Lecture 02 instrument transducers manipal

INSTRUMENTATION AND TRANSDUCERS
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They are those which do not require an auxiliary power device to produce an
output
Piezo electrical crystal measuring acceleration is an example.

In this diagram, the crystal is sandwiched
between 2 metallic electrodes, a fixed mass is
placed on top of the sandwich. The property is
that when a force is applied to them, it
produces output voltage, The mass is fixed ,
force is proportional to acceleration, the output
voltage is proportional to force and hence to
acceleration. This is also called accelerometer,
which converts the acceleration to electrical
voltage

Comparison between electrical and mechanical transducer
Electrical transducer Mechanical transducer
Output signals are electrical in nature Output signals are mechanical in nature
Electrical quantities are voltage, resistance,
capacitance , inductance , phase angle etc.
They are temperature pressure, force,
torque, density
Electrical or electronic components are
used
Spring elements, bellows are used
Flow measurement isn’t possible Flow measurement is possible
It is used for pressure and displacement
measurement
Orifice, ventury tubes are used for velocity
and pressure measurement

Desirable Characteristics of Transducers
For choosing a transducer for any application the
following characteristics should be checked
1) Input characteristics
2) Output characteristics
3) Transfer characteristics
The three characteristics given above are known as
the DESIRABLE CHARACTERISTICS OF A TRANSDUCER

1) INPUT CHARACTERISTICS:
a)Type of input and operating range. The
foremost consideration for the choice of a
transducer is the input quantity it is going to
measure and its operating range. The transducer
should maintain a good resolution throughout its
operating range.
b) Loading effects. The transducer, that is selected
for a particular application should ideally extract no
force, power or energy from the quantity under
measurement in order that the latter is measured
accurately.

2) OUTPUT CHARACTERISTICS:
a) Type of electrical output. The types of output
which may be available from the transducers
may be a voltage, current, impedance or a time
function of these amplitudes.
b) Output impedance. The output impedance Zo
of a transducer determines to the extent the
subsequent stages of instrumentation is loaded.
c) Useful output range. The output range of a
transducer is limited at the lower end by noise
signals which may hamper the desired input
signal. The upper limit is set by the maximum
useful input level.

3) TRANSFER CHARACTERISTICS
a) Transfer function. The transfer function of a
transducer defines a relationship between the
input quantity and the output quantity.
Transfer function = qo = f(qi)
Where qo is the output quantity and qi is the input
quantity
b) Sensitivity.
Static sensitivity
The static sensitivity of an instrument or an
instrumentation system is the ratio of the
magnitude of the output signal to the quantity to
be measured. Its units are counts/volt etc.
depending upon the type of input and output.

FIGURE a)Non feedback(Open loop) system

The transfer function for the desired inputs in a
non-feedback (open loop) system is GD and the
desired input is rD. The output due to desired input
C=GDrD.

Lecture 02 instrument transducers manipal

THE INPUT QUANTITIES ARE CATEGORISED INTO 3 CLASSES
1. DESIRED INPUT
2. MODIFYING INPUT
3. INTERFERING INPUT
 DESIRED INPUTS ARE DEFINED AS QUANTITIES FOR WHICH THE
INSTRUMENT OR MEASUREMENT SYSTEM IS SPECIFICALLY DESIGNED
TO MEASUREAND RESPOND.
THE DESIRED INPUT rD PRODUCES AN OUTPUT COMPONENT CD
=GDrD IN ACCORDANCE WITH THE INPUT,OUTPUT RELATIONSHIP
SYMBOLIZED BY A MATHEMATICAL OPERATOR GD WHICH IS
DEFINED AS A TRANSFER FUNCTION.

 MODIFYING INPUT ISDEFINED AS THE INPUT WHICH CAUSES A
CHANGE IN INPUT OUTPUT RELATIONSHIP FOR EITHER DESIRED
INPUT OR INTERFERING INPUT OR BOTH.
IT IS AN INPUT DENOTED BY rM WHICH MODIFIES GD AND OR GI.
THE SYMBOLS GMDAND GMI REPRESENT THE SPECIFIC MANNER IN
WHICH rM AFFECTS GD AND GI RESPECTIVELY.
 INTERFERING INPUTSREPRESENT THE QUANTITIES TO WHICH THE
INSTRUMENT AND MEASUREMENT SYSYTEM BECOMES
UNINTENTIONALLY SENSITIVE.THE INTERFERING INPUT rI IS
OPERATED UPON A TRANSFER FUNCTION GI TO GET CD = GIrI.

Suppose, due to the modifying input, like
changes in ambient temperature, the transfer
function changes by ∆GD and therefore
modifying transfer function is GMD=GD+ ∆GD.

