Instrumentation and Measurements Eng. Ahlam Damati

Transducers

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Introduction:

Transducers are devices used to transform one kind of energy to another. When a transducer converts a physical quantity (sound, pressure level, optical intensity, magnetic field, etc.) to an electrical voltage or an electrical current we call it a sensor.

When the transducer converts an electrical signal into another form of energy, such as sound, light, or mechanical movement, it is called an actuator.

As an example shown in figure 1, transducers are used in electronic communications systems to convert signals of various physical forms to electronic signals, and vice versa. In this example, the first transducer could be a microphone, and the second transducer could be a speaker.

Figure 1: Transducers in a communication system

A transducer is made of three blocks: an input (physical parameter), a sensor and an output (electrical signal) as shown in figure 2.

Figure 2: Transducer Structure

Classification of transducers:

The classification of transducers is made on the following basis:

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1. Based on the physical phenomenon: Primary transducer and Secondary transducer.

2. Based on the power type Classification: Active transducer and Passive transducer.

3. Based on the type of output: Analog transducer and Digital transducer.

4. Based on the electrical phenomenon is a best Classification of Transducer:

a. Resistive transducerb. Capacitive transducerc. Inductive transducerd. Photoelectric transducere. Photovoltaic transducer

Table 1 is a partial listing of the applications for sensors and transducers.

Table1: Typical sensors applications

There are some factors that should be taken in consideration when selecting a transducer: • It should have high input impedance and low output impedance, to avoid loading effect.• It should have good resolution over is entire selected range.• It should be able to withstand • Small in size and weight.• High sensitivity.• Ability to withstand environmental conditions; pressure, shocks, vibrations etc..• Low cost.

1- Resistive Transducers:

Strain gage:3

It is one of the most popular types of transducers. It has got a wide range of applications. It can be used for measurement of force, torque, pressure, acceleration and many other parameters. The basic principle of operation of a strain gage is that it uses electrical resistance variation in wires to sense the strain produced by a force on the wire. When strain is applied to a thin metallic wire, its dimension changes, thus changing the resistance of the wire. This is explained in figure 3.

Figure 3: Strain gauge transducer

Resistance of an electrical conductor is given by:

R=ρL/A

Where:

R = Resistance in Ω

ρ = Resistivity of the conductor (Ω - cm)

L = Length of the conductor in cm.

A = Cross-sectional area of the metal conductor in cm2

It is clear from the equation that, the electrical resistance can be varied by varying the length L, the cross-sectional area A, the resistivity ρ, or combination of these.

Gage Factor:

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Consider a long straight metallic wire of length L, circular cross section A, with diameter d. When this wire is subjected to a force applied at the two ends, a strain will be generated and as a result, the dimension will change (L changes to L+∆L, d changes to d+∆d and A changes to A+∆A).

The gauge factor K is defined as the unit change in resistance per unit change in length.

K= ∆ R /R∆ L/L

(1.1)

Where:

K = the gauge factor.

R = the initial resistance in ohms (without strain).

ΔR = the change of initial resistance in ohms.

L = the initial length in meters (without strain).

ΔL = the change of initial length in meters.

The term ∆ L/ L in the denominator in eqn.1 is the strain σ , so eqn.1.1 can be written as:

K= ∆ R /Rσ

=¿1+2µ (1.2)

Where µ is the Poisson’s ratio which is defined as the ratio of strain in the lateral direction to strain in the axial direction.

Poisson’s ratio for most metals lies in the range of 0.25 to 0.35 and the gauge factor would then be on the range of 1.5 to 1.7

In strain gauge applications, a high sensitivity is desirable, so a large gauge factor means a large resistance change.

The relationship between stress and strain is given by Hooke’s law in terms of the modulus of elasticity of the material under tension. Defining stress (s) as the applied force per unit area and strain (σ) as the elongation of the stressed member per unit length, Hooke’s law is written as:

σ= sE

(1.3)

where: σ = strain, ∆L/L, no units.

s = stress (kg/cm2).

E = Young’s modulus (kg/cm2).

