USF Libraries
USF Digital Collections

Thermal response of lithium tantalate for temperature measurement

MISSING IMAGE

Material Information

Title:
Thermal response of lithium tantalate for temperature measurement
Physical Description:
Book
Language:
English
Creator:
Agastra, Ardit
Publisher:
University of South Florida
Place of Publication:
Tampa, Fla
Publication Date:

Subjects

Subjects / Keywords:
Modified Wien Oscillator
Pyroelectricity
Signal Amplification
Voltage Output
Dissertations, Academic -- Mechanical Engineering -- Masters -- USF   ( lcsh )
Genre:
bibliography   ( marcgt )
non-fiction   ( marcgt )

Notes

Summary:
ABSTRACT: This thesis describes the study of the thermal response of the pyroelectric material named lithium tantalate or LT (LiTaO3) in aid of this material's possible use for temperature measurement. The temperature range studied was between 5-99oC. The sensor was excited using a silicon rubber heater. The lithium tantalate sensor and the rubber heater were enclosed such that the temperature would reach steady state faster. The enclosure was a small insulated box in order to reduce any extraneous effects on the sensor. The output signal of the lithium tantalate sensor was then amplified by using four different amplifying circuits and the voltage output was studied. The amplifying circuits included Current Mode, double Current Mode, Voltage Mode, and a modified Wien Oscillator. Results demonstrated linear dependencies of the voltage output as a function of temperature for the Voltage Mode and the modified Wien Oscillator. Using the modified Wien Oscillator amplifying circuit the slope of the line a 2.1mV/oC and for the Voltage Mode the slope was 1mV/oC. For both cases it was found that the range for the standard deviation of the measurements was 0.5<&#61555;<1mV and the correlation coefficient R2 was above 0.98. Results are comparable to theoretical results for the same amplifying circuits simulated with OrCAD Family Capture Lite Edition and PSpice 9.2 software. The data showed that the lithium tantalate sensor could be used as a temperature measuring device for the range mentioned above. The resolution of the data is high enough to be able to be detected with modern measuring devices and the standard deviation is low enough to allow for such measurements. Moreover, the linear dependence of the data allows for accurate measurements at each temperature within the range.
Thesis:
Thesis (M.S.M.E.)--University of South Florida, 2011.
Bibliography:
Includes bibliographical references.
System Details:
Mode of access: World Wide Web.
System Details:
System requirements: World Wide Web browser and PDF reader.
Statement of Responsibility:
by Ardit Agastra.
General Note:
Title from PDF of title page.
General Note:
Document formatted into pages; contains 91 pages.

Record Information

Source Institution:
University of South Florida Library
Holding Location:
University of South Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
usfldc doi - E14-SFE0004981
usfldc handle - e14.4981
System ID:
SFS0028214:00001


This item is only available as the following downloads:


Full Text
xml version 1.0 encoding UTF-8 standalone no
record xmlns http:www.loc.govMARC21slim xmlns:xsi http:www.w3.org2001XMLSchema-instance xsi:schemaLocation http:www.loc.govstandardsmarcxmlschemaMARC21slim.xsd
leader nam 22 Ka 4500
controlfield tag 007 cr-bnu---uuuuu
008 s2011 flu ob 000 0 eng d
datafield ind1 8 ind2 024
subfield code a E14-SFE0004981
035
(OCoLC)
040
FHM
c FHM
049
FHMM
090
XX9999 (Online)
1 100
Agastra, Ardit
0 245
Thermal response of lithium tantalate for temperature measurement
h [electronic resource] /
by Ardit Agastra.
260
[Tampa, Fla] :
b University of South Florida,
2011.
500
Title from PDF of title page.
Document formatted into pages; contains 91 pages.
502
Thesis
(M.S.M.E.)--University of South Florida, 2011.
504
Includes bibliographical references.
516
Text (Electronic thesis) in PDF format.
520
ABSTRACT: This thesis describes the study of the thermal response of the pyroelectric material named lithium tantalate or LT (LiTaO3) in aid of this material's possible use for temperature measurement. The temperature range studied was between 5-99oC. The sensor was excited using a silicon rubber heater. The lithium tantalate sensor and the rubber heater were enclosed such that the temperature would reach steady state faster. The enclosure was a small insulated box in order to reduce any extraneous effects on the sensor. The output signal of the lithium tantalate sensor was then amplified by using four different amplifying circuits and the voltage output was studied. The amplifying circuits included Current Mode, double Current Mode, Voltage Mode, and a modified Wien Oscillator. Results demonstrated linear dependencies of the voltage output as a function of temperature for the Voltage Mode and the modified Wien Oscillator. Using the modified Wien Oscillator amplifying circuit the slope of the line a 2.1mV/oC and for the Voltage Mode the slope was 1mV/oC. For both cases it was found that the range for the standard deviation of the measurements was 0.5<<1mV and the correlation coefficient R2 was above 0.98. Results are comparable to theoretical results for the same amplifying circuits simulated with OrCAD Family Capture Lite Edition and PSpice 9.2 software. The data showed that the lithium tantalate sensor could be used as a temperature measuring device for the range mentioned above. The resolution of the data is high enough to be able to be detected with modern measuring devices and the standard deviation is low enough to allow for such measurements. Moreover, the linear dependence of the data allows for accurate measurements at each temperature within the range.
538
Mode of access: World Wide Web.
System requirements: World Wide Web browser and PDF reader.
590
Advisor:
Pyrtle, III, Frank .
653
Modified Wien Oscillator
Pyroelectricity
Signal Amplification
Voltage Output
690
Dissertations, Academic
z USF
x Mechanical Engineering
Masters.
773
t USF Electronic Theses and Dissertations.
4 856
u http://digital.lib.usf.edu/?e14.4981



PAGE 1

Thermal Response of Lithium Tantalate for Temperature Measurement by Ardit Agastra A thesis submitted in partial fulfillment o f the requirements for the degree of Master of Science in Mechanical Engineering Department of Mechanical Engineering College of Engineering University of South Florida Major P rofessor: Frank Pyrtle III, Ph. D. Nathan Crane, Ph. D. Crai g Lusk, Ph. D. Date of Approval: March 24, 2011 Keywords: Pyroelect ricity Signal A m plification Voltage Response Modified Wien Oscillator Voltage Output Copyright 2011 Ardit Agastra

PAGE 2

ACKNOWLEDGEMENTS I would like to thank Dr. Pyrtle for being a great professor and advisor during my USF academic career Your expertise has guided me to complete this thesis without any difficulties. I want to thank my committee members Dr. Crane and Dr. Lusk for their help and support throughout my thesis. I could not ask for better professors to be part of my committee. And to John Shelton I want to say thank you for your knowledge and help a nd I can only hope that one day I could be as knowledgeable as you are. Moreover, my family and friends have done more than I could ask and I want to thank them for that. Thank you everyone for your support!

PAGE 3

i TABLE OF CONTENTS LIST OF TABLES ................................ ................................ ................................ i ii LIST OF FIGURES ................................ ................................ ............................... v ABSTRACT ................................ ................................ ................................ ........ v i i CHAPTER 1: INTRODUCTION ................................ ................................ ........... 1 CHAPTER 2: LITERATURE REVIEW ................................ ................................ 4 2.1 Methods of Thermometry ................................ ................................ .... 4 2.1.1 Resistance Thermometry ................................ ...................... 5 2.1.2 Thermocouples ................................ ................................ ..... 9 2.1.3 Radiation Thermometry ................................ ....................... 12 2 .2 Applications of Thermometers ................................ .......................... 1 5 2.3 P yroelectric it y : Its History and Physics ................................ .............. 1 7 2.4 Pyroe lectric Materials ................................ ................................ ........ 20 2.4.1 Pyroelectric Detectors ................................ ......................... 21 2.4.2 Pyroelectric Crystals ................................ ............................ 21 2.4.3 Pyroelectric Polymers ................................ .......................... 22 2.4.4 Pyroelectric Ceramics ................................ ......................... 22 2.5 Pyroelectric Properties and Figures of Merit ................................ ..... 23 2 .5.1 Pyroelectric Coefficient ................................ ........................ 23 2.5.2 Responsivity ................................ ................................ ........ 24 2.5.3 Noise ................................ ................................ ................... 25 2.5.4 Curie Temperature ................................ .............................. 27 2.6 Pyroele ct ric C urrent State of Research ................................ ............. 28 2.7 Lithium Tantalate ................................ ................................ .............. 30 CHAPTER 3 : MATERIALS AND METHODS ................................ ..................... 33 3. 1 Materials and Instrumentation ................................ ........................... 33 3.2 Experimental Setup ................................ ................................ .......... 39 CHAPTER 4 : RESULTS AND DISCUSSION ................................ .................... 46 4.1 Theoretical Expectations ................................ ................................ ... 46 4.2 Experimental Results ................................ ................................ ........ 49 CHAPTER 5 : CONCLUSION AND SUG ESTIONS ................................ ............ 61 REFERENCES ................................ ................................ ................................ .. 63

PAGE 4

ii APPENDICES ................................ ................................ ................................ ... 67 Appendix A: Collected Data for the Vol tage Mode (V.M.) and the Modified Wien Oscillator (W.O ) ................................ ................... 68 Appendix B: Collected Data for the Current Mode (C.M.) and the Double Current Mode (D.C.M.) ................................ ..................... 7 4 Appendix C: 90% and 95% C on fidence Interval Values for T en V max Measurements at Each Temperature and E ach Amplifying C ircuit ................................ ................................ ........................... 80

