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It is a device for determining the value or magnitude of a quantity or variable.
N1 = 826 ± 5 ( = ± 0.605%)
N2 = 628 ± 3 ( = ± 0.477%)
Sum = 1,454 ± 8 (=± 0.55%)
N1 = 826 ± 5 ( = ± 0.605%) N2 = 628 ± 3 ( = ± 0.477%)
Difference = 198 ± 8 (= ± 4.04%)
These are the errors inherent in measuring instrument because of their mechanical structure.
Components are guaranteed to be within a certain percentage of rated value.
Thus the manufacturer has to specify the deviations from the nominal value of a particular quantity.
It is defined as r = ± 0.6745s where s is standard deviation.Probable error has been used in experimental work to some extent in past, but standard deviation is more convenient in statistical work.
These are due to conditions in the measuring device, including conditions in the area surrounding the instrument, such as the effects of changes in temperature,humidity.
The best approximation method will be made when the number of readings would give the best result.
By definition, average deviation is the sum of absolute values of the value deviations divided by the number of reading.
It is necessary to define a physical quantity both in kind and magnitude in order to use this information for further proceedings. The standard measure of each kind of physical quantity is named as the unit.
The physical embodiment of a unit of measurement is a standard.
For example,the fundamental unit of mass in the international system is the kilogram and defined as the mass of a cubic decimeter of water at its temperature of maximum density of 4°c.
The specification of limiting error is in itself uncertain because the manufacture himself is not sure about the accuracy because of the presence of random errors.
Transducer is a device which converts one form of energy into electrical energy.
A thermocouple converts heat energy into electrical voltage.
On the basis of transduction form used:
Bourdon tube acting as a primary transducer senses the pressure and converts the pressure into displacement.
No output is given to the input of the bourdon tube. So it is called primary transducer. Mechanical device can act as a primary transducer.
The output of the Bourdon tube is given to the input of the LVDT.
There are two stages of transduction, firstly the pressure is converted into a displacement by the Bourdon tube then the displacement is converted into analog voltage by LVDT. Here LVDT is called secondary transducer. Electrical device can act as a secondary transducer.
In the absence of external power, transducer cannot work and it is called a passive transducer.
Example: capacitive, inductive, resistance transducers.
In the absence of external power, transducer can work and it is called active transducer.
Example:
velocity, temperature, light can be transduced with the help of an active transducer.
These transducers convert the input quantity into an analog output which is a continuous function of time.
Thus a strain gauge, an LVDT, a thermocouple or a thermistors may be called analog transducer, as they give an output which is a continuous function of time.
Fundamental units in mechanics are measures of length, mass and time and those are fundamental to most other physical quantities and hence they are called Primary fundamental units.
Measures of certain physical quantities in thermal, electrical and illumination fields are also represented by fundamental units and are used only where those disciplines are involved and hence called auxiliary fundamental units.
The unit of mass is represented by a material standard: the mass of International prototype kilogram consisting of platinum Iridium hollow cylinder.
It refers to a process in which all the inputs(desired,modifying,interfering) except one are kept at some constant values.
The ability to trace the accuracy of the standard back to its ultimate source in fundamental standards of National Institute of Science and Technology is termed “Traceability”.
The happenings or disturbances about which we are unaware and lumped together are called random errors or residual errors.
Since these errors remain even after the systematic errors are taken care of,they are called residual errors.
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When a force is applied to piezo-electric crystals, they produce an output voltage.
A device which converts an electrical quantity into a non-electrical quantity.
A piezo-electric crystal acts as an inverse transducer because when a voltage is applied across its surfaces, it changes its dimensions causing a mechanical displacement.
Static characteristics of a measurement system are, in general, those that must be considered when the system or instrument is used to measure a condition not varying with time.
Many measurements are concerned with rapidly varying quantities and, therefore, for such cases we must examine the dynamic relations which exist between the output and the input .
This is normally done with the help of differential equations. Performance criteria based upon dynamic relations constitute the Dynamic Characteristics.
The input- output relationship of a zero- order transducer is given by
Y(t) = K r(t)
Where r(t) is the input, Y(t) is the output and K is the static sensitivity of the transducer.
Example for zero-order transducer is a potentiometer.
Mathematical model is defined as the mathematical representation of the system and its process.
Frequency response is thus defined as the steady – state output of a transducer when it is excited with sinusoidal input.
The frequency response is represented with the help of two plots namely amplitude radio verses frequency and phase angle shift versus frequency.
The damping ratio V is an important parameter which decides the nature of oscillation in the transducer output.
WhenV =0, the second order system is said to be undamped and the system behaves like an oscillator. WhenV =1, the second order system is said to be critical damped and when V >1 , the second – order system is said to be over damped.
Sensitivity should be taken depending on the operating point. The sensitivity is expressed in
S = output unit/ input unit.
Linearity is a measure of the maximum deviation of the plotted transducer response from a specified straight line.
Accuracy is the closeness to true value whereas precision is the closeness amongst the readings.
Precision is the degree of closeness with which a given value may be repeatedly measured.
When the input to a transducer is increased from zero, there is a minimum value below which no output can be detected .
This minimum value of the input is defined as the threshold of the transducer.
When the input to a transducer is increased slowly from some non-zero arbitrary value, the change in output is not detected at all until a certain input increment is exceeded. This increment is defined as the resolution.
When the input to a transducer which is initially at rest is increased from zero to full-scale and then decreased back to zero, there may be two output values for the same input.
