Download Self-heating and dissipation constant

a) Objectives :To study the parameters of a negative temperature coefficient resistor & their
application in the design of practical measurement systems.
b)Theory :Themistors consist of semi-conducting, poly-crystalline material. In the
production of temperature sensors copper dioxide (CuO2) is preferred. It
demonstrates a severe non- linear drop in resistance for an increase in
temperature: it possesses a negative temperature coefficient. Which is the reason
why these sensors are called NTC resistors. If the (CuO2) is mixed with the
ingredients of a ferroelectric material like (BaTi). The temperature coefficient is
initially negative only for low temperatures. After reaching a threshold
temperature. The temperature coefficient becomes very strongly positive in a
narrow temperature range. For higher temperatures the temperature coefficient
reverse back to negative. These sensors are called PTC resistors. And are mainly
used for triggering purposes.
NTCs have strongly negative temperature coefficients. Which are not constant.
Their resistance changes through several decades for a change in temperature. I.e.
NTC sensors have a high sensitivity. Which is easily 10 times higher than that of
a metal resistance thermometer (whose temp. coefficient. Is positive). The nonlinearity of NTCs and their broad manufacturing tolerances exclude them from
use for precision instruments. 3% types can only be obtained through careful
selection. NTCs have small-time constants resulting from the small dimensions of
the sensor. Similar small-time constants are only available in thermocouples.
However the long-term stability of NTCs is considerably lower.
Resistance at 25 ºC for typical commercial units ranges from 100 Ώ to over
10MΏ . in addition to the choice of resistance values. Choices of power rating.
Physical size and shape. Resistance tolerance are also available. Smallest NTCs
are made in the from of beads. Some are as small as 0.15 mm in diameter. And
may come glasscoated or sealed in the tips of solid-glass probes. NTCs may also
obtained in disk, washer. Or rod forms. Their power ratings typically vary from
few μW to 25W, and can be connected in series-parallel arrangements for greater
power handling.
The shape of the curve relating resistance to temperature is given in general by the
equation : RT = A exp (B/T)
Where
RT
T
A and B
is the thermistor resistance in ohms.
is absolute temperature in Kelvin.
are constants that are experimentally determined.
Self-heating and dissipation constant
We know that we cannot measure resistance without passing current through it,
this will cause what is known as self-heating. However we want the sensor to
measure the temperature of its surroundings only, therefore a precaution is
necessary to keep the effect of self-heating as small as possible.
When a thermistor or a metal-resistance thermometer is to be used in a
temperature measurement or control system there will be two conflicting
requirements:
1. Greatest possible sensitivity from the detector circuit, meaning as large
energizing current as possible, and therefore more self-heating.
2. Limited error, implying a limit to the self-heating.
The dissipation constant is a parameter which help to resolve this conflict by
specifying how much power can be dissipated by the energizing current without
causing more than the permitted amount of self-heating. So it can be defined as:
Dissipation constant = mW of power dissipation due to self-heating which will
cause a temperature rise of 1ºC. it is important to note that this constant depends
on the thermal conduction characteristics of the medium in which the sensor is
placed because if this is high. More power will be needed to raise the temperature
by 1ºC than if it is low .
Linearizing the NTC resistance characteristic
In some applications it is desirable to have a linear relationship between the
thermistor resistance and temperature. A simple way of achieving this is to
connect a resistor of suitable value and has a very low temperature coefficient in
parallel with the thermistor. This resistor is called the linearizing or compensating
resistor (Rc), and is chosen so that the slope of the resistance-temperature curve is
the same at each end of the operating range. The resulting temperature sensitivity
is reduced for the sake of linearity.
c) Results :The results are shown printed in the next pages.
The resistance of the thermistor at room temperature = 4kΩ
The Voltage at the mid range ( 56ºC ) equals 0.201v.
Using this value, & from the circuit, we can get the value of RC :15*RC / ( 100000 + RC ) = 0.201
 RC = 1.358 kΩ
We connect this resistance in parallel with the Thermistor in the linearization part.
In the following page, you can see the graphs of the results printed.
d)Graphs : - Plot the resistance of the thermistor versus θ ºC for no linearization & no
Linearization cases in the above measurements.
In order to do so , I derived an equation from the circuit, which is :RT = 100*V / ( 15 – V )
Req = 100*V / ( 15 – V )
( For no Linearization )
( For Linearization )
Then I copied the tables of temperature & voltage from the CASSY to the Excel
to get the following graphs :-
Non Linearized
3
2
1.5
1
Resistance
2.5
0.5
0
100
80
60
40
20
0
Temp
9
8
7
6
5
4
3
2
1
0
100
80
60
40
Temp
20
0
Resistance
Linearized
e) Questions : 1- Minimum slope is at 75ºC = (.677-1.0101) / ( 74.6-64) = - 0.036 kΩ/ºC
Maximum slope is at 38ºC = - 0.115
Minimum Sensitivity = (0.101 - 0.15) / (74.6 - 64 ) = - 0.0046 v/ºC
Maximum Sensitivity = (0.35 - 0.401) / (41.3 - 38.2) = - 0.016 v/ºC
2- Slope = (7.812 - 7.365 ) / ( 34.1 - 40.1) = - 0.0745 kΩ/ºC
Sensitivity = (0.753 - 0.62) / (60 - 70 ) = - 0.0133 v/ºC
f) Discussion : From the results we obtained, we can see that the relation between the resistance
of the Thermistor & the temperature is not linear ( Fig 1 & 2 ) . In fact it has an
exponential shape, which agrees with the theory.
After adding a compensation resistance in parallel to the thermistor, whose value
is equal to the value of the resistance of the thermistor at mid position ( 1.358 kΩ
at 56ºC ) , we saw that the relation became linear ( Fig 3 ). This process allows us
to use the thermistor as an effective temperature sensor, which can measure the
temperature in the area in which it is located, by obtaining the value of the
resistance & by knowing the slope of the resistance versus temperature.
g) Conclusions :During this lab, we studied the parameters of a negative temperature coefficient
resistor & their application in the design of practical measurement systems. We
detected the exponential relation between the resistance of a thermistor & the
temperature, which is given by :RT = A exp (B/T)
We saw that the resistance decreases with the increase of temperature.
In order to make the thermistor a more useful sensor, we did a linearization
process. This process made the relation between the resistance of the sensor & the
temperature linear.
We faced some errors in our measurements in this lab, this might be obvious from
Fig 3 which is not exactly linear as it should be, this may be due to rounding
errors in calculating the compensation resistance, or an instrumental error due to
the use of the decade box. But those errors are experimentally accepted.