 RDB  Ru R3  R1R2
Ru  R3 R1  R2

 Thevenin’s voltage across

DB
 Ru R1 
 EO  Vi   
 Ru  R3 R1  R2 

EE220 Instrumentation & Measurement 15

Current drawn by measuring
instrument is not negligible
 Voltage across Rm
Rm EO
 mV 
RDB  Rm
Vi Rm Ru R2  R1R3 
 Vm 
Ru R3 R1  R2   R1R2 Ru  R3   Rm R1  R2 Ru  R3 

EE220 Instrumentation & Measurement 16

Example:
 A bridge circuit is used to measure the value of
unknown resistance Ru of a strain gauge of nominal
value 500 Ω. V = 10 V
 Rm = 10 kΩ, R2 = 500 Ω, R1 = 500 Ω, R3 = 500 Ω

EE220 Instrumentation & Measurement 17

Example:
 Calculate the measurement sensitivity in volts/ohm
change in Ru if the resistance Rm of the measuring
instrument is neglected

 Ru R1 
 VO  Vi   
 Ru  R3 R1  R2 
 501 500 
 G
V  10  
 501  500 500  500 
 4.99 mV
 Sensitivity is 4.99 mV/Ω

EE220 Instrumentation & Measurement 18

Example:
 Calculate the measurement sensitivity in volts/ohm
change in Ru if account is taken of the value of Rm

Vi Rm Ru R2  R1R3 
 Vm 
Ru R3 R1  R2   R1R2 Ru  R3   Rm R1  R2 Ru  R3 

 4.76 mV
 Sensitivity is 4.76 mV/Ω

EE220 Instrumentation & Measurement 19

Error Analysis
 In a Bridge circuit the contribution of component
value tolerances to total measurement system accuracy
limits should be known
 Maximum measurement error is determined by first
finding the value of Ru with each resistor set at the
limit of its tolerance which produces the maximum
value of Ru
 Similarly, the minimum value of Ru is calculated
 The required error band is the span between these
maximum and minimum values
EE220 Instrumentation & Measurement 20
Error Analysis
 Ru unknown resistor
 Rv has specified
inaccuracy ±0.2 Ω
 R2 = R3 = 5000 Ω ± 0.1%
 At null position Rv =
520.4 Ω
 Determine the error
band for Ru expressed as
a percentage of its
nominal value
EE220 Instrumentation & Measurement 21
Error Analysis
 Ru = Rv(R3/R2)
 For maximum error
 = 521.44(5005/4995)
 = 522.48 error is +0.4 %
 For minimum error
 = 519.36(4995/5005)
 = 518.32 error is –0.4 %
 Possible error range ±0.4%

EE220 Instrumentation & Measurement 22

Apex Balancing
 Error of ±0.4% is large
and not acceptable
 Apex Balancing is used
to reduce error
 Variable Resistance at
Node C
 For calibration Ru and Rv
replaced by two very
accurate equal resistors

EE220 Instrumentation & Measurement 1

Apex Balancing
 Variable resistance
varied until null
deflection
 Error in R2 and R3
removed
 Error only due to Rv

EE220 Instrumentation & Measurement 2

AC Bridges
 Used to measure
unknown impedances
 Both Null and
Deflection Type exist
 Oscilloscope is used to
detect null point as
magnitude and phase
has to be compared
 Pair of headphones
connected via an
operational amplifier
EE220 Instrumentation & Measurement 3
AC Bridges
 Zu = unknown
impedance
 Zv = variable impedance
 Zu = Zv(R1/R2)
 If Zu is capacitive then Zv
is variable capacitance
1
 Zu 
jCu

EE220 Instrumentation & Measurement 4

AC Bridges
 If Zu is inductive then Zv
is variable inductance
and resistance
 Zu  Ru  jLu
 Pure inductance is not
available
 Inductor coil always has
resistance
 High Q factor coil used

EE220 Instrumentation & Measurement 5

Maxwell Bridge
 Used for measuring
unknown inductance as
variable inductance are
difficult and expensive to
manufacture
 Unknown inductance
Zu  Ru  jLu
 R1 and R2 are variable
resistance

