Sensors

Lecture 5

Basic Sensors and Principles

2

Transducer, Sensor, and Actuator

Transducer: A device that converts energy from one form to another. Transducer can act as a sensor or actuator. • Sensor:

converts a physical parameter to an electrical output (a type of transducer, e.g. a microphone)

• Actuator: converts an electrical signal to a physical output (opposite of a sensor, e.g. a speaker)

Transducer Systems

SensorsActuators

InterfaceCircuits

ControlandProcessingCircuits

PowerSupply

I/O Channel/USER

4

Classification of Transducers

Transducers

On The Basis of principle Used

Active/Passive Primary/Secondary Analogue/Digital

Capacitive

Inductive

Resistive

Transducers may be classified according to their application, method of energy conversion, nature of the output signal, and so on.

5

Piezoelectric

Type of Sensors

Temperature Sensors:Thermistors, thermocouples

Displacement Sensors:resistance, inductance, capacitance, piezoelectric

Electromagnetic radiation Sensors:Thermal and photon detectors

Measurements Techniques

• Before we start….

Something about measurements techniques

Measurement Techniques: Small fractional changes

• Many sensors vary their electrical characteristic by a small fraction over the range over which they are used

– thermister - resistance varies by 4%/C

– Temperature varies by 1mA/K (i.e. 290-300 K = 3% change in current)

VG

x1-

+

R1

R2

R3 R1

R2Rx

Wheatstone bridge

+-

R3

Rx

Vs

Temperature Measurements

There are two main types: contact and noncontact temperature sensors. Contact sensors include thermocouples and thermistors that touch the object they are to measure, and noncontact sensors measure the thermal radiation a heat source releases to determine its temperature. The latter group measures temperature from a distance and often are used in hazardous environments.

Sensor Types: Temperature Measurement

• The human body temperature is a good indicator of the health and physiological performance of different parts of the body.

• Temperature indicates:– Shock by measuring the big-toe temperature

– Infection by measuring skin temperature

– Arthritis by measuring temperature at the joint

– Body temperature during surgery

– Infant body temperature inside incubators

• Temperature sensors type– RTD (Resistor Temperature Detector )

– Thermocouples

– Thermistors

– Radiation and fiber-optic detectors (non-contact type)10

11

RTD Sensors

• What is an RTD ?– Resistance Temperature Detector

– Operation depends on inherent characteristic of metal (Platinum usually): electrical resistance to current flow changes when a metal undergoes a change in temperature.

– If we can measure the resistance in the metal, we know the temperature!

Platinumresistance changes

with temperature

Two common types of RTD elements:

Wire-wound sensing element

Thin-film sensing element

on ceramic substrate

12

Why is Platinum used ?

It is the most stable & near linear resistance versus

temperature function when compared to other metals

like Nickel & Balco

RTD Sensors

(Nickel-Iron Alloy)

13

Question

What does it mean Pt100, = 0.00385?

Pt = Platinum

0.00385 = 0 deg C the probe will read 100 ohms.

at 100 deg C, it will read 138.5 ohms.

Each resistance versus temperature relation for an RTD is qualified by a term known as “alpha”. “Alpha” is the slope of the resistance between 0°C and 100°C. This is also referred to as the temperature coefficient of resistance, with the most common being 0.0038

What would be the resistance at 20C?

the resistance of the sensor at 0 °C

the resistance of the sensor at 100 °C

1. They have very poor thermal sensitivity, that is a change in temperature only produces a very small output change for example, 1Ω/oC or even less.

2. The more common types of RTD’s are made from platinum and are called Platinum Resistance Thermometer or PRT‘s with the most commonly available of them all the Pt100 sensor, which has a standard resistance value of 100Ω at 0oC. The downside is that Platinum is expensive and one of the main disadvantages of this type of device is its cost.

3. Because the RTD is a resistive device, we need to pass a current through them and monitor the resulting voltage. However, any variation in resistance due to self heat of the resistive wires as the current flows through it, I2R , causes an error in the readings.

