Physical Quantities Measurements

(Ch1)

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Definition of Transducer (or Sensor)

• It converts the physical quantity (such as: position, displacement, temperature, force, velocity, …etc.) into corresponding electrical signal which is ready to be used for measurement, amplification, transmission, and control.

• Therefore the function of transducer is:

(1) Sensing the presence, magnitude, and frequency of the physical quantity.

(2) Providing an electrical output that gives accurate quantitative data about its input physical quantity.

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Classification of the Transducers

• According to their application (based on the measured physical quantity), for example: pressure, temperature, displacement, velocity, Light, etc transducers.

• According to their operating principles, For example: Variable resistance slide wire, resistance strain gauge, resistance thermometer, differential transformer, condenser microphone.

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• According to their need to an external power supply (Or according to the method of transduction):

o Passive transducers: in this case the physical quantity changes one or more electrical parameter such as: resistance, capacitance, or inductance. Therefore, it is required an external power supply to generate an electrical signal (voltage or current) proportional to the changed parameter of the transducer.

o Active transducers: this type of transducers directly generate the corresponding electrical signal without need of an external power supply, such as: moving coil generator, thermocouple, photovoltaic cell,….etc.

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Selection of a Transducer

• transducer has to be physically compatible with its intended application. It is selected according to the following criteria:

(1) Operating range : it must cover the range of the input quantity.

(2) Sensitivity : it should be sensitive enough to its input physical quantity changes and have minimum sensitivity to the other physical quantities which not are intended to be measured.

(3) Frequency response : its frequency response must be flat over the needed frequency range of measurement.

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(4) Accuracy : it must satisfy the required accuracy of measurement.

(5) Electrical Requirements : the required length of cables, the required signal to noise ratio.

(6) Environmental capability : its temperature range, pressures, and chocks…

(7) Usage and ruggedness : its ruggedness versus its size and weight.

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Resistive Displacement Transducers

• The object whose position or displacement is to be measured is directly coupled to a sliding contact of a variable resistor (potentiometer)

• Therefore the resistance is changed according to the position or displacement of the object.

• If an external power supply is used, the voltage drop between the sliding contact and one end of the resistance is changed proportional to the position (displacement) of the object from this end.

• This type of transducers is passive.

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Unipolar displacement transducer

Disp. = 0 when wiper W at the reference point B, V0 = VWB

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Bipolar displacement transducer -The reference point is such that R1 = R2 (i.e., the shaft is at mid-stroke), and R3 = R4. -The output voltage VE between the moving wiper W & the fixed wiper C (i.e. VE = VWC). - disp. = 0 when wiper W at the middle of the transducer resistance AB.

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Example:

• A unipolar displacement transducer with a shaft stroke of 3.0 in. has a total resistance of the potentiometer (R1R2) of 5k, and supply voltage VS of 5.0V. Calculate:

a- the value of R2, and its output voltage VO When the wiper is 0.9 in. from the reference point B.

b- the displacement of the wiper if the output voltage is 4 V.

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Solution:

a- V0/VS = Disp/Stroke = R2/(R1+R2)

R2 = (Disp/Stroke) X (R1+R2)

= (0.9 in/3 in) x 5000 = 1500

V0 = [R2/(R1+R2)] x Vs

= (1500/5000) x 5 V = 1.5 V

b- Disp = (V0/Vs) x Stroke

= (4/5) x 3 in = 2.4 in

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Capacitive Transducers

• The capacitance C between two conductive

plates separated by an insulating material of dielectric constant (), of depth (d), and the common area of the plates is A is:

C = A/ d [F, F/m, m2, m]

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• If , A, or d is changed, then the capacitance between the two conductive materials will be changed.

• This type of transducers uses the physical quantity to change the dielectric material (), area of the conductive materials (A), or their separation distance (d).

• Since these transducers require an external power supply to convert the change of the capacitance to an electrical signal, they are passive transducers.

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using a rectilinear capacitor by moving a rod inside a fixed

conducting cylinder (linear displacement transducer)

.

using a rotary capacitor (radial displacement transducer)

.

Methods used to change the common area A

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Methods used to change the dielectric constant ε

When the tank is full of fuel it is represented as a fuel dielectric capacitor. When it is empty it is represented by an air dielectric capacitor. But if it is partially empty it is represented by two parallel connected capacitors.

air dielectric and fuel dielectric capacitors (fuel level transducer)

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Methods used to change the dielectric depth d

The speech pressure moves a movable conducting diaphragm against a fixed conducting plate, therefore

the distance (d) is changed. Therefore the capacitance between the fixed plate and the movable plate is

changed according to the pressure of the speech. (Acoustic pressure microphone transducer)

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d is changed by moving the movable conducting

plate according to the relative difference between

the fluid pressure P1 and the atmosphere

pressure P0. Therefore its capacitance changes

according to the value of P1

(Fluid pressure transducer)

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• Any of the previous transducers can be placed in an AC bridge in order to convert the change of the transducer capacitance into a voltage VO.

• This voltage VO can be used to measure directly the applied non-electrical quantity.

