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CHAPTER ONE INTRODUCTION TO INSTRUMENTAT

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CHAPTER ONE
INTRODUCTION TO INSTRUMENTATION
1.1
Introduction to instrumentation
Instrumentation is the art of science of measurement and control. It is an applied
science that deals with analysis and design of systems for measurement purposes such as
quantify or expressing a variable numerically, determine or ascertain the value
(magnitude) of some particular phenomena, indicate record, register, signal, or perform
some operation on the value it has determined. Measurement is the process of quantifying
input quantity as shown in figure 1.1.
Figure 1.1 Measurement system
A measuring instrument is simply a device that determines the value of quantity
or physical phenomena. The value determined by the instrument is generally, but not
necessarily, quantitative. For example, an instrument for the measurement of the presence
of an object with in a defined area may simply respond "yes" or “no".
Purpose of measurement
The role of measurement in ones country development particularly in the
advancement of science and technology is huge; this is because of the need or eagerness
for understanding of events or physical phenomenon. Once then, the event can be well
harnesses for the welfare of the society or development of the country through analysis
and interpretations leading to innovations. Generally the purpose of measurement is
categorized in to three these are; Monitoring, Controlling processes and operations, and
experimental engineering analysis.
1. Monitoring of process and operations:
Monitoring refers to knowing or understanding the process or operation by
measuring the variables of the process but don’t take any action in the ordinary control
sense of setting these variables to desired point.
1
Example: thermometers, barometers, anemometers used by the weather bureau are used
to provide information of the environment by providing the atmospheric temperature,
pressure and wind speed. Their purpose is to measure and indicate the weather variables
and not to take a control action, such as to set these variables to desired ones.
2. Control of process or operations
Controlling of process or operations refers to attain the variable of interest set as
desired point. Thus knowledge or understanding of the process variable or operation is
required through appropriate measurement and then a control action will be taken to let
the output keep track of set point.
Example: Feed back control shown in figure 1.2 is an automatic controller that is used to
control a system or process in such a way that the output (O) is usually the set point(S) or
keep track of the set point(S). To do so the control system employs a measurement
system which continuously reads the output (O) and produces its own measured output
(MO) that can be compared with the set point (S) to provide an error signal(e). The
controller takes the error signal (e) executes a corresponding manipulating variable (m)
which is used to manipulate the system in such a way that the output (O) is the set point
Figure 1.2 Feed control system or process
Thus it can be said the quality of the control is highly dependent on the quality of
measurement
3. Experimental engineering analysis:
Another important purpose of instrumentation is the desire of measurement for
experimental
engineering analysis for design, development and research that relies on
laboratory testing of one kind for the purpose of validating engineering design, collecting
data for future analysis e.t.c
1.2
System of units and standards
Instrumentation engineering is a multidisciplinary subject; it takes input quantity or
variables from various disciplines such as Electrical, Electronics, Mechanical, Chemical,
2
Hydraulic, and Medical. These variables or physical quantities are described in
magnitude and unit. There are different types of units used, among the common ones are
1. FPS system(foot, pound, second)
2. CGS system(centimeter, gram, second)
3. MKS system(meter, kilogram, second)
4. rationalized MKSA system(meter, kilogram, second ,ampere)
The rationalized MKSA system was adopted in 1968 under the system international
d’units (SI) which is accepted internationally. The SI system of units has seven units
called as fundamental units as summarized in table 1.1
Table 1.1: Fundamental units of SI system of unit
Quantity
SI unit
1. Length
m
2. Mass
Kg
3. Time
sec
4. Current
A
5. Luminous intensity
cd
6. Temperature
K
7. Amount of substance (matter) mol
Broadly units are classified as fundamental units and derived units. Fundamental
units are unit’s fundamental to most other units these units are summarized in table 1.1.
All other units which can be expressed in terms of the fundamental units are called
derived units.
Example: The unit of force is Newton, [N] however it can be described using the
fundamental units
F=ma=mv/t=ms/t2= [kgm/sec2]
Likewise all other units can be derived from the fundamental units. Some times for
studying instrumentation systems, quantities are also described as electrical quantity (EQ)
and non electrical quantity (NEQ)
Example: Non electrical quantity (NEQ), Temperature, Pressure; Force
Electrical quantity (EQ), voltage, current, electrical power
3
Standards of measurement
Measurement, the process of quantifying a variable, is made by comparing the
unknown quantity with a predefined standard. The physical embodiment of a unit of
measurement is called Standard. Standards are available for some of the derived units
besides all the fundamentals units.
For example: The fundamental unit of mass in the international system is kilogram (kg)
and is defined as the mass of a cubic decimeter of water at this temperature of maximum
density of 40c. Thus if the mass of a body is said as 2Kg, the numeric value along with
the unit that describes the weight is said in comparisons with its predefined standard in
this case the kilogram.
Basically Standards are classified in to four these are; international standards
(international accepted), primary standards, secondary standards and working standards.
But according by their function, application and accuracy there are so many working
standards such as national standards (nationally accepted), material standards (gold,
diamond)
1.3
Functional blocks of a measurement system
The purpose of measurement system is to present an observer with a numerical
value corresponding to the variable being measured. To do so a measurement system
comprises four functional blocks at most. These are sensing element, signal conditioning,
and signal processing and data presentation. .
Figure 1.3 Functional blocks of a measurement system
Input
The input variable, also called as true value or real input or measurand, is a physical
quantity or phenomena which is under interest to be measured. It is real physical quantity
or variable from electrical, mechanical, chemical, hydraulic, Medical, geographical e.t.c
such as; temperature, flow, speed e.t.c.
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Sensing element
The true value is sensed or detected by sensing element. Sensor detects change of
input and produces equivalent quantity which is related to the input, in other words it
provides a corresponding change of output for change of input of physical phenomena as
shown in figure 1.3 a.
Example: A strain gauge is a sensing element that detects change of pressure and
provides change in resistance. The change of resistance can be attained in the form of
voltage by using deflection bridge circuit.
(a)
(b)
Figure 1.4 Sensing elements
Often the sensing element is also called as transducer. Literally transducer is any
device that converts one form of energy to another as shown in figure 1.3.b. Specifically
it converts one type of physical quantity, such as temperature, strain, pressure, or light,
into another signal (preferably electrical). Transducers have become convenient,
economical, and highly efficient in operation by converting the various physical
quantities into related electrical values because such electrical values can readily be used
for measuring, amplifying, transmitting, or controlling purposes. In its applied usage, the
term transducer refers to devices of a rather specialized nature. The majority either
converts electrical energy to mechanical displacement and/or convert some non-electrical
physical quantity (such temperature, pressure, etc) to an electrical signal such as voltage
or resistance. Thus a sensor is a transducer but a transducer doesn’t necessarily mean
sensor. Some times it is possible to use stages of sensors (more than one sensor) until the
desired output is obtained.
5
Signal conditioning element and interfacing circuits
The output of a sensor is usually small or not suitable for processing or
presenting. Hence a signal conditioning element is used to condition the output of sensing
in to a convenient form, so that it can be further processed or presented. Among the most
commonly used signal conditioning elements are Deflection bridges, Amplifier,
Modulation, Filtering, Impedance matching, Oscillator, e.t.c and signal conversion;
V/I,I/V,V/F,F/V, and interfacing circuits (DAC/ADC)
Single processing element
The signal processing takes the output of the signal conditioning element and
converts it in to a form more suitable for presentation.
- Digital signal processing , example Micro processor (for computation
purposes
Data/Output presenting element (display/recording)
This presents the measured quantity to the observer. Data can be presented numerically,
graphically or recorded
- Analog indication by means of pointers (deflection pointers)
- Digital indication using displays (LCD, LED)
- Graphically using cathode ray oscilloscopes(CRO)
- Recording the variation of signal as function of tome
1.4
Performance characteristics
The first and for most important step in designing instrumentation system is the
selection of sensor or transducer. Thus knowledge of the performance characteristic of
the sensor or transducer is essential for the proper choice of the transducer. Based on the
responses of sensor or transducer to inputs which are either constant or varying with time
rapidly, the Performance characteristic of sensor or transducer is broadly classified in to
static and dynamic characteristic.
Input (I)
Sensor or
transducer
output (O)
Figure 1.5 Performance characteristic
6
1. Static characteristics: are a set of performance criteria that give a meaningful
description of the quality of measurement while the measured quantity is either
constant or varying slowly.
2. Dynamic characteristics: describe the quality of measurement when the measured
quantities vary rapidly with time.
A conventional approaches is to treat these two characteristics separately because the first
one is expressed in terms of linear equations and the second one in terms of differential
equations
1.4.1 Static characteristics
The static characteristics describe the set of performances when the input is
constant or varying slowly. It is classified as systematic and statistic characteristics; the
former describes for those which can be exactly quantified by mathematical or graphical
means while the later for those which are analyzed by statistical means
1.4.1.1 Systematic characteristics
The systematic characteristic describes those which can be exactly quantified by
mathematical or graphical means. The important systematic characteristic of a sensor or
transducer are;
Range, Span, Sensitivity, Threshold, Resolution, Hysteresis,
Linearity, input impedance or loading effect, Environmental effects.
Range: The input (I) and output (O) ranges are specified by a minimum and maximum
value as, IMIN to IMAX, and OMN to OMAX.
Example: Thermocouple (temperature transducer) have input range 100 0C to
2500C and output range of 4 mv to 10 mv.
Span: is defined as the maximum variation in input or output
Input span: IMAX – IMIN
Output span: OMAX – OMIN
Example: The above transducer have Input span: 1500C and Output span: 6mv
Sensitivity: is the rate of change of output with respect to input. Its unit is expressed in
terms of output unit per input unit
Example: - The sensitivity of mercury in glass thermometer is expressed
mm/0C and for Pressure gauge is in angular degrees/kilopascal (kpa)
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Linearity: is the description of relation between the input and output .A sensor or
transducer is said to be linear if corresponding values of input (I) and output (O) lie on a
straight line
Figure 1.6 Linear characterstics
The mathematical relation is straight line connecting points (IMIN, OMIN) to (IMAX, OMAX) ,
O(I) = KI+a, where k is the Slope, a is the intercept
Eqn(1.1)
Non lineartiy: is a measure of the deviation of the actual transducer response from the
ideal straight line behavriour. It is expressed as N(I)
N(I)= O(I) – (KI+a)
Eqn(1.2)
O(I) = KI + a + N(I)
Eqn(1.3)
Figure 1.7 Non linear characterstics
Non linearty is usaully quanitfied interms of the maximum non linearity as percentage of
full scale deflection (f.s.d).
Max non linerity as =
% of f.s.d
N
X 100%
Eqn(1.4)
OMAX -OMIN
Usally the mathemtacial model for non linear transduer is given by
O(I)
Example:
=
ao +a1I+a2I2 + --- + amIm
Thermocouple E(T)
Eqn(1.5)
=38.74 + 3.319X10 2 T2 +2.071X10-4T3+---
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Non linearty behaviour makes Analysis and design for measurement and conrol purposes
difficult.
Threshold: when the input to a transducer is increasing from zero, there is a minimum
value below which no output can be detected .Threshold is defined as the minimum value
of the input that can be detected by the sensing element (tranducer)
Figure 1.8 Threshold and resolution
Resolution:When the input to a transducer is a slowly varying from non-zero arbitrary
value, the change in input is not detected until a certain input increment is exceeded.
This increment is defined as resolution.
Example: A digital multimter which is set to display 999.9V, the resolution is 0.1V
Hystersis: When the input to a transducer which is intially at rest is increaseed from zero
to fullscale and then decreased back to zero, there may be two output values for the same
input as shown in figure 1.9. this may be due sytem characterstics such as; damping
change, internal friction
Figure 1.9 Hysterisis characterstics
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Input imepdnace /loading effect: A transdeucr used in any measrument may normally
extract some energy from the measuring medium, there by disturbuing the value of the
measured quantity. This effect is called as loading effect.
Example: Voltmeter may be is used to measure volatge across a terminal of a
circuit. Thus due to the internal resistnace of the instrument, current may be
drawn from the media bieng measured this is called the loading effect.
Enviromental effects:
In general, the output depends not only on real input but also on some other
enviromental inputs such as ambient temprature, atmospheric pressure, relative humudity,
supply voltage e.t.c that causes additional non ideal characterstics.Thus equation must be
modified to account for deviations in environmental conidtions from standard.Two type
of enviroment input ares modifying and interferring inputs which causes slope and
intercept change.
1. Modifying input: causes the linear sensitivity of the element to change Thus if IM is
the deviation in a modfying enviromental input from ‘standard’ value (IM is zero at
standard conditions) . Then this produces a change in linear sentivity from K to
K+KM IM , where KM is the sesitivity of sensor or trasducer to modfying input
2. Intefering input: causes the intercept or zero bias of the elemetn to change. Thus of
II is the devation in an interfering enviromental input from standard value (II is zero at
standard condition). Then this produces a charge in zero bais from I at to I +K1 II
where K1 is the sesitivity of sensor or trasducer to interfering input. Km, KI are
refemed to as enviromental coupling constants or resistanties Ideal ones have both
km and ki zero
Figure 1.10 Enviromental effects
1.4.1.2 Statistical characterstics
By the vary nature of random errors, the uncertainity associated with any
measurment can’t be predetermined. The systematic way of speciying this uncertaintiy is
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the stastical method of analysis to determine the accuracy and precision( degree
repeatablity).
precision: is the degree of closness with which a given value may be repeatedly
measured. It is a measure of repeatability of sensor or transducer. when it is used to
meausre the same input at different instnaces the output may not be the same, thus the
deviation from the nominal output in absolute units or fraction of full scale is called
precision error or repeatablity error.
Accuracy: is the measure of the closness of the measured value to the true value.
Random signal system performance are studied interms of mean, mode, median,
varinace, standard deviation.
Errors in measurement
Measurement is the process of comparing an unknown quantity with an accepted
standard quantity. The measurement thus obtained is a quantitative measure of the socalled “true value” or “expected value”. Some factors that affect measurements are
related to the measuring instruments themselves. Others factors are related to the person
using the instrument. The degree to which a measurement conforms to the expected value
is expressed in terms of error of the measurement. Error in measurement (e) is defined as
the algebraic difference between the true value of the variable (or expected value) and the
measured value. Error in measurement in others words is the uncertainty of measured
values. The measured values are enclosed in the error bands, representing the precision of
measurement as shown in figure 1.11.
Figure 1.11 Illustration of error bands
Error may be expressed either as absolute error or as a percent of error
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Percent of error 
Absolute error
 100 %
True value
Eqn(1.5)
Percent of error 
True value - Measured value
 100 %
True value
Eqn(1.6)
It is frequently more desirable to express measurements in terms of relative accuracy
rather than error, or:
Relative accuracy  1 -
Absolute error
True value
Eqn(1.7)
If a measurement is accurate it must also be precise, that is, accuracy implies precision.
The reverse, however, is not necessary true, that is, precision does not necessary imply
accuracy. The precision of a measurement is a quantitative, or numerical, indication of
the closeness with which a repeated set of measurement of the same variable agree with
the average of the set of measurements. Precision can be expressed in a mathematical
sense, or quantitatively, as:
Precision  1 -
Where:
Xn - Xn
Xn
Eqn(1.8)
Xn = the value of nth measurement.
Xn = the average of the set of n measurements.
The accuracy and precision of measurement depend not only on the quality of the
measuring instrument but also on the person using the instrument.
Error, which has been described quantitatively, may be defined as the deviation of a
reading or set of reading from the expected value of the measured variable. Errors are
generally categorized under the three following major headings.
(a) Gross error: These errors are generally human errors using the instruments such as
misreading instrument, incorrect adjustment , improper application of instrument,
computation errors
(b) Systematic errors: due to short comings of the instrument and changes in external
conditions affecting the measurement. These errors are classified as instruments,
environmental effects, or observational errors.
12

Instruments errors: errors due to changes in the proprieties of the components
used in instrument such as friction in the bearing of the meter movement,
incorrect spring tension, improper calibration, or faulty instruments.
Instruments errors can be reduced by proper maintenance, use, and handling

of instruments.
Environmental errors: such errors are due to the environmental conditions in
which instruments may be used. Subjecting instruments to harsh environment
such as high temperatures, pressure, or humidity; strong electrostatic and/or

electromagnetic fields, may have detrimental effects, thereby causing errors.
Observational errors: errors introduced by the observer. Probably the most
common observational errors are the parallax error introduced in reading a
meter scale and the error of estimation when obtaining a reading from a meter
scale
(c) Random errors: These are errors that remain after the gross and systematic errors
have been substantially reduced, or at least accounted for. Random errors are
generally the accumulation of a large number of small effects and may be of real
concern only in measurements requiring a high degree of accuracy. Such errors can
only be analyzed statistically.
Limiting error: the accuracy of a measuring instument is usually specified by its
manufacture as % of full scale reading. thus if the user is not using the instrument in its
full scale the error will be higher than the percentage specified. The limiting error is
defined as the maximum deviation in the reading
For example: The accuracy of a thermometer to measure 0-1500C can be given as + 1%.
The limiting error is thus +1.50C. if the thermometer reads 600C, the maximum deviation
is +1.50C and in percentage it becomes +2.5% (i.e +1.50C/600C x100).
Silimiarly if readings from a number of instrumetns are used to compute or
determine some quantity, each instrumrts accuracy will ontributes reasonable error to the
overall limiting error.
Consider problem computing a quantity  from n independent measurment Ui
=f(Ui)= (U1, U2, … Un) where i=1 … n
Eqn(1.9)
The limiting errors of Ui‘s (+ Ui ) lead to an error of +  in the computed value of .
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+  = f(Ui+U1,U2+ U2 … , Un+Un)
Expanding Eqn(1.10 using Taylor series, we get
f (u1  u1 , u2  u2 ,.....,un  un )  f (u1 , u2 ,....un )  u1
Eqn(1.10)
f
f
f
 u2
 .....  un

u1
u2
un
2
2
1  2 2 f
2  f 
2  f
.....
 ...... Eqn(1.11)
u
u
u






 1
2
n
2
2
2
u2
u1
u n 
In actual practice, the limiting errors U1, U2, …e.t.c ar get are small quantities and
hence higher powers of U are neglible, Eqn(2.1) becomes
f (u1  u1, u2  u2 ,.....,un  un )  f (u1 , u2 ,....un )  u1
f
f
f
 u2
 .....  un
un
u1
u2
The absolute error is given by
  u1
f
f
f
 .....  un
 u2
un
u2
u1
Eqn(1.12)
Example: The power dissipated in a resistor of 50+ 1 is comupted by measuring the
current passing through the resultor using the formula P = I2R. The ammeter used has an
accuracy of + 1% and its full scale reading is 5A. Calculate the limiting error in the
computed value of power, when the ammeter reads 3A.
Solution
The computed power is given by P = I2R=450 watt
But The limiting error for ammeter is 0.05A and resistor is 1, thus the overall limiting
error in computed value can be calculted as
  u1
I 2 R
I 2 R
f
f
 R
 I
 u 2
R
I
u2
u1
= 2 RII  RI 2
= 24 watts
The percenatge error in computed value of power is

 100%  5.33%
P
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1.4.2 Dynamic Characteristics
The dynamic characteristic of a transducer refers to the performance of the
transducer when it is subjected to time varying input. The dynamic behavior
(performance) of a transducer is described by its mathematical model.
The general differential equation describing the dynamic behavior is given by
an
d n y (t )
d n 1 y (t )
d n  2 y (t )


 .........  a0 y (t )  b0 x(t )
a
a

n
2

n
1
dt n
dt n 1
dt n  2
Eqn (1.13)
Where n is the order of the differential equation, x(t) is input, and y(t) is the output
The order of the transducer is the highest value of the differential equation that decided to
which its dynamic behavior belongs. According to the value of n, transducers are
categorized as




Zero order transducer (n=0)
First order transducer (n=1)
Second order transducer (n=2)
Higher order transducer (n>2)
Because of the reason that real signals are either a function of time or frequency,
the dynamic characteristic of transducer is studied by the time and frequency response.
Practically transducers are subjected to inputs which are random in nature. But for
analysis purposes, test inputs are used to determine the dynamic behavior of transducers,
these are; Impulse input, Step input, ramp input, Sinusoidal input
The dynamic performance of measuring instruments gives insight in to speed of
response, Stability, and bandwidth.
1.4.2.2 Time response of transducers
(a) Zero order transducer
The input–output relationship of zero order transducer is given by
a0 y (t )  b0 x (t ) , i.e. when n=0
Eqn(1.14)
The Laplace transform of the equation (1.14) is
a0Y (s )  b0 X (s )  H ( s ) 
Y ( s ) b0

k ,
X ( s ) a0
Eqn(1.15)
15
Where H(s) is transfer function, and K is Static sensitivity
From the transfer function, it is clearly seen that the input-output relationship is expressed
using static sensitivity that is constant. Hence the zero order transducer represent ideal
dynamic performance i.e. the output varies the same as input, thus there is no time lag or
error associated with output response.
(b) First order transducer
The input-output relationship is given by
a1
dy (t )
 a0 y (t )  b0 x (t )
dt
Eqn(1.16)
The Laplace transform of the eqn(1.16) is given by
a1sY ( s)  a0Y ( s)  b0 X (s)
Y (s)( a1s  a0 )  b0 X (s)
H ( s) 
b
a
Y (s)
b0
k
, where k  0 ,   1


a0
a0
X ( s) a1s  a0 s  1
,
Eqn(1.17)
where  is called as time constant and k is the static sensitivity
From the transfer function, the first order transducer is described by two parameters
namely the static sensitivity and the time constant. Hence the response of the transducer
to any input is reasonably influenced by these values.
Example: consider the first order transducer which is subjected to step input as shown
below
x(t )  u (t )  X ( s ) 
1
s
Figure 1.12 step input
The output equation becomes
Y (s ) 
1 k
1
1
k
 k( 
x (s )  .
)
s  1
s s  1
s s 1

Eqn(1.18)
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The inverse Laplace transform of Eqn(1.18) is given by
y (t )  k (1  e
t

)u (t )
Eqn(1.19)
Figure 1.13 First order transducer response to step input
From the transducer response shown in figure 1.13, the output is not exact as the input
rather it is an exponential growth elapsing some time to reach the final or steady state,
which is dependent on the value of the time constant. Actually the output reaches 63.8 of
final value at t   , 98.2% of final value at t  4 , 99.3% of final value at t  5 .
Practically the transducer takes 4 or 5 to reach the final value or steady state value.
Thus the time constant describes the speed of response; its magnitude determines the
speed at which the output reaches the steady state i.e.