RTD

15

– To avoid selfheating the RTD is usually connected into a Whetstone Bridge network which has additional connecting wires for lead-compensation and/or connection to a constant current source. Two types of Whetstone Bridge networks are follow:

– 2-wire: Lowest cost -- rarely used due to high error from lead wire resistance

– 3-wire: Good balance of cost and performance. Good lead wire compensation.

RTD

• 2 wire;

Es is the supply voltage; Eo is the output voltage; R1, R2, and R3 are fixed resistors; and RT is the RTD. In this uncompensated circuit, lead resistance L1 and L2 add directly to RT.

Because the RTD is a resistive device, you must drive a current through the device and monitor the resulting voltage. However, any resistance in the lead wires that connect your measurement system to the RTD will add error to your readings.

RTD Circuits

RTD Circuits

• 3 wire;

In this circuit there are three leads coming from the RTD instead of two. L1 and L3 carry the measuring current while L2 acts only as a potential lead. No current flows through it while the bridge is in balance. Since L1 and L3 are in separate arms of the bridge, resistance is canceled.

In 3 wire configuration you can compensate for the leadresistances. In this bridge configuration, the effects of L1 and L3 cancel each other out because they are located in opposite arms of the bridge. Lead resistance L2 does not add significant error because little current flows through it.

RTD

• Most stable over time

• Most accurate

• Most repeatable temperature measurement

• Very resistant to contamination/ corrosion of the RTD element

• High cost

• Slowest response time

• Low sensitivity to small temperature changes

• Sensitive to vibration (strains the platinum element wire)

• Decalibration if used beyond sensor’s temperature ratings

• Somewhat fragile

Advantages Disadvantages

Thermocouples

A thermocouple is a device consisting of two dissimilar conductors or semiconductors that contact each other at one or more points. A thermocouple produces a voltage when the temperature of one of the contact points differs from the temperature of another, in a process known as the thermoelectric effect.

Thermocouples

• The conversion of temperature difference to electric current and vice-versa is termed as thermoelectric effect.

• When the two junctions of a thermocouple are maintained at different temperatures, then a current starts flowing through the loop known as thermo electric current. The potential difference between the junctions is called thermo electric emf.

• There are three major effects involved in a thermocouple circuit: the Seebeck, Peltier, and Thomson effects.

21

Seebeck Effect

22

The Seebeck effect describes the voltage or electromotive force (EMF) induced by the temperature difference (gradient) along the wire due to diffusion. The change in material EMF with respect to a change in temperature is called the Seebeckcoefficient .

V- Voltage difference between two dissimilar metalsa- Seebeck coefficientTh - Tc - Temperature difference between hot and cold junctions

Seebeck Effect

Seebeck observed that when two dissimilar metal wires are formed into a closed loop and its two junctions are held at different temperatures, it has the ability to deflect a galvanometer needle. The operation of a thermocouple is based on the different Seebeckcoefficients of the dissimilar metals. If the two metals of the thermocouple were alike, or had the same Seebeck coefficient, the net emf produced at its measuring point would be zero.

Peltier effect

24

The reverse of the Seebeck effect is also possible: by passing a current through two junctions, you can create a temperature difference. Peltier effect describes the temperature difference generated by EMF and is the reverse of Seebeck effect.

Thomson Effect

25

Thomson effect is related to the emf that develops between two parts of the single metal when they are at different temperature.

Thus thomson effect is the absorption or evolution of heat along a conductor when current passes through it when one end of the conductor is hot and another is cold. The heat is proportional to both the electric current and the temperature gradient.

Thermocouples

26

Simple, Rugged

High temperature operation

Low cost

No resistance lead wire problems

Point temperature sensing

Fastest response to temperature changes (=1ms)

Least stable, least repeatable

Low sensitivity to small temperature changes

Extension wire must be of the same thermocouple type

Wire may pick up radiated electrical noise if not shielded

Lowest accuracy

Advantages Disadvantages

Thermoelectric Sensitivity

The three most common thermocouple materials used above for general temperature measurement are Iron-Constantan (Type J), Copper-Constantan (Type T), and Nickel-Chromium (Type K). The output voltage from a thermocouple is very small, only a few millivolts (mV) for a 10oC change in temperature difference and because of this small voltage output some form of amplification is generally required.