PAGE 5

iii LIST OF TABLES TABLE 1: Metals used for resistance thermometry and their properties (from Michalski et al. 2001) ................................ ............................ 7 TABLE 2: The E mf values fo r different metals referred to p latinum at 100 o C with a reference temperature of 0 o C (from Michalski et al., 2001) ................................ ................................ ...................... 11 TABLE 3: Temperature (800 1320 o C) and radiation color correlation ( from Michalski et al., 2001) ................................ ......................... 14 TABLE 4: Some properties for germanium and s ilicon (from Michalski et al. 2010) ................................ ................................ ................... 15 TABLE 5: Pyroelectric and piezoelectric point g roups (from Safari et al. 1996) ................................ ................................ ............................ 22 TABLE 6: Some pyroelectric materials and their primary and s econdary pyroelectric coefficients (from Lang 2005) ................................ .... 24 TABLE 7: Pyroelectric materials and their figures of m erit (Xiao et al. 1988) ................................ ................................ ............................ 27 T ABLE 8: Specifications for SPC 2 LiTaO 3 pyroelectric detector .................. 34 TABLE 9: Compone n ts used for the amplification circuits ............................ 38 TABLE 10: Mean and standard deviation of the ten V max measurements at each temperature for the modified Wien Oscillator amplifying circuit ................................ ................................ ........... 51 TABLE 11 : Mean and standard deviation of the ten V min measurements at each temperature for the modified Wien Oscillator amplifying circuit ................................ ................................ ........... 53 TABLE 12 : Mean and st andard deviation of the ten V max measurements at each temperature for the Voltage Mode amplifying circuit ........ 54

PAGE 6

iv TABLE 13: Mean and standard devia tion of the ten V max measurements at each temperature for the double Current Mode amplifying circuit ................................ ................................ ........................... 56 TABLE 14: Mean and standard devia tion of the ten V max measurements at each temperature for the double Current Mode amplifying circuit ................................ ................................ ........................... 57 TABLE 15: 90% confidence interval values in mV for ten V max measurements at each temperature and each amplifying circuit ................................ ................................ ........................... 80 T ABLE 16: 95% confidence interval values in mV for ten V max measurements at each temperature and each amplifying circuit ................................ ................................ ........................... 8 1

PAGE 7

v LIST OF FIGURES FIGURE 1: Graph for temperature vs. W for an arbitrary material that is used for resistance thermometry (from McGee, 1988) ................... 8 FIGURE 2: Simp le thermocouple c ircuit (from Kinzie, 1973) .......................... 10 FIGURE 3: Equivalent circuit for a pyro electric material ( from Nalwa, 1995) ................................ ................................ ............................ 19 FIGURE 4: Magnitudes of voltage noise for a pyroelectric detector as a function of frequency (Whatmore, 1986) ................................ ...... 26 FIGURE 5 : SPC 2 Lithium tantalate p yroelectric sensor ................................ 35 FIGURE 6 : Current Mode amplifying circuit as proposed by Chirtoc et al. (2003) ................................ ................................ .......................... 36 FIGURE 7 : Voltage Mode amplification circuit as proposed by Chirtoc et al. (2003) ................................ ................................ ...................... 36 FIGURE 8 : Amplification circuit as proposed by Chung et al. (1996) .............. 37 FIGURE 9 : Modified a mplification circ uit similar to a proposed Wien O scil lator circuit by Malhame (2002) ................................ ............ 3 8 FIGURE 10 : Setup for amplifying circuits for the Voltage Mode (left) and Current Mode (right) ................................ ................................ ..... 40 FIGURE 11 : Setup for amplifying circuits for a modified Wien Oscillator circuit (left) an d double Current Mode (right) ................................ 41 FIGURE 12: Diagram of the experimental setup ................................ ............... 42 FIGURE 13 : The components and the experimental setup for thermal response of l ithium t antalate ................................ ........................ 43 FIGURE 14 : Circui t studied by Lang et al. (1969) ................................ ............. 46 FIGURE 15 : Voltage vs. time for shunt resistor value much lower than pyroelectric resistance ................................ ................................ 47

PAGE 8

vi FIGURE 16 : Voltage vs. time for shunt resistace higher or equal to the pyroelectric resistance ................................ ................................ 47 FIGURE 17 : Voltage vs. time for shunt resistance equal to the pyroelectric resistance ................................ ................................ 48 FIGURE 18: Response of voltage output vs. time for the Current Mode and double Current Mode ................................ ............................. 49 FIGURE 1 9 : The average maximum voltage vs. temperature for the modified Wien Oscillator with error bars of one standard deviation in each direction vertically and 0.5 o C in each direction horizontally ................................ ................................ .... 52 FIGURE 20 : The minimum voltage measured vs. temperature for the modified Wien Oscillator with error bars of one standard deviation in each direction vertically and 0.5 o C in each direction horizontally ................................ ............................ 43 FIGURE 21 : The maximum voltage measured vs. temperature for the Voltage Mode with error bars of one standard deviation in each direction vertically and 0.5 o C in each direction horizontally ................................ ................................ .... 55 FIGURE 22: The maximum voltage measured vs. temperature for the Current Mode with error bars of one standard deviation in each direction vertically and 0.5 o C in each direction horizontally ................................ ................................ .................. 56 FIGURE 23: The maximum voltage measured vs. temperature for the Double Current Mode with error bars of one standard deviation in each direction vertically and 0.5 o C in each direction horizontally ................................ ................................ .... 57 FIGURE 2 4 : The expected slope of the voltage output using the Voltage Mode amplify ing circuit generated with OrCAD 9.2 Capture CIS Lite Edition and PSpice ................................ ......................... 59 FIGURE 2 5 : The expected slope of the voltage output using the modified Wien Oscillator amplifying circuit generated with OrCAD 9.2 Capture CIS Lite Edition and PSpice ................................ ............ 60

PAGE 9

vii ABSTRACT This thesis describes the study of the thermal response of t he pyroelectric material named lithium t antalate or LT (LiTaO 3 ) in aid use for temperature measurement. The temperature range studied was between 5 9 9 o C. The sensor was excited using a silicon rubber heater The lithium tantalate sensor and the rubber heater were enclosed such that the temperature would reach steady state faster. The enclosure was a small insulated box in order to reduce any extraneous effects on the sensor. The output signal of the lithium tantalate sensor was then amplified by using four differe nt amplifying circuits and the voltage output was studied. The amplifying circuits include d Current Mode, double Current Mode, Voltage Mode, and a modified Wien Oscillator. Results demonstrated linear dependenc i e s of the voltage output as a function of temperature for the Voltage Mode and the modified Wien Oscillator Using the modified Wien Oscillator amplifying circuit the slope of the line a 2 .1 mV/ o C and for the Voltage Mode the slope was 1mV/ o C. For both cases it was found that the range for the stan dard deviation of the measurements was 0.5< <1 mV and the correlation coefficient R 2 was above 0.98. Results are comparable to theoretical results for the same amplifying circuits simulated with OrCAD Family Capture Lite Edition and PSpice 9.2 software.

PAGE 10

viii The data showed that the lithium t antalate sen sor could be used as a temperature measuring device for the range mentioned above. The resolution of the data is high enough to be able to be detected with modern measuring devices and the st andard deviation is low enough to allow for such measurements. Moreover, the linear dependence of the data allows for accurate measurements at each temperature within the range.

PAGE 11

1 CHAPTER 1: INTRODUCTION Ferroelectricity and piezoelectricity are two material properties that are relatively new in science however they are more recognized than pyroelectricity. In terms of time since their discovery, piezoelectricity and ferroelectricity pale in comparison to pyroelectricity. The first two were discovered as a result of pyroelectricity about two millennia after pyroelectricity was first observed by Theophrastus, a philosopher of ancient Greece (Lang, 1999) He recognized that tourmaline, today recognized as a p yroelectric material, attracted other smaller objects when a change in temperature was present. Possible lack of understanding or apathy towards this subject made it difficult for this phenomenon to be recognized worldwide for almost two thousand years (La ng, 2004) Renaissance brought forth the interest in science and pyroelectricity was once again a part of research around the world. The new beginning of pyroelectric studies began in early 18 th century and ever since it has become an important tool of mod ern science. This flo wering in pyroelectric studies eventually leads to the naming of this phenomenon by David Brewster due to the fact that pyro means fire in Greek (Lang, 2005). Particular solids fundamentally bear a spontaneous polarization whose intens ity could be modified with a change in temperature, and this defines whether a material is pyroelectric. If a material, in the presence of a temperature gradient, has a net change in polarization then that is the definition of

PAGE 12

2 pyroelectricity. In better te rms, Lang (1974) defines the spontaneous polarization zero polarization of a material in the absence of an external electric charges will appear on the surface as t o cancel what is happening within the solid. This charge which accumulates on the surface could be measured using an ammeter after placing electrodes on the surface of the pyroelectric solid (Lang, 2005). As mentioned above, temperature is essential in cr eating electricity in a pyroelectric material. Temperature itself is a quantity which has a recent history in terms of its measurement. It was not until the sixteenth century that temperature started being measured using an air thermometer developed by Gal ileo. Accurate t emperature measurement is a recent development because one must first fully understand statistical mechanics or thermodynamics (Quinn, 1990). Since the first breakthrough from Galileo, temperature measurement has been flourishing with numer ous different ways of achieving it. According to Quinn (1990) there are two types of thermometry: primary and s econdary. In primary thermometry it said the temperature measurement is carried out without establishing any temperature dependent variables. An example of this type of thermometry is total radiation thermometry. On the other hand, secondary thermometry includes t he rest of the methods used which do not fall under the previous category. Thermocouple temperature measurement is an example of secondar y thermometry.

PAGE 13

3 In the following paper many different thermometry methods and their applications are discussed Also a review of pyroelectricity and its relevance will be communicated The scope of this thesis entails the correlation between a pyroelectric measurement and the ambient temperature and the main purpose of it is to measure ambient temperature using a pyroelectric sensor. The chosen lithium t antalate sensor will be subjected to a temperature change and the output signal was analyzed and compared to the input temperature. The possible uses of such a correlation include but are not limited to medicine, military, imaging, electronics etc. The foundation of this thesis is based on developing a different method of temperature measurement using the pyr oelectric material lithium t antalate which could be applied in any place where temperature measurement is necessary. Lithium t antalate is a pyroelectric crystal which also exhibits ferroelectric properties. This sensor was enclosed such that the temperature would reach steady state and no extraneous effects would affect the sensor. The temperature was changed using a resistance heater and the sensor response was measured. The response measurement did require amplifying circuit s to amplify the output signal. This circuit was implemented using a breadboard since changes to the circuit might be necessary The amplified signal w as then measured using an oscilloscope. The temperature of the enclosure was measured using thermo couples and was re corded for later use Subsequently the response of the sensor was compared to the temperature and correlations were sought between any characteristic of response against the temperature change.