As its value decreases, the output reaches the steady state quickly
As its value increases the response become sluggish.
(c) Second –order transducer
The input-output relationship of second order transducer is given by
a2
d 2 y (t )
d 1 y (t )

a
 a0 y (t )  b0 x(t )
1
dt 2
dt1
Eqn (1.20)
The laplace transform of the Eqn (1.20) is given by
a2 s 2Y ( s )  a1sY ( s )  a0Y ( s )  b0 X ( s )
Y ( s)
b0
kwn2
,
H ( s) 


X ( s ) a2 s 2  a1s  a0 s 2  2wn  wn2
Eqn (1.21)
Where  n is called natural frequency,  is called as the damping ratio, and k is the static
sensitivity
The denominator s 2  2wn  wn2 is called the characteristic equation since it describes
characteristics of the system dynamic behavior. The system response depends on k,
 n and  values
K is the static sensitivity
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 n Describes frequency of oscillation, it is the frequency at which the output oscillates
 Describes the nature of oscillation
(a)   0 , undamped, The system acts like oscillator i.e. the output oscillates
continuously
(b) 0    1 , under damped , the system oscillations will die down as time elapses
also known as damped oscillation
(c)   1 , critically damped - the system response becomes no oscillatory
(d)   1 , over damped – the response is equal to first order oscillation with out any
oscillations.
Higher order transducers
In practice many transducers have higher order dynamics which can be described
by a higher order d.E. for engineering purpose analysis; they can be represented by either
first order or second order d.E. with certain linerzing assumptions. However when
accurate analysis is required the higher order it can be taken and solved.
18
1.4.2.2 Frequency response of transducers
Frequency response is defined as the steady state output of a transducer when it is
excited with sinusoidal input. The response of a transducer to a frequency input is
important characteristic since most of signals in the real world can be considered to be a
combination of signals of different frequencies and if a transducer is to represent a
variation of quantity realistically it should treat all the frequency components of the
signal equally i.e., the sensitivity should be the same for all frequency. The frequency
response (Fourier transform) can be obtained from the transfer function by replacing the
S=jw. The frequency response is represented with the help of two plots namely;
Amplitude ratio (AR) Vs frequency and Phase angle shift Vs frequency
The gain or Amplitude ratio (AR) is the ratio of output to input
AR = amplitude ratio = Output
Eqn(1.22)
Input
Figure 1.14 Frequency responses of transducers
The frequencies f1 and f2 are called cut-off or half power frequencies or else they are
the frequency at which the amplitude ratio is attenuated by – 3dB. The range of
frequencies of the input signal for which the instrument can responds without distortion.
Graphically correspond with the value of frequency from f1 to f2, where the attenuation
of input signal is -3 db (cut-off frequency) is called as Bandwidth (BW). Bandwidth is
term used to quantity the flat useful regions of the amplitude plot of the frequency
response, it is given by
BW=f2-f1
Eqn(1.23)
It may be noted that an ideal transducer is one whose AR is constant for all
frequencies. In other words the amplitude plot of the frequency response should be flat
for all frequencies.
19
1.5
General Model of transducer
Both dynamic and static characteristics together with general specifications are
very important to make adequate selection of measuring instruments. For example:
1 - Input range.
6 - Time constant.
2 - Output range.
7 - Dimensions and weight.
3 - Power supply requirements.
8 - Robustness.
4 - Precision.
9 - Cost
5 - Accuracy.
10 -Environmental condition of exploitation
and storage.
The performance of the measuring elements during the functioning of instruments under
real conditions is influenced by undesirable environmental effects (temperature, pressure,
humidity, etc). The mathematical output-input relationship (ideally an equation of straight
line in linear elements) is also affected. The environmental conditions generally don’t
produce affectation in the slope of the I-O characteristic, neither the linearity, but they
introduce an undesirable independent term in the input/output equation. For that reason it
is necessary to know the mathematical model of the measuring elements in order to
represent the effect of external factors, noises and interferences in appropriate manner.
The general equation of the ideal straight line is:
O=KI+a
Where:
Eqn(1.24)
O = output signal (e.g. current, voltage, resistance, etc)
I = input signal. (e.g. pressure, temperature, level, etc)
K = linear gain (static gain)
a = independent term
Rewritten the expression (9) we obtain the generalized model of the measuring element,
that is:
O = K I + a + N(I) + KM IM I + KI II
Eqn(1.25)
Where:
II = Interfering input. Represent the undesirable additional input signal to which the
measuring element unfortunately responds.
IM = Modifier input. Represent the alterations or modifications in the I/O relationships
(interferences)
20
N (I) = represents the non-linear mathematical function in nonlinear measurement
elements (For example, hysteresis)
a = Independent term. Correspond with the output signal obtained when the input variable
is zero. Graphically is the interception with the y-axis of the straight line in the I/O
relationships graphic.
KMIMI =Multiplicative error or modifier signal. Factor that has influence in the magnitude
of the output signal as result of modifier input (IM). It changes the slope of the I/O
characteristic.
Figure 1.15 shows the block diagram representation of the generalized model of the
measuring element by considering modifier and interfering inputs.
Figure 1.15 Generalized model
Example 1: Consider the strain gauge transducer shown figure 1.16 where the output
voltage of the Wheatstone bridge Vo is proportional to deformation e,
Figure 1.16 Strain gauge transducer
21
that is:Desired Input = e (deformation)
Desired Output = Vo (voltage)
Suppose that we can define the following interference signals:
1.
Electromagnetic fields: Produced by AC power lines of electric motors.
Electromagnetic fields induce voltages in the measurements circuits causing a variation
of the output voltage (Vo), so you can obtain variations in Vo when there is not
deformation.
2. Environment temperature: Temperature can cause variations in the resistance of the
strain gauge affecting the output voltage of the Wheatstone bridge. We can also see
variations in the Vo without deformation. In this case the temperature is considered as
modifier input.
In both cases is possible to obtain variations in the output voltage without any
variation in the strain gauge sensor. Variations in the supply voltage V to the Wheatstone
bridge can
be also
considered as
modifier
input,
because
it
affects the
Voltage/Deformation relationships.
By analogy with expression (1.25), the mathematical equation for this example is:
R = K e + a + KM T e + KI T
Eqn(1.26)
The Generalized model of strain gauge transducer is shown Figure 1.17 by blocks
diagram.
Figure 1.17 Block diagram of the generalized model of strain Gauge transducer
1.6
Identification of transducer models
Transducer mathematical models are nothing but the differential equation that
describes the dynamics of transducer. Identification is meant obtaining of the transducer
22
from the accessible inputs and outputs. Hence the mathematical model can be obtained
from time response or frequency response of the transducer.
A conventional method of obtaining transducer mathematical model requires
knowledge of components, their interconnection and the physical law governing their
functioning. Of course a number of assumptions are mandatory to derive the equation
representing the model. In many practical situations, the components used their numerical
values, behavior, interconnections and the physical laws may not be precisely known. In
such situations the model can be assumed to be black box whose inputs and outputs are
accessible for measurements and the transducer model can identified.
Example: a thermometer is suddenly dipped in a water bath kept at 100oc the following
data was generated
t( sec)
0
Temp (oc) 30
2
4
6
8
10
12
14
16
18
54
74.2
81
86
93
96
97
98.4
99
a. Identify the thermometer
Solution
The input is step 100 0c and the graph of the collected shows that the response of a 1st
order thermometer, thus the time constant and the sensitivity can be found using
Eqn(1.19) given as
y (t )  k (1  e
t

)u (t )
How ever there is an initial value of the thermometer, thus equation must be modified to
account for the initial value of the thermometer
The input is a step input of: 100-30=70u(t)
T (t )  k (1  e
t

)70u (t )  T (t  o)  k (1  e
lim Tt(t )  70k (1  e
t

t

)70u (t )  300 c Where T is temperature
)u (t )  300 c  1000 c  k  1
And from a step response, normally at time is equal to the time constant the response
reaches 63.2% of its final value which is 0.632x (100-30) =44.2, from the data or graph
30+44.2=74.2 is the value at t=4sec
Thus the transfer function of the thermometer is given by
T (t ) 
k
1

s  1 4 s  1
23
1.7
Noise and Interference
under real time conditions the performance of the measuring elements are
influenced by undesirable environmental effects (temperature, pressure, humidity, etc)
besides the measurement is significantly affected by the general random behavior of
system such as; random variation in the input (Signal) , random variation in the system
(white noise), deterministic disturbances in the system (interference Power frequency
interference, switching circuit (sparking), RF generating circuit (inductor).
The science of instrumentation engineering is mainly concerned with finding
ways of reducing the effects of noise and interference in the circuit
1. Shielding (isolation) : shielding or isolation is a technique which is applied to reduce
or avoid the interfering or modifying inputs (i.e Ii = 0, Im = 0).this is usally done
either by isolating the instrument from these environmental effects or shielding the
instrument with specially fabricated material having the property of isolating the
instrument from any interfering or modifying input.
2. Environmental insensitivity: another important technique is making the instrument to
be insensitive to any modifying or interfering input (i.e. Km = 0, Ki = 0)
3. Methods of opposing input: this is one of the most commonly applied technique in
which instruments make use a technique or means to cancel the effects of undesired
signals.
4. Filtering: filtering is a technique applied to signals so as to pass or reject frequency of
desire. Generally filters categorized as low pass, high pass, band pass, and band reject
filters. Often in instrumentation they are used to filter out undesired signal frequency.
5. Modulation: modulation can be thought of as a technique used change the frequency
content of the original signal so to transmit or reduce the effect of undesired inputs.
various ways of modulations can be applied in conjunction with appropriate filters to
eliminate the effects of noise of interference
6. Averaging : As noise signals are unpredictable averaging them may reduce the
magnitude
7. Correlation: A method used to detect the presence of any periodic signal buried in
random noise. It is used to obtain the relation of the signal and its time shifted signal
24
Problems
1. When two resistors of value 470+ 10%, and 330+ 5%, are connected in (a)
parallel and (b) in series . Calcuate the total (effective) resistance, taking errors in to
consideration and neglecting errors
2. The power factor in a circuit is determined by measuring current, voltage and power.
The reading obtained are 125V on 150V scale voltmeter of accuracy + 005%, 3A on
5A Scale ammeter of accuracy + 005%,225W on 500W wattmeter of accuracy +
0.25%
a. To what % accuracy can you guarantee that the determined power factor
b. For the possible error show the amount of contribution by each instrument.
3. Determine the response of first order transducer when subjected to ramp input X(t) =
t, sketch the response and determine the transient and steady state error
4. Industrial
a
mercury
in
glass
thermometer
is
described
by
the
equation
dh
 h  bT where h is height of the mercury in capillary and T is the temperature at
dt
the thermometer bulb. When the temperature is 25oc the height of mercury is the
capillary is 10mm.If the thermometer is immersed in a bath of boiling water
suddenly. How does the height in the capillary rise?
5. A thermometer at room temperature of 28oc is suddenly immersed in a steaming
water bath of 100oc. Calculate the time constant of the thermometer if it takes 30
seconds to show a reading of 96.4oc.
6. Obtain the response of a second order under damped transducer subjected to step
input. Formulate and define settling time, rise time, peak overshot from the response
7. Many commercial transducers are designed to have a damping ratio of 0.6 to 0.7,
why?
8. A second order transducer has a damping ratio of 0.5 and a natural frequency of
oscillation of 3 radians. The transducer is subjected to a step change in input of unity
what is the maximum output of the transducer.
25
CHAPTER TWO
SENSORS FOR MEASUREMENT AND CONTROL
2.1
Introduction
Sensing element, the first block diagram represented in the functional block
diagram of measurement system, is the basic and main building blocks of a measurement
system. Sensor is defined as a component, device or equipment that detects variation of
input or physical phenomenon and responds (or provides) equivalent electrical or non
electrical quantity corresponding to it.
Often a term transducer is also used for sensing element; literally transducer is
defined as a device that transforms one form or type of energy into another. Example: a
microphone, a photoelectric cell, an automobile horn, or bulb. Sensor is a transducer but
transducer is more than a sensor, if it is used for sensing application both terms are used
interchangeably.
2.2
Classification of sensors
The study of sensors is important, so as to


understand the basic principle operation of measuring instruments
analyze, design and identify measuring instruments
Sensors are used to detect physical quantities or variables of multidiscipline. This makes
the subject to broad, leading to different classifications for studying them. Hence there
are different ways of classifying sensors. In these teaching materials the classification of
sensors used is based on
1. The physical effect employed as resistive, inductive, capacitive sensors
2. The source of energy the used to provide an output as active and passive sensors
3. The physical quantity they convert as displacement sensor, temperature sensor,
speed sensor, pressure sensor e.t.c
26
2.2.1 Based On the Physical Effect Employed
When a physical effect employed on the sensing element causes change in any of
the physical parameter (quantity) that describes the sensing element then a mathematical
relation can be established between the physical effect and the sensing element that under
goes change of its describing parameter. For example: A strain gauge is a sensor that
when subjected to force or pressure its resistance changes
The very common variations of electrical quantities from sensing elements when
subjected to physical effect are
1. Variation in resistance
2. Variation in inductance
3. Variation in capacitance
2.2.1.1
Variation in resistance
Resistance is the character or ability of an element to oppose the flow of current.
Often the resistance of an element is given in either of formula;
R
l
A
 R (  , l , A) Where  is resistivity, l is length and A is cross-
sectional area
R(T )  R0 (1  (T  T0 ) Where R0 is resistance at T0
R(T )  R0 e
 (1 
1 1
)
T T0
Where R0 is resistance at T0
Mathematically the resistance is described as function of the different parameters. Thus if
any physical effect employed causes change in either of these parameter, then the
resistance value will vary in response to the very cause. Apparently a mathematical
relation can established between the physical effect and the resistance. Some of the very
common sensors which work based up on this principle are:




Potentiometer; for linear and angular displacement measurement,
Resistance thermometer( resistance temperature detectors( RTD), thermistor;
for temperature measurement
Strain gauge; for stress measurement such as; pressure ,force ,torque
Photoresistor (photoconductor) , for light intensity measurement
27
Potentiometer
A resistive potentiometer is a resistance wire wound on a former provided with a
sliding contact and excited by dc or ac voltage source. The movement of the slider can be
translational, rotational or combination of these two such as helical motion permitting
measurement of linear or rotational and combination of two. They are the most
commonly used type of sensor mainly for linear and angular displacement measurement
as shown in figure 2.1
Figure 2.1 potentiometer for (a) linear displacement and (b) angular
Displacement measurement
Linear displacement (fig 2.1a)
Angular displacement (fig 2.1b)
V0 
V0 
Vin . X
L
Eqn (2.1a)
V0
K
Eqn (2.2a)

eqn (2.1b)
V0  K  0
V0  K . X
X 
Vin . 0
0 
V0
K
eqn (2.2b)
, Where x and  0 are linear and angular displacement, and K is the sensitivity
The sensitivity is the rate of output voltage per input displacement and is given by
K
Vin . V0

L
X
Eqn (2.3)
The resolution of a potentiometer is the smallest change in displacement that can be
measured or identified. If the excitation is fixed then it is the smallest change in
resistance that can be identified by slider movement.
To measure physical parameters using a potentiometer, there are important factors
that need to be considered in designing or functioning of the instrument. These are;
28

Heat dissipating capacity: Potentiometers are designed on the basic of power rating
which is related directly to their heat dissipating capacity. The maximum input voltage
is limited on account of potentiometer heat dissipating capacity. The maximum input
voltage is limited on account of potentiometer heat dissipating capacity and is give by
Vin  PRT , where RT = Total Resistance of the potentiometer, P= Power

rating of a resistor (P= 5W at 200c)
The loading effect: Potentiometers are linear devices how ever their linearity is
affected by loading effect thus a care must be taken to avoid a loading effect due to
internal resistance of next stage elements such as; measuring instrument like

voltmeter(if used to measure the output voltage).
The resolution and sensitivity.
Exercise: Consider the Linear displacement measurement circuit of fig2.1a with input
voltage of 5-volt the output voltage is 2.5-volt. The total resistance element length is
100mm. The Linear displacement of an object causes the sliding contact to move such
that the output voltage 2.65-volt. Determine the displacement of the object and the
direction to which it moves.
Solution
Given V0  2.5,Vin  2.5, and L  100mm, the displacement X can be obtained from eqn
(2.1a) as
V0 
Vin . X
2.5v  100mm
X 
 50mm , thus the slider is at the middle
L
5v
If the output is now 2.65, it means that displacement to the up direction of figure 2.1a has
occurred, and the total displacement X is given by
X 
2.65v  100mm
 53mm
5v
The sensitivity K is given by
K
Vin . V0
=20

L
X
Exercise: Consider a voltmeter with internal resistance of 50KΩ is used to measure the
voltage across the terminal. How percentage of measured voltage is lost during full
displacement measurement if the total potentiometer resistance is 5KΩ.
29
Resistance thermometer
Resistance thermometers are temperature dependent resistors made from a conductive
or semiconductor element. Resistance temperature detectors (RTDs) and thermistor are
the most common transducers that vary their resistance when subjected to temperature
variation. They are passive transducers requiring an excitation source.
(a)
Resistance-temperature detector (RTD)
Resistance-temperature detector is a temperature sensing device whose resistance
increases with temperature, also referred as positive temperature co-efficient (PTC). As
they are almost invariably made of platinum, they are often called platinum resistance
thermometers (PRTs). Platinum RTD has a nominal resistance of 100 Ω at 00C as
shown in figure 2.2.
Figure 2.2 Resistance-Temperature Curve for a 100 Ω Platinum RTD,   = 0.0038
The mathematical relation between the resistance and temperature of Resistance
temperature detectors (RTD) is given by
R(T )  R0 (1  (T  T0 ) , where R0 is resistance at T0
Eqn (2.3)
Measurement using RTD
Measurement using RTD has to consider the following factors to over come inaccuracy

Since RTD is a passive resistive device, a current is required to pass through the
device to produce a measurable voltage. This current causes the RTD to heat
internally and hence causes as an error, this heating is called as self heating. It is
30
typically specified as the amount of power that will raise the RTD temperature by
10C, or 1 mW/0C. Self heating can be minimized by using the smallest possible
excitation current. The amount of self heating also depends heavily on the medium in
which the RTD is immersed. An RTD can self heat up to 100 times higher in still air

than in moving water
Lead wire resistance can also be a factor Because RTDs are low-resistance devices,
care must be taken in wiring and measuring RTDs to avoid errors caused by lead

resistance
Mechanical strain on the resistance thermometer can also cause inaccuracy
The factors cause significant loss of accuracy especially if manufacturers limits are not
respected, or the design does not properly consider the heat path; thus using small
excitation currents and adopting three- and four-wire, instead of two-wire, connections
can eliminate connection lead resistance effects from measurements as shown in figure
2.3 ; three-wire connection is sufficient for most purposes and almost universal industrial
practice. Four-wire connections are used for the most precise applications as shown in
figure 2.4.
Figure 2.3 Two-Wire and three-wire RTD with Wheatstone bridge
Figure 2.4 Four-Wire RTD Measurements
31
Resistance thermometers are constructed in a number of forms and offer greater stability,
accuracy and repeatability advantages and limitations
Advantages of platinum resistance thermometers:




High accuracy
Low drift
Wide operating range
Suitable for precision applications
Limitations:

RTDs in industrial applications are rarely used above 660 °C. At temperatures above
660 °C it becomes increasingly difficult to prevent the platinum from becoming
contaminated by impurities from the metal sheath of the thermometer. This is why
laboratory standard thermometers replace the metal sheath with a glass construction.
At very low temperatures, say below -270 °C (or 3 K), due to the fact that there are
very few phonons, the resistance of an RTD is mainly determined by impurities and
boundary scattering and thus basically independent of temperature. As a result, the

sensitivity of the RTD is essentially zero and therefore not useful.
Compared to thermistors, platinum RTDs are less sensitive to small temperature
changes and have a slower response time. However, thermistors have a smaller
temperature range and stability.
(b)
Thermistor
A thermistor is a type of resistor whose resistance varies significantly (more than
in standard resistors) with temperature. The word is a portmanteau of thermal and
resistor. Thermistors are widely used as inrush current limiters, temperature sensors, selfresetting over current protectors, and self-regulating heating elements.
Thermistors differ from resistance temperature detectors (RTD) in that the
material used in a thermistor is generally a ceramic or polymer, while RTDs use pure
metals. The temperature response is also different; RTDs are useful over larger
32
temperature ranges, while thermistors typically achieve a higher precision within a
limited temperature range [usually −90 °C to 130 °C].The resistance RT of a thermistor at
a temperature (T) can be expressed by the equation:
R(T )  R0e
( 
1 1
)
T T0
, Where R0 is resistance at T0 or
RT = a e k/T , Where a and b are constants of the material
Eqn (2.5a)
Eqn (2.5b)
Depending on the sign of k thermistors are classified into two types. If k is
positive, the resistance increases with increasing temperature, and the device is called a
positive temperature coefficient (PTC) thermistor, or posistor. If k is negative, the
resistance decreases with increasing temperature, and the device is called a negative
temperature coefficient (NTC) thermistor. Resistors that are not thermistors are designed
to have a k as close to zero as possible (smallest possible k), so that their resistance
remains nearly constant over a wide temperature range.
NTC thermistors are essentially semiconductor devices which behave as thermal
resistors having a high negative temperature coefficient. The sensors are made of sintered
ceramics, usually from mixtures of oxides of iron, manganese, nickel, cobalt, and cooper
in the form of beads or discs as shown in Figure 2.5b.The variation of the resistance with
temperature is non-linear, decreasing with temperature, as shown in figure 2.5a.
Figure 2.5 Thermistor resistance-temperature characteristic and types
As temperature sensors, thermistors normally operate as externally heated devices
wherein the changes in ambient or contact temperatures can be directly converted to
corresponding changes in voltage or current. Because of its smaller size, the device is
ideally suited for measuring temperature distributions or gradients. The measurement of
33
the change in resistance is carried out with a standard Wheatstone bridge network.
Application of thermistors

PTC thermistors can be used as current-limiting devices for circuit protection, as
replacements for fuses. Current through the device causes a small amount of resistive
heating. If the current is large enough to generate more heat than the device can lose
to its surroundings, the device heats up, causing its resistance to increase, and
therefore causing even more heating. This creates a self-reinforcing effect that drives

the resistance upwards, reducing the current and voltage available to the device.
PTC thermistors are used as timers in the degaussing coil circuit of CRT displays and
televisions. When the unit is initially switched on, current flows through the
thermistor and degauss coil. The coil and thermistor are intentionally sized so that the
current flow will heat the thermistor to the point that the degauss coil shuts off in


under a second.
NTC thermistors are used as resistance thermometers in low-temperature
measurements of the order of 10 K.
NTC thermistors can be used as inrush-current limiting devices in power supply
circuits. They present a higher resistance initially which prevents large currents from
flowing at turn-on, and then heat up and become much lower resistance to allow
higher current flow during normal operation. These thermistors are usually much
larger than measuring type thermistors, and are purposely designed for this

application.
NTC thermistors are regularly used in automotive applications. For example, they
monitor things like coolant temperature and/or oil temperature inside the engine and
provide data to the ECU and, indirectly, to the dashboard. They can be also used to

monitor temperature of an incubator.
Thermistors are also commonly used in modern digital thermostats and to monitor the
temperature of battery packs while charging.
Exercise: A platinum resistance thermometer (RTD) has a resistance of 100 at 25oc and
its temperature coefficient of resistance at 25oc is 0.00392/oc.
a. find the resistance at 65oc
b. if the thermometer has a resistance of 150oc find the temperature
34
Strain gauge
Strain is the amount of deformation of a body due to an applied force. More
specifically, strain (ε) is defined as the fractional change in length, as shown in Figure
2.6. A strain gauge takes advantage of the physical property of electrical conductance and
its dependence on not merely the electrical conductivity of a conductor, which is a
property of its material, but also the conductor's geometry. When an electrical conductor
is stretched within the limits of its elasticity such that it does not break or permanently
deform, it will become narrower and longer, changes that increase its electrical resistance
end-to-end. Conversely, when a conductor is compressed such that it does not buckle, it
will broaden and shorten changes that decrease its electrical resistance end-to-end.
Figure 2.6 Strain gauge
Strain gauges find wide application for measurement of stress (pressure or force) and are
hence refereed as strain gauges. From the measured electrical resistance of the strain
gauge, the amount of applied stress may be inferred. A fundamental parameter of the
strain gauge is its sensitivity to strain, expressed quantitatively as the gauge factor (GF).
Gauge factor is defined as the ratio of fractional change in electrical resistance to the
fractional change in length (strain):
GF 
R
R
L
L
R

R
Eqn (2.5)
The Gauge Factor for metallic strain gauges is typically around 2.
35
Photoresistors / Photoconductors
Photoresistor, light dependent resistor (LDR) or cadmium sulfide (CdS) cell is a
resistor whose resistance decreases with increasing incident light intensity. It is also
referred to as a photoconductor. Often it is made of a high resistance semiconductor. If
light falling on the device is of high enough frequency, photons absorbed by the
semiconductor give bound electrons enough energy to jump into the conduction band.
The resulting free electron (and its hole partner) conduct electricity, thereby lowering
resistance.
Figure 2.8 Resistance Vs illumination graph of photoresistor
Photoresistors are available in many different types. Inexpensive cadmium sulfide cells
can be found in many consumer items such as camera light meters, street lights, clock
radios, alarms, and outdoor clocks. They are also used in some dynamic compressors
together with a small incandescent lamp or light emitting diode to control gain reduction.
Lead sulfide (PbS) and indium antimonide (InSb) LDRs (light dependent resistor) are
used for the mid infrared spectral region. Ge:Cu photoconductors are among the best farinfrared detectors available, and are used for infrared astronomy and infrared
spectroscopy.
36
2.2.1.2
Variation in Capacitance
Capacitance is the ability of an element to store electric charges in its electric field.
Basically there are two capacitor models; the parallel plate and coaxial cable
The capacitance value is given by
Parallel plate C 
Coaxial cable C 
0A
d
,
2l
ln( b / a)
Eqn (2.7a)
Eqn (2.7b)
A change in the parameters expressing the capacitors due to any physical effect employed
will cause a change in capacitance. The parallel plate capacitor is used to measure some
physical parameters such as displacement or density of some materials, thickness as
shown in figure 2.9.
Figure 2.9 Parallel plate capacitor
Capacitive displacement sensors “are non-contact devices capable of high-resolution
measurement of the position and/or change of position of any conductive target”. They
are also able to measure the thickness or density of non-conductive materials. Capacitive
displacement sensors are used in a wide variety of applications including semiconductor
processing, assembly of precision equipment such as disk drives, precision thickness
measurements, machine tool metrology and assembly line testing. These types of sensors
can be found in machining and manufacturing facilities
37
Exercise: capacitors are also used for level sensing such as coaxial cable as shown in
figure 2.10. Determine the capacitance as a function of height h.
Figure 2.10 Coaxial cable level sensor
Solution: Both the liquid (having relative permittivity er) and air , form two capacitors
connected in parallel thus the total capacitance as function of height h becomes
2.2.1.3
Variation of inductance
Inductance is the ability of an element to store electric energy in its magnetic
filed. The inductance of a coil winding with N number of turn in a material of
permeability  is given by:
L
N 2 N 2 A

, where l is the length and A is the area of the magnetic material

l
Some of sensor types which provides change of inductance value corresponding to the
physical effect employed are



Inductance force sensor, torque sensor, Inductance displacement sensor e.t.c
Linear variable differential transformer (LVDT)
Magnetostrictive sensors
38
Inductance displacement sensor, force sensor
The figure 2.10 shows some of the inductance sensors which appear in different form to
sense displacement or force.
Figure 2.10 Inductance displacement sensors
Linear variable differential transformer (LVDT)
LVDT is the most commonly used sensor for displacement measurement
applications. It is a transformer consisting a single primary winding and two secondary
windings wound on a tubular ferromagnetic former shown in figure 1.7a.The secondary
winding is connected in such a way that the output is the difference of them. With the
core moving V1 and V2 change with core position X. The output voltage and the
displacement have a linear relationship as shown in figure 1.7c. An iron core slides
within the tube and therefore affects the magnetic coupling between the primary and the
39
two secondary. When the core is in the center, the voltage induced in the two secondary
winding is equal. When the core is moved in one direction from center, the voltage
induced in one winding increase and that in the other is decreased. Movement in the
opposite direction reverses this effect.
Figure 2.11 Linear variable differential transformer (a) Construction
(b) Schematic diagram (c) Output voltage vs displacement.
Because the sliding core does not touch the inside of the tube, it can move without
friction, making the LVDT a highly reliable device. The absence of any sliding or
rotating contacts allows the LVDT to be completely sealed against the environment.
Another One advantage of the LVDT over the inductive bridge-type transducer is that it
produces higher output voltage for small changes in core position.
LVDT are commonly used for position feedback in servomechanisms, and for
automated measurement in machine tools and many other industrial and scientific
applications. The frequency is usually in the range 1 to 10 KHZ.
Magnetostrictive sensor
Ferromagnetic materials like iron, nickel, 68 permallay e.t.c change their magnetic
permeability under mechanical stress. This is known as villari effect the permeability can
increase or decrease depending on the material and the type of stress (compression,
tension or torsion) this property can be made use of, in constructing transducers to
convert a stress to variation in indication. They are used for measurement of force,
torque, up to large tons.
40
2.2.2 Based the energy they used to provide an output
Sensors or transducers are also classified as active or passive sensors based on the energy
they use as passive and active sensor
2.2.2.1 Passive sensors
Passive sensors are those sensors which consume or require electrical energy to
provide an output Example: R, L, C e.t.c so far discussed sensors
2.2.2.2 Active sensors
Active sensors are those which don’t consume rather provide electrical energy
corresponding to input



Thermoelectric (Thermocouple) V(T) temp
Solar cells (photovoltaic cells)
I(E) illumination
Piezoelectric crystals ----
I(F), I(P) or V(P)
Thermoelectric (Thermocouple)
Thermoelectricity is the relationship between the temperature of a substance and
electrical energy. If two different dissimilar metals A and B are joined together and,
subjected to temperatures at their junction, there is a potential difference in electrical
potential across the junction called the contact potential and vice versa
Thermoelectric principles


Change in temp lead to voltage generation
Application of voltage leads to change in temp
The generation of voltage is by see back effect: when any conductor is subjected to a
thermal gradient, it will generate a voltage. This is now known as the thermoelectric
effect or seebeck effect. Using a dissimilar metal to complete the circuit creates a circuit
in which the two legs generate different voltages, leaving a small difference in voltage
available for measurement. That difference increases with temperature, and is between 1
and 70 microvolt per degree Celsius (µV/°C) for standard metal combinations.
The voltage is not generated at the junction of the two metals of the thermocouple but
rather along that portion of the length of the two dissimilar metals that is subjected to a
temperature gradient. Because both lengths of dissimilar metals experience the same
temperature gradient, the end result is a measurement of the temperature at the
thermocouple junction.
41
This contact potential depends on the metals A and B and the temperature T0C of the
junction. The voltage generated is non linear and is given as a power series of the form
ETAB  a1T  a2T 2  ....  anT n , Where a, a2… an constants of the metals
Eqn(2.8)
Thermocouple is closed circuits consisting of two dissimilar metals joined at two ends,
and generate a voltage as function of junction temperatures (T1 and T2). The dissimilar
metals used are alloys, for example , a J-type thermocouple has one iron conductor and
one constantan (a copper-nickel alloy) conductor.
Figure 2.12 J-Type Thermocouple
Thermocouple is one of the most frequently used temperature transducers which are very
rugged, inexpensive, providing accurate measurement over a wide temperature ranges.
Often they generate a very low voltage, but they can also connected in series to form the
so called thermopile. They are widely used for temperature measurement ranging from
home, hospitals to industry, in the ranges from -3000C to 20000C (as summarized in table
2.1). Some of their applications are



in industries, such as furnace, measuring temperature of liquid metals and even in
nuclear reactors,
in medical applications such as monitoring internal temperature during operation,
To monitor or record temperature with data acquisition systems or data loggers
Table2.1. Thermocouple voltage output extremes (mV)
Thermo-
Conductor
Temperature
o
Voltage Range
Seebeck Coeff.
couple type
Positive
Negative
Range ( C)
(mV)
(μV/ oC)
E
Chromel
Constantan
-270to 1000
9.835 to 76.358
58.70 at 0฀C
J
Iron
Constantan
-210to 1200
-8.096 to 69.536
50.37 at 0฀C
K
Chromel
Alumel
-270to 1372
-6.548 to 54.874
39.48 at 0฀C
T
Copper
Constantan
-270to 400
-6.258 to 20.869
38.74 at 0฀C
S
Ptatinum-10% Rhodium
Platinum
-50to 1768
-0.236 to 18.698
10.19 at 600฀C
R
Platinum-13% Rhodium
Platinum
-50to 1768
-0.226 to 21.108
11.35 at 600฀C
42
Thermocouple laws
To ensure proper installation and measurement often it is necessary to consider
the laws governing thermocouples
Law 1: Law of homogeneous material
A thermoelectric current cannot be sustained in a circuit of a single homogeneous
material by the application of heat alone, regardless of how it might vary in cross section.
In other words, temperature changes in the wiring between the input and output do not
affect the output voltage, provided all wires are made of the same materials as the
thermocouple. The voltage generated is function of junction temprature T1 and T2 and
independent of the temperatures of the wires connecting the junction.
Law 2: Law of intermediate materials
If a third metal is inserted in between, provided that the temperature of the introduced
metal is the same, emf generated is the same. The algebraic sum of the thermoelectric
emfs in a circuit composed of any number of dissimilar materials is zero if all of the
junctions are at a uniform temperature. So if a third metal is inserted in either wire and if
the two new junctions are at the same temperature, there will be no net voltage generated
by the new metal.
One application of this law is that a voltmeter can be connected to measure voltage.
Law 3: when a third metal is introduced at the junction provided that the junction
temperature of the introduced metal is the same emf generated is the same.
Advantage of this law is that voltmeter can be connected, and the junctions’ can be either
soldered or brazed
43
Law 4: Law of intermediate metal
The emf generated by two dissimilar homogeneous materials AB
at junctions
temperature T1 and T2 is equal to the sum of emf generated by a third metal introduced
AC and CB at the same junction temperature pf T1 and T2
Law 5: Law of successive or intermediate temperatures
If two dissimilar homogeneous materials produce thermal emf1 when the junctions are at
T1 and T2 and produce thermal emf2 when the junctions are at T2 and T3 , the emf
generated when the junctions are at T1 and T3 will be emf1 + emf2,provided T1<T2<T3.
.
Measuring temperature with thermocouples
To measure a thermocouple seebeck voltage, you cannot simply connect the
thermocouple to a voltmeter or other measurement system, because connecting the
thermocouple wires to the measurement system creates additional thermoelectric circuits.
Thermocouples have some special signal conditioning requirements, including coldjunction compensation, amplification, linearization, filtering, and even isolating because
thermocouples generate a very low-level of output voltages. You should use as large a
gain as possible for the best resolution and noise performance.
Thermocouples generate low-voltage signals, typically in the millivolt range. For
example, a J-type thermocouple outputs –8.1 mV at –210° C and 21.8 mV at 400° C.
Therefore, you must amplify the signal to accurately read and digitize it.
When using thermocouples, you should be aware of several measurement issues
such as the following:




Cold-junction compensation
Nonlinear data
Low-voltage signals
Noisy signals
44
Cold-Junction Compensation
Thermocouples measure the temperature difference between two points, not
absolute temperature. To measure a single temperature one of the junctions—normally
the cold junction—is maintained at a known reference temperature, and the other junction
is at the temperature to be sensed
Thermocouples require some form of temperature reference to compensate for
these unwanted parasitic thermocouples. The term cold-junction comes from the
traditional practice of holding this reference junction at 00C in an ice bath.
Figure 2.13. Traditional temperature measurement with reference junction held at 0oC
In Figure 2.13, the measured voltage depends on the difference in temperatures T1 and
Tref; in this case, T ref is 0oC. Notice that because the voltmeter lead connections are the
same temperature, the voltages generated at these two points are equal and opposing.
Therefore, the net voltage error added by these connections is zero. Under these
conditions, if the measurement temperature is above 0oC, a thermocouple has a positive
output; if below 0oC, the output is negative. When the reference junction and the
measurement junction are the same temperature, the net voltage is zero.
Although an ice bath reference is accurate, it is not always practical. A more
practical approach is to measure the temperature of the reference junction with a directreading temperature sensor and subtract the parasitic thermocouple thermoelectric
voltage contributions. This process is called cold-junction compensation. You can
simplify computing cold-junction compensation by taking advantage of some
thermocouple characteristics such as inserting an extra lead in the isothermal region as
shown in figure 2.14.
45
Figure 2.14. Inserting an extra lead in the isothermal region
There are two techniques for implementing cold-junction compensation–hardware
compensation and software compensation. Both techniques require that the temperature
at the reference junction be sensed with a direct-reading sensor. A direct-reading sensor
has an output that depends only on the temperature of the measurement point.
Semiconductor sensors, thermistors, or RTDs are commonly used to measure the
reference-junction temperature. For example, several industrial terminal blocks include
thermistors that are located near the screw terminals to which thermocouple wires are
connected.
Hardware Compensation
With hardware compensation, a variable voltage source is inserted into the circuit to
cancel the parasitic thermoelectric voltages. The variable voltage source generates a
compensation voltage according to the ambient temperature, and thus adds the correct
voltage to cancel the unwanted thermoelectric signals. When these parasitic signals are
canceled, the only signal that is measured is the voltage from the thermocouple junction.
The major disadvantage of hardware compensation is that each thermocouple type must
have a separate compensation circuit that can add the correct compensation voltage,
which makes the circuit fairly expensive. In hardware compensation, often it also
necessary to use either of the following, so as to minimize inaccuracy.
1. Use a shielded cable from the signal conditioning chassis to the plug-volt meter
device and apply extra shielding to your thermocouple wire.
2. Use low-pass noise filters to attenuate high-frequency noise. Some signal
conditioning cards include 1 Hz low-pass filters on every channel to maximize
rejection of 50 and 60 Hz noise.
3. Use the appropriate controllable gain instrumentation amplifiers to amplify the
46
signal and increase the noise immunity.
Generally with thermocouple measurements, the possible sources of error include
compensation, linearization, measurement, thermocouple wire, and experimental errors.
Solar cells or photovoltaic cells
Solar cells are semiconductor devices which produce electric energy when
illuminated; usually silicon element is used as solar cell. Often DC Voltage is generated
that is proportional to the incident light. Photovoltaic cells are used for production of
electrical energy and as sensing elements they are also used for sensing light light
intensity
Piezo electric sensors
Piezoelectric crystals are special materials which produce charge distribution when
they are subjected to an external pressure or force. These is based on the natural
phenomenon of certain non-metals and electronic compounds, materials like Quartz,
Rochelle Salt, barium titanate develop electric charge when subjected to or force.
The effect is reversible i.e when a charge is applied they are deformed. This
phenomenon is known as piezo electric effect. “Piezo” is a Greek word meaning for or
pressure. The mechanical deformation producing electric charge is basis of many
instruments for measuring acceleration, force and torque.
Figure 2.15 Piezoelecric transducer
Figure 2.15 shows a piezo electrcic transducer where the mass is held by a screw against
the crystal. When the mass accelerates, it applies a force on the crystal. A charge then
occurs on the crystal, in response to the acceleration. Crystals such as sodium potassium
chlorate (rodhium salt) are used because they have high mechanical strength and are
also relatively inexpensive sensor.
47
2.2.3 Based on the quantity they convert
Sensors are also classified based on the quantity they convert such as
displacement sensor, torque sensors, force sensors, optical sensor, proximity sensors,
temperature sensors, speed sensors, level/flow sensors, acceleration/vibration sensors
e.t.c
2.2.3.1 Optical sensors
Optical sensors are one of the most widely used sensing elements that uses the
effect of light (visible or infrared) for sensing or detection of various physical parameters.
Basically they consist of light sources and detectors as shown in figure 2.16. The Light
sources are often light emitting divides (LED’s) and light detectors which is silicon
phototransistors (a semiconductor device that biases when light fall on it) a.
Figure 2.16 Optical sensor
Often optical sensors produce information in digital form hence some times referred
as digital sensors. This is useful because a digital output is compatible with computers
and other digital electronic systems. One of their importance’s lies in the absence of
contact with the physical parameter being detected. Optical sensors have a wide variety
of application in sensing various physical parameters being measured such as; proximity
sensing of object, alarm systems, isolation, control application such as hand dryer and
water control in toilet.
One of the various applications of optical sensors is for angular displacement
measurement in which linear or angular displacement varies the transmission of light
from a source to detector there by providing a means for sensing the physical parameter.
An optical shaft is encodes the angular displacement in to digital form. This is useful
because a digital output is compatible with computers and other digital electronic
systems. There are two main types of encoder devices, the incremental encoder and the
absolute encoder.
48
Incremental encoder
The incremental encoder produces an output signal showing that some
displacement of a shaft has taken place. Further output signals are counted and from these
the angular displacement of a shaft can be measured, relative to some arbitrary datum.
Figure 2.16a shows a typical incremental shaft encoder. The incremental shaft encoder
consists of a disc rigidly attached to the shaft whose displacement is to be measured. The
disc has a number of equally spaced slots, or windows, through which a beam of light can
pass. The rest of the disc is opaque. A light source, consisting of two light emitting
diodes (LED’s), is aligned with the disc. If the light from the LED’s is uninterrupted, it is
detected by the light detectors.
Figure 2.16 (a) Optical incremental shaft encoder (b) Incremental shaft encoder disc
As the shaft rotates, the light shines through the equally spaced windows in the disc, and
is blocked by the opaque sections of the disc. Hence a pulsed light output from the light
detectors is produced. The LED’s and detectors are arranged so that, as the disc rotates,
the phase difference between the pulse trains from the detectors shows the direction of
rotation. The number of pulses detected is proportional to the angle through which the
shaft and disc travel.
The angular displacement of the shaft can be determined relative to an arbitrarily
selected starting point. The resolution depends on how may windows if contains, the
more windows the disc has, the higher the resolution.
Resolution=
3600 or 2
eqn (2.9)
Number of windows
The number of windows on the rotating disc can vary from 60 to well over l000 with
multi-tracks, allowing very good resolution to be achieved. Typical resolutions of optical
incremental shaft encoders are 0.0034 radians (0.2°) to 0.102 radians (6°).
49
Absolute encoders
The absolute encoder produces an output signal which shows the total
displacement of a shaft from a null position. Figure 2.17a shows a typical optical absolute
shaft encoder. It differs from the incremental encoder in that the output signal it produces
is in binary or coded form. This provides an absolute displacement of the shaft.
Figure 2.17 (a) Absolute encoder, (b) Binary absolute encoder disc
A rotating disc, with a number of concentric tracks, is attached to the shaft. A light source
consisting of LEDs is aligned with the tracks of the disc as shown in figure 2.17(b). A
light detector is similarly aligned with the disc and beams to detect the light which passes
through the disc. A “closed” window, which is opaque and so prevents light from the
LED’s reaching the detector, represents a binary '0'. An “open” window, which allows
light from the LED’s through to the detector, indicates a binary '1'. The combinations of
open and closed windows follow a binary sequence from 0 to 2n-l, where n is the number
of tracks.
The binary absolute shaft encoder disc shown in Figure 2.17b has four tracks and
consequently there are four bits in each binary number. The numbers of positions which
can be detected are 16 (24), since the binary sequence runs from 0 to 15 (0 to 24-1).
The resolution is given by
Resolution=
2 or 3600
eqn(2.10)
Number of windows in the disc (16)
50
In this case 16 binary numbers are 0.393 radians or 22.5°. If we use a rotating disc with
eight tracks, giving eight bits in each binary number, the number of positions that can be
detected is 28 = 256. The resolution is then 0.024 radians or 1.41°.
In practice there are problems with this type of binary absolute encoder. The exact
alignment of the window edges in each track is difficult to achieve, and consequently
errors are sometimes introduced. These errors occur at the boundaries between windows
and, in some cases, it is possible to make a 180oerror in determining the shaft angular
displacement. A major disadvantage of the binary absolute encoder is that on many
occasions more than one window will change condition for one increment. This is
because of the nature of the binary number system. Examples of this are;
Example
0011
to
0100
3
to
4
0111
to
1000
7
to
8
The most significant change is from 1111 to 0000 (15 to 0 in base 10). Hence if the
absolute encoder system misreads one window, it can lead to serious errors in position
measurements. To overcome this, the Gray Code (named after Frank Gray of Bell
Laboratories) was developed. This produces a sequence where only one 'bit' or 'window'
changes condition between consecutive positions.
Table 2.2 Gray code and binay code sequence
Decimal
Gray code
binary code
1
0000
0000
2
0001
0001
3
0011
0010
4
0010
0011
5
0110
0100
6
0111
0101
7
0101
0110
8
0100
0111
Angular optical encoders have applications in numerically controlled machines,
such as computer controlled lathes or millings machines. They are also used in robotics
and positioning systems. A common application of relative optical encoders is in the
computer mouse.
51
2.2.3.2 Proximity sensors
Proximity measurement refers to indicating whether an object is present with in a
defined area close to the sensor, and from it angular or linear displacement, speed and
velocity, acceleration can be measured. Proximity sensors are also used to measure
rotation by indicating where a point on a shaft is present, the sensor does sense the point
and using the relation with respect to time, the displacement and revolution can be
determined.
Proximity sensors are widely used in manufacturing, often monitoring the
position, detecting presence or non-presence of components doing assembly, and they are
also used to count products, for example items on a conveyor belt to be palled in a set
size of box. Some of the types of proximity sensors are Micro switches, Variable
reluctance proximity sensor, and Reed switch
Variable resistance proximity sensor (magnetic pickups)
The sensor contains of a small electromagnetic coil held in a protection sassing,
mounted in a fixed position close to the shaft. It can detect the presence of a ferrous metal
Figure 2.18 Variable reluctance proximity sensors (magnetic pickups)
The figure shows variable resistance proximately sensor detecting the immediate
presence of a gear tooth. When the tooth passes close by the pick up, an output voltage is
produced caused by variations in its magnetic field. The output is a pulse and may be
52
displayed on a voltage or current meter. Typical variable resistance proximity sensor can
sense up to 2.5 mm. some of the very common applications are crank angle sensing,
ignition timing of engine, in disk drives in computers, speed sensing in motors
Advantage of these sensors is that they can be made very small and so deployed where
other sensors may not fit. Since these devices have to be close to the physical parameter
to be measured, they suffer from unwanted signals or noise.
Reed Switch sensor
Reed Switch consists of two small ferromagnetic reeds hermetically sealed (air tight)
in a glass tube. The reeds are thin, and flexible and as they are ferromagnetic they
become magnetized in the presence of a magnetic a magnetic felid. The reeds may have
normally open or change over contacts depending on the application
The angular rotation of a shaft can be determined using a reed switch by embedding
or attaching a permanent magnetic to a shaft and the reed switch is fixed near the shaft, so
that when the shaft rotates the magnet passes close by. As the magnet passes, the reed
switches make or break a circuit and produces a pulsed output. These processes can be
used to determine angular displacement, velocity or acceleration using approximate
signal conditioning. Reed switches have application speed and distance measurement of
bicycle, automatically breaking of circuits to shut a machine off when a guard is
removed, and in switches on doors and windows for burglar alarms.
Hall Effect sensor
A Hall Effect sensor is a transducer that varies its output voltage in response to
changes in magnetic field. Hall sensors are used for proximity sensing, positioning, speed
detection, and current sensing applications.
In its simplest form, the sensor operates as an analogue transducer, directly
returning a voltage. When a current carrying conductor or semiconductor is acted by a
magnetic field positioned at right angles to it, the electrons passing through the conductor
are acted up on by a force which concentrates them more to one side of the conductor
than the other. This variation in current distribution creates an emf across the conductor.
The generated emf is proportional to the strength of the magnetic flux and can be used as
a principle for proximity sensing.
53
Figure 2.19 Hall Effect sensors
The generated transverse voltage or hall voltage is given by
VH 
K H BI
,
t
eqn (2.11)
where VH is hall voltage, B is magnetic field, I is the current, t is the thickness
They are used for measurement of current, power and as switches for different purposes.
For example current meters; electricity carried through a conductor will produce a
magnetic field that varies with current, and a Hall sensor is used to measure the current
without interrupting the circuit. Typically, the sensor is integrated with a wound core or
permanent magnet that surrounds the conductor to be measured.
Frequently, a Hall sensor is combined with circuitry that allows the device to act
in a digital (on/off) mode, and may be called a switch in this configuration. They have
wide applications in industries, and consumer equipment such as printers use them to
detect missing paper and open and for high reliability keyboards.
Micro switch
These are mechanical switches that operate with very little movement of operating
plunger so are sensitive and particularly suitable for use as direct contact proximity
sensors. The contacts may be normally open, close or change over. This opening or
closing contacts is used to make or break and circuit.
54
2.2.3.3 Pressure sensors
Both pressure and stress have a similar basic definition. i.e, they are a measure of
a force acting on an area, the difference is however;


The force acting by flowing air or fluid is usually referred to as pressure.
The force caused by or acting on a solid object is usually referred to as stress.
Because of the weight of air, everything on the surface of the earth is under pressure
which is known as atmospheric pressure. The standard value of atmospheric pressure at
sea level is 1.01325 X 105 N.m2. The term gauge pressure is used for measurement,
which used atmosphere at its zero points. Absolute pressure is then the sum of gauge
pressure and atmospheric pressure.
There are so many types of sensor used for measurement of pressure these are;




Liquid manometers
Barometers
Elastic pressure sensor
Capacitive sensors, piezoelectric sensors , strain gauges
Manometers
Technically a manometer is any device used to measure. However, the word
manometer is commonly used to mean a pressure sensor which defects change by means
of liquid in tube. Manometers are differential pressure sensors. A differential pressure
sensor measures the difference between a pressure being applied to it and a reference
pressure (often atmosphere)
A barometer is a pressure sensor used to measure atmosphere pressure. Hence they
have to be sensitive enough to measure absolute points. They are mainly used for
metrological purposes
Elastic pressure sensors
Elastic sensors are so called because something flexes, stretches, or temporarily
deforms when a pressure is being applied. Elastic sensors initially convert pressure in to a
displacement. This allows displacement sensors to be used to condition the output signal
from the pressure sensor. Some pressure sensors are referred to by the method they use to
measure this displacement such as piezoelectric and capacitive pressure sensors. When
55
electronic displacement sensors are used, the method of detecting charge is usually by
means of diaphragm. Elastic pressure sensors measure differentially.
Figure 2.20 Elastic pressure sensors
2.2.3.4 Temperature measurement
Temperature is the degree of hotness of any body, substance or medium compared
with another. The Measuring temperature is usually to compare the degree of hotness to a
fixed reference point using a temperature sensor. Often there are two thermodynamic
scales which are used for temperature measurement namely; Kelvin thermodynamics and
scale Celsius thermodynamic scale. The Kelvin thermodynamics scale (referred with unit
Kelvin or K) uses absolute zero as its reference point and the Celsius thermodynamic
scale (referred with unit degree Celsius, oc) uses the freezing(0oc) and the boiling
point(100oc) of water as a point of references. The absolute zero is the lowest temperature
any substance can reach in other words molecules of substance contain no heat energy at
absolute zero referred as 273.15K.
Commonly temperature measurement device are called thermometer and
sometimes pyrometer if they measure high temperature. The most commonly used types
of temperature measurement devices work based on or by means of
56




Liquid expansion ; mercury in glass thermometer
Metal expansion; bimetallic strip
Thermoelectricity; thermocouple
Electrical resistance (resistance thermometer detectors(RTD) , Thermistor
Mercury in glass thermometer
Liquid expansion thermometer work on the principle that certain liquids change
their in volume (expand) by large amount when they are subjected to temperature. The
most commonly used type of liquid is mercury. The mercury-in-glass thermometer shown
in figure 2.21, widely used in laboratory and industry, is one of the simplest temperature
measuring devices.
Figure 2.21 Mercury in glass thermometer
It utilizes the volumetric expansion of mercury with temperature as a means of indicating
temperature. Above the liquid is gas or vacuum which compress when the liquid expands.
Other than mercury, alcohol or synthetic oils are also used. Mercury in glass thermometer
have typical a temperature range of approximately 238k to 783 k. Alcohol in glass
thermometer 193k to 343 k. The mercury in glass thermometer is widely used especially
in medical and veterinary applications for measurement of human body, air temperature
often for domestic applications. To ensure safety, strength and as well read remotely, for
industrial applications often the liquid in metal instead of glass thermometer is used.
Bimetallic strip
The expansion property of materials when subjected to temperature is also used
for measurement of temperature. The bimetallic strip is a device made of two dissimilar
metals strips having different expansively (called coefficient of expansion) which are of
the same length, connected and secured together by riveting, welding or bonding, and the
expansively of a material is the fraction of its inguinal dimension by which the substance
57
expanses for degree rise in temperature. The two metals which form the strip are usually
an iron-nickel alloy with a very small expansively, and a metal with high expansively,
such as brass.The bending of the bimetallic strip is due to the different coefficient of
expansion of the metals. Brass has high expansibility hence expands significantly more
than the iron-nickel alloy for the same temperature rise as shown in figure 2.22.
Figure 2.22 Bimetallic-strip
The bimetallic strip have application as thermometer, thermostats (a device which
keeps a system or a substance at a constant temperature) and automatic flashing units for
motor vehicle direction indictors and automatic flashing unit for advertising signals,
Bimetallic thermometer
The bimetallic thermometer is commonly used wherever the industrial mercuryin-glass thermometer is employed. The construction of a bimetallic-strip element
provides a rugged yet accurate and simple device for the indication of temperature. A
bimetal is composed by two strips of metal having a different coefficient of thermal
expansion as shown in figure 2.22. The deflection of bimetal with temperature is nearly
linear, depending mainly on the coefficients of linear thermal expansion. The form of the
industrial bimetallic thermometer is shown in figure 2.23.
Figure 2.23 Industrial bimetallic thermometer
The bimetal is wound in the form of a helix, with one end fastened permanently to
the outer casing and the other end connected to the pointer stem. A pointer is attached to
the upper end of the stem and sweeps over a circular dial to indicate the temperature.
58
Heat radiation
The property of all hot substance emits heat radiation can be used to measure the
temperature of the body with out having direct contact. When a substance or body is at
above a suitable temperature, we can see it glow. This is heat energy being transferred
from the substance by radiation of electromagnetic rays. If the substance changes color or
becomes brighter, it indicates that more heat energy is radiating off the substance – it is
hotter.
A body which completely absorbs any heat or light radiation falling on it is
known as a blackbody (blade body only exist in theory).The amount of energy given off
by the surface of a particular substance is called its emissivity (E) is the ratio of the
radiation emitted by a given surface to the radiation emitted by the surface of a slave
body heated to the dimension less number between 0 and 1. A black body would have an
emissivity of E=1. Knowing the emissivity of a substance, then measuring the
electromagnetic radiation it is possible to measure temperature.
At a given wavelength, brightness will vary with temperature. The radiation can
be measured by looking at its intensity or color. Devices which measure temperature in
this has are referred to as radiation pyrometers. Radiation pyrometer energy measure is
used to high temperature. One major advantage in that there is no contact with the
substance whose temperature they are measuring.
The disappearing filament optical pyrometer
The disappearing filament optical pyrometer compares the visible electromagnetic
radiation given off by the hot body with the light emitted by the lamp. The lamp is
calibrated so that its filament brightness corresponds to know temperature. Adjusting the
current to the lamp will adjust the brightness. When the filament disappears it means that
the temperature is the same. The current to the lamp at which the filament disappears is
thus indication of the temperature of the body. These type of sensors have application in
measurement of temperature of molten metal’s, furnaces and heat treatment
Infrared pyrometer
They use the in force electromagnetic rays emitted by a hot body and measure the
interring of them by thermocouple or thermopile. Thermopile is groups of thermocouples
are bright together for measurement so as to increase sensitivity.
59
2.2.3.5 Speed measurement
A tachometer refers to any device used for measuring the rotation of a shaft (from
the Greek word takhos, meaning speed). A tachometric generator is a machine which,
when driven by a rotating mechanical force, produces an electrical output proportional to
the speed of rotation. For measuring speed, tachometric generators are usually connected
to the rotating shaft. There are several methods of doing this, for example by direct
coupling, or by means of belts or gears (although any rotational amplification must be
taken into consideration). They produce an output which primarily relates to speed and
since speed is the rate of change of displacement, and a measure of displacement can be
obtained by integrating the tachometer output over time. Tachometric generators are
generally referred to as A.C or D.C tachogenerators, or A.C or D.C tachometers.
Figure 2.24 DC Tachometric generator
Figure 2.24 shows a D.C tachometric generator. It is essentially a small D.C generator,
which produces a moderate D.C output voltage. It is designed optimally to give greater
accuracy as a speed measuring instrument rather than the generation of electricity.
Tachometers are often constructed from lighter materials such as fiberglass to reduce
their total mass. It is important to make these devices as light as possible so the mass of
the tachometer does not affect the speed of the system being measured.
The output signal from D.C tachometers usually requires electronic circuitry to
remove electrical noise. The output signal can then be displayed on a voltmeter calibrated
in terms of speed or displacement. A characteristic of D.C tachometers is that the polarity
of the output voltage shows the direction of rotation of the shaft. The range of
measurement is between about 0–600 radians per second (0–6000 revolutions per
minute). They need regular maintenance because certain parts, particularly the brushes,
are prone to wear, and also the strength of permanent magnets tends to weaken over time.
60
As its name implies the AC tachogenerator is an electrical generator that produces an AC
output.
Figure 2.25 A.C Tachometric generator
Figure 2.25a) shows a typical A.C tachogenerator arrangement with a permanent magnet
(rotor) rotating within a stationary coil (stator winding). In normal operation the rotor
would be connected to and driven by the shaft to whose angular speed is to be measured,
(same as d.c. tachogenerator) schematically as shown in Figure 2.25b. The output, V0 is
an alternating signal, the amplitude and frequency of which are both proportional to the
speed of rotation. Using suitable signal processing circuits, either amplitude or frequency
may be used to give an indication of speed.
The A.C tachometer compared with the D.C tachometer, has the disadvantage of
requiring more involved signal conditioning. Also, the direction of rotation cannot be
obtained from the output signal. However, A.C tachometers are simpler, less expensive,
and more reliable. They require less maintenance and, when the frequency is used to
measure speed, they give long term accuracy even if the strength of the permanent
magnet weakens. The A.C tachogenerator does not have the high noise content in its
output signal which is normally associated with the D.C tachogenerator. Both A.C and
D.C tachometric generators are widely used in automated production systems, machine
tools, and for monitoring large electricity generators. Figure 2.26 shows one of its
applications.
Figure 2.26 Block diagram of the speed measurement.
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2.2.3.6 Level Measurement
Measurement and/or control of liquid level is an important function in many
industrial processes and in more exotic applications, such as the operation and fueling or
large liquid fuel rocket motors. Figure 2.27 illustrates some of the more common
methods of accomplishing this measurement.
Figure 2.27 Common methods of level measurement
The simple float of figure 2.27-a) can be coupled to some suitable motion
transducer to produce an electrical signal proportional to the liquid level. Figure 2.27-b)
shows a "displacer" which has negligible motion and measures the liquid level in term of
buoyant force by means of a force transducer. Since hydrostatic pressure is related
directly to the liquid level, the pressure-sensing schemes of the figure 2.27-c) and 2.27-d)
allows measurement of the liquid level in open and pressure vessels, respectively. In the
"bubbler" or purge system of figure 2.27-e), the gas pressure downstream of the flow
restriction is the same as the hydrostatic head above the bubble-tube end. The flow of gas
is quite small; a bottle of nitrogen used as a source of pressurized gas may last six months
or more.
62
Capacitance variation (figure 2.27-f) has been employed in various ways for level
sensing, for essentially non-conducting liquids (where the resistance is sufficient high)
obtaining satisfactory results. For conductive liquids the probe must be insulated to
prevent short circuiting of the capacitance by the liquid resistance. Capacitance levelsensing techniques have been used with many common liquids, powdered or granular
solids, liquid metals (high temperatures), liquefied gases (low temperatures), corrosive
materials such acids, and in very high pressure processes. Figure 2.27-g) illustrates the
use of radioisotopes for level measurement. Since the absorption of  -ray or  -ray
radiation varies with the thickness of absorbing material between the source and the
detector.
Figure 2.27-h) shows the method of using hot-wire or carbon resistor elements for
the measurement of liquid level in discrete increments. The basic concept is that the heattransfer coefficient at the surface of the resistance element changes radically when the
liquid surface passes it. This changes its equilibrium temperature and thus its resistance,
causing a change in bridge output voltage. By locating resistance elements at known
height intervals, the tank level may be measured in discrete increments. Such
arrangements have been used in filling fuel tanks of large rocket engines with cryogenic
liquids fuels. Ultrasonic techniques can also be applied to liquid-level sensing, as in
figure 2.27-i). Ultrasonic devices utilizing wave propagation principles to obtain a digital
output representing the measured value of the variable (liquid level of the tank in the
example illustrated).
63
2.2.3.7 Flow Measurement.
The measurement of the flow rate and flow quantity of materials is made
primarily for the purpose determining the proportions of materials introduced to a
manufacturing process and the amount of materials evolved by the process. Secondarily,
flow measurements are made for the purpose of cost accounting usually for steam and
water services.
Laminar and turbulent flow
Experimental observations have shown that two distinct types of flow can exist.
The first is laminar flow, or viscous or streamline flow this is shown for a circular pipe in
figure 2.28-a). Here the particles move in a highly ordered manner retaining the same
relative positions in successive cross sections, thus the laminar flow in a circular pipe can
be regarded as a number of annular layers: the velocity of these layers increases from
zero at the pipe wall to maximum at the pipe centre with significant viscous shear stresses
between each layer. A graph of layer velocity υ versus distance r of layer from center has
a parabolic shape.
The second type of flow, turbulent flow, is shown in figure 2.28-b). This is highly
disordered; each particle moves randomly in there dimensions and occupies different
relative positions in successive cross sections. As a result, the velocity and pressure at a
given point in the pipe are both subject to small random fluctuations with time about their
mean values. The viscous friction forces which cave the ordered motion in laminar flow
are much smaller in turbulent flow.
Figure 2.28 Illustration of laminar and turbulent flows
64
Reynold’s number:-Reynold’s number tells us whether the flow in a given situation is
laminar or turbulent. It is the dimensionless number.
Re 
vl