27

Thermistors

• Thermistors are semiconductors made of ceramic materials whose resistance decreases as temperature increases or vice a versa.

• Advantages

– Small in size (0.5 mm in diameter)

– Large sensitivity to temperature changes (-3 to -5% /oC)

– Temperature differences in the same organ

– Excellent long-term stability characteristics (R=0.2% /year)

• Disadvantages

– Nonlinear

– Self heating

– Limited range28

ThermistorsTHERMal resISTORS

Thermistors are made of semiconductor materials (metallic

compounds including oxides such as manganese, copper,

cobalt, and nickel, as well as single-crystal semiconductors silicon and germanium).

Contrast <<--->> Common carbon resistors, made from carbon powder mixed with a phenolic binder glue.

Leads, coated Glass encased Surface mount

Assume a simple linear relationship between resistance and temperature for the following discussion:

ΔR = k ΔT

where

ΔR = change in resistance

ΔT = change in temperature

k = first-order temperature coefficient of resistance

Thermistors

Thermistors can be classified into two types depending on the sign of k.

If k is positive, the resistance increases with increasing temperature, and the device is called a positive temperature coefficient (PTC) thermistor, Posistor.

If k is negative, the resistance decreases with increasing temperature, and the device is called a negative temperature coefficient (NTC) thermistor.

Thermistors

Thermistor-choice is based on the nominal resistance you want at the operating temperature range, on the size, and on the time constant.

Time constants are about 5 - 10 seconds.

Thermistors

Thermistors

A little easier to read

Thermocouple

-0.50

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

0 10 20 30 40 50 60 70 80 90

Temperature (∘C)

Vo

lta

ge

(m

V)

Thermistor

0.00

20.00

40.00

60.00

80.00

100.00

120.00

0 10 20 30 40 50 60 70 80 90

Temperature (∘C)

Resis

tance (

KΩ

)

RTD

100.00

105.00

110.00

115.00

120.00

125.00

130.00

135.00

0 10 20 30 40 50 60 70 80 90

Temperature (∘C)

Re

sis

tan

ce

(Ω

)

Self heating of thermistor1.The voltage source is turned on, producing a current through the series combination of resistors, Rt and Ra.2.The current flowing through the thermistor generates some heat because thermistor dissipates electrical power.3.The heat causes a temperature rise in the thermistor.4.The temperature rise in the thermistor causes the resistance of the thermistor to decrease (NTC).5.The decrease in resistance causes and increase in current through the thermistor.6.The increased current through the thermistor generates more heat.7. The additional heat raises the temperature even higher.

That means that the temperature it measures is not the surrounding temperature, but one that is higher. This phenomenon is called self heating.

When using thermistor circuits, you want to minimize self-heating. You do that by minimizing the current through the thermistor. Given a choice, choose the situation where the thermistor has the smallest amount of current flowing through it.

Self heating of thermistor

Circuit Connections of Thermistors

• Bridge Connection to measure voltage

• Amplifier Connection to measure currents

37

R1

R2

R3

Rt

va

vbV

Thermistors Resistance

• Relationship between Resistance and Temperature at zero-power resistance of thermistor.

= material constant for thermistor, K (2500 to 5000 K) To = standard reference temperature, KTo = 293.15 K = 20C = 68F

is a nonlinear function of temperature

(a) Typical thermistor zero-power resistance ratio-temperature characteristics for various materials.

38

]/)([

000 TTTT

t eRR

)/(%1

2K

TdT

dR

R

t

t

50 0 50 100 150 200

0.001

0.01

0.1

1

10

100

1000

Temperature, ° C(a)

Res

ista

nce

rat

io, R

/R2

5º

C

Temperature Sensor Options• Resistance Temperature Detectors (RTDs)

– Platinum, Nickel, Copper metals are typically used

– positive temperature coefficients

• Thermistors (“thermally sensitive resistor”)

– formed from semiconductor materials, not metals

• often composite of ceramic and metallic oxide (Mn, Co, Cu Fe)

– typically have negative temperature coefficients

• Thermocouples

– based on dissimilar metals at diff. temps

Semiconductors Temperature Sensor

• Are small and result from the fact that semiconductor diodes have voltage-current characteristics that are temperature sensitive.