PAGE 14

4 CHAPTER 2: LITERATURE REVIEW This literature review entail s a look at temperature measurement, some methods of ther mometry, and how they are u sed today. Moreover, an in depth look is taken on pyroelectricty, its history and physics, and its importance in Also, a brief review of lithium t antal a te is provided. In addition, new advancements in both fields are discussed. Both, temperature and pyroelectricity are in the center of this thesis as a different method to relate pyroelectricity to temperature is sought and possibly a new technique of temperature measurement could be developed 2.1: Methods of Thermometry As mentioned in the introduction, there are many different methods of temperature measurement. The pas t five centuries have seen a bloom in temperature measurement technology and thus there are numerous techniques by which one can measure temperature. In this section three different methods of thermometry are discussed : resistance thermometry, thermocouple, and radiation thermometry. These three methods were chosen because they are three of the most important and widely used methods today. The science behind each method is discussed and the ir importance is described

PAGE 15

5 2.1.1 : Resistance Thermometry R esistance thermometry relates a change in electrical resistance of a material to a change in temperature. Acc ording to Michalski et al. (2001) Sir Humphrey Davy was the first scientist to repor t in 1821 a correlation between the res istance of a material (platinum in this case ) and a change in temperature The beginnin g of resistance thermomet ry is accredited to a publication by H. L. Callendar in late 19 th century on the dependence of electrical resistance of platinum on temperature. Despite some previous lack of success on a similar subject by Lord Kelvin and James Ma xwell, H. L. Callendar pursued what he believed to be a new method of temperature measurement (Quinn, 1990) H is success in this subject was a milestone in resistance thermometry as it became a subject of heavy research af ter his publication Although there are counter examples most commonly the resistance of a material increases with an increase in temperature. This is attributed to the fact that an increase in temperature causes an increase in vibrations within an atom and thus the movement of free electrons is restricted (Michalski et al., 2001). With the assumption that temperature is the factor that affects the resistance of a material, then we can say that the equation for the resistance as a function of temperature is given by: R = R o [1 + A + B 2 +C 3 ] Usually the coefficients A, B, and C are considered to be independent of temperature and their equations are given by: A = 1/R o ( R / ) = o

PAGE 16

6 B = 1/2R o ( R / ) = o C = 1/ 6 R o ( R / ) = o In the above equations R is the resistance and o is the reference temperature which is often taken to be 0 o C. This is the case for the temperature sensing element s of a resistance thermometer called resistance thermometer detectors or RTDs. In addition to having a reference temperature of 0 o C, the equation for an RTD c an be simplified further when the constant C is disregarded. With that said, there are a few factors to keep in mind when designing a resistance thermometer According to McGee (1988), a few of these characteristics include but are not limited to : 1. high resistance per unit temperature 2. stable physical properties 3. adequate mechanical strength 4. possibly no hysteresis or path dependence These characteristics are necessary in man ufacturing a n RTD whose uses range from simple every day measurements to very complex ones The fore mentioned characteristics are also part of the material selection process which forms the basis for s uch designs. When considering a wide range of temperature measurem ent metals are the primary material choice for designing a resistance thermometer. These metals include but are not limited to: platinum, copper, and nickel. The table below shows each metal, its operating t emperature, and the resistivity at 0 o C.

PAGE 17

7 Table 1. Metals used for resistance thermometry and their properties (from Michalski et al. 2001) Metal Operating Temperature ( o C ) Resistivity ( m) Normal Special Nickel 60 to 150 60 to 180 0.09 to 0.11 Platinum 200 to 850 260 to 1000 0.10 to 0.11 Copper 50 to 150 50 to 150 0.017 to 0.018 Note: Reproduced from Michalski et al. 2010. Although not mentioned on this table, a nother important figure of merit for such metals is the ratio of the resistance at 100 o C to the resistance at 0 o C called R 100 /R 0 This figure of merit is real ly important in determi ning the purity of the material and thus gives a better understanding (Quinn, 1990) In addition, another ratio W is used to compare materials. W is a resistance ratio and its equation is given by: W=R/R o Where R is the resistance at any temperature and R o is the initial resistance. This ratio of resistances provides a great way of comparison between materials with different initial resistances. The figure below shows what the resistance ratio W would look like for an arbitrary material that is used for resistance thermometry (McGee, 1988)

PAGE 18

8 Note: Reproduced from McGee 1988. Figure 1. G raph for t emperature vs. W for an arbitrary material that is used for resistance thermometry ( from McGee, 1988) In addition to metals, ceramics are widely used in resistance thermometry. A thermistor is considered to be a semiconductor with its resistance being many times more sensitive than that of metals. Some drawbacks that thermistors introduce are nonlinearity and decreased stability but they are inexpensive and re adily available for purcha se Moreover, they are used for applications where the precision of temperature measurement is at a minimum (Michalski et al., 2001) Although thermistors are of importance in some applications, platinum resistance thermometers are the most reliabl e and widely used form of resistance thermometry. Platinum has been and is to this day the most frequently used material for resistance thermometers because of its wide range of use and the linearity between its resistance and temperature. It makes platinu m resistance thermometers very practical in many resistance thermometry applications. 0 200 400 600 800 1000 1200 0 0.27 0.54 0.81 1.08 1.35 1.62 1.89 2.16 2.43 2.7 Temperature W Temperature vs W

PAGE 19

9 2.1.2 : Thermocouples Thermocouple temperature measurement is a method of thermometry that dates back to the findings of T. J. Seebeck in 1821. He discovered the effect which now takes his name in which he explains that two unalike metals create a current when their junctions are at two different temperatures (Quinn, 1990) According Michalski et al. ( 2001 ) two dissimilar thermal and electrical co nductor s joined at one end create a thermocouple. It is the end where the two conductors meet that the measuring point in created and the two open ends are considered reference points. Thermocouple temperature measurement only measures the temperature difference between the reference point and the measuring point and thus the reference temperature must be known. Usually a reference point is taken as the freezing point or the boiling poi nt of water (0 o C and 100 o C respectively) with the former being the most preferred reference point The temperature difference between the free end s and the junction point create a different voltage in each conductor. The introduction of a third electrical conductor is necessary to measure the voltage difference between the two dissimilar conductors (Kinzie, 1973) Depending on the conductors used, a table for the voltage between conductors against temperature is created. This would be used as a reference when using thermocouples. The tables are different for each set of conductors used. A simple therm ocouple circuit is depicted in F igure 2. It shows two dissimilar material s X and Y and T 1 an d T 2 could be arbitrarily the reference temperature and the temperature being measured.

PAGE 20

10 Note: Reproduced from Kinzie 1973. Figure 2. Simple the rmocouple circuit ( from Kinzie, 1973) Materials selection is very important for thermocouple temperature measurement. Material choice determines the properties of the measuring system. It is necessary to optimize between the following properties of thermoelectric materials in order to get the best performing thermocouple: 1. high permissible working temperature 2. high resistance to oxidation 3. low resistivity 4. high melting temperature 5. possible linear relationship between electromotive force ( Emf ) and temperature Moreover, i t is extremely important to select two materials which create the highest Emf (electromotive force) or Seebeck voltage range Table 2 shows some commonly used materials and the Emf values referred to platinum. T his makes for the most appropriate thermocouples.

PAGE 21

11 Table 2. The E mf values for different metals referred to p latinum at 100 o C with a reference temperature of 0 o C (from Michalski et al., 2001) Metal Emf (mV) Metal Emf (mV) Constantan (55%Ni 45%Cu) 3.51 Iridium 0.65 Nickel 1.48 Rhodium 0.70 Cobalt 1.33 Silver 0.74 Palladium 0.57 Copper 0.76 Platinum 0 Gold 0.78 Aluminum 0.42 Iron 1.98 Lead 0.44 Chromel 2.81 Note: Reproduced from Michalski et al. 2010. The mo st common thermocouples used are type K and type E. Type K thermocouples are created by using one conductor made of nickel chromium (Chromel) and the other made of nickel aluminum. This is the most widely used thermocouple due to its range of use Type E thermocouples on the other hand, use nickel chromium (Chromel) and copper nickel (Constantan) conductors respectively. This type of thermocouple is the preferred one in the United States since it has the highest range of Emf out of all metal thermoco upl e combinations (Michalski et al. 2001). Kinzie (1973) explains in detail of a few applications of thermocouples. The author discusses thermocouple uses in fluid temperature measurement, manufacturing processes and heat appliance safety. Moreover, thermoco uple temperature measurement is not limited to the applications mentioned above as it is used in many other smaller but nonetheless important applications. Thermocouples are widely used due to the fact that they are low cost and reasonably reliable in many applications. One disadvantage that thermocouples introduce is lack of precision in certain temperature ranges. Overall,

PAGE 22

12 thermocouples are easy to use and available to everyone The extent of use of thermocouples is very important in many applicat ions. 2.1.3 : Radiation Thermometry One may have heard of radiation pyrometry or infrared pyromtery and may have wondered if there is a difference between the two. These are two names which are used as synonyms for the method of thermometry by means of the rmal radiation. Unlike the thermocouple or resistance temperature measurement, radiation thermometry could be explained explicitly through equations relating temperature to spectral radiance (Quinn, 1990). This method of thermometry is a noncontact method in which the de vice used does not touch the material whose temperature is being measured. Moreover, because the equations for this method could be written explicitly, it falls under primary thermometry. The fundamentals of radiation thermometry come from the Stefan Boltzmann law of thermal radiation. According to this law, the energy flux leaving a surface (W/m 2 The most important aspect of thermal radiation is the emissivity of the target (Z hang et al., 2010). To understand the process of thermal radiation and how emissivity plays a role one must first study blackbody radiation. A blackbody is used as a comparison device when discussing radiation. It is a perfect surface in which three import ant steps happen: 1. it absorbs all incident radiation 2. no other surface can emit more radiation

