Transducer i i

8/16/2019 Transducer i i

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Velocity Transducer

Use the principle of electromagnetic induction: linear and angular velocity transducer

Linear velocity measurement Angular velocity measurement

Basic equation relating voltage generated to velocity of a conductor in a magneticfiled can be expressed as

BlvV T =

V T = the voltage generated by the transducer B = the component of the flux density normal to the velocityl = the length of the conductor v = the velocity


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Velocity Transducer Permanent magnet-core

N S

Linear velocity transducer

LVT is equivalent to a voltage generated connected in series with an inductance LT and a resistance R T and here R M is the input resistance of a recording instrument

vS V i R Rdt di

L vT M T T ==++ )(

S v = the voltage sensitivity (mV/(in/s) )v = the time dependent velocity (in/s)i = the current flowing in the circuit

V T

i

LT RT

R M V o

Equivalent circuitV T

Assume a sinusoidal input velocity, the frequency response can be obtained

( ) ( ))arctan(here )()(

22 M T M T

v M M o

R R

L

L R R

vS R RiiiV

+−=

++

∠==

ω φ

ω

φ ω ω


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0)()( inminm =−+′−′+′′ x yk x yb ym

= natural frequency

= damping ratio

Accelerometer

spring

damper

Seismicmassm

y(t )

Movable work piece

x in (t )

mk

bmk

F xm z k z b z m in

m

m

mn

mm

2=

=

−=′′−=+′+′′

ζ

ω

Let z = y - x in

m

k ( y-x )

bm

( y-x ) My

,, , ,

0

-y

+y

Most accelerometers use the mass-spring-damper system,under a steady acceleration, the mass will move, stretchingor compressing the spring until the force exerted by springbalance the force by the force due to acceleration

ak m

yma yk

m

m

=∆=∆

21

nmk m

ω =Here = static sensitivity

So the measurement of steady acceleration is just a

displacement problem.

For dynamic behavior: the system is a second order system


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Accelerometer

Accelerometer using a potentiometer Strain gage accelerometer

Piezoelectric accelerometer

F

q+

q-

F S q q=

D = piezoelectric strain constant

C

F S

C q

V q== electrode

F xm z k z b z m in −=′′−=+′+′′ mm


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Piezoelectric EffectA piezoelectric material produces an electric charge when its subject to a force orpressure. The piezoelectric materials such as quartz or polycrystalline bariumtitanate, contain molecules with asymmetrical charge distribution. Therefore,under pressure, the crystal deforms and there is a relative displacement of the

positive and negative charges within the crystal.

P = 0O

(a)

P = 0

Force

(b)

Cubic unit cell has a center of symmetry

From Principles of Electronic Materials and Devices, Second Edition , S.O. Kasap (© McGraw-Hill, 2002)http://Materials.Usask.Ca

P = 0 PO

y

x

(a) (b)

A

B

A'

B'

P = 0P

(c)

A''

B''

Hexagonal unit cell has no center of symmetry


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Piezoelectric Effect

Charge, q develops can be determined from the output V oF

q+

q-

electrode

AP S F S C V q qqo ===

C = capacitance S q = charge sensitivity A = area P = applied pressured = distance between electrode

dP S dP S

AP C

S V V

r

qqo === ε ε 0

Quartz: Young’s modulus 86 GPa, resistivity 10 12 Ω .m and dielectric constant = 40.6 pF/m


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Piezoelectric Effect

Piezoelectricsensor

AmpLeads To

Voltmeter

q V o R P C P C L C A R A

Charge generator

Sensor Amplifier

Schematic diagram of a measuring system with a piezoelectric sensor


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Pressure Transducer

Pressure transducers - use some form of mechanical device thatstretches proportionally in response to an applied pressure. Straingages, LVDT, potentiometers, variable inductance, or capacitance

convert this displacement into an electrical signal.

Mechanicaldevice

PositionSensor pressure

Displacement

Electricaloutput

-Diaphragm-Bellows-Bourdon Tube

-Potentiometric-Resistive (strain gauge)-Inductive (LVDT)-Capacitive-Optical


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Pressure Transducer

Bourdon tube is a curve metal tube having an elliptical cross section that mechanicallydeforms under pressureBellow is a thin-walled, flexible metal tube formed into deep convolutions and seal atone end.Diaphragm is a thin elastic circular plate supported about its circumference.