• Temperature measurement ranges that are small compared to thermocouples and RTDs, but can be quite accurate and inexpensive.

Thermal Sensor Vendors

Minco

Pyrotek

Omega

Watlow

Texas Instrument

National Semiconductor

Maxim

Determining Factors

Low Power

Serial Interface

Small

Accurate

Wide temperature range

Extras

I2C Interface

Temperature Alarms

Texas Instrument SpecsTMP 100/101

I2C Interface -55º to 125ºC range ±1º accuracy (±3º max) ±0.0625ºC resolution 2.7 to 5.5 operating voltage 45 to 75 µA operating current,

0.1 to 1µA shutdown current 40ms/320ms conversion

rate(9/12 bit) 25/3 conversions per second

(9/12 bit) Online sample request 6 pin SO23 package Needs 400kHz clock for I2C

Interface

MaximMAX6625/MAX6626

I2C Interface

-55º to 125ºC range

±1º accuracy (±2º max)

±5/0.0625ºC resolution(625/626)

3.0 to 5.5 operating voltage

250µA to 1mA operating current, 1µA shutdown current

133ms conversion rate

Online sample request

6 pin SO23 package

National SemiconductorLM75/LM76

I2C Interface -55º to 125ºC range ±2/ ±1º accuracy 9 bits/ 12 bits or ±0.0625ºC

resolution 3/3.3 to 5.5 operating voltage 0.25 to 0.5 µA operating current,

4/5µA shutdown current 100ms/400ms conversion

rate(9/12 bit) Online sample request 8 pin SOP package Needs 400kHz clock for I2C

Interface

Temperature measurement: An electronic medical thermometer

• Use thermistor to measure temperature in range 35-40 ºC.

• Thermistor changes its resistance on temperature change.

• The change in resistances measured and digitally displayed on thermometer in terms of temperature.

An electronic medical thermometer: Block Diagram

10 k

RSsensor

SV

oV Vref

ADC

35 36 37 38 39 40

temperature

0.1

0.2

0.3

0.4

0.5

v0�v xam

0

128

255

CDA

tuptuo

An electronic medical thermometer

• parameters– < 0.1 ºC sensitivity required

– 8-bit ADC/ 12 bit is also in use

– Typical Thermistor RS=10kW at 35 ºC

– Temperature coefficient (suppose )

• 4% per ºC

• At 40 ºC RS=10k x 1.045=12.166kW

5.0

549.01000012166

12166

min

max

V

VV S

• Variation is 0.05/0.549=9%– 9% of ADC dynamic range is used

– 23 counts for 5 ºC =0.22 ºC/count

– Approximately linear 35 ºC to 40 ºC

– Voltage at 40 ºC: Vmax=0.549V

SS

so V

RR

RV

1

• Or in graphical format– only levels 0-232 are unused:– Levels 233-255 are in use

35 36 37 38 39 40

temperature

0.5

0.549

v0�v xam

235

240

245

250

255

CDA

tuptuo

• For this application– voltage across thermister is high

– ADC has high input impedance

– ADC is close to thermister

• Thermister voltage can be applied directly to ADC without amplification

• But the poor use of the ADC dynamic range means that the required resolution (0.1 ºC ) is not achieved...

0.22

10 k

RSsensor

SV

SS

so V

RR

RV

1

oV

ADC

• A solution is to subtract the bias voltage with a differential amplifier.

• The voltage range is unchanged, but the voltage at the ADC input at the minimum temperature of 35 ºC is now zero volts

• Using a differential amplifier with a gain of 10 with a Vref of 0.5V is now 0.49V, making good use of the ADC dynamic range

Vo

x10+-

Smax

min

4

'

V49.0

0

2

1

1010

V

V

VTR

TRV S

S

So

10k

10k

10k

RS

0.5VS

ADC

VrefV’o

VS

VS/2

Fiber-Optic Temperature Sensors

• Small and compatible with biological implantation.

• Nonmetallic sensor so it is suitable for temperature measurements in a strong electromagnetic heating field.