PAGE 23

13 3. all radiation is emitted isotropically (same intensity in all directions) These are the three reason s why a blackbody is called the ideal radiator and all real s urfaces are compared to it (DeWitt et al., 1988). With that established we can say that emissivity has a range between 0 and 1 with a blackbody having an emissivity value of 1. But getting the exact emissivity of a surface is an arduous task. O ver the year s techniques to overcome this problem have been created Some techniques to reduce emissivity problems include dual wavelength pyrometers, multi spectral thermometry and reflective mirrors (McGee. 1988). According to Zhang et al. ( 2010 ) the equation relating temperature, emissivity and the total radiation excluding reflection is given by: L em = T 4 / where L em the total radiation emitted, is the emissivity of the body, T is the temperature of the body, and is the Stefan Boltzmann constant. Because a real surface radiation is being measured, the directional emissivity and the total radiance temperature never surpass and at most would equal that of a blackbody (Zhang et al. 2010). One of the earliest and pr obably the simplest methods of radiation thermometry was the use of vision to detect the color emitted by the body in question. With a well trained eye, one can estimate the temperature of a body within a few degrees and it is said that the human eye could distinguish a color difference that corresponds to a 1 o C change in temperature. This could be useful

PAGE 24

14 for heat treatment processes (Plumb, 19 72) Table 3 demonstrates the correlation between thermal radiation color and the temperature of the body. Table 3. Temperature (800 1320 o C) and radiation color cor relation ( from Michalski et al., 2001) Temperature ( o C) Color 800 830 Orange/carmine 830 880 Dark orange 880 1050 Orange 1050 1150 Yellow/orange 1150 1250 Yellow 1250 1320 White/ yellow Note: Reproduced from Michalski et al. 2010. Since the first days of thermal radiation many attempts have been made towards improving the main problems of thermal radiation. According to Zha ng et al. ( 2010 ) s ome of the more relevant problems are: 1. establish the target emissivity 2. surface conditions 3. angle of view 4. reducing contiguous radiation and other effects The methods of improvement are solved by using two types of pyro meters. Manually operated pyrometers are one method of pyrometry and include filament disapp earing and two color pyrometers (Michalski et al., 2001) In filament disappearing pyrometry the brightness of a lamp filament is changed by adjusting the current input. The current is adjusted until the filament color becomes one with the background color and the current then is compared to the temperature. In t wo color pyrometry, the ratio of the radiance emitted at two different wavelengths is measured and thus inducing a temperature measurement. These two methods solve the problem s the surface conditions might create (Plumb, 1972 ) The rest o f the problems are answered by automatic pyrometers which

PAGE 25

15 are divided into two categories: optical and thermal or total radiation. The automatic optical pyrometers take advantage of the light em itted by the body and the thermal radiation pyrometers use the whole thermal radiation range to measure temperature (Quinn, 1990). Moreover, p hotoelectric pyrometers use materials such as Germanium and Silicon to measure temperature. They are limited by the range of wa velength they could operate in. The table below shows these two material s and some of their properties. Table 4. Some proper ties for germanium and s ilicon (from Michalski et al. 2010) Wavelength, Material Maximum Sensitivity ( m) Maximum Operating Value ( m) Resistance ( ) Time Constant ( s) Germanium 1.2 1.8 -1 Silicon 0.9 1.2 10 7 ~ 1 Note: Reproduced from Michalski et al. 2010. Some of t he most important materials used in radiation thermometry are ferroelectric and pyroelectric materials. Pyroelectric materials intrinsically carry optical and thermal properties which could be related to temperature. Thus a pyr oelectric sensor was chosen and thermal radiation was used to perform the studies is searc h of a new way of measuring tem perature. 2.2: Applications of Thermometers Thermometry is useful in any application in which t emperature measurement is necessary The possibilities for temperature measurement are virtually endless. New research is being conducted on a daily basis in search of different methods of temperature measurement. Innovative temperature measurement techniques have been created in recent years which have many

PAGE 26

16 different applications. According to Zhang et al. (2 010 ) s ome of these techniques include but are not limited to: 1. ultrasonic thermometry (uses changes in the speed of sound to measure temperature 2. microwave radiometry (uses energy in the microwave range to measure temperature) 3. spectroscopic thermometry (uses visible light to measure temperature) 4. acoustic thermometry (uses changes in the speed of sound to measure temperature) Some of these methods are currently in use and others are yet to be put on the market for commercial use. Nonetheless, applications for such systems have been defined. For temperature measurement techniques such as the one mentioned in the previous section, applications are numerous. According to Zhang et al. (2010), radiation thermometry is widely used in metal processing industries such as steel and aluminum production. Moreover, the authors go in detail for a few more uses of radiation thermometry. Some of these uses include: 1. medical thermometry 2. sensing of earth surface temperature 3. thermal imaging in firefighting 4. military night vision

PAGE 27

17 T hese are just a few applications where thermometry is exceptionally important. Scientists will continue to develop new methods for new application and the field of thermometry will keep growing. More accurate temperature measurement techniques will be soug ht after. Demands for such techniques will continue to increase as temperature measurement is important in numerous applications. 2.3: Pyr o electricity : Its History and Physics The first writings on pyroelectricity date back to the days of the ancient Greeks when Theophrastus noticed that tourmaline attracted other materials in the presence of a fire (Lang, 1981). The next studies on this occurrence were not performed until the b eginning of the renaissance. A few centuries later David that pyro means fire in Greek (Lang 1974). The studies on pyroelectricity of the past century have brought to light som e very important applications Some other phenomena such as ferroelectricity and thermoelectricity were discovered by scientists whose previous works included pyroelectricity. The difference between ferroelectricity a nd pyroelectricity will be explained in a later section. In the early 1900s scientists discovered that pyroel e ctric materials could be used for infrared imaging. This was a step that would escalate the number of pyroelectric studies performed. It has led to numerous applications which range fro m medical imaging to space missions and beyond (Lang, 2005). Like many other phenomena, e verything in pyroelectricity begins at the atomic level. It is known today that the distance between positive and negative

PAGE 28

18 charges is called the electric dipole moment. The total measure of the electric dipole moments for a system is referred to as its polarity (Yan et al., 2007). Change in temperature either increas es or decreases the energy in a system of atoms and therefor e alters the crystal structure within. In the presence of a temperature change (Lovinger, 1983) Supposing that we can get a crystal to be cut in such a way that the negative and positive charges of the system are oriented towards the largest face in area of the crystal, we can then attach electrodes on this area in order to measure the electrical potential (Smith & Amon, 2007). This electrical potential can only be measured if a pyroelectric material is subjected to a chan ge in temperature. Lang (2005) give s a more detailed look at how one could measure the pyroelectric current generated by a material. It is also necessary to point out that the polarization created by these materials is spontaneous and dies off after a crit ical temperature is reached (Lang, 1974 ) Pyroelectricity, therefore, should not be mistaken for thermoelectricity in which a fixed temperature profile allows a stable electrical potential. In thermoelectricity, a change in temperature causes electrons or electron holes to travel from one side to the other thus generating an electrical current (Kinzie, 1973) In pyroelectricity, a change in temperature causes electrons from the ambient to be attracted to the surface of the material due to changes occurring within the material (Lang, 2005) Thus, in thermoelectricity the electrical potential is generated by the electrons which reside inside the volume as compared to pyroelectricity where electrons are accumulated on the surface.

PAGE 29

19 A si mple representation of the equivalent circuit for a pyroelectric material or detector is given in Figure 3. Note: Reproduced from Nalwa 1995. Figure 3. Equivalent circuit for a pyroelectric material ( from Nalwa, 1995) In the figure above the pyroelectric current is given by I p its resistance R p and its capacitance C p The pyroelectric current is usually in the range of p ico amperes and its resistance is in the order of 10 12 ohms or higher. The capacitance varies with temperature and is in the order of p ico farads (Kohli, 1998). The current flowing in a circuit due to the presence of the pyroelectric material can be presented by the following equation i p =A p (dT/dt) where A is the area of the electrodes placed on the material, p is the pyroelectric coefficient acting perpendicular to the electrodes and dT/dt is the change of temperature with respect to time (Dietze et al., 2008). Most pyroelectric materials generate currents in the range of p ico amperes and can reach micro ampere s in some cases Although these currents are relatively low, they are high enough to be used in numerous applications. Often other circuit components are used in parallel or in series with the material in order to improve the output signal of a device (Sha ldin et al., 2007). In order to improve the performance of pyroelectric materials a method called poling is often used. In poling one can change the dipoles in such a way

PAGE 30

20 that they are oriented in the same direction and thus increasing the possible cu rrent generated by the material. According to Batra et al. ( 2008 ) there are six types of poling: plasma, hysteresis, electrical, thermal, corona, and electronic beam poling. All six of these poling procedures are used in poling of composites but electrical poli ng is widely used in crystals and other material groups. In electrical poling, a high electrical current is passed through the material to reorient the dipole moments within the material. Safari et al. ( 1 996 ) de monstrated polin g effects on a material. For a material that has not been poled the dipoles within the crystal structure point in random directions whereas in a poled material t he dipoles are oriented to complement the electrical field applied during poling. Poling is a process which can improve th e current output of the pyroelectric material as well as improve the responsivity of the device (Li et al.,2008). It is beneficial to mention that ferroelectric materials are very similar to pyroelectric materials. As a matter of fact all ferroelectric materials are pyroelectric materials but not all pyroelectric materials are ferroelectric. This is the case because all ferroelectric materials have spontaneous polarization which can be reversed in the presence of an electric field. On the other hand, the re are some pyroelectric materials that do not possess this quality therefore they are not ferroelectrics (Fedosov & Von Seggern, 2008). 2.4: Pyroe lectric Materials Py roelectric materials are often known for their piezoelectric and ferroelectric properties. Three big groups can summarize the pyroelectric

