chapter 2 sensors 1 au351.ppt - t ucharnnarong.me.engr.tu.ac.th/charnnarong/my classes/au351/chapter...

ตวัตรวจวดัและเคร ือ่งบนัทกึ

1

คณะวิศวกรรมศาสตร์

มหาวิทยลยัธรรมศาสตร์

Chapter 2Recording systems and sensors

Recording instruments are used in an electronic measurement system to display an output (Qo ) that is proportional to the quantity (Qi ) being measured.

Transducer Recorder

QoQi

Measurement and Instrumentation



What important? (1) accuracy (2) easy interpretation (3) rapid process

In general, the characteristics that describe the behavior of a recording instrument are

1. Input impedance

2. Sensitivity

3. Range

4. Zero drift

5. Frequency response



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Input impedance, Z

Input impedance z controls the energy removed from the system by the recording instrument in order to display the input voltage.


Consider a simple dc voltmeter used to measure the voltage v of a source. The power loss p through the meter is given by

p = v2 / Zm

Transducer+ -

Zm = Rm + i Xm

Resistance

Capacitance / Inductance



For dc and quasi-static measurements

Z = R+i X ~ R (since X0)


vi

Zs

Zm

+

-

Transducervoltage

Thevenin’s equivalent circuit

1+(Rs/Rm)vm = vi

vm ~ vi

* High impedance is preferred

(Rm >>Rs)


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Sensitivity

The sensitivity S of a voltage recording instrument is given by

a change in voltage being measured

a change in output reading

Example A voltmeter is used to measure the voltages of a transducer

+ -vi

d


S = = d / vi Qi

QO

S = =Qi

QO

High sensitivity is required to give sufficiently large d for accurate readout



RangeThe range, which represents the maximum voltage that can be recorded, is determined from

+ -vi

dr

vi,max = dr / S

vi = d / S

As illustrated by the above equation, when

the sensitivity S is high, the range vi will be low;

conversely, if

the range is high, the sensitivity will be low.



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Zero driftis a variation in the output of an instrument which is not caused by

any change in the input

Zero input“0”

Readout“0”

Instabilities in the circuits of a recorder




Frequency response

Input Out put

Static

Dynamic



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Frequency response


Recording instrument

vi = Ai exp(jt) vo = Ao exp(j[t+])

Input signal Output indicator

A = amplitude of a signal

= phase angle

Amplitude distortion

NdB = 20 log10(Ao/Ai)

For instance, a recorder specification indicates that the frequency response isWithin ±3 dB from 0 to 100 Hz



Frequency response


When NdB = +3dB,

Ao/Ai = 103/20= 1.413 Ao=1.413Ai +41%

When NdB = -3dB,

Ao/Ai = 10-3/20= 0.707 Ao=0.708Ai -29%

In general, limits of ± 0.4dB should be maintained to reduce recorder error to less than ± 5%


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Analog recording system



galvanometer

voltmeter Strip chart


Galvanometer


มหาวิทยลยัธรรมศาสตร์ Measurement and Instrumentation

is a device that is used to detect a current.

Torque, T = N I A B sin

where N = a number of turns of the coilI = current

A = cross-sectional area of the current loop = angle between the normal of the cross-sectional area and the magnetic field

Note: In general, the coil is arranged so that

Torsion spring: T = k


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Analog Voltage meters



The galvanometer can be used as a dc voltmeter by inserting a resistor in series with the instrument.

voltmeter

Galvanometer

R

Input Dc voltage

V = I x R

Digital recording systems



Transducer

Conditioningcircuits

Amplifier

ADCA/D converter

Analog Digital

Display processing



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1 0 1 1 0 0 1 0

Digital codes


Maximum count C = 2n – 1 (numbers of comparator)

Resolution,R = Vrange / 2n

N-bit binary word permits a count of 2n



R = 10 / 24 = 0.625 v

Example A /D converter

Input ranges from 0 to 10 volts4-bit converter

C = 24 – 1 = 15

R= 0.625 0 0000

1 0.63 C1 0001

2 1.25 C2 0010

3 1.88 C3 0011

4 2.50 C4 0100

5 3.13 C5 0101

6 3.75 C6 0110

7 4.38 C7 0111

8 5.00 C8 1000

9 5.63 C9 1001

10 6.25 C10 1010

11 6.88 C11 1011

12 7.50 C12 1100

13 8.13 C13 1101

14 8.75 C14 1110

15 9.38 C15 1111

16 10.00


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Example: 4-bit wordCode Count

0000 0

0001 1

0010 2

0011 3

0100 4

0101 5

0110 6

0111

1000

7

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Convert the decimal number 3 to binary

2 ) 3 12 ) 1 1

0


Convert the binary 0101 to decimal

= 23x0 + 22x1 + 21x0 + 20x1= 0 + 4 + 0 + 1 = 5

Digital recording instrument



Digital multi-meter

Data logger

Data acquisition system

Digital oscilloscope



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Sensors and Transducers Sensors are physical elements that employ some natural phenomenon by which they sense the variable being measured.

