control assignment - calibration of insulated and uninsulated thermistors

7/29/2019 Control Assignment - Calibration of Insulated and Uninsulated Thermistors

1/13

Daniel James Watkins [Static and Dynamic Calibration of an Insulated and Un-insulated Thermistor]

BEng Mechanical Engineering Page 1

Introduction

One of the most common types of physical measurements is temperature. Temperature can be

measured in many environment and channel counts. There are various types of temperaturemeasuring sensors and components. Depending on the temperature range, desired accuracy and

expense; appropriate sensors must be selected (National Instrument, 2011).

There are three types of Semiconductors classifications; elemental semiconductors, compound

semiconductors and junction semiconductors. Thermistors are compound semiconductors that are

used for temperature measurements and identify a special resistor that varies in resistance with

temperature (McGee, 1988).

Background Theory

Thermistors

Thermistors are resistors that contain high rate of change of resistance with temperature. Typically,

they are inexpensive ceramic compounds that are highly sensitive to temperature change.

Regardless of the high sensitivity, they are commonly used for temperature control within the

temperature range from approximately -100 to 500C (McGee, 1988). Mostly, themistors are

compound semi-conductors that contain complex conduction processes. Compound semiconductors

are usually ceramic in which solid solutions of transition metal oxides are used (McGee, 1988).

Thermistors are employed in many electronic devices to control the temperature response or to

compensate for temperature changes in electronic circuits. In term of temperature measurement, tominimize Joule heating which cause the thermistor to have a higher temperature than its

surroundings, the current flows through a thermistor should be small (McGee, 1988). Sufficient

current to casue Joule heating is desirable in the case of temperature control, switching purposes

and fluid flow measurements or any other properties that have an effect on heat transfer from the

thermistor. The internal heating is negligible when a small voltage is applied to a thermistor,

therefore, its temperature will practically be the same as its surrounding temperature (McGee,

1988). Themistors contain negative temperature coefficients of resistance, therefore, the Joule

heating causes the resistance to drop, increases the current and increases heat transfer from the

thermistor.

The relationship between the Voltage and current is nonlinear due to the resistor R (Figure 1.1) is

not constant. When the voltage increased, the heat transfer increases which will compensate for the

Joule heating and a point will be reached where the maximum voltage will appear for any particular

souce of current (Figure 1.1 and 1.2). The current-voltage relationship becomes unstable when the

resistance of the thermistor drops and impulsive increases in current take place in between point B

and C (Figure 1.3). The electrical power Nprovided to the thermistor equals to the heat dissipated to

the surroundings P along the V-I curves. The V-I curves is extremely useful in many thermistor

circuit applications.


2/13



Figure 1.1: The voltage drop V across thermistor depends on the current I, the source resistance R,

and the temperature of T (McGee, 1988). [Figure Abstracted from: McGee, T. (1988) Principles andMethods of Temperature Measurement, New York: John Wiley & Sons, p.210]

Figure 1.2: Voltage-current response of the thermistor showing the thermistor resistance and

temperature at different current levels (McGee, 1988). [Figure Abstracted from: McGee, T. (1988)

Principles and Methods of Temperature Measurement, New York: John Wiley & Sons, p.211]


3/13



Figure 1.3: Stable (C) and unstable (B) points of a simple thermistor circuit (McGee, 1988). [Figureabstracted from: McGee, T. (1988) Principles and Methods of Temperature Measurement, New York:

John Wiley & Sons, p.211]

In temperature measurement applications, the current must be kept at minimal to minimize self-

heating errors. This requires a small voltage applied or current limiting. The voltage and current

measurement errors increase as their value is decreased. In many applications, a compromise is

needed between minimizing self-heating errors and minimizing resistance measuring errors (McGee,

1988).

Most thermistors contains a negative coefficient relating resistance with temperature, however,Positive-Temperature-Coefficient (PTC) thermistors are available and used due to their greater

sensitivity. PTC thermistors contain positive coefficient only over a limited temperature range,

beyond this range, the coefficient is negative (Leigh, 1991). The typical curve for a negative and

positive-temperature coefficient thermistor is shown in Figure 1.4 and 1.5.

Figure 1.4: Typical resistance/temperature curve for a negative-temperature-coefficient thermistor

(Leigh, 1991)[Figure abstracted from:Leigh, J. (1991) Temperature Measurement & Control, Herts:Peter Peregrinus Ltd., p.25].


4/13



Figure 1.5: Typical resistance/temperature curve for a positive-temperature-coefficient thermistor

(Leigh, 1991)[Figure abstracted from:Leigh, J. (1991) Temperature Measurement & Control, Herts:

Peter Peregrinus Ltd., p.25].