Null-type and deflection-type
instruments
 In deflection type instruments, the value
of the quantity being measured is
displayed in terms of the amount
movement of a pointer. The pressure-
measuring device shown is an example of
a deflection type instrument.
 An alternative type of pressure gauge is
the deadweight gauge which is a null-type
instrument. Here, weights are put on top
of the piston until the downward force
balances the fluid pressure. Weights are
added until the piston reaches a datum
level, known as the null point. Pressure
measurement is made in terms of the
value of the weights needed to reach this
null position.

Sensitivity
Sensitivity is the ability of the transducer to generate
an output for a given change in input.
Sensitivity =Change in output / Change in input
E.g. A thermocouple that increases output
voltage by 3mV per degree Celsius temperature
change has a sensitivity of 3mV/ C

Analogue and digital instruments
 An analogue instrument gives an output that
varies continuously as the quantity being
measured changes. The output can have an
infinite number of values within the range that
the instrument is designed to measure. The
deflection-type of pressure gauge is an example
of an analogue instrument.
 As the input value changes, the pointer moves
with a smooth continuous motion. Whilst the
pointer can therefore be in an infinite number of
positions within its range of movement, the
number of different positions that the eye can
discriminate between is strictly limited, this
discrimination being dependent upon how large
the scale is and how finely it is divided.

Analogue and digital instruments
 A digital instrument has an output that varies in discrete steps and so can only have a
finite number of values. The rev counter is an example of a digital instrument. A cam is
attached to the revolving body whose motion is being measured, and on each
revolution the cam opens and closes a switch. The switching operations are counted by
an electronic counter. This system can only count whole revolutions and cannot
discriminate any motion that is less than a full revolution

Sensitivity of a sensor is defined as the
change in output for a given change in input,
usually a unit change in input.
Sensitivity represents the slope of the transfer
function.
Also is used to indicate sensitivity to other
environment that is not measured.

Sensitivity = dqo/dqi
When calibration curve is linear, the sensitivity of the instrument
can be defined as the slope of the calibration curve. In this case
the slope will be constant over the entire range of the
instrument. However if the curve is non linear, the slope varies
with input shown in the fig.

c) Hysteresis. It is a phenomenon which
depict different output effect while
loading and unloading whether it’s a
mechanical system or an electrical system
or any system. It’s a non coincidence of
loading and unloading curves

Hysteresis
• Hysteresis is the deviation of the sensor’s output at
any given point when approached from two
different directions

• When the input of the instrument is slowly varied
from 0 to full scale and the back to 0, its output varies
as shown in fig.(a)

• In the case of the instruments which are used on
both sides of 0 (+ve & -ve applied input) the variation
of output is shown in fig.(b)

• At constant Columb’s friction, the input-
output relationship are like the ones shown
in fig.(c) & fig.(d)

Statement. The law states that for two dry
solid surfaces sliding against one another,
the magnitude of the kinetic friction exerted
through the surface is independent of the
magnitude of the velocity (i.e., the speed) of
the slipping of the surfaces against each
other.

• The maximum input hysteresis & maximum output
hysteresis is shown in fig.(e)

Accuracy
Accuracy can be expressed as a comparison of the
static error of the transducer compared to the actual
value (at full scale) expressed as a percentage of full
scale. (Accuracy may also be expressed in other
ways.)
% Accuracy (Measured value – Actual value) x
100/ Actual value
=
E.g. A temperature transducer that reads 102 C at full
scale, when the temperature is 100 C, has an
accuracy equal to 2% of full scale.

Range
The highest and lowest values that the
transducer is designed to measure.
E.g. A Temperature transducer may have
a range of –50 C to +50 C
Span
The difference between the upper and lower
values the transducer is designed to measure.
•E.g. A Temperature transducer that has a range
of –50 C to +50 C has a span of 100 C

Range and Span
• Range: lowest and highest values of the
stimulus
• Span: the arithmetic difference between the
highest and lowest values of the input that
being sensed.
• Input full scale (IFS) = span
• Output full scale (OFS): difference between
the upper and lower ranges of the output of
the sensor.
• Dynamic range: ratio between the upper and
lower limits and is usually expressed in db

Range and Span (Example)
• Example: a sensors is designed for
: -30 °C to +80 °C to output 2.5V to
1.2V
• Range: -30°C and +80 °C
• Span: 80- (-30)=110 °C
• Input full scale = 110 °C
• Output full scale = 2.5V-1.2V=1.3V
• Dynamic
range=20log(140/30)=13.38db

Errors and Accuracy
•Errors: is the difference between the result
ofthemeasurement and the true value of the
quantity being measured
error= measured value –true value
• As a percentage of full scale (span for
example) error is calculated as;
e = Dt/(tmax-tmin)*100
where tmax and tmin are the maximum and
minimum values the device