Transducers are electromechanical devices that convert a mechanical change into a change in an electrical signal.

Sensor characteristics for the selection process

1. Size Smaller is better, because of enhanced dynamic response and minimum interference with the process

2. Range Extended range is preferred.

3. Sensitivity Higher output devices have the advantage of requiring less amplification




Sensor characteristics

4. Accuracy

5. Frequency response

6. Stability

Devices that exhibit errors of 1% or less is preferred.

Wide-response (both static and dynamic loading) sensors are preferred.

Low drift in output over extended periods of time and with changes in T and RH is essential.



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Sensors characteristics

7. Temperature limits

8. Economy

9. Ease of application

The ability to operate under a wide temperature range is important.

Reasonable costs are preferred.


Reliability and simplicity are significant factors.



Sensors used in transducer design

1. Potentiometer is the slide-wire (or wire-wrapped) resistor that is used to measure displacements for linear motion and angles for angular motion.


Vo = (x / l) Vi

Vo

Vi xl

slide-wire resistor

l VPotentiometer


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2. Differential transformers , based on a variable-inductance principle, are also used to measure displacement.

Vi

Linear Variable Differential Transformer, LVDT


Magnetic

AC

f = 50-25000, Hz

l VLVDT



3. Resistance strain gage is a thin metallic-foil grid used

to measure the strain of an object.


The strain gage can be adhesively bonded to the surface of a structure. When the structure is loaded, strains develop and are transmitted to the foil grid. As a result, the resistance of the foil grid changes in proportion to the load-induced strain.

Force L R Strain gage


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3. Resistance strain gage


R =L

A

The resistance of a uniform metallic conductor can be expressed as

where = the specific resistance of the metalL = the length of the conductorA = the cross-sectional area of the conductor

Differentiating R and dividing by the resistance R gives

For the case of a uni-axial tensile stress state,

dR

R

d

dL

L

dA

A= + -

a = dL L

t = - dL L

Poisson’s ratio




The gage factor (Sg) is

[Sg ~ 2 for metallic strain gauges]

The output of a strain gage (R) is usually converted to a voltage signal with a Wheatstone bridge


Sensitivity of the conductor can be written as

SA = = + (1+2) R/R

a

/a

Wheatstonebridge

Powersupply

L Strain gage VoR

Vi

Sg = R/R


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VO

Vs

Vo = Vs [ - ]R3

R3+Rg

R2

R1+R2


If R1=R2=R3=R4=Rg and Rg/Rg<<1,then

Vo = ¼Vs (Rg/Rg)

Vo = ¼Vs Sg



4. Capacitance sensors

C = [pF] k K A h

h

where A = area of the sensor headk = 0.00885 for dimension in millimetersK = dielectric constant (K = 1 for air)


The capacitance sensor consists of a target plate and a second plate called the sensor head. These two plates are separated by an air gap of thickness ha and form the two terminals of a capacitor.


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4. Capacitance sensors (cont.)

C +C = [pF] k K A h+h


If the separation between the head and the target is changed by an amount h, then the capacitance C becomes

which can be written as

However, the impedance of the capacitor is linear in h.

C/C = -h/h1+(h/h)

nonlinear relationship

ZC / ZC = h / h



5. Piezoelectric sensors

F

q = Sq x A x p [pC]


A piezoelectric material produces an electric charge when it is subjected to a force or pressure.

Sq = charge sensitivity, A = cross section area of the material, p = applied pressure


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5. Piezoelectric sensors (cont.)

vo = q / C


If the external surfaces of piezoelectric material are coated with metallic electrodes as shown in the figure, the output voltage vo is developed and related to the charge q by

or

where

vo = Svhp

Sv = voltage sensitivity of the sensor = Sq/kK



6. Resistance temperature sensors

Resistance Temperature Detectors (RTD) Material: Metals, such as Platinum, Nickel or Copper

ThermistorsMaterial: Semiconducting materials, such as oxides of copper, cobalt, manganese, nickel, or titanium

R/R0 = c1(T-T0) + c2(T-T0)2 + … + cn(T-T0)n

1/T = c1 + c2 ln(R) + c3 ln3(R) (3rd order approximation)


The change in resistance of materials with temperature provide the basis of resistance temperature sensors.