Gallium Arsenide (GaAs) semiconductor temperature probe.

The amount of power absorbed increases with temperature

61

Displacement Measurements

• Used to measure directly and indirectly the size, shape, and position of the organs.

• Displacement measurements can be made using sensors designed to exhibit a resistive, inductive, capacitive or piezoelectric change as a function of changes in position.

62

Displacement Measurements

• Examples– diameter of part under stress (direct) – movement of a microphone diaphragm to quantify liquid

movement through the heart (indirect)

• Primary Transducer Types (As previous slide)– Resistive Sensors (Potentiometers & Strain Gages)– Inductive Sensors– Capacitive Sensors– Piezoelectric Sensors

• Secondary Transducers– Wheatstone Bridge– Amplifiers

Measure linear and angular position

Resolution a function of the wire construction

Measure velocity and acceleration

Displacement: Resistive sensors -potentiometers

2 to 500mm From 10o to more than 50o

Strain Gauges

• Definition: resistive element that changes resistance proportional to an applied mechanical strain

Compression = decrease in length by L and an increase in cross sectional area.

Rest ConditionL = length

L - L = length Compression

Strain Gauges

Strain Gauges

Tension = increase in length by L and a decrease in cross section area.

Rest ConditionL = length

TensionL + L = length

Resistance of a metallic bar is given in length and area

– where• R = Resistance units = ohms (Ώ)

• ρ = resistivity constant unique to type of material used in bar units = ohm meter (Ώm)

• L = length in meters (m)

• A = Cross sectional area in meters2 (m2 )

A

pLR

Gauge Factor (GF) = a method of comparing one transducer to a similar transducer

Gauge Factor

Gauge Factor

• where

– GF = Gauge Factor unitless

– ΔR = change in resistance ohms (Ώ)

– R = unstrained resistance ohms (Ώ)

– ΔL = change in length meters (m)

– L = unstrained length meters (m)

LL

RR

GF

Gauge Factor

• Where ε strain which is unitless

• GF gives relative sensitivity of a strain gauge where the greater the change in resistance per unit length the greater the sensitivity of element and the greater the gauge factor.

LL

RR

GF

Example of Gauge Factor

• Have a 20 mm length of wire used as a string gauge and has a resistance of 150 Ώ.

• When a force is applied in tension the resistance changes by 2Ώ and the length changes by 0.07 mm.

• Find the gauge factor:

71.3

2007.0

1502

W

W

mmmm

LL

RR

GF

Resistance of a metallic bar is given in length and area

• Example: find the resistance of a copper bar that has a cross sectional area of 0.5 mm2 and a length = 250 mm note the resistivity of copper is 1.7 x 10-8Ώm

W

W

0085.0

1000

15.0

1000

1250

10*7.12

2

8

mm

mmm

mm

mmm

mA

LR

Piezoresistivity

• Piezoresistivity = change in resistance for a given change in size and shape denoted as h

• Resistance in tension =

• Resistance increases in tension

L = length; ΔL = change in L; ρ = resistivity

A = Area; ΔA = change in A

AA

LLhR

• Resistance in compression =

• Resistance decreases in compression

L = length; ΔL = change in L; ρ = resistivity

A = Area; ΔA = change in A

AA

LLhR

Example of Piezoresistivity

• Note: Change in Resistance will be approximately linear for small changes in L as long as ΔL<<L.

• If a force is applied where the modulus of elasticity is exceeded then the wire can become permanently damaged and then it is no longer a transducer.

Example of Piezoresistivity

• Thin wire has a length of 30 mm and a cross sectional area of 0.01 mm2 and a resistance of 1.5Ώ.

• A force is applied to the wire that increases the length by 10 mm and decreases cross sectional area by 0.0027 mm2

• Find the change in resistance h. –Note: ρ = resistivity = 5 x 10-7 Ώm

Example of Piezoresistivity

W

WW

W

24.1

74.25.1

1000

1*)0027.001.0(

1000

1*)1030(

10*52

2

7

h

h

mm

mmm

mm

mmm

mhR

AA

LLhR

Application

1: By mounting is suitably on the walls of cardiac muscle, the force of the contraction of the cardiac muscle can be measured continuously. 2: To measure blood pressure in the heart, The strain gauge is mounted on the tip of the catheter which is inserted in the heart through a vein. In front of the strain gauge there is diaphragm the deflection of which varies with blood pressure. And in turn alters the strain gauge resistance.