Advantages and disadvantages of Thermistors

The advantages of thermistors include; High Sensitivity,Small physical sizeand resistance at ambient

temperature may be specified in a range of 0.1-300 k. However, the disadvantages of thermistors

are their limited temperature range and their modest upper usable temperature (Leigh, 1991).

Static and Dynamic Characteristics Respond

The term Static characteristics of an instrument refer to the steady state reading that it gives when it

has settled down. These types of characteristics may be stated in terms of accuracy, linearity, etc.

The expression of Dynamic Characteristics illustrates the behaviour of an instrument in the time

between when the measured quantity changes and a steady reading are provided (Figure 1.6)

(Bolton, 1991).

Figure 1.6: Dynamic responses [Figure abstracted from: Bolton, W. (1991) Industrial Controls &

Instrumentation, Essex: Longman Group UK Limited, p.9]


5/13



Experimental Apparatus

Laboratory 1: Characterise the static performance of two sensors, insulated thermistor and un-insulated thermistor.

Equipment provided:

Hot water

Thermocouple acting as a thermometer

Beaker

Digital Voltage Meter

Experiment procedure:

1. Fill beaker with hot water and place one of the two thermocouple wire in the beaker and

another outside the beaker at room temperature.

2. Slowly poor in cold water into the beaker to reduce the temperature of the water, therefore,

changing the net voltage values on the voltmeter.

3. Take readings and obtain the temperature and voltage values. Note that the thermocouple

acts as a thermometer which in turns, two readings are obtained Temperature and voltage

change.

4. Repeat the experiment several times until desire data are obtained.

5. Repeat the above procedures for but with form insulated thermistor.

Figure 2.1: Experiment 1 Set-Up


6/13



Laboratory 2: Investigate the dynamic performance of the two temperature sensors, following a

step change in temperature.

Equipment Provided:

Hot Water

Beaker

Computer with data acquisition system

Experiment Procedure:

1. Prepare the computer data acquisition system.

2. Fill in the beaker with hot water.

3. Start the computer measurement system; wait one or two second before placing the

thermistor inside the beaker and wait until all samples has been taken.

4. Set the samples and the rate and time for the themistor to measure at 1000 samples at the

rate of 50 samples per second.

5. Repeat the test until desire results are obtained.

6. Repeat the procedures for Insulated thermistor experiment except that the test will run at

720 samples at the rate of 1 sample per second.

7. Obtain all results to be further process.

Figure 2.2: Experiment 2 Set-Up


7/13



Results and Discussion

Experiment 1: Static Calibration

Graph 1.1: Static Calibration with no insulation results

Graph 1.2: Static Calibration with Insulation results

Graph 2 shows the sensor output (V) against the temperature (C) which indicates the values of

voltage for the insulated and un-insulated thermistor. The information obtained may be used to

conduct calculations which include static sensitivity (K) for un-insulated and insulated thermistor.

R = 0.9351

0

0.5

1

1.5

2

2.5

3

3.5

0 20 40 60 80 100

Voltage

Output(V)

Temperature (C)

Static Calibration with Insulation

Set-1

Set-2

All

Poly. (All)


8/13



This can be achieve by the use of gradient best fit line which correspond for the static sensitivity k

(V/C)

Calculation:

Ideal Straight line equation can be calculated as follow:

minmax

minmax)(II

OOKslopeLineStraightIdeal (1.1)

minmin)( IKOaInterceptLineStraightIdeal (1.2)

)1(/041.0

2590

2.174.31 resultsSetCVK

)2(/039.02590

22.177.32 resultsSetCVK

040.0Ave rageK

23.0a

63.2

Ideal

Ideal

O

aIKO

Un-insulated Thermistor span:

minmax IIspanInput (1.3)

65

2590

spanInput

spanInput

minmax OOSpanPutOut (1.4)

57.2

2.177.3

SpanPutOut

SpanPutOut


9/13



Un-insulated thermistor linearity:

)( minminmax

minmaxmin II

II

OOOO

(1.5)

)2565(259

2.177.32.157.2

58.137.1

Insulated thermistor span:

43.0

33.175.1

65

2590

SpanOutput

SpanOutput

SpanInput

SpanInput

Insulated thermistor Linearity:

27.091.0

)25.65(2590

33.175.133.141.0

From observation of the graph, there was error occurred during the experiment. The static

sensitivity was calculated as 0.04 V/C. It can be said that the un-insulated thermistor was more

suitable for the static calibration.