PAGE 31

21 materials which include crystals, polymers, and ceramics although minerals and biological materials are some other groups which have been considered (Fuka da, 1989) All these groups have their own advantages and their specific uses. This section will give an overview of each group, describe some materials and their uses, and give some advantages for each material. 2.4.1: Pyroelectric D etectors Pyroelectric detectors use pyroelectric materials to measure changes in t emperature by measuring changes in heat radiation. The heat radiation is detected by the pyroelectric material which in turn sends a signal to the rest of the components. The information is then f iltered by the other circuit elements, giving off a reading for the temperature change. Determining the electrical response is not an easy task. Analysis of these electrical and thermal components is required in addition to calculating the losses (Lau et a l., 2008). While this proves to be a tough task, pyroelectric applications are too beneficial not to create pyroelectric detectors. 2.4.2: Pyroelectric Crystals Crystals in general are divided into thirty two groups in which 20 groups show piezoelectric pr operties. Out of those 20 groups, 10 show spontaneous polarization and these are the pyroelectric crystal groups. A better understanding of the crystallographic groups is given in Table 5 Some pyroelectric crystals include Lithium T antalate, triglycine su lfate, and strontium barium niobate. Crystals are beneficial because they give a high voltage response and most of

PAGE 32

22 the crystals have high Curie temperatures which give a higher range of use (Shaw et al., 2007). Table 5. Pyroelectric and piezoelectric point groups (from Safari et al. 1996). Crystal Structure Non centrosymmetric Piezoelectric Pyroelectric Triclinic 1 1 Monoclinic 2, m 2, m Orthorhombic 222, mm2 Tetragonal 4, 422, 4mm, 42m 4, 4mm Trigonal 3, 32, 3m 3, 3m Hexagonal 6, 622, 6mm, 6m2 6, 6mm Cubic 23, 43m Note: Reproduced from Safari et al. 1996. 2.4.3: Pyroelectric Polymers The most recognizable polymer used in pyroelectric applications is polyvinylidene fluoride (PVDF). This polymer is widely used in medical applications due to the fact that its density is about that of human tissue and water. In addition, polymers are very flexib le and can be of use in many other applications (Safari et al., 1996). Another advantage of polymers such as PVDF is that they are commercially available in large area thin films. Polymers are good contenders for applications such as intruder alarms and single element devices (Whatmore, 1986). 2.4.4: Pyroelectric Ceramics Lead zirconate titanate is a very useful ferroelectric oxide and is one of the most studied pyroelectric materials. PZT is a ceramic and offers different benefits

PAGE 33

23 over other materials. It has advantages over crystals in the sense that it is easy and fairly inexpensive to manufacture and is chemically and mechanically strong (Batr a et al. 2006). Moreover, ceramics allow for use in higher temperature ranges due to their high Curie temperatures. 2.5 : Pyroelectric Properties and Figures of Merit Material p roperties characterize an engineering material. They are what engineers and scientists first look at when making a material selection. The blueprint of a material is withheld within its properties and each material has its own distinct blueprint. Diamond is known for its hardne ss for example and copper is known for its corrosion resistance and these properties decide when and where such material will be used. Similarly, pyroelectric materials have their own properties that describe everything about the material. An understanding of the material properties is fundamental in any engineering discipline This section of the paper explain s some of the most important properties of pyroelectric mat erials and devices and why they are important 2.5.1: Pyroelectric Coefficient The pyroele ctric coefficient is the relation between the change in temperature and the change in polarization of a material. The pyroelectric coefficient has units of C/Kcm 2 According to Wong ( 1993 ) there are two types of pyroelectric coefficient: one experimentally measured and the other one defined thermodynamically. They are given in the following forms p y (e xperimental) =1/A (dQ/dT) p y (thermo) =dP/dT

PAGE 34

24 where dQ/dT and dP/dT represent the change in charge and the change in polarization with respect to t emperature respectively (Uchino, 2000) The experimental pyroelectric coefficient is usually lower in value than the thermodynamic one. There is a distinction which should be made between two types of electrical responses in a pyroelectric material. Prima ry pyroelectricity is due to the change in temperature when keeping a constant volume for the material. But when temperature changes so does the volume which creates a secondary pyroelectricity due to the piezoelectric effect (Zheng et al., 2008). Table 6. Some pyroelectric materials and their primary and secondary pyroel ectric coefficients (from Lang 2005). Material Primary ( C/m 2 K ) Secondary ( C/m 2 K ) BaTiO 3 260 60 LiNbO 3 95.8 12.8 LiTaO 3 175 1 Tourmaline 0.48 3.52 Note: Reproduced from Lang 2005. The pyroele ctric coefficient is the single most important property when choosing a pyroelectric material. 2.5.2: Responsivity Responsivity is a measure of how well a detector is performing. The responsivity of a device is a measure of the ratio of t he total voltage output compared to the total power input. This feature of a pyroelectric detector tends to decrease when heat radiation frequencies reach above 200 Hz. The higher this attribute the better the detector works (Chvatal et al., 2009). T his characteristic

PAGE 35

25 for infrared detectors was studied in more detail by Batra et al. ( 2008 ) This property of pyroelectric detectors shows a great deal about the detectors themselves as well as their performance capabilities. Whatmore (1986) studies pyroele ctric devices in detail. He explains that for a pyroelectric detector the voltage response R v is one of the more important aspects and is given theoretically by R v =(RpA G(1+ 2 t 2 ) 1/2 (1+ 2 e 2 ) 1/2 ] where G is the thermal conductance R is the pyroelectric resistance p is the pyroelectric coefficient t is the thermal time constant e is the electrical time constant is the emissivity A is the active area is the frequency Moreover, the theoretical voltage response maximizes when the =( e t ) 1/2 It should be noted that detectors are manufactured for specific tasks thus this is a general property of a detector. Other properties might be more useful when developing a pyroelectric detector. 2.5.3: Noise Noise becomes a problem when trying to get a small signal output from a device. For pyroelectric devices, Whatmore ( 1986 ) explained that there are four

PAGE 36

26 dominant sources of noise to consider. They are temperature noise (noise generated by temperature when t he system is in equilibrium Johnson noise ( nois e created by the pyroelectric conductance ) amplifier noise (noise generated by amplifying circuit) and finally current noise. The equivalent noise for a detector is given by Batra et al. ( 2008 ) as V N 2 = V T 2 + V J 2 + V i 2 + V A 2 Furthermore, a graph showing each noise as a function of frequency was proposed by Whatmore ( 1986 ) and is shown in the figure below Note: Reproduced from Whatmore (1986). Figure 4 Magnitudes of voltage noise for a pyroelectric detector as a function of frequency (Whatmore, 1986). It is safe to say that from the graph that the Johnson noise dominates after 20 Hz and before that the current noise dominates. All the noises should be at their lowest for a good performin g detector It is important to note that for this thesis the frequency used in 60 Hz. At this frequency the voltage noise is approximately

PAGE 37

27 four orders of magnitude smaller (~10 7 V) than the signal that is being measured (10 3 V). It is assumed that the noise ha s neg ligible effects on the output signal. 2.5.4: Curie Temperature The Curie temperature would be thought of as a limitation of the pyroelectric material in the sense that the spontaneous polarization of the material dramatically decreases as the temperature is increased to the Curie zero (Ram os et al., 2007). Careful attention should be paid to the Curie temperature of a material because it could be the limiting factor for the app lication in which the pyroelectric material is being used. Detectors in general use different types of materials due to the different properties and figures of merit materials exhibit (Kao, 2004) Table 7 shows some pyroelectric materials and their respec tive figures of merit. These are some of the widely used pyroelectric materials. These properties include the pyroelectric coefficient, loss tangent (a way to quantify the energy dissipation within a material) strain, and Cu rie temperature. Specific applications of such materials require careful attention to certain figures of merit. Table 7. Pyroelectric materials and their figures of m erit ( from Xiao et al. 1988) Material p (10 4 C/m 2 K) tan T c ( o C ) PVF 2 0.27 0.015 12 170 TGS 5.5 0.025 55 49 PZT 3.8 0.003 290 230 Note: Reproduced from Xiao et al. 1988.