Bourdon tube pressure sensor


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Pressure Transducer

Diaphragm pressure sensor Capacitive pressure sensor

Capacitive pressure sensor


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Flow Transducer

Volume flow rate:

Mass flow rate: Qdt

dmQ ρ ==m

dt dV

Q =

Velocity: AQ

v =

Where is the density of fluid and A is the cross section of the pipe

122 P P k Q −=

Q = Volumetric flow ratek = Constant is set by the geometry

P 2 = high-side pressure P 1 = low-side pressure

Restriction Flow sensors

Orific plate

venturi

An intentional reduction in flow will cause ameasurable pressure drop across the flow path


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Flow Transducer

Defection type Flow sensor Spin type Flow sensor

Electromagnetic Flow sensor


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Level Transducer

Continuous level:indicate the precise level, proportionally along the entire

height of the tankDiscrete level

indicate only when the tank reaches the predefined level

Discrete level transducer


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Level Transducer

Capacitive level sensor

Level measurement bypressure sensor

Level measurement by

force sensor

Level measurement by

differential pressure sensor


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Temperature Transducer

• Thermocouple• RTD• Thermistor • Integrated circuit (IC) sensor


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ThermocoupleThermocouple:

a simple temperature sensor consists of two dissimilarmaterials in thermal contact (junction), the electrical potential

(Seebeck voltage) is developed that is proportional to thetemperature of the junction .

Metal#1

Metal#2

SensingJunction

V

∆ T

V = s∆ T

s: Thermoelectric coefficient(material dependence)

Reference junction at 0ºCReference junction


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Thermocouple


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Thermocouple

In practice, we can’t measure Seebeckvoltage directly because we mustconnect voltmeter to the thermometer ,and the voltmeter leads themselvescreate a new thermoelectric circuit.Voltmeter

Copper

Constantan

+

-

Cu

Cu

J 1

J 2

J 3

Equivalent circuit

V 3 = 0

≡

V = V 1 - V 2

Cu

ConstantanJ 2

Cu

+

-+ -V 2

V 1V J 1J 1

Cu

ConstantanJ 2

J 3

Cu

Cu

+ -

+

-

V 3

+ -V 2

V 1

How can we know the temperature at J 1?

Equivalent circuit


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Thermocouple•Using ice bath

Cu

ConstantanCu

J 2IceBath

J 1

Cu

ConstantanCu

J 2IceBath

J 1

Voltmeter

+

-

Since T 2 = 0; V 2 = 0

V = V 1 = V Cu/constantan (T 1)

The thermoelectric circuit is used to sensed an unknown TemperatureT1, while junction 2 is maintained at a known reference temperature T 2.It is possible to determine T 1 by measuring voltage V.

V

Accurate conversion of the output voltage V , to T 1-T 2 is achieved eitherby using calibration (lookup) tables or by using a higher order

polynomialn

nV aV aV aaT T ++++=− L2

21021

Where a 0, a 1, ···, a n are coefficients specified for each pair ofthermocouple materials, and T 1-T 2 is the difference temperature in oC

We can use calibration table forTC or polynomial eq. to find T 1

V 1-

+


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•The insertion of an intermediate metal C into junction 1 does not affect the outputvoltage V o, provided that the two junctions formed by insertion of the intermediate(A/C and C/B) are maintained at the same temperature T 1

•A Thermocouple circuit with temperatures T 1 and T 2 produces an output voltage(V o)1-2 = f(T 1 – T 2), and one exposed to temperatures T 2 and T 3 produces anoutput voltage ( V o)2-3 = f(T 2 – T 3). If the same circuit is exposed to temperaturesT 1 and T 3 , the output voltage ( V o)1-3 = f(T 1 – T 3) = ( V o)1-2 + (V o)2-3 .

Principles of Thermocouple Behavior

T 1

T 2

Material A

Material BMaterial B

V o

T 1

T 3 Material C

T 1 T 2

Material A

Material B Material B(V o)1-2

T 2 T 3

Material A


T 1 T 3

Material A


= +

(d) Intermediate metal in junction

(e) Voltage addition from identical thermocouples at different temperatures

T 1 T 2

Material A

Material B Material BV o

≡


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•A thermocouple circuit fabricated from materials A and C generates anoutput voltage ( V o) A/C when exposed to temperatures T 1 and T 2, and asimilar circuit fabricated from materials C and B generates an output

voltage ( V o)C/B . Furthermore, a thermocouple fabricated from materials A and B generates an output voltage ( V o) A/B = (V o) A/C + (V o)C/B

Principles of Thermocouple Behavior

T 1 T 2

Material A

Material C Material C(V o)A/C

T 1 T 2

Material C

Material B Material B(V o)C/B

T 1 T 2

Material A

Material B Material B(V o)A/B

= +

(f) Voltage addition from different thermocouples at identical temperatures


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Thermocouple


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Thermocouple

Themoelectric voltages: Chromel-Alumel Type K (Table A.2)Copper-Constantan Type T (Table A.3)Iron-Constantan Type J (Table A.4)


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• Commercial ICs are available for a wide variety of TC

AD594: Type J (iron-constantan)AD595: Type K (chromal-alumel)These ICs give approximate output

Thermocouple•Using hardware compensation (electronic ice point reference)

V

1o C

mV 10 T V ≈

Fe

ConstantanCu

J1

Cu

Voltmeter

+

- J 3

J 2

integrated

tempertauresensor

R H

Commercial IC


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Cu

ConstantanCu

J 1

Cu

Voltmeter

+

- J 3

J 2

Thermistor or RTD

Thermocouple•Using software compensation

V V 1+

-

)()( 2/CuConstantan1tanCu/Constan T V V T V −=

+

+-

-

From calibration tables: V Cu/constantan (100 oC) = - V constantan/Cu (100 oC) = -4.277 mV