Strain Gauge Applications:5

1. Strain gauges are used to measure the amount of stress an airplane can handle until it fails.2. They are used to keep bridges in good condition; people have put sensors on bridges to monitor the

weak points of a bridge. These sensors tell us if a bridge gets weak at some points so that they can be fixed before the bridge can break. This is most useful to civil engineers.

3. Strain gauges are used to keep rails in good condition. These strain gauges are put on the rails in vertical, longitudinal, and lateral positions to measure different forces. Again, this is most useful to civil engineers.

Example 1:

A resistance strain gage with a gage factor of 2 is fastened to a steel member subjected to a stress of 1,050 kg/cm2. The modulus of elasticity of steel is approximately 2.1x106 kg/cm2. Calculate the change in resistance ∆R of the strain gage element due to the applied stress.

2- Capacitive Transducers:

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a) Parallel-Plate Capacitor:

Capacitance is a function of effective area of conductor, the separation between the conductors and the dielectric strength of the material. The capacitance of a parallel-plate capacitor is given by:

C=εr ε o A

d

where: εr = dielectric constant of the insulating medium, for air εr =1

εo =permittivity of air or free space = 8.854 x 10-12 F/m.

A = the area of the plate, (m2).

d = the plate spacing, (m).

Since C is inversely proportional to d, any change in d will cause a change in C. A change in capacitance can be done by varying any of the following parameters:

1. Changing the distance between the two parallel electrodes (d).2. Changing the dielectric constant, permittivity, of the dielectric medium.3. Changing the area of the electrode (A).

Some transducers work by making one of the capacitor plate’s movable, either in such a way as to vary the overlapping area or the distance between the plates. Other transducers work by moving a dielectric material in and out between two fixed plates to detect and transmit the physical position of mechanical parts via electrical signals as shown in figure 4.

Figure 4: Capacitive Transducers.

Example 1:

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An electrode-diaphragm pressure transducer has plates whose area is 5 × 10-3 m2 and whose distance between plates is 1 × 10-3 m. Calculate its capacitance if it measures air pressure. The dielectric constant of air is ε r =1.

Solution:-

Example 2:

A capacitive transducer uses two quartz diaphragms of area 750mm2 separated by a distance of 3.5 mm. A pressure of 800 KN/mm2 when applied to the top diaphragms produces a deflection of 0.6 mm. The capacitance is 370 PF without pressure. Find the value of capacitance after the application of 800 kN/m2 pressure?

Since,

C1=εr ε o A

d1 and C2=

εr ε o Ad2

then,

C1

C2=

d2

d1

d2=3.5 mm−0.6 mm=2.9 mm

C 2=C1 ×d1

d2=370 pF × 3.5 mm

2.9mm = 446.5 pF

b) Coaxial-Cylindrical Capacitor:

A coaxial-cylindrical capacitor consists of two coaxial cylinders with the outer radius of the inner cylinder defined as D1, the inner radius of the outside cylinder as D2 and the length as L as shown in figure 5.

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C =εr εo Ad

=(1 ) (5 x 10−3 m2 ) (8 .854 x 10−12 F /m)1 x10−3 m

= 44 .25 pF

Figure 5: Cylindrical-Capacitive Transducer.

The capacitance value is given by the following relation:

C=2 π εo ε r L

ln( D2

D1 )where L: the length of the cylinder.

D1: diameter of the inner cylinder.

D2: diameter of the outer cylinder.

Figure 6 shows different types of capacitive transducers. The angular rotation, the cylindrical, and the thin diaphragm. The dielectric is either air or vacuum. Such devices are often used as capacitance microphones.

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Figure 6: Capacitance transducers

Example 3:Capacitive transducer is made up of two concentric cylindrical electrodes. The inner cylinder has a diameter of 3 mm and the outer one has a diameter of 3.1 mm. The length of the electrodes is 20mm and the dielectric medium is air. Find the change in the capacitance if the inner electrode is moved by 2 mm.

Uses of Capacitive Transducer:

The following are the uses of capacitive transducer:

1. The capacitive transducer uses for measurement of both the linear and angular displacement. It is extremely sensitive and used for the measurement of very small distance.