• For example the fluid pressure can be measured as shown in the next figure:

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• The capacitive fluid pressure transducer is connected as one arm (C) of AC bridge then the unbalance voltage (VO) indicates the pressure of the fluid.

• When P1 = P0, C = C0, the bridge is balanced, and VO = 0V

• If P1 > P0, C > C0, therefore VO < 0V, and vice versa.

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Inductive Transducers

This type of transducers include both types: Passive and Active transducers

Passive Inductive Transducers • If a core is displaced in proximity to a coil, the

self inductance (L) of the coil will be changed proportionally to the distance of the core from the coil.

• If this inductance is used in an AC bridge the output voltage VO will be changed according to the change of the coil inductance (L), i.e., due to the change of the distance of its core (X).

• This is the principle of operation of an electronic micrometer. 2/25/2018 20

Electronic Micrometer circuit diagram If X = R , then L4 = L3 , VL4 = VL3 , and VO = 0V If X > R , then L4 < L3 , VL4 < VL3 , and VO > 0V If X < R , then L4 > L3 , VL4 > VL3 , and VO < 0V

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Self Generating Inductive Transducers

• If a coil (rotor) is rotated in a permanent magnet (PM), or a PM is rotated inside a coil, a voltage is induced in the coil.

• This voltage is proportional to the velocity of rotation of the rotor (E = BLV) , where :

o E is the induced voltage [V],

o B is the magnetic field strength of PM [Tesla],

o L is the length of the coil [m]

o V is the velocity of rotation of the rotor [m/Sec]

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• If the object whose velocity is to be measured is mechanically coupled to the rotor, the output voltage (E) is directly proportional to the RPM of the object. This is the idea of the tachometer.

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Temperature Transducers

They can be divided into the following categories:

• Resistance temperature detectors (RTD)

• Thermistors

• Thermo-couples

Note : The conversion between the temperature scales is as follows :

• (F-32) = C = K-273.15

• Water freezes at: 0 C, 32 F, or 273.15 K,

• Water boils at: 100 C, 212 F, or 373.15

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Resistance Temperature Detectors (RTD) • They are resistive elements which have a positive

temperature coefficient (+ve TCR) • It is also called Temperature Dependent Resistor

(TDR). It is a passive transducer. R = R0 (1+ ∆ T)

• Where : R is its resistance at the measured temperature T [Ω].

• R0 is its resistance at the reference temperature T0 [Ω].

• is its TCR coefficient = (∆R/ ) / R0 • ∆T is the difference between the measured and

reference temperatures = T - T0 2/25/2018 25

- The temperature can be measured using an RTD transducer.

- The voltage VRTD across the RTD resistor is proportional to the temperature to be measured, and VO = VRTD.

- Therefore VO can be used to measure directly this temperature. 2/25/2018 26

Thermistors • It is a semiconductor resistive materials, which have a

negative temperature coefficient of resistance (-ve TCR).

• It is a passive transducer since an external power supply is needed to convert the change of resistance to a voltage or current.

• It is a non-linear over the temperature range but it may be available with better than 0.2% linearity over (0 to 100°C) temperature range. – R = R0 (1+ ∆ T) = R0 (1- ∆ T)

– Where : R is its resistance at the measured temperature T [Ω].

– R0 is its resistance at the reference temperature T0 [Ω].

– = (Δ R/ ) / R0, it is its TCR coefficient

– ∆T = T-T0, it is the difference between the measured and reference temperatures [].

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• The resistance RT of the thermistor is inversely proportional to the temperature to be measured, and the current I is inversely proportional to the resistance RT.

• Therefore I can be used to directly measure this temperature.

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Thermocouples

• When a pair of wires made of different metals are joined together at one end, a voltage difference between the wires at the other end is found.

• This voltage depends on the temperature difference between the two ends of the wires and on the wire materials

• This type of transducers is a self-generating transducer.

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• The reference junction is kept at room temperature T0 and the sensing junction is put where the temperature T is being measured.

• Then the induced voltage is connected to a measuring instrument which is calibrated to measure the temperature directly instead of voltage.

• The produced emf (E) is given by:

E= C (T-T0) + K (T2-T20)

– Where: E is the induced EMF in [mV] , – C and K are thermocouple constants in [mV/C], and

[mV/C2] respectively. – T and T0 are temperatures at the hot and cold

junctions in [C] respectively.

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Photoelectric Transducers

Phototubes

It operates on the principle of photoemission:

• Incident photons enter the tube and strike its photo cathode, and electrons are emitted from the surface of the photo cathode.

• These photo emitted electrons are attracted to a positively charged anode, and a current (proportional to the incident light) passes in the external biasing circuitry as shown in the next figure

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• The phototube transducer is a self generating transducer.

• Its advantages are its linearity (induced current versus the incident light) and simplicity.

• But its main disadvantage is its low sensitivity which is overcome by the photo-multiplier tubes.

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Photo-Voltaic Cell (Solar Cell) • It is sometimes called solar cell. It provides a

current if it is connected to a load. • Its application is sensing light in the punched

cards or as infrared detectors. • It is a self generating active transducer.