PAGE 38

28 2.6 : Pyroelectric Current State of Research Recent years have seen pyroelectric research advance to new levels. This section takes a look at recent papers and an overview of their areas of research. Mischenko et al. (2008) looks i nto harvesting waste energy and turning it into electrical energy using the pyroelectric phenomenon. The authors propose the idea of usi ng a pyroelectric material in places where heat is lost such as air conditioning to convert that heat into electricity. At this point efficiencies for this conversion are very low but there is room for improvement. This is a very young area of study bu t th ere is a lot to be discovered. Continuing on those steps, Vanderpool et al. (2008) take a look at c onversion of waste heat directly into electricity. In this paper, a prototypical energy converter is simulated and studied by solving two dimensional energy, mass, and momentum equation using the finite element method. Results demonstrate that there is an energy efficiency increase with an increase in specific heat and density of the working fluid and the pyroelectric material. They calculated a p ossible effic iency of 40% for Carnot Cycle Moreover, Guyoma r et al. (2009) take a look at the h arvesting of thermal energy using a pyroelectric material. A method called synchronized switch harvesting on inductor (SSHI) is used to perform experiments. For the Carnot cycle the efficiency of energy harvesting is about 0.05%. In this case the power pro duced for a temperature change of 7K is more than 0.3 mW for an active material that has a mass of 8g. Temperature frequency seems to be the limiting

PAGE 39

29 factor is this case. Large temperature variations are necessary to increase the efficiency and low speed o f heat transfer makes it difficult to achieve that. Qiu lin et al. (2009) take a look at gas sensors as an important application of pyroelectric materials. These sensors can be used to measure the amount of gas in the environmental level, in biomedical de vices, and automobiles. In this article, thin film pyroelectric materials are studied for this particular use. The pyroelectric sensor detects infrared waves of the gas produced then coverts it into an electrical signal. This paper studies the detection of methane gas and the results show that these pyroelectric sen sors are good candidates for such tasks Epstein et al. (2009) introduce t he electrocaloric effect (ECE) which is a phenomenon similar to pyroelectricity. When an electric field is applied to an elec t rocaloric material the temperature rises and when the field is decreasing, the temperature goes down. In this paper, the properties of electrocaloric materials are studied for application such as refrigeration, heat pumps, and electrical generators. The efficiency of refrigerators and generators using thin film electrocaloric materials are studied. It is shown that the efficiency increases with an increase of the thermal co nductivity between the heat switches. These Lead zirconate titanate and polyvinylidene fluoride are two ma terials that are studied in paper by Cuadras et al. (2010). The author s propose these two materials as thermal energy harvesting sources to supply a low power autonomous sensor. The sensors are used as current sources with output impedances. Heating and cooling of the sensor is created by air currents. The

PAGE 40

30 generated currents were in the order of 10 7 Amperes. This current is collected in a capacitor for cooling and heating cycles. The energy collected was measured up to 0.5 mJ, which is enough to power a sensor making measurements such as mentioned above. Recent studies conce rning pyroelectric materials concentrate more on applications of pyroelectric materials in such areas as infrared detection, gas monitoring and energy harvesting. Not many studies concentrate on the effects of temperature on such materials. This thesis will require the use of a pyroelectric sensor and study the temperatu re dependence of its properties in hope of develop ing a new method for temperature measurement. 2.7. Lithium Tantalate All ferroelectric materials are considered to be pyroelectric but not vice versa. This means that the direction of the dipole moments could be reversed in the presence of an electric field but the rest of the properties of ferroelectric material s follow pyroelectric behavior. As was mentioned above, lithium t antalate or usually known as LT is a ferroelectric crystal. LT has a Curie temperature of ~610 o C and is one of the most widely used pyroelectric/ferroelectric materials. Lithium Tantalate is u sed in many different applications such as human detection, military, and security (Nougaret et al., 2009) and lately it has received a lot of attention for electro optical applications (Sa tapathy et al., 2011). Lithium t antalate is widely used in such app lication s due to the following properties: 1. high mechanical stability (Sokoll et al., 1997) 2. low thermal expansion (Sokoll et al., 1997)

PAGE 41

31 3. high signal noise ratio (Norkus et al., 2010) 4. reproducibility of sensor properties (Norkus et al., 2010 ) Some fabrication methods for lithium t antalate include ion beam etching, sol gel method, and radio frequency magnetron sputtering (RFMS) In ion beam etching a similar process to sand blasting is created where single atoms to ablate the material away (Soko ll et al., 1997). In the sol gel method or chemical solution deposition as it may be called, a solution is used to crea te a gel like structure and then the material itself (Satapathy et al., 2011). Other methods include deposition by RFMS thermal evaporat ion, and laser ablation (Nougaret et al., 2009) LT can be fabricated to fit m any application s and is readily available. Most o f the recent studies involving lithium t antalate are concerned with applications of this material have been studied, studies today concentrate of electro optic application s Kohli et al. (199 8 ) has studied the electrical an d pyroelectric properties of LT. Most of the experimental results on this study are concerned with how a property varies with a change in frequency. They studied the relative permittivity (how well energy is stored within the material) of a capacitor creat ed from this material and its variance with temperature for the range 110 610 o C. Results showed a linear dependence of the relative permittivity for ranges 110 310 o C and 350 550 o C. Nothing has been mentioned on how this could be used for possible temperatu re measurement. Moreover, these results are out of the scope of this thesis as the range of temperature studied in this thesis is 0 100 o C. Furthermore, Jacob et al. (2004) studied the permittivity and

PAGE 42

32 loss tangent of lithium tantalate as a function of temp erature. Tests were performed for a frequency 11.44 GHz and for temperatures up to 300K. Again, this temperature range is out of the scope of this thesis. Moreover, lack of state of the art testing equipment would not allow for such measurements at the temperature range of 0 100 o C. This thesis is based solely on the th ermal response of this material and it could be looked at as a starting point for temperature measurement using lithium tantalate. In this thesis, a ny extraneous effects on the lithium t an talate sensor were eliminated and the response will be purely dependent on the temperature change. Moreover, all types of noise were minimized by the manufacturer of the sensor. The main purpose was to study only the temperature effects on the se nsor whil e other effects were eliminated or at the least are kept at a minimum.

PAGE 43

33 CHAPTER 3: MATERIALS AND METHODS In this chapter the materials, instrumentation, and the methods that were necessary to complete this thesis are discussed A detailed look at the materials and instrumentations used are provided. Moreover, a step by step presentation of the experimental setup is given. This chapter is presented in such a way that someone could easily reproduce this experiment. 3.1: Materia ls and Instrumentation After careful research of pyroelectricity and pyroelectric materials it was decided that the best materi al to use for this project was lithium t antalate (LiTaO 3 ). A few important factors were considered when making the selection. One factor was that secondary pyroelectricity of LiTaO 3 is almost zero and is the lowest among the most common ly used materials as shown in T able 6. This allows one to study in higher accuracy the temperature dependent properties of this material/sensor as the volumetric effects will be neglected. Moreover, lithium t antalate has a high Curie temperature (~ 610 o C) which allows for higher temperature studies (although not necessary for this thesis due to its scope ). Another advantage of such a sensor is its h igh current response This means that the current or voltage output of the sensor compared to the power input is relatively high when compared to other sensors. The sensor was ordered from a manufacturer located in Orego n and the company name is Spectrum Detector. According to their manual some additional advantages of such a sensor are:

PAGE 44

34 1. fast response time 2. small and portable 3. used in current mode and voltage mode circuits 4. highly sensitive This sensor is named SPC 2 meaning it is a discrete pyroel ectric d etector with a diameter of 2mm According to the manufacturer, this sensor has a broadband of 0.1 to 100 m. Moreover, it is specifically manufactured to be used as an optical pyrometer, laser energy meter, and infrared gas sensor. The purpose of th is thesis is to show that this sensor could be used something other than what is specified by the manufacturer : a starting point for possible temperature measurement. Furthermore, s ome of the specifications for this sensor according to the man ufacturer are shown in Table 8 below and F igure 4 shows a close up photograph of the sensor. Table 8. Specifications for SPC 2 LiTaO 3 pyroelectric detector. Parameter Magnitude Diameter (mm) 2 Area (mm 2 ) 3.14 Capacitance (pF) 2 2 Thermal 3db Frequency (Hz) 1.6 Current Responsivity ( A/W) 0.45 Maximum Average Power (mW) 50 Note: Reproduced

PAGE 45

35 Fig ure 5 SPC 2 Lithium T antalate p yroelectric sensor In order to measure t he temperature response of the Lithium T antalate sensor mentioned above I must have the sensor enclosed in such a way that any conve ctive and optical effects on the sensor would be neglected. I chose a well insu lated box with dimensions of 5 1 Polyurethane was used to insulate the walls of the enclosure. This was used due to the fact that it has a high enough temperature limit (~120 o C) to be used for this thesis. Two sheets of polyurethane with dimension 5 were used to insulate the top a nd the bottom of the box, width. The reason for choosing such a small box is to make sure that ste ady state temperature would be achieved faster. A type k thermocouple was chosen for temperature measurement of the ambient inside the enclosure. The accuracy of the thermocouple was 0.4% of the temperature being measured. For the measurements made i n this thesis the highest uncertainty would be at 99 o C (0.004*99 o C=0.396 o C). The temperature was read from an Omega HH12A digital thermometer. The uncertainty of the

PAGE 46

36 digital thermometer is half of its resolution (0.5*1 o C=0.5 o C). The digital thermometer thus is the limiting instrument for the measurements made in this thesis. A silicon rubber heater was used to increase the temperature within the enclosure. This heater was purchased from Omega.com. Moreover, a mini fridge was used to decrease the temperature of t he sensor below the room temperature In order to amplify the signal output, four different amplifying circuits were used The first two are called Voltage Mode and Current Mode and are propos ed by Chirtoc et al. (2003). Rep resentation s of these two ampl ifying circuits using OrCAD 9.2 Capture CIS Lite Edition are given in Figure s 5 and 6 Note: Reproduced from Chirtoc et al. (2003). Figure 6 Current Mode amplification circuit as proposed by Chirtoc et al. (2003). Note: Reproduced from Chirtoc et al. (2003) Figure 7 Voltage Mode amplification circuit as proposed by Chirtoc et al. (2003).

PAGE 47

37 Moreover, a double Current Mode amplifying circuit was used as proposed by Chung et al. (1996) An illustration of this circuit using OrCAD 9.2 Capture CIS Lite Edition is given in Figure 7 Note: Reproduced from Chung et al. (1996). Figure 8 Amplification circuit as proposed by Chung et al. (1996). A nd last but not least I used an amplification circuit using a modified Wien Oscillator as proposed by Malhame (2002). A demonstration of this circuit using OrCAD Capture CIS Lite Edition 9.2 is given in Figure 7. The difference between this amplifying circuit and the Wien Oscillator is that the pyroelectric sensor is replacing a capacitor and resistor in series.