10/13



Experiment 2: Dynamic Calibration

Graph 2.1: Dynamic Calibration without insulation

Graph 2.2: Dynamic Calibration with insulation

0

0.5

1

1.5

2

2.5

3

0 5 10 15 20 25

Sens

oroutput(V)

Time (s)

Dynamic Calibration with out Insulation

Test 4

Test 3

Test 2

1.41.45

1.5

1.55

1.6

1.65

1.7

0 200 400 600 800

Voltage(V)

Samples

Dynamic Calibration with Insulation


11/13



The graph of the results obtained for un-insulated indicated that the maximum value is 2.9 with the

minimum value of 1.40.

The Y value from the graph can be calculated as follow:

VY

Y

22.2

4.1632.04.17.2

The time constant of 0.632 (value of step change) indicates in percentage form of 63.2%

To find the X value, straight line was plotted at 90 degrees against the Y value at 2.2. The X value

was found to be 5.5 seconds (Time Constant)

5.5 Seconds (time constant), Sampling rate = 50 Samples/1 Second = 50 samples/sec

The time constant ( ) is estimated at 5.5 seconds from the un-insulated graph which represent the

dynamic performance for first order instrument.

The results obtained from the computer software displayed that the maximum value of insulated

test is 1.66 with the minimum value of 1.44.

).(115

115

6.1

44.1632.044.166.1

antconstTime

X

Vy

y

Mathlab software and Laplace Transform was used to calculate time constant in both cases. The

time constant for un-insulated themistor was found to be less than the insulated one.

Conclusion

Overall, the results obtained for both Static and Dynamic experiments were fairly accurate.

However, there were minor errors occurred which may have cause by human in term of inaccurate

data observation, systematic or self-heating etc.

It was observed for the static calibration that the un-insulated thermistor was the best option to be

used for the experiment due to its least error. For the dynamic calibration, the time constants were

compared and the un-insulated thermistor was found to be more appropriate for the dynamic

calibration.

Also, from the experimental observation, it can be stated that the instrument system might

encounter some error due to chemical reaction, dirt and dust in the laboratory environment.

Therefore, the instrument system should be examined at particular time intervals maintaining the

international standards. The regular reports of the instrument examined should be preserved further

accuracy


12/13



Reference

Bolton, W. (1991) Industrial Controls & Instrumentation, Essex: Longman Group UK Limited,

p.8-10.

McGee, T. (1988) Principles and Methods of Temperature Measurement, New York: John

Wiley & Sons, p.206, 466-474, 504-511.

Sachse, H. (1975) Semi-Conducting Temperature Sensors and Their Applications, New York:

John Wiley & Sons, INC., p.159-165.

Leigh, J. (1991) Temperature Measurement & Control, Herts: Peter Peregrinus Ltd., p.24-26.

Childs, P. (2001) Practical Temperature Measurement, Oxford: Butterworth-Heinemann,

p.39-41.

Benedict, R. (1984) Fundamentals of temperature, Pressure, and Flow Measurements, 3rd

ed. 1984: John Wiley & Sons, Inc., p.146.

Figliola, R. and Beasley, D. (2006) Theory and Design for Mechanical Measurements, 4th ed.

New York: John Wiley & Sons, Inc., p.12-15.

National Instruments (2011) Temperature Measurement, [online] Available at:

http://www.ni.com/temperature/ [Accessed: 10th Dec 2011].


13/13



Appendices

Sensors Calibration

Calibration consists of determining the indication or the output of a temperature sensor with

respect to a standard sufficient number of known temperatures so that, with acceptable means of

interpolation, the indication or output of the sensor will be known over the whole range of

temperature used (Benedict, 1984, p146). The problem areas of calibration are immediately

apparent; four main points must be available:

1. Means for measuring the output of the temperature sensor

2. A satisfactory temperature standard

3. Controlled temperature environments

4. A scheme for interpolating between calibrations points (Benedict, 1984).

As Benedict (1984, p147) described, the environments for calibration distributed into two classes

depending on the method of determining the temperature of the test sensor.

Firstly, the sensor is exposed to a fixed-point environment so that under particular conditions,

naturally exhibits a state of thermal equilibrium whose temperature is established numerically by

the IPTS without recourse to a temperature standard. Secondly, the test sensor and temperature

standard are simultaneously exposed to a controlled-temperature environment whose temperature

is established by the standard instrument (Benedict, 1984).

Static Calibration

Static calibration is the most common type of calibration. For this procedure, known value is input to

the system under calibration and the system output is recorded. The term Static implies that the

values of the variables involved remain constant. In static calibrations, only the magnitudes of the

known input and the measured output are important (Figliola et al. 2006).

Dynamic Calibration

Dynamic variables are time dependent in their magnitude and frequency content. Dynamic

calibration determines the relationship between an input of known dynamic behaviour and the

measurement system output. Normally, these calibrations involve applying sinusoidal signal or a

step change as the known input signal (Figliola et al. 2006).

control assignment - calibration of insulated and uninsulated thermistors

Documents