Hysteresis effects can be minimized by taking readings corresponding to ascending and descending values of the input and then taking their arithmetic average.
The range of the transducer is specified as from the lower value of input to higher value of input.
The span of the transducer is specified as the difference between the higher and lower limits of recommended input values.
It is defined as time required for the system to rise from 0 to 100 per cent of its final value.
q = qo [ 1- exp(1-t/t)]
=100[ 1- exp(1-1.5 /3.5)] = 34.86°c.
Time to reach equilibrium conditions = 5t = 10s.
Time constant t= 10/5 =2s.
q = qo [ 1- exp(1-t/t)]
0.5= 1-[exp(-t / 2)]
t= 1.39s.
Basically a resistance potentiometer, or simply a POT, (a resistive potentiometer used for the purposes of voltage division is called a POT) consists of a resistive element provided with a sliding contact.
The POT is a passive transducer.
The gauge factor is unit resistance change per unit strain, which is due to three factors as revealed by the above equation.
It is a ratio of changing length to original length.
It is a ratio of stress and strain, dR/R / dl/l
A resistance thermometer consists of a resistive element which is exposed to the temperature to be measured.
If the conductors or metals are used to measure the temperature, they are known as resistance thermometers and if semiconductors are used then they are known as thermistors.
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Resistance thermometer bridges may be excited with either d.c.or a.c .The direct or rms alternating current through the thermometer is usually in the range of 2 to 20 mA.
This current causes an I2R heating which raises the temperature of the thermometer above its surrounding, causing the so called self-heating error.
Othername of resistance variation type transducers is hot wire anemometer. In general anemometers are devices used for measurement of velocity of flow.
It is used avoid the fluctuation, we need dynamic compensation circuits for the hotwire anemometer.
Mixture of metallic oxides such as manganese, nickel, cobalt, copper, iron and uranium.
Transducers based on the variation of inductance are another group of importance devices used in much application.
In these transducers self-inductance or the mutual of a couple of coils is changed when the quantity to be measured is varied.
The Linear Variable Differential Transformer (LVDT) is the most common mutual inductance element.
This can be considered to be a versatile transducer element for most of the electromechanical measuring systems with regards to resolution, hysteresis, dynamic response, temperature characteristics, linearity and life.
Ideally the output voltage at the null position should be equal to zero. However, in actual practice there exists a small voltage at the null position.
The primary is excited with alternating current. This induces a voltage in to the secondary.
The amplitude of this output voltage varies with the mutual inductance between the two coils and this varies with the angle of rotation.
Another common version of the variable reluctance principle.
This is an accelerometer for measurement of accelerometer for measurement of acceleration in the range ± 4g. Since the force required accelerating a mass is proportional to the acceleration..
To detect motion on both sides of zero, a fairly involved phase- sensitive demodulator would be required.
To eliminate the demodulator the iron core and springs were adjusted so that core was offset to one side by an amount equal to the spring deflection corresponding to 4 g acceleration.
Many industrial variables like displacement, pressure, level, moisture, thickness etc. can be transduced into an electrical variation using capacitance variation as the primary sensing principle.
It is also a transducer which converts sound energy into electrical energy.
Example is condenser microphone.
C= 2pe0 [e1 h1 + e2 h2 / loge (r2/r1) ]
Where, h1= height of liquid
h2= height of cylinder
e1=relative permittivity of liquid
e2= relative permittivity of vapour above liquid r2= inside radius of outer cylinder
r1= outer radius of inner cylinder
e0= relative permittivity of free space
This transducer converts input quantity into an analog output which is a continuous function of time.
Thus a strain gauge, LVDT, thermocouple, thermistors, may be called as analog transducer.
These transducer convert input quantity into an electrical output which is in the form of pulses.
They convert pressure or force into electrical charge.
These transducers are based upon the natural phenomenon of certain non-metal and di-electric components.
Primary quartz, Rochelle salt, ammonium di-hydrogen phosphate (ADP), and ceramics with barium titanate, di-potassium tartrate, potassium di-hydrogen phosphate and lithium sulfate.
Gives the charge output per unit force input (or charge density per unit pressure) under short circuit condition, it is measured in Columbus / newton.
G-coefficient representing the generated e.m.f gradient per unit pressure input.
It is obtained by multiplying the g-coefficient by young’s modulus valid for the appropriate crystal orientation of the material, and thus measures the e.m.f gradient per unit mechanical deformation, or (V/m) / (m/m ).
Iron , nickel, 68 permalloy and ferroxcube ect .
The permeability can increase or decrease depending upon the material, type of stress , and the magnetic flux density in the sample.
Fiber optic cable consists of outer core and inner cladding.
Data is transmitted in the form of light.It is used for measuring displacement,torsion.
Digital transducer gives digital outputs. Analog transducers outputs are continuous functions of time.
If these analog transducers are to be interfaced with digital devices, then one has to use analog to digital converters.
The number of tracks must be increased and the length of each coded should be reduced, which would require fine brushes.
A piezo electric material is one in which an electric potential appears across certain surfaces of a crystal if the dimensions of the crystal are changed by the application of the mechanical force.
Digital encoding transducer or digitizer enables a linear or rotary displacement to be directly converted into digital form without intermediate form of analog to digital (A/D) conversion.
In this case output deviates from the correct value by a constant factor over the entire range of transducer.
3. Transducer response
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