Application: Biomechanics

Force Plates/DynamometersA force is a device that measures the ground reaction forces (GRF) exerted by a subject standing (or walking) on it. Force plates are used for gait analysis, diagnosis of foot impairment, studies of balance, sports medicine, and design of medical shoes.Force plates consist of a top plate which is separated from the bottom frame by force transducers at each corner. The forces exerted on the top surface (of the plate) are transmitted through the force tri‐axial transducers (operating in transverse (Z), antero‐posterior (X) andvertical (Y) directions).

Application: Weighing

In weighing/scaling machine there is a sensor which converts force or weight into an electrical signal. This sensor is the load cell which is classified as a force transducer. The strain gage is the heart of a load cell.

Application: Kidney DialysisA typical kidney dialysis system may depend on one or several load cells to ensure that the filtration system has perfect balance and timing. The dialysis system must remove contaminated blood, clean it, and recirculate the clean, reoxygenated blood. Load cells used for this type of system are typically in-line, small, and work by monitoring flow changes by sensing the weight of a hanging bag to ensure the dialysis procedure is performed safely every time. The load cell is attached to the end of a hanging bag. The bag is connected to the dialysis machine via two flexible tubes. One tube is used for the flow inlet and the other is for discharge. Each load cell is connected to a programmable logic controller or computer to monitor the flow by weight measurement. Using the load cell information, the system automatically processes and controls the dialysis procedure while collecting data for further analysis when needed.

Application: RehabilitationA load cell attached to a gripping or tension device can indicate exact changes in an affected muscle and how much progress is being made after each therapy session. This allows the therapist to customize the types of therapy to the needs of the patient. These load cells vary in size from 1 to 4 in. diameter, with measurement ranges of 50–1000 lb. There are many system configurations designed for this purpose, but all have two things in common: the patient exerts force against some object that is connected to the load cell, and the load cell sends the resulting measurement to a readout device or computer. The computer then converts the signal from analog to digital to produce an accurate, real-time display.

Types of Strain Gauges: Unbonded and Bonded

• Unbonded Strain Gauge : resistance element is a thin wire of special alloy stretch taut between two flexible supports which is mounted on flexible diaphram or drum head.

• When a Force F1 is applied to diaphramit will flex in a manner that spreads support apart causing an increase in tension and resistance that is proportional to the force applied.

• When a Force F2 is applied to diaphramthe support ends will more close and then decrease the tension in taut wire (compression force) and decrease resistance will decrease in amount proportional to applied force

Types of Strain Gauges: Unbonded and Bonded

• Bonded Strain Gauge: made by cementing a thin wire or foil to a diaphragm therefore flexing diaphragm deforms the element causing changes in electrical resistance in same manner as unbonded strain gauge

Types of Strain Gauges: Unbonded and Bonded

• When a Force F1 is applied to diaphram it will flex in a manner that causes an increase in tension of wire then the increase in resistance is proportional to the force applied.

• When a Force F2 is applied to diaphram that cause a decrease the tension in taut wire (compression force) then the decrease in resistance will decrease in amount proportional to applied force

Types of Strain Gauges: Unbonded and Bonded

1. Unbonded strain gauge can be built where its linear over a wide range of applied force but they are delicate

2. Bonded strain gauge are linear over a smaller range but are more rugged

– Bonded strain gauges are typically used because designers prefer ruggedness.

Comparison: Unbonded and Bonded

Typical Configurations

R2 = SG2R4 = SG4

R3 = SG3

C+-

A

B

Vo

R1 = SG1

DES

Electrical Circuit Mechanical Configuration

4 strain gauges (SG) in Wheatstone Bridge:

Strain Gauge Example

• Using the configuration in the previous slide where 4 strain gauges are placed in a wheatstone bridge where the bridge is balanced when no force is applied,

• Assume a force is applied so that R1 and R4 are in tension and R2 and R3 are in compression.