Photo-Conductive Cells (Photocells) • It is a passive transducer, whose resistance is

decreased upon striking by a light, its symbol and characteristics are shown in the next figure

•

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Note : •The incident illumination is measured in lumen/m2 (Lm/m2) or Lux.

•But for the invisible light it is measured in [watt /m2].

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The main photocells application is controlling a relay circuit. :

• Upon striking a light, the resistance of the photocell decreases and the current passing through it increases, consequently the relay is energized.

• When the light is interrupted, the resistance of photocell increases and the current passing through it decreases to a level that the relay is deenergized, as shown in the next figure:

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Example • The circuit of controlling a relay consists of : 30V supply (VS),

a photocell, resistance R, and a relay (ignore its resistant).

• Calculate the resistance R if VS delivers 10 mA when the cell is illuminated with 400 Lm/m2

• The relay is deenergized when the photocell is dark (illuminated with 0 Lm/m2), find the level of dark current, if the characteristics of the photocell is given as follows:

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Solution:

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• When the photocell is illuminated with 400 Lm/m2 : Rcell = 1 k, I = 10 mA, and the relay is energized

Since I = Vs / (R + Rcell) The resistance R = (Vs/I) – Rcell = (30V / 10 mA ) – 1 k = 2 k

• When the photocell is dark : Rcell = 100 k

I = Vs / (R + Rcell) = 30/ (2 k + 100 k) = 0.3 mA and the relay is deenergized

Photodiodes and Phototransistors

• If the normal semiconductor diode is reversed biased, a very small reverse current ( 1A in case of silicon diodes) passes.

• But in case of photodiodes if it is reversed biased, a reverse current passes proportional to the intensity of light striking the diode (its V-I characteristics is shifted)

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• If the diode does not reverse biased and is illuminated a voltage drop is established across it, therefore, it behaves as a photovoltaic device(solar cell). But if it is reverse biased it behaves as a photoconductive device

• Thus, the photodiode behaves as a passive transducer when it is reverse biased, and as an self generating transducer when it is forward (or not) biased.

• The main advantage of the photodiode as a photoconductive over the photoconductive cell is its faster time response, so it is used in high frequency applications. Its main disadvantage is its low sensitivity, which is overcome by the phototransistors.

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• The Photodiode illumination characteristics shows that : for the same load R the polarity of diode voltage VD is changed from negative to positive at the highest level of illumination.

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Example:

• A photodiode is connected in series with a 200 resistance and a 0.5 V supply. The supply polarity reverse-biases the device.

• Determine the diode currents ID, and voltages VD at 1500, 10000, and 20000 Lm/m2 illuminations.

Solution :

• When ID = 0, VR = IDR = 0V, then VD = -0.5V

• Plot point A on characteristics, at ID = 0 and VD = -0.5V

o When VD = 0,

ID = (Vs / R) = (+0.5 V / 200 ) = 2.5 mA (reverse current)

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• Plot point B at ID = 2.5 mA and VD = 0V.

• Then draw the load line through A and B.

• From the load line we get VD, and reverse currents ID o At 1500 lm/m2 ID = 0.25 mA and VD = - 0.43V

i.e. diode is reverse biased and operates as photoconductive cell o At 10000 lm/m2 ID = 2 mA and VD = - 0.22V

i.e. diode is reverse biased and operates as photoconductive cell o At 20000 lm/m2 ID = 3.6 mA and VD = + 0.22V

i.e. diode is forward biased and operates as photovoltaic cell

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Phototransistors • When the light falls on the base region of the phototransistor it

frees electron-hole pairs which lowers the barrier potential across its both junctions. Thus the flow of electrons from the emitter region to base and to the collector regions is increased.

• the output characteristics of the phototransistor and its symbol are shown bellow :

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• The photodiodes and phototransistor can be used as a photo-detectors for the applications as punched cards and tape readouts.

• The phototransistor, because of its high sensitivity, can be used to control a relay by light, as seen in the next Figure:

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• As the intensity of light increases, I1 increases, thus transistor T2 will be conducting providing higher current that energizes the relay.

• But when the light decreases, I1 decreases, T2 enters its cut off region, and the relay is deenergized

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Piezoelectric Transducers

• The word piezoelectricity means electricity resulting from pressure.

• It is derived from the Greek piezo, which means to squeeze or press

• When a symmetrical crystalline materials, such as quartz, are placed under stress, they produce an emf.

• This electromechanical property is used in piezoelectric transducers, where a crystal is placed between: – A solid base, and

– A force summing member

as shown in the next slide

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V0

• An externally applied force, entering the transducer through its pressure port then through the force summing element, applies pressure to the top of a crystal.

• This produces an emf across the crystal, proportional to the magnitude of the applied pressure.

• It is a self generating active transducer since it doesn’t need external power supply.

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• It is used in high-frequency accelerometers, since it has a very high frequency response.

• Its major disadvantage is that it cannot be used to measure static conditions.

• The induced emf equals to zero if the applied pressure does not change.

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Thank You

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