PAGE 48

38 Note: Reproduced from Malhame (2002). Figure 9 Modified a mplification circ ui t similar to a Wien O scillator circuit proposed by Malhame (2002). The components used to build these amplifying circuits were purchased from RadioShack. A summary of these components is given in Table 9. Table 9. Compone n ts used for the amplification circuits. Component Type Value Amount Resistor watt 5% 10 6 1 1 10 5 7 Capacitor ceramic plate 10 9 F 4 10 10 F 1 Operational Amplifier 741 OP AMP mini DIP IC NA 5 Electrical Breadboard No. 276 001 5V max 2 A few additional instruments were necessary for measurement of the signal. A DC power supply was used to supply power to the breadboard and its components. Moreover, another AC power supply (60Hz) was used t o supply power to the silicon rubber heater. The power output of the AC power su pply was m onitored using a digital voltmeter. An oscilloscope purchased from Agilent Technologies was used to measure the signal output And last but not least a

PAGE 49

39 personal computer was used to document the data and produce the necessary graphs. The data was recorded into Microsoft Office Excel 2007 and the gr aphs were generated 3.2: Experimental Setup Before beginning the experiment the amplifying circuits needed to be constructed using the components purchased from RadioShack (resistors, capacitors, operational amplifiers, and electrical breadboards). Careful attention was paid to the design of the circuits when using of the breadboard and the operational amplifiers A small misplacement of the components on the breadboard result in the wrong measurement. Also, the connection of the components to the operational amplifier is very important. It is a good idea to double or triple check the construction of the amplifying circuits. In order to reduce the time it would take to gather data, it was beneficial to have all four circuits built before starting to collect data. Th us one would be able to keep the temperature at steady state and switch circuits rather than keep the same circui t and change temperature (in the previous method the cost is somewhat higher than the latter one but time would be reduced significantly ) With that said, th e Voltage Mode and t he Current M ode were constructed on the sam e breadboard as seen in Figure 9

PAGE 50

40 Figure 10 Setup for amplifying circuits for the Voltage Mode (left) and Current Mode (right). The numbers in this figure represent the following: 1. Signal input to the Voltage Mode 2. Signal i nput to the Current Mode 3. Operational amplifier for Voltage Mode 4. Signal output for Current Mode 5. Signal output for Voltage mode 6. Operational amplifier for Current Mode 7. The connection of the positive end of the DC power supply. Red wire connects the positive end to both sides of the breadboard. 8. The connection of the negat ive end of the DC power supply. 9. Ground connection for oscilloscope connection.

PAGE 51

41 A different electrical breadboard and components were used to construct the modified Wien Oscillator and the double Current Mode circuits. A representation of the se two amplifyi ng circuits is shown in Figure 10 (modified Wien Oscillator left, and double Current Mode right). The list given for Figure 9 applies to Figure 10 except the Voltage Mode is replaced by the modified Wien Oscillator and the Cur rent Mode is replaced with the d ouble Current Mode. Figure 11 Setup for amplifying circuits for a modified Wien Oscillator circuit (left) and double Current Mode (right). With the circuits completed, the next step was to the setup of the enclosure and the components inside it This setup is only pertinent for temperature measurements above the room temperature (23 o C in this case). The reason behind choosing the enclosure was to keep the sensor, the heater, and the thermocouple in the same place such that any extraneous heating or cooling effects on the sensor would b e negl ig i ble Moreover, an enclosed space small

PAGE 52

42 enough such that i ts volumetric temperature would change rapidly and reach steady state faster was necessary This is important because it saves a great deal of time. As mentioned in the previous section, a small enclosure with a volume of 20 in 3 was chosen and was well ins ulated. The lithium t antalate sensor and a thermocouple attached to its side ( with the meas uring end of the thermocouple not touching the sensor) were placed inside the enclosure Across from them, at a distance of ~2 inches, the silicon rubber heater was placed. The senor output was then connected through copper wires to the ground and to the signal input of the amplifying circuits. The heater was powered by the AC power source mentioned in the previous section and the thermocouple was connected to a digital thermometer. A diagram of the complete setup is given below. Figure 12 Diagram of the experimental setup.

PAGE 53

43 The enclosure used for temperature measurements below room temperature was a small refrigerator with an area of 1.7 ft 3 The pyroelectric sensor and the thermocouple were enclosed in a plastic wrapping to reduce condensation and similarly the wire connections were insulated by means of electrical tape for the similar reason s With the enclosures and the amplifying circuits completed, the experimental setup was almost complete. To better understand the experimental setup Figure 11 is displayed below. Figure 1 3 The components and the e xperimental setup for thermal response of l ithium t antalate. In this picture all the necessary instrumentations are shown with the exception of the small refrigerator The numbered instruments and components are the following: 1. AC power supply 2. DC power supply

PAGE 54

44 3. Digital thermometer 4. Digital Voltmeter 5. Breadboard consisting of the modified Wien Oscillator and the double Current Mode 6. Breadboard consisting of the V oltage Mode and Current Mode 7. Oscilloscope 8. Enclosure 9. Silicon rubber heater 10. Lithium t antalate pyroelectric sensor 11. Sony Vaio personal laptop for recording the data The parts listed above are connected in the following fashion. The lithium t antalate sensor, silicon rubber heater, and the thermocouple are placed inside the enclosure. The the rmocouple is connected to the digital thermometer. The heater is powered by the AC source and the power input to the heater is monitored by a digital voltmeter. The sensors output signal is connected to the input of the amplifying circuit. The DC power sup ply is connected to the breadboard and the output signal of the amplifying circuit on the breadboard is connected to the oscilloscope. The oscilloscope s output then is recorded in Microsoft Office Excel 2007 The procedure for temperature measurement is as follows: 1. Construct the amplifying circuits 2. Construct the enclosure 3. Connect everything as mentioned in the paragraph above

PAGE 55

45 4. t 5. Turn on everything 6. Set the DC power source to the desired voltage 7. Con nect the oscilloscope to the ground and to the output of the desired amplifying circuit 8. 9. 10. Take 10 measurements each at a minute apart and record the dat a. 11. Repeat step 9 for the rest of the circuits and record the data 12. Take the mean and the standard deviation of the data 13. Increase the AC power supply until the desired temperature inside the enclosure is reached 14. Wait 30 minutes and make sure the temperature does not change in order to assume steady state temperature 15. Repeat steps 7 14 for all desired temperature measurements 16. For measurements below room te mperature, repeat steps 1 15 using t he small refrigerator in lieu of the heater. This step by step process of data collection is the conclusion of the materials and methods chapter. It is important to mention that the standard deviation and the mean of the ten data points are necessary for data int erpretation.

PAGE 56

46 CHAPTER 4: RESULTS AND DISCUSSION 4.1 : Theoretical Expectations Lang et al. (1969) has studied the use of a pyroelectric sensor in parallel with a shunt resistor. The figure below shows the circuit which is studied by them. The emphasis is put on the importance of the shunt resistor R s Note: Reproduced fro Lang et al. (1969). Figure 1 4 Circuit studied by Lang et al. (1969). For this thesis, this type of configuration was used as part of the Voltage Mode and modified Wien Oscillator amplifying circuits but not for the Current Mode and the double Current Mode as simulated results show higher slopes for the voltage output for the former amplifying circuits There are three cases on how the shunt res istor affects the voltage vs. time curve. The first is when R s <
PAGE 57

47 Note: Reproduced from Lang et al. (1969). Figure 1 5 Voltage vs. t ime for shunt resistor value much lower than pyroelectric resistance Note: Reproduced from Lang et al. (1969). Figure 1 6 Voltage vs. time for shunt resistace higher o r equal to the pyroelectric resistance 0 1 2 3 4 5 6 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Voltage Time Voltage vs. Time for R s << R p 0 5 10 15 20 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Voltage Time Voltage vs. Time for R s R p

PAGE 58

48 Note: Reproduced from Lang et al. (1969). Figure 1 7 Voltage vs. time for shunt resistance equal to the pyroelectric resistance Because the pyroelectric resistance of the sensor used for this thesis is in the order of >10^12 ohms and the shunt resistances are in the order of 10^5 ohms, it was expected for the voltage response with time to f ollow the form seen in Figure 15 Since the sensor is allowed to reach steady state the voltage output at a certain temperature was expected remain the same with time The voltage output should only change with a ch ange in temperature. Moreover, this behavior should be expected for the two circuits which are i mplementing the shunt resistor : Voltage Mode and modified Wien O scillator As mentioned above, t he shunt resistor was used for these two amplifying circuits because the simulation using OrCAD and PSpice showed higher slopes for them as compared to other two. On the other hand, t he Current Mode and the double Current Modes should be expected to follow the form given on the figure below due to the fact that no shunt resistor is present. Lack of a shunt resistor would cause the voltage output with time to reach a peak t hen decay to zero with time. Thus, the voltage output 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Voltage Time Voltage vs. Time for Rs = Rp

PAGE 59

49 for these two amplifying circuits would be expecte d to follow a linear behavior with a slope closer to zero unlike the Voltage or the Wien Oscillator modes Note: Reproduced from Tuo a yar (2007). Figure 18 Response of voltage output vs. time for the Current Mode and double Current Mode OrCAD Family 9.2 Capture CIS Lite Edition and PSpice were used to simulate the correlation between the current generated by the sensor and the voltage output. This allow s comparisons to be made between theoretical and experimental results. 4. 2: Experimental Results As mentioned in the previous chapter, all temperature measurements were taken at steady state. If the temperature of the enclosure did not change for thirty minutes, this was assumed as achieving steady state. After the latter was reached, ten measurements of the minimum voltage and maximum voltage were taken at one minute intervals These measurements were recorded in Microsoft Office Excel 2007. The mean and standard deviation of all the measurements 0 0.02 0.04 0.06 0.08 0.1 0.12 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Voltage output Time (ms) Expected Voltage Output vs Time for Current Mode and double Current Mode

PAGE 60

50 were calculated using Excel. In this case the standard deviation of the ten measurements taken is the only statistical method necessar y to describe the behavior of the data The voltage output from the sensor was measured at sixteen different temperatures (5, 10, 15, 23, 31, 36, 41, 47, 53, 60, 67, 73, 80, 87, 94, and 99 o C ) The t en measurements which were taken at each temperature were also taken for each of the four amplifying circuits. A fter the measurements were made and recorded the averages at each temperature were calculated and plotted. Out of eight possibilities ( maximum voltage and minimum voltage for all four circuits) three demonstrated linear behavior with noticeable slopes and the rest exhibited linear behaviors with slopes close to zero The three modes which exhibite d linear behavior were the measurements for the maximum voltage and minimum voltage of the modified Wien Oscillator and the maximum voltage for the Voltage mode. Table 10 displays the V max (maximum voltage) average the standard deviation for all temperatures for the modified Wien Oscillator From this table, a linear behavior of the voltage maximum throughout the temperature range is observed. Moreover, the standard deviation has a range between 0.5 and 1.0mV. This plays a big role on how useful t his data could be. To understand the importance of the standard deviation we must take a look at the plot of the maximum voltage against temperature wh ich is given in Figure 19 As can be seen the data is linear with a slope of 2.1 2736 mV. The slope in this case represents the resolution of the collected data. We are getting a response of 2.1 2736 mV/ o C with a standard deviation between 0.5 and 1mV.