2. It is used for the measurement of the force and pressures. The force or pressure, which is to be measured, is first converted into a displacement, and then the displacement changes the capacitances of the transducer.

3. It is used as a pressure transducer in some cases, where the dielectric constant of the transducer changes with the pressure.

4. The humidity in gases is measured through the capacitive transducer.

The following figure 7 explains one application of the coaxial-cylindrical capacitive transducer for measuring the water level of a tank.

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Figure 7: Coaxial cylindrical capacitive sensor for liquid-level measurement

3. Inductive Transducers:

Inductive transducers may be either of the self-generating or passive type. The self-generating type utilizes the basic electrical generator principle, a motion between a conductor and magnetic field induces a voltage in the conductor (generator action).

Passive inductive transducers: They require an external source of power. The action of the transducer is principally one of modulating the excitation signal. The Differential transformer is a passive inductive transformer, well known as Linear Variable Differential Transformer (LVDT). It consists basically of a primary winding and two secondary windings, wound over a hollow tube and positioned so that the primary is between two of its secondary coils. Figure 8 shows the LVDT.

Figure 8:

Linear Variable Differential Transformer (LVDT).An iron core slides within the tube and therefore affects the magnetic coupling between the primary and the two secondary coils. When the core is in the center, the voltage induced in the two secondary coils is equal. When the core is moved in one direction from center, the voltage induced in one winding is increased and that in the other is decreased. Movement in the opposite direction reverses this effect as shown in figure 9.

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Figure 9: An example of LVDT wiring

In figure 10 the windings are connected "series opposing." That is, the polarities of V1 and V2 oppose each other. Consequently, when the core is in the center so that V1 = V2, there is no voltage output, Vo=0.

When the core is moved in one direction from the center, the voltage induced in one winding is increased and that in the others is decreased. Movement in the opposite direction reverses the effect. When the core is away from center toward S1, V1 is greater than V2

and the output voltage Vo will have the polarity of V1. When the core is away from center toward S2, V2 is greater than V1, and the output will have the polarity of V2. That is, the output ac voltage inverts as the core passes the center position. The farther the core moves from center.

Thus, the amplitude of Vo is a function of distance the core has moved. If the core is attached to a moving object, the LVDT output voltage can be a measure of the position of the object. The farther the core moves from the center, the greater the difference in value between V1 and V2, and consequently the greater the value of Vo.

Figure 10: The windings of LVDT

The main applications of inductive transducers are in:

1. Position Detection: such an example is in washing machine displacement.2. Speed Sensing: A tachometer is an inductive transducer that directly converts speed or velocity into

electrical signal.3. Distance Measurement.

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4. Resistance Temperature Detector (RTD):It is a device which used to determine the temperature by measuring the resistance of pure electrical wire. This wire is referred to as a temperature sensor. If we want to measure temperature with high accuracy, RTD is the most accurate temperature sensor. RTD is manufactured from Platinum, Nickel, Copper and tungsten. A typical RTD is shown in figure 11.

Figure 11: A typical RTD

The variation of resistance of the metal with the variation of the temperature is given as:

Rt=Ro (1+αΔt+ β Δt2+γΔt 3+…) (4.1)

where: Rt and R0 are the resistance values at toC and t0oC temperatures.

α, β, and γ are the constants depends on the metals.For Platinum: α=3.94×10-3 and β=-5.8×10-7 which is a very small value.Δt = t˚C - to˚C

This expression is for huge range of temperature. For small range of temperature, the expression can be written as:

Rt ≈ Ro (1+αΔt ) (4.2)

where α is the temperature coefficient of a resistance.

In RTD devices; Copper, Nickel and Platinum are widely used metals. These three metals have different resistance variations with respect to temperature variations. That is called resistance-temperature characteristics as shown in figure 12. Platinum has the temperature range of 650˚C, and then the Copper and Nickel have 120˚C and 300˚C respectively. For Platinum, its resistance changes by approximately 0.4 ohms per degree Celsius of temperature.