EE220 Instrumentation & Measurement 6

Maxwell Bridge
 R3 fixed resistance
 C fixed capacitance
 At null point
 Zu = R2(R3/Z1)
1
 Z1  R1 ||
jC
R1
 Z1 
1  jR1C
R2 R3 1  jR1C 
 Zu 
R1
EE220 Instrumentation & Measurement 7
Maxwell Bridge
R2 R3 1  jR1C 
 Zu 
R1
 Real component
R2 R3
 u
R 
R1

 Imaginary component
 Lu  R2 R3C
 Quality Factor ‘Q’ of coil
L
 Q  u  CR1
Ru

EE220 Instrumentation & Measurement 8

Hay Bridge
 Similar to Maxwell
Bridge
 Used for measuring
Inductance with high Q
 R4 and C4 are connected
in series
 Less sensitive to
frequency

EE220 Instrumentation & Measurement 9

Hay Bridge
R3
 Z1  R2
Z4
 R3 
 Z1  R2  
 R4  1 / jC4 
 R3 
 Z1  R2  
 R4  j / C4 
 R4  j / C4 
 Z1  R2 R3  2 
2 2 
 R4  1 /  C4 

EE220 Instrumentation & Measurement 10

Hay Bridge
 R4  j / C4 
 Z1  R2 R3  2 
2 2 
 R4  1 /  C4 

 Real Term

 R4 
 R1  R2 R3  2 
2 2 
 R4  1 /  C4 

R2 R3  1 
 R1   
2 2 2 
R4  1  1 /  R4 C4 

EE220 Instrumentation & Measurement 11

Hay Bridge
 Imaginary Term

 1 /  2 C4 
 L1  R2 R3  2 
2 2 
 R4  1 /  C4 
R2 R3  1 /  2C4 
 L1  2  2 2 2 

R4  1  1 /  R4 C4 

 Quality Factor ‘Q’ of coil

L1
1
 Q 
R1 C4 R4
EE220 Instrumentation & Measurement 12
Hay Bridge
R2 R3  1 
 R1   
2 
R4  1  Q 
 1 

 L1  R2 R3C4  
2 
 11/ Q 

 For large ‘Q’ factor

 L1  R2 R3C4

EE220 Instrumentation & Measurement 13

Schering Bridge
 Similar to Maxwell Bridge
 Used for measuring
Capacitance
 L1 is replaced with C1
 R3 is replaced with
variable C3
 R4 and C4 series
combination replaced
with parallel combination

EE220 Instrumentation & Measurement 14

Schering Bridge
Z3
 Z1  R2
Z4
1 / jC3 
 R1  1 / jC1  R2
R4 / 1  jR4C4 
1  jC1R1 R2 1  jR4C4 
 
jC1 R4 jC3
1  jC1R1 R2 1  jR4C4 
 
C1 R4C3

EE220 Instrumentation & Measurement 15

Schering Bridge
1 R
 Real term  2
C1 R4C3
R4C3
 C1 
R2

 Imaginary term

C1 R1 R2 R4C4
 
C1 R4C3
R2C4
 R1 
C3
EE220 Instrumentation & Measurement 16
Schering Bridge
 Quality Factor ‘Q’ of
capacitor
 Q  1 / C4 R4

EE220 Instrumentation & Measurement 17

Deflection type AC Bridge
 Zu = unknown
impedance
 Z1 = variable impedance
 R2 and R3 are fixed
resistance
 If Zu is capacitive then Z1
is variable capacitance
 If Zu is inductive then Z1
is variable inductance
Vs
 I1  Vs I2 
Z u  Z1 R2  R3
EE220 Instrumentation & Measurement 18
Deflection type AC Bridge
 At null deflection
 Vo  I1Zu  I 2 R3

 Zu R3 
 Vo  Vs   
 Z u  Z1 R3  R2 

 For capacitance

 1 / Cu R3 
 Vo  Vs   
 1 / Cu  1 / C1 R3  R2 

EE220 Instrumentation & Measurement 19

Deflection type AC Bridge
 
 Vo  Vs  C1  R3 
C C R  R 
 1 u 3 2 

 For inductance

 Lu R3 
 Vo  Vs   
 Lu  L1 R3  R2 

EE220 Instrumentation & Measurement 20

Resistance Measurement
 Devices that convert measured quantity into a change
in resistance include
 Wire-Coil Pressure Gauge
 Strain Gauge