Where:
υ = flow velocity, l = characteristic length
ρ = density, η= dynamic viscosity
The value of Re implies laminar or turbulent flow. Re < 2x103 Laminar flow, Re > 104
Turbulent flow, 2x103 < Re < 104
Transition region
Head-type flow meters
One of the most well knows types of flow meter correspond with head-type flow meters.
They have a common feature, so they produce a pressure difference (head-difference)
when a fluid flow is maintained through them. The differential pressure so obtained has
an accurate relationship to the mean dynamic pressure within the conduit and hence to the
square of the flow rate.
The head-type flow meters covers:
1. Orifice-plate tube
2. Venturi-tube
3. Pitot-tube
4. Flow nozzle
Orifice-plate meter
The orifice meter is the most common type of head flow measuring device for
medium and large-pipe sizes. The orifice plate inserted in a pipe line causes an increase
in the flow velocity and a corresponding decrease in the pressure. The flow pattern shows
an effective decrease in the cross-section of flow beyond the orifice plate with the
maximum pressure. The particular position where the velocity is maximum and the static
pressure is minimum is known as vena contracta.
The orifice plate inserted in the line is basically a thin plate of metal with circular
opening with different configurations (figure 2.29). The concentric orifice plate consists
of a central hole in a metal plate concentric with the circumference of the plate (see figure
2.30).
65
Figure 2.29 Orifice plate styles.
Figure 2.30 Installation scheme of orifice plate
By measuring the different pressure using pipe tapping locate at distances D and D/2 in
the upstream and downstream respectively is possible to obtain the flow rate. The
materials used for orifice plates are mild steel, stainless steel, phosphor bronze, or gun
metal, depending upon the application. The main advantages of an orifice meter its
simple construction and high reliability. The limitations are its poor accuracy, calibration
changes appreciably with wear, high pressure loss, and possible maintenance problems
with blocked tapping. Since the pressure losses are high, the device is not recommended
for high velocities. The effect of inserting an orifice plate in a fluid stream causes an
abrupt change in the stream area accompanied by a fairly high pressure loss. In cases
where such pressure loss is not acceptable, it is preferable to use an element possessing a
gradual stream area change, such as the Venturi tube, which is described below.
Pitot – tube
The Pitot is one of the earliest devices developments for flow measurement. It consists of
a cylindrical probe inserted into the fluid stream. In this device, the velocity head is
converted into an impact pressure, and the difference between the static pressure and the
impact pressure is a measure of the flow rate. Pitot tubes are widely used for air-speed
measurements on board an aircrafts.
66
The sketch of the Pitot tube is shown in figure 2.31, it consists simply of a tube supported
in the pipe with the impact opening of about ⅛ to ¼ in diameter arranged to point directly
forward the oncoming fluid. The process taking place in the fluid is one of converting the
"velocity" head to an additional static head. If therefore the pressure difference (p2 - p1)
can be measured the velocity of the fluid in the stream tube may be found by knowing the
density of the flow.
Figure 2.31 Pitot tube
The main advantages of the Pitot tube are that installation is relatively simple and they
one readily adaptable for flow measurements made in very large pipes or ducts. They can
be employed in either open-channel streams or pipes. The pressure loss caused by the
Pitot tube is, of course very small. The main disadvantage of the Pitot tube is that it
cannot be used in fluids containing solid particles.
Venturi tube
The basic design of Venturi tube comprises three sections: the converging conical
section at the upstream, cylindrical throat, and the diverging recovery outlet cone at the
downstream. Figure 2.32 illustrates a standard configuration of a Venturi tube. The inlet
cone tapers down from the pipe area to the throat section of smaller area to produce the
necessary increase in velocity and decrease in pressure. The cylindrical throat provides a
point of measurement of his decrease in pressure where the flow rate is steady. The
diverging outlet cone expands from the throat to the pipe are resulting in pressure
recovery. Pressure measurements are carried out at the upstream entrance to the cone and
at the throat.
67
The dimensions of Venturi tube are relatively large, and its cost is also high. Since the
device is sufficiently resistant to abrasion, it is well suited for suspended liquids.
Figure 2.32 Standard configuration of the Venturi tube
The Venturi tube has the highest accuracy of all pressure-differential flow elements when
it is properly installed and calibrated, and its reproducibility is high. The permanent
pressure loss in a Venturi tube is usually much lower than in an orifice of the same
capacity. Further, the Venturi is lees subject to wear and abrasion and is lees likely to
become clogged with sediment.
Flow nozzle
The flow nozzle is a primary flow-metering device wherein a pressure difference is
created during the flow. Flow nozzles combine the simplicity of the orifice plate with the
low losses of the Venturi tube, and hence are preferred in many applications. It
approximates to a Venturi tube with a curved form of approach, as shown in figure 2.33,
giving a gradual change of sectional area, having the same order of discharged
coefficient. However, the absence of the downstream expansion cone brings the pressure
loss to the same order as that for an orifice plate.
Figure 2.33 Flow nozzle
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The fabrication complexities are less than that of a Venturi tube. At high velocity flows,
the performance is better than the orifice device. The curved profile of the nozzle renders
its usefulness whenever fluids with suspended solid matter are encountered. The
following general characteristics of differential pressure flow meters should be borne in
mind when deciding on the most suitable meter for a given application.
1. No moving parts, robust, reliable and easy to maintain, widely established and
accepted.
2. There is always a permanent pressure loss due to frictional effects. The cost of the
extra pumping energy may be significant for large installations.
3. These devices are non-linear this limits the useful range of a meter to between 25
and 100 % of maximum flow. At lower flows the differential pressure
measurement is below 6 % of full scale and is clearly inaccurate.
4. Can only be used for clean liquids, where is well established turbulent flow.
5. Considerable care must be taken with the installation of the meter, minimum
lengths of straight pipe upstream and downstream of the meter, the geometry of
the flow meter, the arrangement of the pressure pipes connecting the flow meter
to the differential pressure device.
A typical modern flow meter system using differential pressure sensor is shown in figure
2.34. It consists of the differential pressure sensing element, differential pressure
transmitter, interface circuit and microcomputer. Transmitter received the ΔP pressure
signal as input giving a DC current output signal (typically 4 -20mA). The interface
circuits consist of an amplifier, signal conditioning circuit, and analogue-to-digital
converter. The computer reads the input binary number, converts it into differential
pressure ΔP and then calculates the measured flow rate Qm, according with the formulas
and constants values of fluid density, dynamic viscosity, temperature of the fluid, etc,
stored in memory.
Figure 2.34 Microcomputer used for flow measurement with differential pressure
sensing element.
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Rotameters
Rotameter is considered variable-area meter, it consist of a vertical tube with
tapered bore in which a “float” assumes a vertical position corresponding to each flow
rate through the tube (see figure 2.35). For a given flow rate, the float remains stationary
since the vertical forces of differential pressure, gravity, viscosity, and buoyancy are
balanced. This balance is self-maintaining since the meter flow area (annular area
between the float and tube) varies continuously with vertical displacement; thus the
device may be thought of as an orifice of adjustable area. The downward force (gravity
minus buoyancy) is constant and so the upward force (mainly the pressure drop times the
float cross-section area) must be constant also. Since the float area is constant, the
pressure drop must be constant. For a fixed flow area, ΔP varies with the square of flow
rate, and so to keep ΔP constant for differing flow rates, the area must vary. The tapered
tube provides this variable area. The float position is the output of the meter and can be
made essentially linear with flow rate by making the tube area vary linearly with the
vertical distance. Rotameters thus have an accurate range of about 10:1, considerably
better others flow meters. Accuracy is typically ± 2 % full scale with repeatability about
0.25 % of reading. Assuming incompressible flow and the area of float relatively smaller
than the area of the tube, we can estimate the flow by the expression:
Q = K (At-Af)
Eqn(2.8)
where: At = area of tube (cm2),
Af = area of float (cm2)
K= constant value, depending of discharge coefficient, local gravity and specific
weight of float and flowing
fluid.
If the tube is shaped so that At varies linearly with the float position (x), then:
Q = K1 +K2 x
Eqn(2.9)
The floats of rotameters may be made of various materials to obtain the desired density
difference, for metering a particular liquid or gas. Floats shaped to include turbulence
can give viscosity insensitivity over a 100:1 range.
70
Figure 2.35 Rotameter with electrical output.
If a pneumatic or an electrical signal related to the flow rate is desired, the float motion
can be measured with suitable displacement of the transducer as is shown in figure 2.35.
Flow rates beyond the range of the largest rotameter may be measured by combining a
rotameter in a bypass arrangement.
Mechanical flow meters
Mechanical flow meters rely on the flow to induce a mechanical motion of elements
within the flow path. The magnitude of the motion is taken as a measure of the flow
volume or flow rate. Numerous designs have been involved, and two of the most popular
configurations are the positive displacement meters and turbine meters.
Positive-displacement meter
Positive displacement flow meters are primarily designed as flow quantity meters, as
opposed to flow rate meters, for the measurement of volume flow, incorporating pistons,
sliding vanes or meshing elements. Some of the common types are illustrated in figure
2.36. All of these constrain the flow path preventing leakage past the moving elements
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and the body of the flow meter. The meters are self-powered and drive mechanical
counters. The upstream flow conditions are of no importance, and these can be used for
viscous fluids. One of the most popular types is the rotary piston meter which has a large
flow range (50:1), long life, low frictional loss, and an accuracy of 1 % of reading. Being
a precision device, the cost is high. Also, the fluid should be clean. The pressure drop in
the meter is high.
Figure 2.36 Positive displacement meters
Turbine-type flow meters
A turbine flow meter (figure 2.37) consists of a multi-bladed rotor suspended in the fluid
stream; the axis rotation of the motor is parallel to the direction of flow. The liquid
impinges on the blades and causes them to rotate at an angular velocity approximately
proportional to flow rate. The blades usually between four and eight in number are made
of ferromagnetic material and each blade forms a magnetic circuit with the permanent
magnet coil in the meter housing. This gives a variable reluctance tachogenerator; the
voltage induced in the coil is a sine wave whose frequency is proportional to the angular
velocity of the blades.
Figure 2.37 Turbine meter
72
The instantaneous frequency is a measure of the flow rate, and the total number of
pulses over a period of time is a measure of the total flow, these measurements can be
made very accurately because of their digital nature.The theory of operation of the
turbine transmitter is complex. Turbine meters behave essentially as first-order dynamic
systems for small changes about an operating point. However, the time constant
(typically 2 to 10 ms at maximum factor) is inversely proportional to the operating-point
flow rate.
The most serious disadvantage of these meters is their susceptibility to damage
with particles suspended in the fluid, and any damage to the blade requires recalibration.
Also, there should be at least a 15-diameter length straight pipe upstream to the meter, to
obtain the required flow pattern. These are expensive and useful for fluids in a limited
viscosity range.
Electromagnetic flow meter
The electromagnetic flow meter is ideally suited for measuring the flow rate of
fluids in installations where the other common methods of measurement are
unsatisfactory. The principle feature is that it does not present any obstruction to the flow
of liquid. The electromagnetic flow meter is based in the principle of Faraday’s law of
electromagnetic induction. A schematic arrangement of the flow meter is shown in figure
2.38. The flow tube lies in a magnetic field of uniform flux density. Two electrodes are
inserted in the tube, their surfaces beings flush with the inner surface of the tube and in
contact with the fluid. As the conductive fluid flows through the insulated tube, it will be
considered as a series of flat conductor discs passing through the magnetic field inducting
an e.m.f across the electrode. The induced voltage is generated in a direction mutually
perpendicular to both the velocity plane of the conducting liquid and phase of the
magnetic field, independent of Reynold’s number, viscosity and density of the liquid.
This value multiplied by the cross-sectional area of the pipe gives the volume flow rate.
In principle, both AC and DC magnetic fields can be used but DC method has the danger
of electrolytic polarization at the electrodes.
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Figure 2.38 (a) Schematic arrangement of a magnetic flow meter (b) Section showing
electrodes and magnetic field.
The main advantage of the devices is that its construction is simple and rugged with no
moving parts, and hence the hysteresis is nil and head loss is low. If the process liquid is
an electrolyte, it is relatively insensitive to changes in the fluid density, temperature,
pressure, viscosity and flow disturbances. The only condition is that the pipe should
always be full.
The device has an essentially linear fast response independent of the properties of
the fluid except for electrical conductivity. It has a range of 10:1, with good accuracy and
reliability. It is ideal for bi-directional measurements and particularly suited for
measuring flows of corrosive acids and alkalis as well as slurries with coarse or fine
suspended materials. The main limitations are that the fluid must be conductive and the
electrical output signal is of a low level (usually a few micro volts), requiring high
amplification and special instrumentation. Further the device tends to be expensive for
small pipe sizes.
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Ultrasonic flow meter
Ultrasonic flow meter use two distinct measurement principles: Doppler
frequency and transit time. Figure x shown two different arrangements of ultrasonic flow
meters.
In the Doppler method, an ultrasonic transducer is bounded to a pipe wall to
transmit an ultrasonic signal in the flow. Particles suspended in the fluid impart a
frequency shift proportional to the particle velocity. Knowing the values of the angle 
and the distance between transmitter and receiver, and by measuring the difference in the
repetition frequency with a suitable electronic counter, the velocity of the fluid can be
computed.
In the transit time flow meter, an ultrasonic transducer is mounted at an angle or
parallel to the pipe wall. When ultrasonic waves pulsed for a very short duration are
transmitted across the fluid, the velocity of the ultrasonic waves is increased or decreased
by the fluid velocity depending upon the direction of the fluid flow. So, the time delay
between transmitter and receiver depends of the direction of the flow and flow velocity.
The electronics unit and display is calibrated so that the time delay is shown in terms of
the flow rate of the fluid.
Figure 2.39 Ultrasonic flow meter arrangements
Although expensive, ultrasonic flow meters are highly accurate, and stable. They can be
used with many liquids, conducting and non-conducting and can be measure flow
continuously in both directions and also they can be used in any pipe size. The
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measurement is not sensitive to the viscosity, pressure, and temperature variations. They
do not disrupt the flow, and are often portable. Other advantages are fast response, wide
frequency range and versatility. However particles of suspended matter in the liquid are
required for either ultrasonic technique to work successfully. Ultrasonic flow meters
cannot be used with gases.
Problems
1. What is the resolution (in voltage and in radians ) of a potentiometer for a 360 single
turn wire which has 150 number of turns per cm and with 20 v excitation
2. What is the resolution (in voltage and in radians ) of 50 turn helical wire wound
potentiometer with 20v excitation and 5cm diameter ,
3. A linear resistance potentiometer is 50mm long and is uniformly wound with a wire
of total resistance of 5kohm under normal conditions, the slider at the center of the
potentiometer, Determine
i. The linear displacement when the resistance of the potentiometer as measured
by the Bridge is 1.85kohm.
ii. The Resolution of the potentiometer in mm, the minimum measurable
iii. Consider a voltmeter with internal resistance of 50Kohm is used to measure the
voltage across the terminal. How percentage of measured voltage is lost during
full displacement measurement.
4. A potentiometer transducer with a stroke length of 5cm has a total resistance of 10k.
The voltage across the potentiometer is 7.5v. When the wiper is 2 cm from one end
what is the output voltage of the potentiometer from the end.
5. A LVDT has a voltage excitation of 10v at 400Hz having a maximum range
movement of +1.5cm and output range of 2.5v. Calculate the output voltage when the
core is +1cm away from null
6. A LVDT has a voltage excitation of 6v rms when the displacement is 0.4X10-3.
Determine the sensitivity of this instrument in volts/mm. A 10 volt voltmeter with
100 scales division and in which two tenths a division is used to read the output.
Determine the resolution o f the voltmeter
7. A thickness measuring device transducer has parallel plate capacitive sensor having a
pair of plates of area of 10cmX20cm, which are separated by a distance of 0.02cm. A
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mica sheet of thickness 0.01±0.00cm is being passed between the plate’s .calculate
the variation of capacitance when the dielectric constant of mica is 8 and the
permittivity of air is 8.85X10F/m.
8. A capacitive transducer is made up of two concentric cylinder plates with inner and
outer concentric diameter of 5mm and 5.2mm respectively. The length of the
electrode is 25mm. Calculate the capacitance value if the outer cylinder is pulled by
5mm, what is the capacitance change.
9. A peizo electric transducer has a capacitance of 1000pf and a charge sensitivity of
4X10-6 coulumb/cm. The connecting cables has capacitance of 400pf. the display
device has an input impedance of 1M resistance and 50pf connected in parallel
i. What is the voltage sensitivity of the piezoelectric transducer alone
ii. What is the high frequency sensitivity in V/cm of the entire system
iii. What is the lowest frequency that can be measured with 2 percent error
10. Capacitor pressure sensors use the electrical property of a capacitance to measure the
displacement of a diaphragm. The diaphragm is an elastic pressure sensor displaced
in proportion to changes in pressure. It acts as a one plate of a capacitor.
77
CHAPTER THREE
SIGNAL CONDITIONING AND INTERFACING CIRCUITS
3.1
Introduction
The output of sensors is usually small or not suitable to directly process or present
it. Thus conditioning or suiting of the signal is necessary. Signal conditioners are circuit
that takes the output of a sensor or transducer and converts it in to a form more suitable
for further processing or presenting. Usually the output is current, voltage or frequency
Some of the very commonly used type of signal conditioning and interfacing circuits
are; Deflection bridge, Instrumentation Amplifier(INA), filters, V/I,I/V,V/F,F/V and as
interfacing circuits, ADC, DAC
3.2
Deflection Bridge
The Deflection Bridge finds an extensive application in electrical instrumentation
for conditioning the output of sensors typically if the sensor output is variation of
resistance, inductance and capacitance. The deflection bridge has four arms of impedance
designated as ZA, ZB, ZN and ZX. One of these, ZX is the unknown impedance that
usually forms the sensor as shown in Figure. 3. 1
Figure 3.1 Deflection Bridge
Initially all impedances values of the deflection bridge are adjusted in such a way
that the measured voltage at the detector is zero ( Vab  0 ), at this moment the bridge is
called at balanced condition or null condition which is used a reference point. When the
impedance comprising the sensor under goes variation, then the terminal voltage varies
accordingly ( Vab  0 ), and the bridge is called at off balance or imbalance accounting for
the change or variation of the sensor. The departure from the initial balance or reference
is taken as measure of the non electrical quantity under interest.
78
The operation of the deflection bridge lies in the two states or conditions of the
bridge namely balanced and unbalanced condition in which is the first is a reference
(starting from zero) while the imbalance accounts for the measurement of the physical
parameter under going change.
Mathematically
At balanced condition, Vab  0 , which is a reference point(start) for measurement
I1Z1  I 2 Z 2
I1 Z 4  I 2 Z 3
Eqn(3.1)
Eqn (3.2)
Dividing equation (3.1) by equation (3.2)
r
Z1 Z 2