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Figure 12: resistance-temperature characteristics curve of the three different metals

Example 1:

Platinum RTD has resistance of 100Ω at 25˚ C. Find:

1. The resistance at 65 ˚C if Platinum has resistance temperature coefficient of 0.003922. If the RTD has resistance of 150 Ω, find the temperature.

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Advantages of RTDs:

1. Greater sensitivity to small temperature changes. 2. High accuracy, stability, and resistance to thermal shock.3. Wide temperature operating range (-200°C to 900°C for platinum) 4. Excellent linearity 5. Easily manufactured to different degrees of accuracy

Disadvantages of RTDs:

1. High cost2. Self-heating effect: This means heating of the material due to flow of current which causes reading

errors.

RTD Applications:

1. Textile production.2. Plastics processing.3. Air, gas and liquid monitoring.

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6. Thermistor:

Thermistor is a type of resistor whose resistance changes rapidly with the small change in temperature. In other words, it is a type of resistor in which the flow of electric current changes rapidly with small change in temperature. The word thermistor is derived from the combination of words “thermal” and “resistor”.

Figure 13 shows different types of thermistors, its symbol in a circuit, and its resistance-temperature relationship.

Figure 13: Thermistor

Unlike RTD’s, thermistor shows decrease in resistance value with temperature increase. Its resistance is given by the following relation:

R=Ro eβ ( 1

T− 1

To) (6.1)

Where R: resistance at temperature T in Kelvin.

Ro: resistance at temperature To in Kelvin.

β: material constant ranges from (3000-5000) ˚k.

notice that T(˚K)=T(˚C)+273

Example 1:

If resistance of thermistor at -100˚C is 200 KΩ, find the value of the resistance at 400 ˚C if β=4000 ˚k.

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Example 2:

Find the value of β for a thermistor whose R(25˚C )=10 KΩ and R(50˚C )=3.3 KΩ.

Example 3:

At room temperature (25˚C), the voltmeter reads Vout= 2 V, the unknown temperature of a material is measured using a thermistor and the voltmeter reads 4 V. If Vin=20 V, β=4000 ˚k, R2=1000Ω, Rv=100 Ω, what is the temperature of the measured material?

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Example 4:

At room temperature (25˚C), the voltmeter reads Vout= 0.805V, the temperature of a material is measured using a thermistor and the voltmeter reads 1.325 V. If Vin=20 V, β=4000 ˚k, R2=1500Ω, Rv=100 Ω, what is the temperature of the measured material?

Advantages of thermistors:

1. High sensitivity: the resistance of thermistors changes rapidly with small change in temperature.2. Low cost.3. Small size.4. Can be used in very narrow locations.

Disadvantages of thermistors:

1. Thermistors are not suitable over a wide operating range.2. The resistance versus temperature characteristics is non-linear.

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Applications of thermistors:

1. Thermistors are used in medical equipment.2. Thermistors are used in hot ends of 3d printers.3. Thermistors are used in home appliances such as ovens, hair dryers, toasters, refrigerators, etc.4. Modern coffee makers use thermistors to accurately measure and control water temperature.5. Thermistors are used in computers.6. Thermistors are used as temperature sensors.7. Thermistors are used as inrush current limiter.

5. Photoconductive cell -Photo resistor :

Photoconductive cell is a sensor that detects light. It is small, inexpensive, low-power, easy to use. It is often referred to as Light Dependent Resistors (LDR). The common type of photoconductive material is Cadmium Sulphide (CdS) which is used in LDR photocells. Its conductivity is a function of the incident electromagnetic radiation. The LDR changes its electrical resistance from a high value of several thousand Ohms in the dark to only a few hundreds of Ohms when light is incident on it. Figure 14 shows the relationship between the resistance and the illumination for an LDR.

Figure 14: Photoconductive cell (LDR)

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The essential elements of a photoconductive cell are the ceramic substrate, a layer of photoconductive material, metallic electrodes to connect the device into a circuit, and a moisture-resistant enclosure. This is shown in figure 15.