EE220 Instrumentation & Measurement 1

Resistance Measurement
 Resistance Thermometer (RTD):Resistance
thermometers, also called resistance temperature
detectors (RTDs), are sensors used to measure
temperature by correlating the resistance of the RTD
element with temperature. Most RTD elements consist
of a length of fine coiled wire wrapped around a ceramic
or glass core.
 Thermistor: A thermistor is a type
of resistor whose resistance varies significantly
with temperature, more so than in standard resistors.

EE220 Instrumentation & Measurement 2

Resistance Measurement
 Standard devices and methods used for measuring
change in resistance
 DC Bridge Circuit
 Commonly used for measuring medium range values
 Best accuracy ( ±0.02%) provided by Null Wheatstone
Bridge
 Deflection type Bridges have inferior accuracy and have
non-linear output

EE220 Instrumentation & Measurement 3

Resistance Measurement
Used for measuring
 Voltmeter-Ammeter small resistances
Method
 Measured DC voltage is
applied across an
unknown resistance and
measuring the current
flowing
 Inaccuracy of up to ±1 %

Used for measuring

large resistances
EE220 Instrumentation & Measurement 4
Resistance Measurement
 Resistance-Substitution Method
 Unknown resistance is replaced by a variable resistance
 Variable resistance is adjusted until the measured circuit
voltage and current are the same as existed with the
unknown resistance in place
 The variable resistance is equal in value to the unknown
resistance

EE220 Instrumentation & Measurement 5

Resistance Measurement
 Two terminals ‘+’ and ‘-’ are
shorted
 Variable resistor adjusted to give
‘zero’ deflection

EE220 Instrumentation & Measurement 6

Resistance Measurement
 Unknown resistor connected
across ‘+’ and ‘-’
 Wide range of measurement
Milliohm to 50 MΩ

EE220 Instrumentation & Measurement 7

Resistance Measurement
R1 VB Ru VB  Vm
 Vm  VB  1 Ru  R1
R1  Ru Vm R1 Vm

 VB applied voltage. VM cross R1

 Inaccuracy is ±2 %, Vm : multimeter voltage

EE220 Instrumentation & Measurement 8

Inductance Measurement
 Device that converts measured quantity into a change
in Inductance is Inductive Displacement Sensor

EE220 Instrumentation & Measurement 9

Inductance Measurement
 Inductance is measured using
AC Bridge circuit
 When Bridge is not available
 Unknown inductance connected
in series with a variable
resistance
 Circuit excited by sinusoidal
voltage of known frequency
 Variable resistance adjusted
until voltage across unknown
inductance is equal to voltage
across resistance
EE220 Instrumentation & Measurement 10
Inductance Measurement
 VR  VL
 IR  IZ L
 R 2
 r 2
 L 2

 L  R 2  r 2 / 2f

EE220 Instrumentation & Measurement 11

Capacitance Measurement
 Devices that convert measured quantity into a change
in capacitance include
 Capacitance Level Gauge (using 555 timer circuit)
 http://www.digikey.com/en/articles/techzone/2011/sep/liquid-level-sensing-is-
key-technology-for-todays-systems---part-1

EE220 Instrumentation & Measurement 12

Capacitance Measurement
 Capacitance Displacement Sensor

EE220 Instrumentation & Measurement 13

Capacitance Measurement
 Capacitance Moisture Meter

EE220 Instrumentation & Measurement 14

Capacitance Measurement
 Capacitance Hygrometer (measures moisture content
in the air)

EE220 Instrumentation & Measurement 15

Capacitance Measurement
 Capacitance is measured using
AC Bridge circuit
 When Bridge is not available
 Unknown capacitance
connected in series with a
resistance
 Circuit excited by sinusoidal
voltage of known frequency
 Current flowing through
Resistor and Capacitor is the
same