, where r is called the arm ratio
Z4 Z3
At off balance, Vab  0
Vab  I1 Z1  I 2 Z 2 ,
 Z1
Z2 

Vab  
VS
 Z1  Z 4 Z 2  Z 3 
.
Eqn (3.3)
Bridge circuits in which two series-connected adjustable circuits elements are
located in a single arm adjacent to the unknown arm (e.g. ZB) are called ratio-arm
bridges. Bridge circuits in which two shunt-connected adjustable elements both located in
the arm opposite the unknown (e.g. ZA) and the product of impedance in the remaining
arms is either purely real or purely imaginary are called product-arm bridges.
Generally in order to attain the relation ship governing the operation of the bridge,
circuit analysis is necessary to obtain three basic information’s
1. The relation ship among the impedance when the bridge is at balanced condition
2. The sensitivity of the bridge i.e. the output voltage per unit change of impedance
3. Loading effect:
The obtained information will help design appropriate deflection bridge that
encompasses calibration, compensation (environmental effects such as temperature,
humidity), adjustment of sensitivity and the provision of adjustment of output voltage to
zero.
79
Types of Deflection Bridge
There are so many types of deflection bridges in use today for measurement
purposes. Deflection brides are classified depending up on

Energy source as DC or AC bridges and their measurement applications
such as , DC bridges( Kelvin double, Wheatstone Bridge) and AC bridges


(Wein, Schering , Maxwell and Owen bridges)
The impedances as resistive, or reactive (inductive, capacitive) bridges
Depending up on the number of sensors present on the bridge arm as
quarter, half and full Deflection Bridge
(a) DC Bridges
With a d-c galvanometer used as a detector and resistive arms the bridge of Figure
3.1 becomes a dc bridge known as Wheatstone bridge. It is almost the standard means of
measuring resistance based on resistance variations over wide ranges. By means of a
suitable variation of the values of RA and RB, the ratio arms, RX can be detected. The
ratio RN/RA should be so chosen that the unknown resistance is determined. The
Wheatstone bridge is usually used to measure resistance values ranging from 1 ohm to
1mega ohm with accuracy of 0.02 percent. Special difficulties can be encountered in the
measurement of very low and very high resistance or resistance variations. For low
resistance the Kelvin double bridge (Fig. 3.2) which is a modification of the Wheatstone
bridge can reduce the uncertainty introduced by the resistance of leads and contacts.
Where r is the resistance of connection between RB = S which is assumed to be very
small
Figure 3.2 Kelvin double bridge
Variations in the unknown resistance and the effects of contact and lead resistance are
greatly minimized. Still, the effects of what are known as thermoelectric emfs can be
80
easily eliminated. By reversing currents through RB = S and RX = X, and averaging the
values detected for X, more accurate values of X can be obtained. Values of resistance
which can be measured by the Kelvin Bridge may range from 1micro ohm to 1o with
accuracy of 0.1 percent. When the resistance being measured is very high, the bridge
galvanometer becomes a relatively insensitive indicator of unbalanced conditions. This is
because of the high source impedance that the bridge presents to the galvanometer.
(b)AC Bridges
Detectors commonly used in d-c bridges are vibration galvanometers (with sensitivities
of 50Hz to 1 KHz), earphones (from about 250Hz), and tunable amplifier detectors (from
about 10Hz to 100 KHz). For wider bandwidths, CROs with relatively high sensitivities
could also be used. Based on these balance conditions various a-c bridges are used in
practice under the broad classification of capacitance and inductance bridges. Some
examples are shown in Figure 3.3.The Wien Bridge (Fig. 3.3a) finds use in the
measurement of frequency in the audio ranges, capacitance measurement of 1nf to
1oomicro farad with fault limits up to 0.1 percent can be measured. It is also useful in the
precision determination of capacitance, since the standards of frequency and resistance is
known to a very great accuracy.
Figure 3.3 AC bridges (Wein, Schering, Maxwell and Owen bridges)
The Schering Bridge (Fig. 3.3b) is extensively used for measuring the capacitance
and power factor of condensers such as cables or insulators up to 500kv. The Maxwell
and Owen bridges (Fig. 3.3c, d) are particularly useful for measurements of inductances
of o.1mH to 10H.
81
3.2.1 Design of Resistive Deflection Bridge
The resistive deflection bridge usually is exited by DC sources and depending up
on the number of sensors present on the bridge arm it is called as quarter, half and full
deflection Bridge as shown in figure 3.4a,b&c. these circuits are very commonly used in
electrical instrumentation to convert a variation of resistance into voltage
Quarter-bridge
This arrangement, with a single element of the bridge changing resistance in response to
the measured variable
Figure 3.4a Quarter-Bridge Circuit
Half-bridge
This arrangement, with a two element of the bridge changing resistance in response to the
measured variable
Figure 3.4b Half Bridge Circuit
Full-bridge
This arrangement, with a four elements of the bridge changing resistance in response to
the measured variable
Figure 3.4c Full-Bridge Circuit
82
Design of Resistive Deflection bridges
Considering the quarter bridge which has one sensor as shown in figure 3.5
Figure 3.5 Quarter Deflection Bridge with R1 as sensor
The resistance R1 is the sole sensor undergoing variation, if Imin and Imax are the
minimum and maximum values of measured values of measured variable and RImin and
RImax are the corresponding sensor resistance then
VIm in
VIm ax




1
1


VS
R4
R3
1 R 
1  R
2 
Im in





1
1


VS
R4
R3
1 R 
1  R
2 
Im ax

VIm ax  VIm in




1
1


VS
R
R
1 4 R 
1  4 R

Im ax
Im in 
Eqn (3.4)
Eqn (3.5)
Eqn (3.6)
Often the bridge is designed to meet the following specifics
1. VIm in  0 , often we need the resistive deflection bridge balanced at I=Imin
R
R
R4
 3  R4  3  RIm in
R2
RIm in R2
2. The electrical power dissipated in the sensor must not exceed the maximum
power
3. The non linearity must be with in the limited value , the ratio r3/r2 gives in
sight in to the non linearity
83
For any input I the output (terminal) voltage Vab is given by




1
1


VS
R4
R3

1
1


RI
R 2 

Eqn (3.7)




1
1
VS

Vab  
1  R3 RIm in 1  R3

R2 
 R R


I
2
Eqn (3.8)
 1
R
V
R
1 
Where r  3 , x  I and v  ab

v
R2
RIm in
VS
1 r 
1  r
x


Eqn (3.9)
Vab
Substituting R4 
R3
 RIm in in Eqn (3.7)
R2
Vab  1
1 



VS 1  r
1 r 
x


Since r is fixed Eqn (3.9) is a function of variable x
v( x) 
x
1
1
1



1 r x  r 1 r
1 r
x
Eqn (3.10)
The degree of non linearity is dependent on r i.e. the graph v versus x is dependent on
the value of r . The design should consider achieving high sensitivity
Example: consider quarter bridge strain gauge circuit shown in figure 3.6 which
comprises a strain gauge sensor R3 in its arm for strain measurement
Figure3.6 Quarter bridge strain gauge circuit
84
In a strain gauge, the relation between strain, gage factor and resistance is given by
R
 F . Where F is gauge factor and e is strain, R is the unstrained resistance
R0
R  F . .R0
However; R is usually small x 
RI
R  R
 I
1
RIm in
RIm in
Hence we require the sensitivity to be as high as possible at x  1 ,
To maximize the sensitivity the partial differential equation v by x should be equal to
zero i.e.
v
x
v
x
x 1
x 1
0

Eqn (3.11)
  x
1 


  0  r 1
x  x  r 1  r  x 1
Thus r  1 implies R3  R2 , R4  RIm in  Ro i.e R4 is set at a value equal to the unstrained
strain gauge resistance and the two arms of the bridge R2 and R3 are set equal to each
other. Thus, with no force applied to the strain gauge, the bridge will be symmetrically
balanced and the voltmeter will indicate zero volts, representing zero force on the strain
gauge. As the strain gauge is either compressed or tensed, its resistance will decrease or
increase respectively, thus unbalancing the bridge there by producing an indication at the
voltmeter.
The output voltage is then
v
v
x
1
1  x 1 1

 
   x  1 Since r  1
x  r 1  r 2  x  1 4
Eqn (3.13)
 1 R
1  RI

 1  .
4  RIm in
 4 R0
Vab 
VS R VS
.
 .F . ,
4 R0
4
Eqn (3.14)
From Eqn (3.14) it is seen that relation between the ouput ( Vab ) and input (strain) is linear
and the sensitivity of the quarter bridge is given by
K
Vab


VS
.F
4
Eqn (3.14)
85
Effect of lead wire resistance
The distance between the strain gauge and the two lead wires connecting it to the bridge
circuit may be substantial, and the wire resistance has a significant impact on the
operation of the circuit. As shown in figure 3.7 the effects of lead wire resistance is
illustrated by addition of resistor connected series with the strain gauge:
Figure3.7 Quarter bridge strain gauge circuit
The strain gauge's resistance (Rgauge) is not the only resistance being measured,
the wire resistances Rwire1 and Rwire2, being in series with Rgauge, also contribute to
the resistance of the lower half of the arm of the bridge, and consequently contribute to
the voltmeters indication. This, of course, will be falsely interpreted by the meter as
physical strain on the gauge. While this effect cannot be completely eliminated in this
configuration, it can be minimized with the addition of a third wire, connecting the right
side of the voltmeter directly to the upper wire of the strain gauge. Thus the resistance of
the top wire (Rwire1) is “bypassed" and the voltmeter is connected directly to the top
terminal of the strain gauge, leaving only the lower wire's resistance (Rwire2) to
contribute any stray resistance in series with the gauge.
Figure3.8 Quarter bridge strain gauge circuit
86
Practically the third wire carries no current (due to the voltmeter's extremely high internal
resistance) and its resistance will not drop any substantial amount of voltage
Compensation for temperature
Another kind of measurement error associated with the strain measurement is due
environmental effects such as temperature. An unfortunate characteristic of strain gauges
is that its resistance change with changes in temperature. This is a property common to all
conductors, some more than others. Thus, the quarter-bridge circuit as shown (either with
two or with three wires connecting the gauge to the bridge) works as a thermometer just
as well as it does a strain indicator. By using a "dummy" strain gauge in place of R2, the
effects of temperature change can be cancelled. As both elements of the rheostat arm will
same resistance change in response to temperature changes the effect of temperature can
be avoided. For example, Figure 3.9 illustrates a strain gauge configuration where one
gauge is active (RG + ΔR), and a second gauge is placed transverse to the applied strain.
Therefore, the strain has little effect on the second gauge, called the dummy gauge.
However, any changes in temperature will affect both gauges in the same way. Because
the temperature changes are identical in the two gauges, the ratio of their resistance does
not change, the voltage V0 does not change, and the effects of the temperature change are
minimized.
Figure 3.9 Use of Dummy Gauge to Eliminate Temperature Effects quarter bridge strain
gauge circuit with temperature compensation
Resistors R1 and R3 are of equal resistance value and the strain gauges are identical to
one another. With no applied force, the bridge should be in a perfectly balanced condition
and the voltmeter should read 0 volts. Both gauges are bonded to the same test specimen,
but only one is placed in a position and orientation so as to be exposed to physical strain
87
(the active gauge). The other gauge is isolated from all mechanical stress, and acts merely
as a temperature compensation device (the "dummy" gauge). If the temperature changes,
both gauge resistances will change by the same percentage, and the bridge's state of
balance will remain unaffected. Only a differential resistance (difference of resistance
between the two strain gauges) produced by physical force on the test specimen can alter
the balance of the bridge. Wire resistance doesn't impact the accuracy of the circuit as
much as before, because the wires connecting both strain gauges to the bridge are
approximately equal length. Therefore, the upper and lower sections of the bridge's
rheostat arm contain approximately the same amount of stray resistance, and their effects
tend to cancel:
Figure3.10 Three lead wire quarter bridge strain gauge circuit
With temperature compensation
Even though there are now two strain gauges in the bridge circuit, only one is responsive
to mechanical strain, and thus we would still refer to this arrangement as a quarterbridge. However, if we were to take the upper strain gauge and position it so that it is
exposed to the opposite force as the lower gauge (i.e. when the upper gauge is
compressed, the lower gauge will be stretched, and vice versa), we will have both gauges
responding to strain, and the bridge will be more responsive to applied force. This
utilization is known as a half-bridge.
Increasing the sensitivity and linearity
Alternatively, one can double the sensitivity of the bridge to strain by making both
gauges active, although in different directions. This is illustrated in figure 3.11,that a
bending beam application with one bridge mounted in tension (RG + ΔR) and the other
mounted in compression (RG - ΔR). This is called half-bridge configuration, whose
circuit diagram is also illustrated in Figure3.11, yields an output voltage that is linear and
88
approximately doubles the output of the quarter-bridge circuit.
Figure3.11 Half bridge strain gauge circuit
Since both strain gauges will either increase or decrease resistance by the same
proportion in response to changes in temperature, the effects of temperature change
remain canceled and the circuit will suffer minimal temperature-induced measurement
error:
V0
GF

Vi
2
In applications where such complementary pairs of strain gauges can be bonded to the
test specimen, it may be advantageous to make all four elements of the bridge "active" for
even greater sensitivity. This is called a full-bridge circuit as shown in figure 3.12.
V0
 GF
Vi
Figure3.12 Full bridge strain gauge circuit
Both half-bridge and full-bridge configurations grant greater sensitivity over the quarterbridge circuit, but often it is not possible to bond complementary pairs of strain gauges to
the test specimen. Thus, the quarter-bridge circuit is frequently used in strain
measurement systems. When possible, the full-bridge configuration is the best to use.
89
This is true not only because it is more sensitive than the others, but because it is linear
while the others are not. Quarter-bridge and half-bridge circuits provide an output
(imbalance) signal that is only approximately proportional to applied strain gauge force.
Linearity, or proportionality, of these bridge circuits is best when the amount of
resistance change due to applied force is very small compared to the nominal resistance
of the gauge(s).With a full-bridge, however, the output voltage is directly proportional to
applied force, with no approximation (provided that the change in resistance caused by
the applied force is equal for all four strain gauges). Strain gauges may be purchased as
complete units, with both strain gauge elements and bridge resistors in one housing,
sealed and encapsulated for protection from the elements, and equipped with mechanical
fastening points for attachment to a machine or structure. Such a package is typically
called a load cell
Example A quarter strain gauge bridge has a strain gauge of resistance R1=200Ω and
gauge factor G=1.9, while R2, R3 and R4 are fixed resistance at 200Ω. The strain gauge
experiences a tensile strain of 400micro strain. If the input voltage is 4 Ω determine the
change in output voltage ΔV.
Solution
Given at the balanced condition R1=R2=R3=R4=200Ω, and GF=1.9
For e=400x10-6 , the resistane change is
ΔR=GF.e.R= 0.152 Ω
The output voltage is
1 V .R
V  . i
 0.76mV
4 R
90
3.3
Amplifiers
Since most of the electrical signals produced by most sensors or transducers are
low voltage or power level, often it is necessary to amplify them before they are used for
further processing, indication or recording. An Amplifier is an electronic device or group
of devices used to increase the size of a voltage or current signal without changing the
signals basic characteristics.
Operational amplifiers (OPAMPs) are special types of amplifiers which essential
component of both practical and precision instruments. Their characteristics make opamp to find wide application in instruments as signal conditioning and signal conversion
circuits such as ; Instrumentation Amplifier(INA), filters, oscillator, integrator,
differentiator, V/I,I/V,V/F,F/V,ADC,DAC
3.3.1 Operational amplifier (OPAMP)
Opamp have two inputs indicated by – and + sign which stands for inverting and noninverting inputs as shown figure 3.13.
Figure 3.13 Schematic diagram of operational amplifier (OPAMP)
An ideal OPAMP have characteristics of
(a) high input amplification: thus weak or poor signal can be largely amplified
(b) high input impedance: thus current is not drawn from the input
(c) low output impedance: there is no voltage drop at the output
(d) low offset voltage: low drift
The output voltage is given as
vo  Av 2  v1 
Eqn (3.15)
This is ideal opamp have same amplification (A) for both inputs thus the ouput voltage is
the difference of the inputs meaning if there is a common voltage(Vc) to both input
terminals then it will be cancelled How ever in practice there is amplification called as
common gain for common voltages, thus the output is
vo  Av 2  v1   AcVc
Eqn (3.16)
91
The degree of deviation form the ideal opamp is specified by common mode rejection
ratio (CMRR)
CMRR 
A
Ac
Eqn (3.17)
The common voltage is not limited to steady state or intentionally effect rather could be
any signal equally applied to both inputs paths such as noise voltage pick. Thus in any
case the use of amplifiers with high CMRR ratio and careful attention to the symmetry in
the lead wire are helpful in reducing errors.
Common opamp circuit configurations
Some of the most common circuit configuration where Opamp is used to for
suiting signal are; Voltage comparator Inverting amplifier Non inverting amplifier
Summing amplifier Voltage follower Differential amplifier Integrating amplifier
Differentiating amplifier, Current to voltage converter, Voltage to current converter,
Voltage to frequency converter, Frequency to voltage converter
a. Voltage comparator
This is used for comparing input voltages, it is a differential amplifier
If v2>v1 the output voltage is positive
If v2<v1the output voltage is negative
If v2=v1, then the output voltage is zero
Figure 3.14a Voltage comparator
Consider a sine wave is applied to v1 and v2 is zero, the output will be high for the
positive parts of the sine wave, negative for the negative part and zero when equal, thus
the output becomes square wave. Such type of comparator circuit is often refereed to as
zero crossing detectors
b. Inverting amplifier
The out put is an inverted (opposite polarity) form of the input voltage
R 
v o  v1  2 
 R1 
Figure 3.14b Inverting amplifier
92
c. Non inverting amplifier
The out put is the non inverted form of the input
 R 
vo  v2 1  2 
 R1 
Figure 3.14c Non inverting amplifier
d. Summing amplifier
The output is the sum of the input voltages
vo  v1
R
R3
 v2 3
R2
R1
Figure 3.14d Summing amplifier
e. Voltage follower
The output is the same as the input. The advantage of the circuit is lies in high input
impedance avoiding loading effect that may occur; it is also referred to as buffer circuit.
vo  v1
Figure 3.14 e Voltage follower
f. Differential amplifier
The output is used to amplify the difference of inputs
vo 
R3
(v2  v1 )
R1
Figure 3.14f Differential amplifier
93
The difference amplifier output can be determined by superposition theorem i.e the
output is due to an inverting amplifier and non-inverting amplifier inputs.
-
-
The inverting amplifier produces
R 
voi   v1  3 
 R1 
Eqn (3.18)
The non-inverting amplifier produces
 R4   R3 
von  v2 
 1  
 R2  R4   R1 
Eqn (3.19)
The output is the sum of the outputs produced by each input.
 R3 
 R4   R3 
vo  v oi  v on  v 2 
 1    v1  
 R1 
 R2  R4   R1 
Eqn (3.20)
vo 
Eqn (3.21)
If R3  R4 ,& R1  R2 then the output becomes
R3
(v 2  v1 )
R1
g. Integrating amplifier
vo  
v1  t
RC
Figure 3.14g Integrating amplifier
h. Differentiating amplifier
vo  
v1  c  R
t
Figure 3.14h Differentiating amplifier
94
i. Current to voltage converter
vo   I  R
Figure 3.14i Current to voltage convertor
j. Voltage to current converter
I' 
v1
R1
Figure 3.14j Voltage to current convertor
k. Voltage to frequency converter
Figure 3.14k Voltage to frequency converter
l. Frequency to voltage converter
Figure 3.14l Frequency to voltage converter
95
3.3.2 Instrumentation Amplifier (INA)
An instrumentation amplifier (INA) is specially designed amplifier to have
differential gain, high input impedance, and high CMRR ratio. Basically it is buffered a
differential amplifier so as to have high input impedance.
Figure 3.15 Instrumentation amplifier
The output voltage can be easily found by analyzing the circuit as shown in figure 3.16
Figure 3.16 Instrumentation amplifier
The voltage difference
v  v2
v  v2
vo1  vo 2  1
R2  v1  v 2  1
R2
R1
R1
R
R 
 v1  v 2  2  1  2 
R1 
 R1
 2R 
 v1  v 2 1  2 
R1 