)()()( 2/CuConstantan2Cu/Cu1tanCu/Constan321

T V T V T V V V V V V

++=++=

0

Ex assume that the arbitrary reference temperature T 2 is maintained at100 oC and that an output voltage V = 8.388 mV is recorded. Find T 1

T2 must be known

• This method relies on a computerprogram that contained calibrationtables of TC

• Thermistor or RTD is used to gainthe absolute temp. of reference junction (ambient temperature).

mV665.12)277.4(388.8)( 1tanCu/Constan =−−=T V

From calibration tables: V Cu/constantan =12.665 mV would be produced by a

temperature of T 1 = 261.7oC


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• Commercial ICs for various TC

AD594: Type J (iron-constantan)AD595: Type K (chromal-alumel)

These ICs give approximate output

Thermocouple•Using hardware compensation (electronic ice point reference)

V

1o CmV

10 T V ≈

Fe

ConstantanCu

J1

Cu

Voltmeter

+

- J 3

J 2

integrated

tempertauresensor

R H

Commercial IC

Fe

Constantan

J 1J 3

J 2

Amp

Tempsensor

Signalconditioning

+V

out

to meter


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Resistive Temperature Detectors (RTDs)

An RTD: All metals produce positive change in resistance for apositive change in temperature

R = R0[1 + α 1(T - T 0) + α 2(T - T 0)2 + … + α n(T - T 0)n ]

Where R0 is the resistance at the reference temperature T 0 . α n is the temperaturecoefficient

ex. For a Pt wire, α 1 ~3.95 x 10 -3/K, α 2 ~5.83 x 10 -7/K2

Resistance-temperature curves fornickel, copper and platinum.

For a limited range of temperature, thelinear form can be used

R = R0[1 + α 1(T - T 0)]

The sensitivity to temperature

S = R0α 1

For a Pt wire, this corresponds to a change

of only ~0.4%/ oC


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RTD: Common Errors

• Lead-wire effectsUse short lead wire ( R L < 1% of RTD )Use three or four lead-wire system

• Stability

• Self-heating

• Sensitivity of the RTD to strain

Self-heating occurs because of the power dissipation in sensor, P D=I 2 RT

The increase in temperature from self-heating ∆T due to P D=I 2 RT is

D T δ = ∆

Where δ is heat dissipation factor (mW/K)

To minimize self-heating effect, the power dissipation must be limited.

Normally, this error can be negligible since the strain sensitivityof the sensor is small comparison with the temperaturesensitivity

Stability may become a source of error when the upper temperature is exceeded


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RTD

V r

R1

R4

R2

100 ΩRTD

Rw1

Rw2

Rw3

DVM

i

i

Wire1

Wire2

Wire3

Wire4

100ΩRTD

Constantcurrentsource i = 0

i = 0T DVM iRV =


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Thermistor

Thermistors: temperature-dependent resistors that are based onsemiconductor materials such as oxides of nickel, cobalt, or manganese andsulfides or irons, aluminum or copper. They are designated as NTC whenhaving a negative temperature coefficient and as PTC when having a positive

temperature coefficient.

Mechanism:Variation of the number of charge carrier and mobility with temperatures

NTC thermistor: the dependence of R with temperature is almost exponential:

0(1/ 1/ )0

T T R R e β −=

Where R0 = the resistance at the reference temperature T 0 andβ = the characteristic temperature, usually ranges from 2000 to 4000 K.

β is also temperature dependent parameter.T and T 0= absolute temperature, K


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Thermistor

The equivalent TCR or relative sensitivity:

2

1 1dRS

R dT R T β

α = = = −

Which shows a nonlinear dependence on T . At 25 oC and taking = 4000K, α = -4.5% /K, which is more than ten times higher than that of PT100probe ( α = +0.35% /K). if R o = 2000 Ω then ∆ R ∆ T = 90 Ω Κ . Therefore, theeffect of lead resistance is less than in thermistor compare to RTD.

RT Constantcurrentsource

V oConstantvoltagesource

R V o

RT

Steinhart-Hart relation:

Where A, B and C = coefficient determined from calibration curves

31 ln (ln )T T B R C RT = + +

Simpler relation: C A R BT −−= ln


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Integrated-Circuit Temperature Transducer

IC temperature sensors: combine the temperature sensing elementand the signal-conditioning electronics

LM335 outputs: 10 mV/K or 2.73 V + 10 ( mV/ o C) T LM34 outputs: 10 mV/ oF

AD592 outputs: 1 µ A/K or 273 µ A + 1 ( µ A /oC) T

LM34 V out

V supply

LM335 +

-V z

Rbias

V supply

V out

AD590 or

AD592

V supply

V out =(10 mV/o C) T +2.73 V

I out

1 k

9.5 k

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