Errors and Accuracy Example:
• Accuracy: is the extent to which the
measured value might be wrong and
normally expressed in percentage
• Example: A thermistor is used to
measure
temperature between –30 and +80 °C and
produce an output voltage between 2.8V and
1.5V. Because of errors, the accuracy in
sensing is ±0.5°C. so the measured value
may be high than or lower than by 0.5 °C

STATIC ERROR
The most important characteristic of an instrument is
its accuracy which is the agreement of the
instrument reading with the true value of the
quantity being measured. The accuracy of an
instrument is measured in terms of the error. Static
error is defined as the difference between the
measured value and true value of the quantity.
δA = Am – At
Ɛ0 = δA
Ɛr = (δA / At) = (Ɛ0 / At)
At = Am /(1 + Ɛr)
Since, Ɛr << 1
At = Am (1 - Ɛr)

DYNAMIC CHARACTERISTICS
• Dynamic characteristics of a measuring system relates
to its performance when the measurand is a function of
time.
• The dynamic response of a measurement system when
subjected to dynamic inputs which are function of time
depends very much on its own parameters apart from
the nature and complexity of the function.
• Thus the dynamic response of a measurement system
consists of two components, one due to its
characteristic parameters and the other due to the
nature of the input function.

DYNAMIC ERROR
• It is defined as the algebraic difference between the
indicated / recorded value and its true value at any
instant when the measuranda is a measure of time.
• It is a function of time and this error is zero only for the
zero order system.
• For measuring the higher order, their output signals
consist of two components, one pertaining to the
transient state, other to the steady state.

Linearity
Linearity refers to the change in output compared to
the change in input. If the change in output is
proportional to the change in input, the transducer
is said to be linear.

tNon linearity means that the output is not
constant with respect to the input signal.
o o the input signal.
• Out
Input
Input
Input
Output

Null Type Instrument.
Definition: An instrument in which zero
or null indication determines the magnitude of
measured quantity such type of instrument is
called a null type instrument.
It uses a null detector which indicating
the null condition when the measured
quantity and the opposite quantity are same.

In deflection type instruments, the value of
the quantity being measured is displayed in
terms of the amount movement of a pointer.
The pressure-measuring device shown is an
example of a deflection type instrument. An
alternative type of pressure gauge is the
deadweight gauge which is a null-type
instrument.

Null-type and deflection-type instruments
In deflection type instruments, the value of the quantity
being measured is displayed in terms of the amount
movement of a pointer. The pressure-measuring device
shown is an example of a deflection type instrument.
An alternative type of pressure gauge is the deadweight
gauge which is a null-type instrument. Here, weights are
put on top of the piston until the downward force
balances the fluid pressure. Weights are added until the
piston reaches a datum level, known as the null point.
Pressure measurement is made in terms of the value of
the weights needed to reach this null position.

Analog and Digital Instruments:
An analogue instrument gives an output that
varies continuously as the quantity being
measured changes. The output can have an
infinite number of values within the range that
the instrument is designed to measure. The
deflection-type of pressure gauge is an example
of an analogue instrument.
An instrument whose output is in digital form is
when there is a need to be interfaced to a control
computer. Analogue instruments must be
interfaced by an analogue-to-digital (A/D)
converter.

A cam is a rotating or sliding piece in
a mechanical linkage used especially in transforming
rotary motion into linear motion

SELECTION CRITERIA OF THE TRANSDUCERS
• Operating principle
•Sensitivity
• Operating range
•Accuracy
•Errors
•Environmental capability
•Insensitive to unwanted Signal
• Stability
•Cost

Generalized
Measurement System

An instrument may be defined as a device or a
system which is designed to maintain a functional
relationship between the prescribed properties of
physical variables and must include ways and
means of communication to a human observer.

The performance of a measurement system can be
described in terms of static and dynamic
characteristics. Most of the measurement systems
contain three main functional elements:
i) Primary sensing elements
ii) Variable conversion elements
iii) Data presentation elements

1.Primary sensing element:The quantity under
measurement makes its first contact with the primary
sensing element of a measurement system.
The measurand is first detected by a primary sensor.
This is done by a transducer.
2.Variable conversion element:The output of a
primary sensory element may be an electrical signal of
any form. It may be voltage, frequency or other
electrical parameters. Sometimes this output is not
suited to the system for the instrument to perform the
desired function. It may be necessary to convert this
output to some other suitable form.
Eg. Suppose output is analog form, then we have to
convert it into digital form.

3.Variable manipulation element:
The function is to manipulate the signal
presented to it preserving the original nature
of the signal. Manipulation means change in
numerical value of signal.
4.Data transmission element:When the
functional elements of the measuring system
are spatially separated then it becomes
necessary to transmit signals from one
element to another.This function is performed
by data transmission element. It is an essential
functional element where remote control
operation is desired.

Lecture 02 instrument transducers manipal

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