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Temperature measurements

Temperature sensor

T L , R, v, etc



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1. Expansion methods

L = L0 T

When materials are subjected to temperature changes ( T) they expand or contract according to

is the temp. coeff. of expansion [mm/°C]

rc h(A –B) (T2-T1)

Metal B

Metal A

rc

h Bimetallic strip


Automobile air conditioning system

Condenser

Evaporator

Compressor

Expansion valve


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Use of bimetallic thermostat in automobile air conditioning system



2. Electrical ResistanceResistance thermometers consist of a sensor element that exhibits a change in resistance with a change in temperature

2.1 Resistance Temperature Detectors (RTD) A typical RTD consists of a wire coil sensor with a framework for support and a sheath for protection. The sensor is a resistive element that exhibits a resistance-temperature relationship given by the expression

For a limited range of temperature,


NickelTungsten

Copper

Platinum

°CTemperature

R/R0 = c1(T-T0) + c2(T-T0)2 + … + cn(T-T0)n

R/R0 c1(T-T0)


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PT 100 temperature probe

Note: RTDs have a high accuracy and a wide operating range. However, they have a low response time.

PT100s are resistance thermometers which are fabricated from platinum. The operating temperature ranges from -200 °C to 850 °C, while the resistance of PT100 at 0 °C is 100 ohms.




2.2 Thermistors are fabricated from semiconducting materials, such as oxides of nickel, cobalt, or manganese. The resistance-temperature relationship for a thermistorcan be expressed as

where is a material constant [K]T is an absolute temperature [K]

Note: ranges from 3000 to 5000 K

R = R0 e(1/T – 1/T0)

Rt


“The resistance decreases exponentially with an increase in temperature”


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*** Thermistors have a high sensitivity, a fast response time, and good accuracy and resolution. However, they typically achieve a high precision within a limited temperature range.



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3. Thermoelectric(or thermocouple) is a temperature sensor that consists of two different metals in thermal contact. The thermal contact, called a junction, may be made by twisting wires together or by welding, soldering, or brazing two material together. A junction between two metals produces a voltage related to a temperature difference.

Material A

Material B Material Bemf

Seebeck effect

Junction 2Junction 1


Material A

Material B

Junction

Thermocouple

The operation of a thermocouple is basedon a combination of thermoelectric effectsthat produce a small open-circuit voltagevo when two thermocouple junctions aremaintained at different temperatures.The voltage vo can be represented by anequation having the form

where C1 and C2 are thermoelectric constants



vo = C1(T1-T2) + C2(T12-T2

2)


Seebeck effect is a phenomena in which any conductor will generate a voltage when it is subjected to a thermal gradient.

Source:http://www.efunda.com/designstandards/sensors/thermocouples/thmcple_theory.cfm

vo C1(T1-T2)


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Peltier effect occurs when a current flows in the thermocouple circuit. The presence of the current I in the thermocouple circuit produces the

well-known self-heating effect, where the Joule heat transfer, q,is

However, the Peltier heat transfer, qP ,is in addition to the Joule heating

effect and is given by

q = i2R [W]

where AB = Peltier coeff.Junction 2Junction 1 i

Material A

Material B Material B

Peltier effect

vs

qp,inqp,out


qP = ABi [W]



Thermoelectric cooling uses the Peltier effect to create a heat flux between the junction of two different types of materials.



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Reference junction

Measuring Junction

T

1

T2

vo




Relationship between voltage and temperature



25



Thermocouple probe

(Sheath)

Tip of a probe 1. Grounded2. Ungrounded3. Exposed


(Thermocouple)

(Insulator)



Characteristics of probe’s tips

Ungrounded tip(separated from the sheath wall

by a layer of insulation)

Grounded tip(direct contact with the sheath wall)

Exposed tip(protrudes outside the sheath wall)

is used in corrosive fluids where the temperature is changing slowly.

is used in corrosive fluids where moderate response is required.

is used for noncorrosive gases where rapid response is necessary.



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4. Radiative Temperature Measurementemploys the principles of radiation to measure surface temperatures with out contacting the body.

“Radiation” is the electromagnetic waves and particles emitted from the surface of a body.


max T = 2898 m.K

E (

)

Radiation power (E) is related to the absolute temperature and the wavelength as shown in the above figure

E()

h = Planck's constant (6.626 x 10-34 Js)c = Speed of Light (3 x 108 m/s)= Wavelength (m)k = Boltzmann Constant (1.38 x 10-23 J/K) T = Temperature (K)



E T

The power of the radiation Eb from an ideal (black) surface is obtained from

where

For grey surface,

Eb =Int[E(),

ET = (T) Eb

= is the Stefan-Boltzmann constant [5.67x10-8 W/m2-K4]


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Radiation MethodsPyrometer

- Optical pyrometer : compares the brightness of image produced by temperature source with that of reference temperature lamp.