EE220 Instrumentation & Measurement 16

Capacitance Measurement
 I R  IC
 VR / R  VC 2fC

VR
 C
2fRVC

EE220 Instrumentation & Measurement 17

Frequency Measurement
 Devices that converts measured quantity into a change
in Frequency
 Variable reluctance velocity transducer
 Transit-time ultrasonic flow meter

EE220 Instrumentation & Measurement 18

Frequency Measurement
 Digital Timer Counter
 All frequencies between d.c. and several GHz can be
measured
 Oscilloscope
 Wien Bridge

EE220 Instrumentation & Measurement 19

Digital Timer Counter
Divider circuit provides
different
Gatetime base toby
is enabled
measure different
the divider circuit
frequency ranges
for specified time
limit for counting
pulses

Oscillator provides
Shapera circuit
very
accurate and stable
converts oscillator
frequency either
signal
100tokHz
square
or 1 MHz wave signal
Amplifier triggerCounter
circuit counts
amplifies unknownthe unknown
signal and converts it pulses
signal
into square wave signal
EE220 Instrumentation & Measurement 20
Digital Timer Counter

EE220 Instrumentation & Measurement 21

Wien Bridge
 Z3 = Series RC circuit
 Z4 = Parallel RC circuit
 At balance
 Z3 = Z4(R1/R2)
 R  1  R4  R1 
 
jC3 1  jR4C4  R2 
3

1  jR3C3 R4  R1 
  
jC3 1  jR4C4  R2 

EE220 Instrumentation & Measurement 1

Wien Bridge
1  jR3C3 R4  R1 
   
jC3 1  jR4C4  R2 
 R1 
 1  jR4C4  jR3C3   R3C3 R4C4  jC3 R4  
2

 R2 
 R1 
 Imaginary Term R4C4  R3C3  C3 R4  
 R2 
R1 C4 R3
  
R2 C3 R4
R1
 In Wien Bridge R4 = R3 and C4 = C3 2
R2
EE220 Instrumentation & Measurement 2
Wien Bridge
 R1 
 1  jR4C4  jR3C3   R3C3 R4C4  jC3 R4  
2

 R2 

 Real Term 1   2 R3C3 R4C4  0

 In Wien Bridge R4 = R3 and C4 = C3

1 1
 
2
f 
R4C4 R3C3 2RC

EE220 Instrumentation & Measurement 3

Operational Amplifiers
 Characteristics of an Ideal
Op-Amp
V+

 Infinite Open-loop Gain

Aout = 
 Infinite Input Impedance Vp Vn Vo
Vcc

Zin = 
Vcc
 Zero Output Impedance V-
Zout = 0
 Infinite Band-width fo = 
 Zero Noise Generation
EE220 Instrumentation & Measurement 4
 See Multisim
Inverting Amplifier simulation of
Inverting Amplifier
vs  vn vo  vn
  0 if

Rs Rf
Rf
 Rf 
 vo  vs   is
in
 Rs 
+Vcc

vn
Rs
Rf
 Av  vp
Rs
Vs -Vcc
Vo

 Input Resistance Rs

EE220 Instrumentation & Measurement 5

 See Multisim
Non-Inverting Amplifier simulation of Non-
 vo  Inverting Amplifier
 v n  R s  
 Rf  Rs 
if

 Rf  Rs 
 v o  v n  
Rf

 Rs  in +Vcc

vn
Rs
 vn = vg (if no current flows
in the +ve terminal i.e. Rg
vp
-Vcc
input resistance is very Vg
Vo

high)
 Rf 
v o  v g   1
 Rs 
EE220 Instrumentation & Measurement 6
Problems in Op-Amps
 Offset Current
 Input Impedance is less than infinity
 Small offset current flows
 Solution
 Compensation Resistor is used

EE220 Instrumentation & Measurement 7

Offset Current Compensation
vs  vn vo  vn
   In if

Rs Rf
Rf
 Rf 
 vo  vs    I n R f
R is
in
 s 
+Vcc

vn
Rs

 Compensation Resistor vp

Rc  Rs || R f Vs -Vcc
Vo

EE220 Instrumentation & Measurement 8