Eqn (3.22)
Eqn (3.21)
Eqn (3.23)
96
The front end of the instrumentation amplifier is a difference amplifier that can be
analyzed by superposition theorem i.e. the output is due to an inverting amplifier and
non-inverting amplifier.
-
-
The inverting amplifier produces
R 
voi  vo1  4 
 R3 
Eqn (3.24)
The non-inverting amplifier produces
 R4   R4 
von  vo 2 
 1  
 R3  R4   R3 
Eqn (3.25)
The output is the sum of the outputs produced by each input.
 R4 
 R4   R4 
vo  v oi  v on  v o 2 
 1    vo1  
 R3 
 R3  R4   R3 
R 
vo  vo 2  v o1  4 
 R3 
 R  R 
 R  R 
vo  v1  v 2 1  2   4   v 2  v1 1  2   4 
 R1   R3 
 R1   R3 
Eqn (3.26)
Eqn (3.27)
The INA is having additional buffer amplifiers to the inputs so as to make Rin infinity at
both V1 and V2 especially as compare to the front differential amplifier. In practice these
differential signals typically emanate from sensors such as resistive bridges or
thermocouples.
97
3.4 Interfacing circuits
The signal processing takes the output of the signal conditioning element and
converts it in to a form more suitable for presentation. The analog to digital converter
(ADC) and digital to analog converter (DAC) makes important part of instruments as
interfacing analog and digital electronic equipments such as computer, data acquisition
systems, and data loggers.
Figure3.17 Interfacing circuits diagram representations
The purpose of analog-to-digital converter or ADC is to generate a train of pulses
proportional to the analog input. It electronically translates analog signals into digital
(binary) quantities. While a digital-to-analog converter, or DAC, performs the
conversion of digital signal in to analog electrical signal such as voltage output. Together,
they are often used in digital systems to provide complete interface with analog sensors
and output devices for control systems. It is much easier to convert a digital signal into an
analog signal than it is to do the reverse. Therefore, we will begin with DAC circuitry and
then move to ADC circuitry.
3.4.1 Digital to Analog Conversion (DAC)
There are two most commonly used type of DAC; these are
a) R/2nR DAC/ binary-weighted-input DAC
b) R/2R ladder DAC
3.4.1.1 The R/2nR DAC/ binary-weighted-input DAC
The R/2nR DAC circuit, otherwise known as the binary-weighted-input DAC, is
an inverting summer op-amp circuit which have the input resistor values set at multiple
powers of two: R, 2R, and 4R…. 2nR and supplied by voltages V,
98
Figure 3.18 The R/2nR DAC/ binary-weighted-input DAC
The output voltage is given by
vout  (v0 
v1 v2
v
  ....  nn )
2 4
2
Eqn (3.28)
Usually v0  v1  v2 ....  vn , then for a n binary bit inputs the analog output voltage is
given
vout  (b0 
b1 b2
b
  ....  nn )v0 , where b0 is MSB and bn is LSB
2 4
2
Eqn (3.29)
If we drive the inputs of the circuit with digital gates so that each input is either 0 volts or
full supply voltage, the output voltage will be an analog representation of the binary
value of these three bits. Each input voltage has exactly half the effect on the output as
the voltage before it. In other words, input voltage V1 has a 1:1 effect on the output
voltage (gain of 1), while input voltage V2 has half that much effect on the output (a gain
of 1/2), and V3 half of that (a gain of 1/4). These ratios are the same ratios corresponding
to weights in the binary numeration system.
Example: For a reference voltage of 5v and 3 bit binary inputs the analog output voltages
is summarized in table 3.4.1
Table 3.4.1 The R/2R DAC output voltage
Binary input
b0b1b2
000
001
010
011
100
101
110
111
Analog output
v0
0.00 V
-1.25 V
-2.50 V
-3.75 V
-5.00 V
-6.25 V
-7.50 V
-8.75 V
99
To increase the resolution of R/2nR DAC (more bit conversion), it is required to
add more input resistors which has value of power-of-two sequences. However; the DAC
becomes bulky and also requires high precision resistor values, thus for large number of
bit conversion it is impractical. Besides all logic gates must have same voltage outputs
both in the "high" and "low" state. If one gate is outputting +5.02 volts for a "high" while
another +4.86 volts, the analog output of the DAC will be adversely affected. Likewise,
all "low" voltage levels should be identical, ideally 0.00 volts. For these reason it is
recommended that to use CMOS gates and that input/feedback resistor values are chosen
so as to minimize the amount of current each gate has to source or sink.
3.4.1.2 The R/2R DAC
An alternative to the binary-weighted- input DAC is the so-called R/2R DAC,
which uses fewer unique resistor values. A disadvantage of the former DAC design was
its requirement of several different precise input resistor values, one unique value per
binary input bit. However in “ladder” type of DAC we require only two resistor values of
R and 2R as shown in figure 3.19
Figure 3.19 The R/2R DAC
One leg of the DAC is grounded while all the legs of the DAC are connected to the
switches having 1 and 0 states meaning:


When the corresponding switch is connected to VREF, bit Ik=1
When the corresponding switch is connected to GND, bit Ik=0
Example: Consider the 4 bit DAC shown figure 3.20(a) which has the MSB and LSB
bits ON. In each case redrawing of the circuit will give ease to find the output voltage.
Figure 3.20b and figure 3.20c are the redrawn circuits when MSB and LSB are ON
respectively
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Figure 3.20 A 4 bit R/2R DAC
The one connected to VREF will generate a current that flows towards the inverting
input of the op-amp which will be halved by the resistor network at each node. Therefore,
the current contribution of each input is weighted by its position in the binary number.
The analog output is summarized in table 3.4.2
Table 3.4.2 The R/2R DAC output voltage
Binary input
b0b1b2
000
001
010
011
100
101
110
111
Analog output
v0
0.00 V
-1.25 V
-2.50 V
-3.75 V
-5.00 V
-6.25 V
-7.50 V
-8.75 V
101
3.4.2 Analog to Digital Converter (ADC)
Introduction
The purpose of the ADC is clearly to generate a train of pulses proportional to the
analog input. Connecting digital circuitry to sensor devices is simple if the sensor devices
are inherently digital themselves. Switches, relays, and encoders are easily interfaced
with gate circuits due to the on/off nature of their signals. However, when analog devices
are involved, interfacing becomes much more complex. What is needed is a way to
electronically translate analog signals into digital (binary) quantities, and visa- versa. An
analog-to-digital converter, or ADC, performs the former task while a digital-to-analog
converter, or DAC, performs the latter. An ADC inputs an analog electrical signal such
as voltage or current and outputs a binary number. In block diagram form, it can be
represented as such:
Figure 3.21 Analog to digital converter (ADC)
There are so many types of ADC used for conversion processes
1. Flash or parallel ADC
2. Counter ADC
a. Digital ramp or stair step-ramp ADC
b. Successive approximation ADC
c. Tracking ADC
3. Slope integrating ADC
a. single slope integrating ADC
b. dual slope integrating ADC
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3.4.2.1 Flash ADC
The flash is also called the parallel ADC, basically comprises of comparator and
priority encoder as shown in figure 3.22.
Figure 3.22 Flash ADC or parallel A/D converter
The operation is simple that analog input signal is compared with a reference
voltage by the comparator, and the result is encoded by the priority encoder, which
produces digital outputs are attained. The flash ADC comprises of 2N-1 comparators for
N bit binary outputs.
Example: 3-bit flash ADC circuit with reference voltage Vref is used to convert analog
signal Vin as shown in Figure 3.23. The reference voltage is divided in to seven stage of
voltage each separated 1/8vref (voltage divider rule), the analog input voltage is
compared with voltages at each nodes and then compared by the comparator,


If the vin exceeds the vref at each comparator, the comparator outputs will
be high
If the vin is less than vref at each comparator, the comparator outputs will
be low
The priority encoder generates a binary number based on the highest-order active
input, ignoring all other active inputs. For this particular application, a priority encoder is
realized by a set of Exclusive-OR gates and the encoder circuit is made from a matrix of
diodes when operated, the flash ADC produces a digital output that looks like in figure 3.
23.
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Figure 3.23 8 bit Flash ADC or parallel A/D converter
The flash ADC is simple in construction and operation besides it is most efficient
of the ADC technologies in terms of speed, being limited only in comparator and gate
propagation delays (e.g., very fast 8-bit ADCs capable of 20 million conversions/sec).
Unfortunately, for N number of bit output it requires 2N-1 number of comparators, thus
for large N it is very expensive and component intensive. Another advantage of the flash
converter, often overlooked, is the ability for it to produce a non- linear output. With
equal- value resistors in the reference voltage divider network, each successive binary
count represents the same amount of analog signal increase, providing a proportional
response. For special applications, however, the resistor values in the divider network
may be made non-equal. This gives the ADC a custom, nonlinear response to the analog
input signal. No other ADC design is able to grant this signal-conditioning behavior with
just a few component value changes.
Example: Determine the binary output of A 3-bit flash ADC Priority encoder subjected
to comparator pattern
a. For comparator outputs of 0001111, priority encoder generates 100
b. For comparator outputs of 0111111, priority encoder generates 110
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3.4.2.2 Counter ADC
These are commonly used types of ADC which basically comprises of digital to
analog converter (DAC), counter and comparator for conversion process. Their operation
is by means of the counter connected to DAC which produces analog signal that can be
compared with analog signal to be digitized and when they become equal, the counter
will stop counting and its current binary output is the digitized form of the analog signal.
The types of counter ADC are digital or stair step ramp, successive approximation, and
tracking ADC
Digital ramp ADC
Also known as the stair step-ramp or simply counter ADC comprises three basic
elements theses are; binary counter, a digital-to-analog converter (DAC), and an analog
comparator. The basic idea is to connect the output of a free-running binary counter to the
input of a DAC, then compare the analog output of the DAC with the analog input signal
to be digitized and use the comparator's output to tell the counter when to stop counting
and reset. Figure 3.24 shows a digital ramp ADC.
Figure 3.24 Digital ramp ADC
As the counter counts up with each clock pulse, the DAC outputs a slightly higher (more
positive) voltage. This voltage is compared against the input voltage by the comparator.

If the input voltage is greater than the DAC output, the comparator's
output will be high and the counter will continue counting normally.
105

If the input voltage is equal or lower than the DAC output, the
comparator's output will be low and the counter will be reset and the latch
will execute a binary output
The effect of this circuit is to produce a DAC output that ramps up to whatever level the
analog input signal is at, output the binary number corresponding to that level, and start
over again. This ADC is relatively slow since conversion time could be up to 2N, where
N is the resolution of the ADC
Successive approximation ADC
One method of addressing the digital ramp ADC's shortcomings is the so-called
successive-approximation ADC. The only change in this design is a very special counter
circuit known as a successive-approximation register. Instead, of counting up in binary
sequence, this register counts by trying all values of bits starting with the most significant
bit and finishing at the least-significant bit. Throughout the count process, the register
monitors the comparator's output to see if the binary count is less than or greater than the
analog signal input, adjusting the bit values accordingly. The way the register counts is
identical to the "trial-and-fit" method of decimal- to-binary conversion, whereby different
values of bits are tried from MSB to LSB to get a binary number that equals the original
decimal number.
Operation is based on a binary search



Initially, the register provides an output corresponding to half the range (1000…0)
If the analog input is greater, then MSB=1, else MSB=0
The register performs the same operation from MSB to LSB
Figure 3.25 Successive approximation ADC
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The advantage to this counting strategy is much faster results: the DAC output converges
on the analog signal input in much larger steps than with the 0-to-full count sequence of a
regular counter. The inner workings of the successive-approximation register (SAR) is
shown in figure 3.26, note that the SAR is generally capable of outputting the binary
number in serial (one bit at a time) format, thus eliminating the need for a shift register.
Figure 3.26 Successive approximation register (SAR) internal working
Note how the updates for this ADC occur at regular intervals, unlike the digital ramp
ADC circuit. One of the important characteristics is that the conversion requires only N
steps, where N is the resolution of the ADC.
Tracking ADC
A third variation on the counter-DAC-based converter theme is the tracking ADC
which instead of a regular "up" counter driving the DAC, the circuit uses an up/down
counter. The counter is continuously clocked, and the up/down control line is driven by
the output of the comparator. So,


When the analog input signal exceeds the DAC output, the counter goes into
the "count up" mode.
When the DAC output exceeds the analog input, the counter switches into the
"count down" mode.
Either way, the DAC output always counts in the proper direction to track the input
signal as shown in figure 3.27.
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Figure 3.27 Tracking ADC
An advantage of this converter circuit is speed, since the counter never has to
reset. This ADC has a much faster update time than any of the other "counting" ADC
circuits. Also note how at the very beginning of the plot where the counter had to "catch
up" with the analog signal, the rate of change for the output was identical to that of the
first counting ADC. Also, with no shift register in this circuit, the binary output would
actually ramp up rather than jump from zero to an accurate count as it did with the
counter and successive approximation ADC circuits.
Perhaps the greatest drawback to this ADC design is the fact that the binary
output is never stable: it always switches between counts with every clock pulse, even
with a perfectly stable analog input signal. This phenomenon is informally known as bit
bobble, and it can be problematic in some digital systems. This tendency can be
overcome, though, through the creative use of a shift register. For example, the counter's
output may be latched through a parallel- in/parallel-out shift register only when the
output changes by two or more steps. Building a circuit to detect two or more successive
counts in the same direction takes a little ingenuity, but is worth the effort.
3.4.2.3 Slope (integrating) ADC
So far, it has been able to escape the sheer volume of components in the flash
converter by using a DAC as part of ADC circuitry. However, this is not the only option.
It is possible to avoid using a DAC and substitute it with an analog ramping circuit
(called as integrator) and a digital counter with precise timing. This is the basic idea
behind the so-called integrating ADC. Instead of using a DAC with a ramped output, we
can use an op-amp circuit called as integrator to generate a saw tooth waveform which is
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then compared against the analog input by a comparator. The types slope integrating
ADC are; single slope and dual slope
Single-slope integrating ADC
The single slope integrating ADC basically comprises ramp integrator,
comparator and a counter to convert analog to digital signals. The ramp integrator
generates saw tooth wave form and the time it takes for the saw tooth waveform to
exceed the input signal voltage level is measured by means of a digital counter clocked
with a precise-frequency square wave (usually from a crystal oscillator). The basic
schematic diagram is shown in figure 3.28
Figure 3.28 Slope (integrating) ADC
When the ramp signal is equal to the analog signal the comparator output will be zero
hence the latch output at that event is the digital equivalent of analog signal.
An integrator circuit can be simply realized by opamp comprising Resistor and
capacitor, as shown figure 3.28. In reality, a latching circuit timed with the clock signal
would most likely have to be connected to the IGFET gate to ensure full discharge of the
capacitor when the comparator's output goes high.
Operation of Single-slope integrating ADC

When the comparator output is low (input voltage greater than integrator
output), the integrator is allowed to charge the capacitor in a linear fashion.
Meanwhile, the counter is counting up at a rate fixed by the precision clock
frequency. The time it takes for the capacitor to charge up to the same voltage
level as the input depends on the input signal level and the combination of –
Vref, R, and C.
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
When the comparator output goes high i.e. the capacitor reaches that voltage
level, the counter's output is feed into the shift register for a final output. And
the IGFET is triggered "on" by the comparator's high output, discharging the

capacitor back to zero volts.
Thus the integrator output voltage falls to zero, the comparator output switches
back to a low state, clearing the counter and enabling the integrator to ramp up
voltage again.
This ADC circuit behaves very much like the digital ramp ADC, except that the
comparator reference voltage is a smooth saw tooth waveform rather than a "stair step:
The single-slope ADC suffers all the disadvantages of the digital ramp ADC, with the
added drawback of calibration drift. The accurate correspondence of this ADC's output
with its input is dependent on the voltage slope of the integrator being matched to the
counting rate of the counter (the clock frequency). With the digital ramp ADC, the clock
frequency had no effect on conversion accuracy, only on update time. In this circuit,
since the rate of integration and the rate of count are independent of each other, variation
between the two is inevitable as it ages, and will result in a loss of accuracy. One
advantage of this circuit is that it avoids the use of a DAC, which reduces circuit
complexity. An answer to this calibration drift dilemma is found in a design variation
called the dual slope converter.
Dual slope integrating converter
The dual-slope integrating ADC comprises of four basic elements these are; an integrator,
a zero-crossing detector, a binary counter, Logic gates and switches as shown in figure
3.29.
Figure 3.29 Dual slope integrating ADC and ramping diagram
110
The integrator circuit is driven positive and negative in alternating cycles to ramp
down and then up, rather than being reset to 0 volts at the end of every cycle. The
integrator has two direction of ramping

In one direction of ramping, the integrator is driven by the positive analog input
signal (producing a negative, variable rate of output voltage change, or output
slope) for a fixed amount of time, as measured by a counter with a precision
frequency clock.