Radiation MethodsPyrometer

- Infrared pyrometer : measures a source temperature by measuring the voltage output from a temperature detector


Lens

Focusing mirrorTemperature detectorFocus spot

Surface


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Radiative Temperature Measurement

Advantages - max temperature up to 3500 C

- non-contact measurement- no installation

Disadvantages- accuracy depending on

- relatively high cost




Thermocouple RTD ThermistorAdvantages - self-powered

- simple- durable- Wide temp. range- Wide variety- inexpensive

- most stable- most accurate- more linear

- fast response- high sensitivity

Disadvantages - non-linear- low voltage- Ref. junc. required- least sensitivity- least stable

- expensive- ext. power required- self-heating

- non-linear- ext. power required- Self-heating- limited temp. range

Advantages and disadvantages of the most common temperature sensors



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Pressure measurements

Pressure sensor

P L , R, c, etc




Pressure represents a contact force per unit area. It acts inward and normal to the surface of any physical boundary that a fluid contacts.

F

AA

FP [ N/m2 or Pa]

Pressure scales1. Absolute pressure scale

is the pressure that is quantified relative to the absolute zero pressure.

2. Gauge pressure scale is the pressure that is quantified relative to the

atmospheric pressure.



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Absolute

vacuumPabs = 0

Pvac

Pabs

Patm

Pgage

PabsPatm= 101.325 kPa= 14.969 psia= 760 mm Hg abs

Relative pressure scales

absatmvac PPP

atmabsgage PPP




Pressure in a moving fluid

Static pressure, Psis the pressure exerted by a stationary fluid.

The force in the static pressure is due to themotion of fluid particles (microscopic view)

Dynamic pressure, Pdrepresents fluid kinetic energy which

depends on the fluid motion (macroscopic view).

PT = P0 = Ps + Pd

PT = Total pressure

P0 = Stagnation pressure

Pd = V 2 / 2

where



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Automotive pressure sensors

Source: http://www.sensata.com/sensors/automotive-pressure-sensor-ap2.htm



Basic pressure measuring devices

1. Barometer consists of an inverted tube containing a fluid and is used to measure atmospheric pressure.

h

ghPPP Hgvacuumatm

ghP Hgatm

6.13/2 OHHgHgS

At 1 atm, hHg = 760 mm.



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2. Manometer is an instrument used to measure differential

pressure based on the relationship between pressure and the hydrostatic equivalent head of fluid.

)( 1212 hhgPPP

A B C

1 2

h

12 PP Case A

Case B atmPhgP 1

Case C hgPPP atmvac 1




3. Bourdon-type pressure gage Bourdon tube (coiled tube) is a curved metal tube having an

elliptical cross section that mechanically deforms under pressure

A‐A

ความดนั

Bourdon Gage

atmabsgage PPP

Patm

0gageP at 1 atm

0 Pa


Bourdon tube


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Pressure transducer

1. Displacement-type

converts a measured pressure into deformation of an elastic element used in the transducer.

1.1 Diaphragms-type

1.2 Bellows and Capsule


Displacement-type(elastic element)

P L



Pressure transducer1.1 Diaphragm-type utilizes a clamped circular plate as the

elastic element. The deformation of the diaphragm is converted into electrical signal by either LVDT or strain gages.

P L VDiaphragm LVDT



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Pressure transducer

1.2 Bellows and Capsule are a thin-wall flexible metal tube of which one end is held fixed and pressure is applied internally. A pressure difference will cause the change in length of the elastic element.

Bellow

VO

ViP L VBellow Potentiometer




Pressure transducer2. Piezoelectric Crystal Elements converts pressure electric

charges. The charge amplifier is used to convert an eletriccharge, q into an output voltage.

P1

P2

t

Crystal

Electrode

Electrode

A

*** can be used to measure either quasi-static or dynamic response.Max pressure up to 100,000 psiMax temperature ~ 350 C



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Figure 1: In a typical automotive sensor application for Manifold Absolute Pressure (MAP), a piezo-electric pressure sensor and signal conditioning IC link to the ECU via a 3-wire interconnect.

Manifold absolute pressure sensor (MAP) provides instantaneous manifold pressure information to the engine's electronic control unit (ECU). The data is used to calculate air density and determine the engine's air mass flow rate, which in turn determines the required fuel metering for optimum combustion (see stoichiometry) and influence the advance or retard of ignition timing.

Source: http://www.eetimes.com/document.asp?doc_id=1272786



Pressure transducer

3. Capacitive pressure sensor uses a diaphragm and pressure cavity to create a variable capacitor to detect strain due to applied pressure, capacitance decreasing as pressure deforms the diaphragm. Common technologies use metal, ceramic, and silicon diaphragms..



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chapter 2 sensors 1 au351.ppt - t ucharnnarong.me.engr.tu.ac.th/charnnarong/my classes/au351/chapter...

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