• Derive the equation to depict the change in voltage across the bridge and find the output voltage when each resistor is 200 Ώ, the change of resistance is 10 Ώ and the source voltage is 10 V

+

Strain Gauge Example

R2 = R - h R4 = R +h

R3= R-h

C+-

A

B

Eo

R1 = R +h

D

VVEo

R

hEs

R

hEs

R

hR

R

hREsEo

hRhR

hR

hRhR

hREsEo

RR

R

RR

REsEo

5.0200

1010

2

2

22

43

4

21

2

W

W

Circuit Derivation:

Es

Piezoelectric Sensors

93

When a pressure is applied to a polarized crystal, the resulting mechanical deformation and displacement of charges results in an electrical charge.

They are sensitive to more than one physical dimension. Therefore, it sometimes becomes necessary to compensate for unwanted Effects. For instance, sophisticated pressure sensors often use acceleration compensation elements. Those compensations are based on thefact that the measuring elements may experience both, pressure and acceleration events. A second measuring unit is added to the sensor assembly that only experiences acceleration events. By carefullymatching those elements, the acceleration signalIs subtracted from the combined signal of pressureand acceleration to derive the true pressure information

• External (body surface) and internal (intracardiac) phonocardiography

• Detection of Korotkoff sounds in blood-pressure measurements

• Measurements of physiological accelerations

• Provide an estimate of energy expenditure by measuring acceleration due to human movement.

General Applications

94

C/Nconstant,ricpiezoelect

k

kfq

Vo

To find Vo, assume system acts like a capacitor (with infinite leak resistance):

A

kfx

C

kf

C

qV

r

o0

x

AC r0

Capacitor:

(typically pC/N, a material property)

k for Quartz = 2.3 pC/N

k for barium titanate = 140 pC/N

95

As mentioned previously, an external force cause a deformation of the crystal results in a charge which is a function of the applied force. In its operating region, a greater force will result in more surface charge. This charge results in a voltage Vo , where q is the charge resulting from a force f, and C is the capacitance of the device.

Models of Piezoelectric Sensors

Piezoelectric polymeric films, such as polyvinylidence fluoride (PVDF). Used for uneven

surface and for microphone and loudspeakers.96

deflectionx

constantalityproportion

K

Kxq

View piezoelectric crystal as a charge generator:

Rs: sensor leakage resistance

Cs: sensor capacitance

Cc: cable capacitance

Ca: amplifier input capacitance

Ra: amplifier input resistanceRa

Transfer Function of Piezoelectric Sensors

97

Convert charge generator to current generator:

dt

dxK

dt

dqis Kxq

Ra

R

V

dt

dxK

dt

dVC

iii

iii

oo

Rsc

Rcs

1

j

jK

jX

jV so

Ks = K/C, sensitivity, V/m

= RC, time constant

Ra

Transfer Function of Piezoelectric Sensors

98

Limitation

R

V

dt

dxK

dt

dVC

iii

iii

oo

Rsc

Rcs

Consider the equation, it indicates that the steady state response to a constant deflection is zero. It means static displacement cant be measured by piezoelectric material. This can be visualized by considering step displacement function (next slide)

Voltage-output response of a piezoelectric sensor to a

step displacement x.

Decay due to the finite

internal resistance of the

PZT

When a force is applied to the sensor at t =0, the sensor output (Kx/C)start decaying

with time, due to limited internal resistance. When force is released the restoration

occurs equally and opposite direction. This cause a sudden drop in charge and

undershoot occur. The decay and undershoot can be minimized by increasing the

time constant =RC.

100

Piezo Electric Pulse Transducer

Piezo-electric element convert force applied to the active surface of the transducer from the finger blood pressure pulse, into an electrical signal.

Detects expansion and contraction of the finger circumference, due to changes in blood pressure Typical output is 50–200 mV but can

reach as high as 500 mV

Piezo Electric Pulse Transducer

Finger pulse transducer is a very sensitive instrument. Even slight movements by the volunteer can result in noisy recordings. The subjects should keep their hand as still as possible between stimuli.