Then, in the other direction, with a fixed reference voltage (producing a fixed rate
of output voltage change) with time measured by the same counter.
The counter stops counting when the integrator's output reaches the same voltage as it
was when it started (the fixed-time portion of the cycle). The amount of time it takes for
the integrator's capacitor to discharge back to its original output voltage becomes the
digital output of the ADC circuit,
The sequence of operation of dual-slope integrating ADC can described as


Counter is reset and switch is connected to the analog input


The integrator generates a negative ramp whose slope is proportional to
the analog input
The comparator goes HIGH, enabling clock pulses into the counter
When counter overflows, it resets to zero and the control circuit switches the
switch to a reference negative voltage


This causes the integrator to generate a positive slope ramp
When this ramp reaches zero, the comparator goes low and stops the
counter, whose value represents the analog input
The dual-slope method can be thought of analogy in terms of a rotary spring used to
measure the rotary speed of a shaft. Initially the spring is at a relaxed state, and then it is
turned, or "wound up," by the rotating shaft (input signal) for a fixed amount of time.
Then it is allowed to unwind at a fixed rate, thus the time it takes to unwind is directly
proportional to the speed at which it was wound.
This technique of analog-to-digital conversion escapes the calibration drift problem
of the single-slope ADC because both the integrator’s integration coefficient ("gain") and
111
the counter's rate of speed are in effect during the entire "winding" and "unwinding"
cycle portions.
Even though slow rate of conversion dual-slope ADCs have the advantages of
providing very high resolution, insensitive to clock drift (RC drifts) and high-frequency
noises. It is widely used in digital multi-meters.
3.4.3 Performance characteristics of ADC circuits
The most important consideration in selecting or designing an ADC is their
performance characteristics which is described by resolution, Sample frequency (or
conversion rate) and step recovery
Resolution
Resolution is the number of binary bits output by the converter. An ADC with a 10bit output can represent up to 1024 unique conditions of signal measurement. Over the
range of measurement from 0% to 100%, there will be exactly 1024 unique binary
numbers output by the converter (from 0000000000 to 1111111111, inclusive). Similarly
an 11-bit ADC will have 2048 representing which is twice of 10 bit resolution.
Resolution is very important in instrument employing ADC such as data acquisition
systems (circuits designed to interpret and record physical measurements in electronic
form).
Example: Suppose we were measuring the height of water in a 40-feet capacity tank
using an instrument with a 10-bit ADC having 1024 possible states (1023 steps). To
determine how much physical water level will be represented in each step of the ADC,
0.039101 feet per step. This step value of 0.039101 feet represents the smallest amount of
tank level change detectable by the instrument. Admittedly, this is a small amount, less
than 0.1% of the overall measurement span of 40 feet.
Sample frequency or conversion rate
This is simply the speed at which the converter outputs a new binary number. Like
resolution, this consideration is linked to the specific application of the ADC. Depending
up on the signal to be measured (slow or fast varying) the sample frequency need to
fulfill the nyquist criterion so that substantial part of the signal is not missed during the
conversion process.
112
Example: If the converter is being used to measure slow-changing signals such as room
temperature, it could probably have a very slow sample frequency and still may perform
adequately. Conversely, if it is being used to digitize an audio frequency signal cycling at
several thousand times per second, the converter needs to be considerably faster.
Theoretically the highest-frequency waveform that an ADC can capture is the socalled Nyquist frequency, equal to one half of the ADC's sample frequency. If an ADC
circuit has a sample frequency of 5000 Hz, the highest-frequency waveform it can
successfully resolve will be the Nyquist frequency which is 2500 Hz. But if the ADC is
subjected to an analog input signal whose frequency exceeds the Nyquist frequency
(2500 Hz), then the ADC will output a digitized signal of false low frequency. This
phenomenon is known as aliasing. The Nyquist frequency is an absolute maximum
frequency limit for ADC, and does not represent the highest practical frequency
measurable. To be safe, one shouldn't expect an ADC to successfully resolve any
frequency greater than one- fifth to one-tenth of its sample frequency.
A practical means of preventing aliasing is to place a low-pass filter before the
input of the ADC, to block any signal frequencies greater than the practical limit, so that
the ADC circuit is prevented from seeing any excessive frequencies and hence will not
digitize them. Generally it is better to have such frequencies go unconverted than to have
them be "aliased" and appear in the output as false signals.
Step recovery
The step recovery is a measure of how quickly an ADC changes its output to match a
large, sudden change in the analog input. In some converter technologies especially, step
recovery is a serious limitation. For example the tracking converter has a typically fast
update period but a disproportionately slow step recovery. An ideal ADC has a great
many bits for very fine resolution, samples at lightning-fast speeds, and recovers from
steps instantly. It also, unfortunately, doesn't exist in the real world. Of course, any of
these traits may be improved through additional circuit complexity, either in terms of
increased component count and/or special circuit designs made to run at higher clock
speeds. Different ADC technologies, though, have different strengths.
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Problems
1. In unbounded strain gauge of circuit shown in figure 3.12 the nominal resistance is
120Ω each and the gaga factor is 2.4. If the excitation voltage is 10v, what is the open
circuit output voltage for tensile strain of 0.001?
2. For resistive half and full bridge derive the expression for the output voltage and their
sensitivity.
3. The instrumentation amplifier is available in the form of controllable also called as
programmable. Sketch the circuit diagram of such type of INA and drive the equation
relating the input and its output. What its advantage over the INA discussed in section
3.3.2.
4. Determine the analog voltage of a 3 bit binary weighted DAC if the reference voltage
is 5v, and having feedback resistor value of 800  and the input resistance R=1 k  .
5. design a 4 bit R/2R DAC of your own and determine the analog output for each
binary combination of input
6. Design a 3 bit flash ADC having a reference voltage of 5v. And determine the output
binary digital outputs for each stage of analog input. How much is the resolution?
7. Rank the ADC , Single-slope integrating, dual-slope integrating, counter, tracking,
successive approximation, flash from best to worst in terms of
a. Resolution/complexity ratio:
b. Speed
c. Step recovery
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CHAPTER FOUR
OUTPUT PRESENTATION
4.1
Introduction
A measuring instrument is simply a device for determining the value of a quantity
or physical phenomenon. The purpose served by the instrument is, first, to determine or
ascertain the value (magnitude) of some particular phenomena. The instrument may be
required to indicate or record the value of the measured quantity in different forms such
as graphically or numerically.
The output presentation is classified in to display, recording or both.
1. Display or indicating
a. pointer deflection
b. Graphically
c. numerically, alpha numerically
2. Recording
a. chart recording
b. magnetic digital recording
3. Data acquisition systems and data logging
4.2
Display or Indicating
Display or indicating is one of output presentation mechanism in which a device
gives an instantaneous visible indication of the signal from sensor, in other words it is a
real time device that indicates the phenomena happing at present, and it does not save it
for future use or reference. Often the output presentation is either in analog or digital
display form. The analog display instruments usually uses pointer deflection or graphical
means of presenting, while the digital display instruments use numbers such as using the
seven segment light emitting diodes (LED) or liquid crystal display (LCD).
4.2.1 Pointer deflection
Pointer deflection display or Indicating refers to an instrument that indicates the
measured variable in calibrated scale by pointer defection as shown in figure 4.1. The
value of the quantity is presented to the observer on the scale to any fraction with the
limitations of the instrument and the human eye.
115
Figure 4.1 Pointer deflection display
Basically the pointer deflection displays are analogue electrical and electronic
instruments. They are portable electromechanical instruments having a wide application
ranging from home appliances equipments to industries. There are four types of these
meters built around the following principles of operations:
1. The permanent magnet moving coil (PMMC) movement mechanism, which
responds to average or direct current only;
2. The moving iron vane (MIV), fixed coil movement mechanism, which responds
to DC or AC currents.
3. The moving magnet fixed coil (MMFC) movement, which again responds to
direct current only; and
4. The electrodynamometer (EDM) movement with one fixed coil and one moving
coil, that responds to direct or alternating currents.
4.2.2 Cathode ray oscilloscopes
The oscilloscope, or more generally the cathode ray oscilloscope (CRO), is the
most versatile electronic measuring instrument which displays electrical signals as a
wave form with high accuracy and precision. It is an indispensable instrument for the
measurements of frequency, time duration, and phase differences at audio and higher
frequencies Besides the CRO can mainly be regarded as a true analog instrument in that it
serves both as a voltmeter and as an electrical-to-optical transducer
Figure 4.3 Cathode ray oscilloscopes
116
The oscilloscope displays the wave form on a cathode ray tube, which is also found in
television sets and computer monitors. The basic structures of a general purpose cathode
ray tube (CRT) are illustrated in Figure 4.3
4.2.3 Numerical/digital display
Rather than showing the measured value in terms of pointer deflection or wave
form, digital display instruments indicate the output as number. The electronic circuitry
of these digital instruments uses the analog to digital converter (ADC) and display driver
to present the number to the observer as shown in figure 4.3. The display driver is an
electronic circuit that is used to drive the seven segment light emitting diodes (LED) or
light crystal display (LCD).
Figure 4.3 Block diagram of digital Indicating Instrument
The seven segment display is a method of forming the characters ot 0 to9 by selectively
highlighting and blanking appropriate segments arranged in the form of 8.
The light emitting diode (LED) is one of the very commonly numeric displays
comprising of diodes which glows when supplied with very small current. They are made
of semiconductors such as gallium phosphide or gallium arsenide with additional small
impurities. There are different colures of LED such as Green, red, orange and yellow are.
Single LED is also used to show two states such as high and low or on and off. LED are
small, inexpensive and reliable. And have a fast responses time as compared to LCD.
These days due to the advances of technology in LCD, LED is getting replaced by LCD.
The liquid crystal displays (LCD) are a film of liquid crystals sandwiched between two
transparent electrodes. Applying a potential difference across the electrodes causes the
refractive index of the liquid to change. Selectively energizing the individual segment
forms different characters, alphanumeric or more complex characters are produced by
using a sixteen segment display or a dot matrix array
The main advantage of LCD is relatively low cost and low power consumptions (can
117
be power by battery), how ever their time response is much slower than LED example
typical LED responses in 100 nanoseconds while LCD 10micro seconds. Now a days
LCD are the most widely used in many display screens such as watches, mobile and
meters.
4.3
Recording
Recording is another way of output presentation mechanism in which is a device
is used to make permanent record of a measured value or signal. Recording is useful for
analysis, interpretation or monitoring of data. The recording of measured variable can be
in the form of graphical or numerical on paper or chart, or on magnetic tape, disk or
semiconductor memory. Recorders are categorized as chart recorders and magnetic
recorders.
4.3.1 Chart recording /Graphical recording
Chart recording is a mechanism by which an instrument makes a written record,
usually on paper, of the value of the measured quantity against some other variable or
against time. Chart recorders also referred as a graphical recorder which plots or draws
measured variations of electrical or non-electrical quantities with respect to time over
seconds, minutes, hours, or days. In many instances, the recording is needed to check the
performance of industrial processes or electrical power generation and distribution
systems.
Important features of the basic graphical recorders are: input impedance,
timescale, event markers, and writing mechanism. The use of amplifier ensures the input
impedance to the recorder is maintained relatively high. The writing mechanism can be
an ink pen with a capillary feed system, or heated stylus recording the variations of the
input (Vin) on a heat sensitive paper. Other recorders, commonly known as photographic
or ultraviolet (UV) recorders, use a light beam as a pointer leaving traces on photographic
papers. Recorders known as multi-channel recorders contain a number of writing pens in
all making marks simultaneously on a wide roll of paper thereby permitting easy
comparison of several simultaneous functions. The common chart recorders are Moving
coil chart recorder (galvanometric chart recorder), Servo chart recorder, XY plotter, Ultra
violent chart recorder, Thermal array recorder. Figure 4.3 shows some of the chart
recorders
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Moving coil chart recorder
Figure 4.3Chart recorders.
These recorders are built around a moving coil instrument where the indicating
pointer is replaced by a writing pen movement on a graduated paper moving at a constant
speed. The tip of the pointer leaves marks on the paper thereby forming a permanent
record of the amplitude of the input signal with respect to time as shown in Fig. 4.3a.
Servo chart recorder
Servo chart recorders are common and accurate way of recording data. It uses a
pen to draw a trace proportional to the signal being monitored as shown in figure 4.3c.
The pen driven by a belt connected to a servomotor traverses the paper linearly along a
guide rail. The pen is connected to wiper of a linear potentiometer which monitors the
pens displacement. An electrical circuit compares the output from the potentiometer and
compares it to the signal from the transducer. The difference in voltage is thus the error
signal. The circuit then drives the servo motor, which moves the pen, until the error
signal is zero. Hence a trace proportional to the input signal is produced (closed-loop
control system).
XY recorder/plotter
The X-Y plotter also known as the flat bed plotter is an analogue device which
produces a graph showing the relation between two input signals as shown in figure 4.3c.
In XY plotter the paper is held in a fixed position on a flat bed. Two voltage signals x and
119
y are applied through their respective terminals of X and Y. the pen which is hold in the
transverse bar moves according to the inputs in the two dimensions of input. XY plotters
are fairly slow and are also not used to record signal against time. The static performance
of such an instrument is described by accuracy, resolution, functions of an X-Y
recorder’s electronic and mechanical characteristics. The slow speed and acceleration in
response to the capture rapid and transient signal input determine the dynamic response.
Other important features include chart size, number of pens,
4.3.2 Magnetic tape recorders
The principle of recording with instrumentation magnetic tapes is illustrated in
Figure 4.4. There are three main components: a core with a small nonmagnetic gap, a coil
wound on the core, and a thin magnetic coating sitting on a base. The latter can be a wire,
but inmost application it consists of a flexible plastic tape.
Figure 4.4 Magnetic tape recording
The magnetic coating is a thin layer of iron oxide (Fe2°3) particles, and the core is made
of laminated steel alloys. The core assembly carrying the winding is called a tape
recording head. With current flowing in the coil, a magnetic flux will bridge cross the
non-magnetic gap, thus magnetizing the iron oxide particles as they pass the gap.
Because the magnetic coating is purposely selected for its high remanence, the iron
particles will remain magnetized in the direction of tape travel with the magnitude of flux
impressed upon the tape as it moves in front of the non-magnetic gap. Hence, a recording
of the applied signal will have been realized. When the same tape is passed through the
front gap of a similar playback head, it will cause variations in the reluctance of the
winding, and thereby inducing a voltage which ideally is required to be a faithful
reproduction of the recorded signal. A functional diagram of a complete magnetic taperecorder is shown .in Fig. 4.5. While two different heads are needed for accurate
instrumentation recording and reproduction, only one combined head is used for coarse
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instrumentation works as well as for audio recordings. With one head, one needs only to
switch from a record to reproduce (playback) mode. At the same time the direction of
tape travel has accordingly to is set by the sense of rotation of the motor moving the tape
transport.
Figure 4.5 Magnetic tape recorder
Four factors contribute to the accuracy of magnetic tape recording, particularly for
instrumentation and data processing purposes. These are; the magnetization
characteristics of the magnetic recording medium, the tape speed, the bandwidth of the
recorded signal, and the gap width. All these factors are considered together to minimize
errors and distortions.
Digital recording
Magnetic tapes are also commonly used for digital recording of binary data encoded in
terms of "1s" or "0s", both in instrumentation and data processing systems. Three broad
methods of digital recording can be briefly described as follows:
a) Return to zero (RZ) systems which employ one direction of saturation for" 1”,
while magnetization to saturation in the opposite direction then represents "0"
b) Non-return to zero (NRZ) systems which regard changes in the direction of
magnetization as "1", while no changes in magnetization are taken as "0".
c) Phase encoding (FE): systems in which one sense of magnetization is
regarded as" 1”, while the opposite sense is regarded as "0”
For each method, the density .of recording is measured in terms of so many bits
per tape length. The unit often used in bits per inch (BPI), typical values being 8000 BPI,
and 1600BPI for NRZ and phase encoded systems, respectively. The recorded binaries
represent decimals or alphanumeric characters using one of the standard binary codes.
Also, the record and reproduce amplifiers are very simple, and the only requirements are
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maintenance of accurate tape and head alignments. For computer application, recording is
mostly made in a block form, meaning that a block of information is recorded at one
time, in place of conventional or incremental recording where data is continuously stored
on the tape. As the recorded binaries are typically obtained by digitizing input analog
signals, the latter can be recovered by use of digital to analog converters.
Alternative recording systems which are gaining wide applications use the same
principles as already described for magnetic recording, but with the flexible tapes
replaced by rigid disk packs, diskettes or floppy disks, all operated with use of movable
heads to scan magnetically coated surfaces. Storage capacities measured in kilo (i.e.
thousand), millions, and possibly billions of bytes (i.e 8-bit words), and access times
ranging from 35 to 100 ms are the two important features of these recording devices.
Data recorded on these devices is therefore much more voluminous than those recorded
in tapes, and can also be accessed much faster
4.4
Data acquisition systems
In instrumentation, data acquisition is the process of acquiring data of interest
(measuring variables) for purposes of measurement and control often recording for later
study and analysis such as further processing. The advancement of semiconductor
technology has made instrumentation systems to comprise the features of computing in
output presentation mechanisms. A data acquisition refers to a process where information
is converted in to a form that can be handled by computer
4.4.1 Computer and data acquisition systems
A Computer data acquisition system is a system where a parameter or parameters
are detected by a sensor or transducer is suitably conditioned and converted in to a form
that can be stored or processed by a computer. The use of computer provides advantages
of quality measurement and control by reducing error. Computers are useful in solving
complex mathematical models, performing repetitive analysis or manipulations quickly
with high accuracy and precision. By the inclusion of multiplexers, data acquisition
system can be made to acquire several physical parameters at a time. A multiplexer
(MUX) is a switch that routes information from several sources to one common
destination.
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Figure 4.6 Data acquisition system
Figure 4.6 shows a data acquisition system in which analog measurement from sensors is
converted in to digital and then fed to a computer for storage, real time display, or
recording for further analysis. A sample and hold device is necessary to ensure the
sampled value is held constant during the time needed for conversion of the analog to
digital output. Simple data acquisition systems are referred to as data loggers.
4.4.2 Data logger
Data logger (also data recorder) is an electronic device that records data over
time or in relation to location either with a built in instrument or sensor, or via external
instruments and sensors. Increasingly, but not entirely, they are based on a digital
processor (or computer). They generally are small, battery powered, portable, and
equipped with a microprocessor, internal memory for data storage, and sensors. Some
data loggers interface with a personal computer and utilize software to activate the data
logger and view and analyze the collected data, while others have a local interface device
(keypad, LCD) and can be used as a stand-alone device.
Data loggers vary between general purpose types for a range of measurement
applications to very specific devices for measuring in one environment or application
type only. It is common for general purpose types to be programmable; however, many
remain as static machines with only a limited number or no changeable parameters.
Electronic data loggers have replaced chart recorders in many applications.
One of the primary benefits of using data loggers is the ability to automatically
collect data on a 24-hour basis. Upon activation, data loggers are typically deployed and
left unattended to measure and record information for the duration of the monitoring
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period. This allows for a comprehensive, accurate picture of the environmental conditions
being monitored, such as air temperature and relative humidity.
Data logging versus data acquisition
The terms data logging and data acquisition are often used interchangeably. However, in
a historical context they are quite different. A data logger is a data acquisition system, but
a data acquisition system is not necessarily a data logger.

Data loggers typically have slower sample rates. A maximum sample rate of 1 Hz
may be considered to be very fast for a data logger, yet very slow for a typical data

acquisition system.
Data loggers are implicitly stand-alone devices, while typical data acquisition system
must remain tethered to a computer to acquire data. This stand-alone aspect of data
loggers implies on-board memory that is used to store acquired data. Sometimes this
memory is very large to accommodate many days, or even months, of unattended
recording. This memory may be battery-backed static random access memory, flash
memory or EEPROM. Earlier data loggers used magnetic tape, punched paper tape,

or directly viewable records such as "strip chart recorders".
Given the extended recording times of data loggers; they typically feature a time- and
date-stamping mechanism to ensure that each recorded data value is associated with a
date and time of acquisition. As such, data loggers typically employ built-in real-time
clocks whose published drift can be an important consideration when choosing

between data loggers.
Data loggers range from simple single-channel input to complex multi-channel
instruments. Typically, the simpler the device the less programming flexibility. Some
more sophisticated instruments allow for cross-channel computations and alarms
based on predetermined conditions. The newest of data loggers can serve web pages,

allowing numerous people to monitor a system remotely.
The unattended and remote nature of many data logger applications implies the need
in some applications to operate from a DC power source, such as a battery. Solar
power may be used to supplement these power sources. These constraints have
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generally led to ensure that the devices they market are extremely power efficient
relative to computers. In many cases they are required to operate in harsh
environmental conditions where computers will not function reliably.

This unattended nature also dictates that data loggers must be extremely reliable.
Since they may operate for long periods nonstop with little or no human supervision,
and may be installed in harsh or remote locations, it is imperative that so long as they
have power, they will not fail to log data for any reason. As such data loggers are
almost completely immune to the problems that might affect a general-purpose
computer in the same application, such as program crashes and the instability of some
operating systems.
Applications of data logging include:









Unattended weather station recording (such as wind speed / direction, temperature,
relative humidity, solar radiation).
Unattended hydrographic recording (such as water level, water depth, water flow,
water pH, water conductivity).
Unattended soil moisture level recording. Unattended gas pressure recording.
Road traffic counting.
Process monitoring for maintenance and troubleshooting applications.
Monitoring of relay status in railway signaling.
For science education enabling 'measurement', 'scientific investigation' and an
appreciation of 'change'
Load profile recording for energy consumption management.
Water level monitoring for groundwater studies.
Data Loggers are changing more rapidly now than ever before. The original model of a
stand alone data logger is changing to one of a device that collects data but also has
access to wireless communications for alarming of events, automatic reporting of data
and remote control. Data loggers are beginning to serve web pages for current readings email their alarms and FTP their daily results into databases or direct to the users.
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Examples

A flight data recorder (FDR), a piece of recording equipment used to collect specific
aircraft performance data. The term may also be used, albeit less accurately, to
describe the cockpit voice recorder (CVR), another type of data recording device

found onboard aircraft.
An event data recorder (EDR), a device installed by the manufacturer in some
automobiles which collects and stores various data during the timeframe immediately



before and after a crash.
A voyage data recorder (VDR), a data recording system designed to collect data from
various sensors on board a ship.
The growing, preparation, storage and transportation of food. Data logger is generally
used for data storage and these are small in size.
In automobiles, all diagnostic trouble codes (DTCs) are logged in engine control units
(ECUs) so that at the time of service of a vehicle, a service engineer will read all the
DTCs using Tech-II or similar tools and will come to know problems occurred in the
vehicle.
Problems
1. some types of voltmeters and ammeter have both types of analog and digital display
what advantage do you think such meters have
2. Common error in pointer deflection meters is the parallax error. What is parallax
error, and describe the way to overcome parallax error.
3. Computer based oscilloscopes are available which have the features of standard
cathode ray oscilloscopes, what advantages do you think computer based
oscilloscopes offer as compare to the standard CRO.
4. Describe briefly the principle of operation of each of pointer deflection meter
discussed in section 4.2.1 by static and dynamic performance characteristics of
instruments
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