# BIOE 3270 Lecture Notes - Lecture 4: Human Body Temperature, Thermal Expansion, Step Function

5 pages48 viewsWinter 2011

School

University of ManitobaDepartment

Biosystems EngineeringCourse Code

BIOE 3270Professor

PaliwalLecture

4This

**preview**shows page 1. to view the full**5 pages of the document.**Dynamic Response of Measuring Instruments

Transducer:

A device that converts a signal from one physical form to a corresponding signal having a different physical form

Physical form: mechanical, thermal, magnetic, optical, electrical

Transducers are energy modifiers or converters

Sensor: receives a stimulus and responds

Dynamic Characteristics: The properties of the system transient response to an input.

y=f(x)

The dynamic response is typically modeled by a constant – coefficient linear differential equation

ax

dky(t)

dtkKa2

d2y(t)

d2ta1

dy(t)

dt aoy(t)x(t)

I practice, these models are limited to zero, first, and second order

Zero Order Instruments: have an output that is proportional to the input at all times

Static gain of the instrument (measure of its sensitivity)

o Example would be a strain gage where

R

L

A

(output is proportional to the length of the wire.

No delays

The sensor only changes the amplitude of the signal

Unit Step Function:

x(t)=0,

t0

x(t)=1, t>0

o For a zero order instrument, y(t)=Kx(t) y(t)=0, for

t0

; and y=K for t>0 therefore response of a zero

order instrument to a unit step function with height k, would be K

First Order Instruments: output is given by a non-homogeneous first-order differential equation

d

dt y(t)y(t)Kx(t)

o

is called the time constant of the instrument

o The response of a first order instrument to the unit step function

d

dt y(t)y(t)K

x(t)=1

Initial condition y(0)=0

y(t)K(1et

)

When t=

y(

)K(1e)0.632K

Second Order Instrument: second order non-homogenous differential equation

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d2

dt2y(t)2

d

dt y(t)

2y(t)K

2x(t)

- constant, damping factor if the instrument

- angular frequency of the instrument

Temperature Measurement

Two necessities for temperature measurement:

o Reference temperature

o Rule for measuring the difference between a certain temperature from the reference point

Temperature Scales:

Fahrenheit: Devised by Gabriel Fahrenheit

o Earliest standard scale

o Wanted to fix human body temperature at 100 degrees + he wanted whole numbers for the

freezing and boiling points

32o F – freezing pt. of water

212o F – boiling pt. of water

98.6o F – human body temperature

Celsius: devised by Andres Celsius

o Set out to fix the boiling point of H2O @ 0o an freezing pt. @ 100(this was later reversed)

o It became popular because if the 100 division

o The unit called ‘centigrade’

o In 1947 the general committee on Weight & Measures ruled that the unit be called ‘Celsius’

Kelvin: William Kelvin

o Discovered the principle of energy as it related to the heat of the matter

o This led to the idea of ‘absolute zero’, a temperature below which it is impossible to go since the

matter would have zero energy at this point.

o 1oC difference in temperature = 1 K temperature difference

273.16 K = 0.01oC & 611 Pa (Triple point of water)

o A unique combination of temperature and pressure at which the solid, liquid and vapor phases co-

exist at equilibrium

Four Basic temperature measurement methods:

1. Thermal expansion: e.g. Hg thermometer

2. Thermoelectricity: e.g. thermocouple

3. Resistance: e.g. thermistor

4. Radiation: e.g. pyrometers

Choice of a particular thermometer depends on:

o Accuracy

o Recording requirements

o Control

o Requirements

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