Figure 15: Typical construction of plastic coated photoconductive cell

Light Dependent Resistor Voltage Divider Network:

A Light Dependent Resistor is generally connected in series with a resistor with a single DC voltage supply across it as shown in figure 16. The connection is shown below. In the absence of light, the resistance of a light dependent resistor is as high as 10 M Ω. In the presence of sunlight, the resistance of a light dependent resistor will fall to 100 Ω

The current in a series connection is same and as the resistance of the light dependent resistor changes due to the light intensity, the output voltage will be determined by using the voltage divider formula.

V out=V ¿

R1

R1+RLDR

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Figure 16: Light Dependent Resistor Voltage Divider Network

Example:

Suppose an LDR has a resistance of 100 Ω in bright light and 200 KΩ in the shade.

Case 1:10 KΩ at the top and LDR at the bottom

IT SHOULD WORK AS DARK SENSOR THAT MEANS, LED OFF

IN LIGHT AND LED ON IN DARK.

When LDR is in light, resistance of LDR is 100 Ω

Vo= (0.1*9)/ (10+0.1) = 0.0891 V (NOT ENOUGH TO TURN

ON THE TRANSISTOR)

When the LDR is in shade, resistance of LDR is 200 KΩ

Vo= (200*9)/ (10+200) = 8.57 V (ENOUGH TO TURN ON THE TRANSISTOR)

We can clearly see that the output voltage is large when the resistance of LDR is high. This voltage would

be enough for a transistor to turn on a LED. Hence, this circuit works as an Automatic Dark sensor.

Case 2: 10 K Ω at the bottom and LDR at the top.

IT SHOULD WORK AS LIGHT SENSOR, THAT MEANS, LED ON

IN LIGHT AND LED OFF IN DARK.

When LDR is in light, resistance of LDR 100 Ω

Vo= (10*9) /(10+0.1)21

= 8.91 V (ENOUGH TO TURN ON THE TRANSISTOR)

When the LDR is in shade, resistance of LDR is 200 KΩ

Vo= (10*9)/ (10+200) = 0.428 V (NOT ENOUGH TO TURN ON THE TRANSISTOR)

We can clearly see that the output voltage is large when the resistance of LDR is low. This voltage would

be enough for a transistor to turn on a LED. Hence, this circuit works as Automatic Light sensor.

Application:

As a switch: The most obvious application for an LDR is to automatically turn on a light at certain light level. For example the circuit shown in the figure explains a simple method of constructing a circuit that turns on when it goes dark. The increase in resistance of the LDR in relation to the other resistor which is fixed as the light intensity drops will cause the transistor to turn on. The value of the fixed resistor will depend on the LDR used, the transistor used and the supply voltage.

If a LED is connected as a load then it will turn on in dark and turn off in presence of light.

Advantages:

1. Available in low cost plastic encapsulated packages as well as hermetic packages. 2. Responsive to both very low light levels (moonlight) and to very high light levels (direct sunlight).3. Low noise distortion4. Easy to use in DC or AC 5. Usable with almost any visible or near infrared light source such as LEDS, neon, fluorescent,

incandescent bulbs, lasers, flame sources, sunlight, etc.6. Available in a wide range of resistance values.

Disdvantages:

Highly inaccurate with a response time of about tens or hundreds of milliseconds.

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6. Photodiode:

A photodiode is a device that helps in conversion of light into electric current. It is a pn-junction semiconductor which is designed to function in reverse bias. When light is incident on a Photodiode, the electrons and holes are separated and will allow the junction to conduct. Current is produced in the photodiode when photons are absorbed and a small amount of current is also produced when there is no light present.

Photodiodes are constructed like any other conventional junction diodes. A typical photo diode and its characteristic curve are shown in figure 17 below.

Figure 17: Photodiode

Advantages:

1. The linearity of the diode is good with respect to incident light.2. Noise is low.

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3. The response is wide spectral.4. Light weight and compact.5. Long life.

Applications: Photodiodes find application in the following:

1. Cameras: flash control.2. Medical devices: x-ray detection.3. Safety equipment: flame monitor, airport x-ray.4. Optical communication devices: fiber optic link.5. Position sensors.6. Industry: bar code scanners.

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