PAGE 61

51 Table 10. Mean and standard deviation of the ten V max measurem ents at each temperature for the modified Wien Oscillator amplifying circuit. Temperature ( o C) Mean (V) Standard Deviation (V) 5 1.4182 0.000788811 10 1.4297 0.000823273 15 1.4424 0.000699206 23 1.4623 0.00082327 31 1.4828 0.000632456 36 1.50 34 0.000843274 41 1.5208 0.000918937 47 1.5329 0.000875595 53 1.5408 0.000918937 60 1.5522 0.000918937 67 1.5621 0.000567646 73 1.5753 0.000823273 80 1.5872 0.000632456 87 1.59 81 0.000875595 94 1.61 0.000666667 99 1.6203 0.000674949 Moreover, the correlation coefficient for this data is R 2 =0.9823 with R 2 =1 being a perfect correlation of the data. This means that all the data has an almost perfect linear dependence. With t he standard deviation being smaller than the resolution and the linear dependence of the data almost perfect, w e could say the maximum voltage measurement for the modified Wien Oscillator could be used for temperature measurement for this temperature range.

PAGE 62

52 Figure 19 The average maximum voltage vs. temperature for the modified Wien Oscillator with error bars of one standard deviation in each direction vertically and 0.5 o C in each direction horizontally Similarly, Table 11 shows the V min average and the standard deviation for the modified Wi en Oscillator mode and Figure 20 shows a plot of this data. Correspondingly, the standard deviation of this dat a has a range between 0.5 and 1 mV and the lin ear dependence of the data is R 2 =0.9929. The slight difference between the maximum voltage and minimum voltage for the modified Wien Oscillator mode is the slope or resolution. The resolution is slightly high er for the maximum voltage (0.2021 mV ) with the resolution of the V min graph being 1.92526mV Furthermore, t he minimum voltage has a slightly better linear dependence than the maximum voltage. Either quant ity could very easily be used for temperature measurement of temperatures between freezing and boiling points of water. y = 0.0021x + 1.4177 R = 0.9823 1.4 1.45 1.5 1.55 1.6 1.65 0 20 40 60 80 100 120 V max (V) Temperature ( o C) Temperature vs. V max (Wien Oscillator)

PAGE 63

53 Table 11 Mean and standard deviation of the ten V min measurements at each temperature for the modified Wien Oscillator amplifying circuit. Temperature ( o C) Average (V) Standard Deviation (V) 5 1.1875 0.000849837 10 1.1981 0.000737865 15 1.2101 0.000567646 23 1.2218 0.000788811 31 1.2475 0.000849837 36 1.2606 0.000843274 41 1.2718 0.000918937 47 1.2817 0.000823273 53 1.2918 0.000918937 60 1.3 0.000632456 67 1.3161 0.000875595 73 1.3261 0.0005 80 1.341 0.000666667 87 1.3543 0.000823273 94 1.3616 0.000843274 99 1.3704 0.000699206 Figure 20 The minimum voltage measured vs. temperature for the modified Wien Oscillator with error bars of one standard deviation in each direction vertically and 0.5 o C in each direction horizontally y = 0.002x + 1.1835 R = 0.9929 1.15 1.2 1.25 1.3 1.35 1.4 0 20 40 60 80 100 120 V min (V) Temperature ( o C) Temperature vs. V min (Wien Oscillator)

PAGE 64

54 Equally, Table 12 and Figure 21 show the V max data for the Voltage mode. Similar to the two previous measurements, there is a linear dependence of this data with a correlation coefficient of R 2 =0.9952. This linear dependence is the best out of all three modes but there is a disadvantage to this mode compared to the other ones. The resolution or the slope of this data is alm ost half of the resolution of the modified Wien Oscillator at 0.99053mV The standard deviation of the data is similar to the other two measurements Although this method could be used for temperature measurement in the range specified above it could be misleading since the slope s and the standard deviation s of the data sets are almost the same. Table 12 Mean and standard deviation of the ten V max measurements at each temperature for the Voltage Mode amplifying circuit. Temperature ( o C) Average (V) Standard Deviation (V) 5 0.4923 0.000823273 10 0.4951 0.000737865 15 0.5026 0.000516398 23 0.5081 0.000737865 31 0.5149 0.000737865 36 0.5209 0.000737865 41 0.5236 0.000516398 47 0.5279 0.000875595 53 0.5347 0.000823273 60 0.5415 0.000849837 67 0.5499 0.000875595 73 0.5579 0.000875595 80 0.566 0.000942809 87 0.5719 0.000737865 94 0.579 0.000666667 99 0.5864 0.000516398

PAGE 65

55 Figure 21 The maximum voltage measured vs. temperature for the Voltage M ode with error bars of one standard deviation in each direction vertically and 0.5 o C in each direction horizontally For the Current Mode and double Current Mode the tables and graphs are given below. As expected, they have linear behaviors with slopes of nearly zero for the temperature range. Moreo ver, the correlation coefficie nts for the graphs are very low with R 2 =0.4077. The voltage output and the standard deviation for the double Current mode is twice that of the Current Mode. The standard deviation for both circuits is much larger than the res olution (slope of the line) thus these two circuits cannot be used for temperature measurement. y = 0.001x + 0.4848 R = 0.9952 0.48 0.5 0.52 0.54 0.56 0.58 0.6 0 20 40 60 80 100 120 V max (V) Temprerature ( o C) Temperature vs. V max (Voltage Mode)

PAGE 66

56 Table 13 Mean and standard deviation of the ten V max measurements at each temperature for the Current Mode amplifying circuit. Temperature ( o C) Average (V) Standard Deviation (V) 5 0.4869 0.000875595 10 0.487 0.000816497 15 0.4881 0.000875595 23 0.487 0.000816497 31 0.4878 0.000918937 36 0.4874 0.000843274 41 0.4868 0.000918937 47 0.486 0.000471405 53 0.4863 0.000948683 60 0.4863 0.000823273 67 0.486 0.000942809 73 0.4861 0.000994429 80 0.4864 0.000699206 87 0.4861 0.000994429 94 0.4866 0.000966092 99 0.4865 0.000971825 Figure 22 The maximum voltage measured vs. temperature for the Current Mode with error bars of one standard deviation in each direction vertically and 0.5 o C in each direction horizontally y = 1E 05x + 0.4874 R = 0.4077 0.4845 0.485 0.4855 0.486 0.4865 0.487 0.4875 0.488 0.4885 0.489 0.4895 0 20 40 60 80 100 120 Vmax (V) Temperature ( o C) Temperature vs. V min (Current Mode)

PAGE 67

57 Table 14 Mean and standard deviation of the ten V max measu rements at each temperature for the double Current Mode amplifying circuit. Temperature ( o C) Average (V) Standard Deviation (V) 5 0.9738 0.00175119 10 0.974 0.001632993 15 0.9762 0.00175119 23 0.974 0.001632993 31 0.9756 0.001837873 36 0.9748 0.001686548 41 0.9736 0.001837873 47 0.972 0.000942809 53 0.9726 0.001897367 60 0.9726 0.001646545 67 0.972 0.001885618 73 0.9722 0.001988858 80 0.9728 0.001398412 87 0.9722 0.001988858 94 0.9732 0.001932184 99 0.973 0.001943651 Figure 23 The maximum voltage measured vs. temperature for the Double Current Mode with error bars of one standard deviation in each direction vertically and 0.5 o C in each direction horizontally y = 3E 05x + 0.9748 R = 0.4077 0.969 0.97 0.971 0.972 0.973 0.974 0.975 0.976 0.977 0.978 0.979 0 20 40 60 80 100 120 V max (V) Temperature ( o C) Temperature vs. V max (double Current Mode)

PAGE 68

58 Moreover, 90% and 95% confidence intervals are given for the ten measurements at each temperature for all the amplifying circuits These confidence intervals are given in Appendix C on Table 15 and Table 16 for 90% and 95% respectively For the Wien Oscillator the values for a 95% CI are on average at 0.553mV and for a 90% CI are on average 0.484mV. W ith the slope of the data for the Wien Oscillator being at 2.12736mV, it is observed that the range of the voltage output at a certain temperature deviate s by 0.484mV with 90% confidence and by 0.553mV with a 95% confidence. This shows that all measurement s are three to four times smaller than the slope of the line at both confidence intervals thus allowing for an accurate temperature measurement for this mode. Similarly, the Voltage Mode has a slope of 0.99053mV and the confidence interval values at 95% an d 90% are 0.615mV and 0.464mV respectively. This also implies that no data is larger than the slope thus allowing for accurate temperature measurement although it is not as accurate as the Wien Oscillator. On the other hand, the Current Mode and the double Current Mode have slopes much smaller than the confidence interval values. This shows that the error is too large for each temperature thus neither amplifying circuit could be used for temperature measurement. These tables and figures conclude the r esults chapter. It has been shown that all three modes (modified Wien Oscillator V max and V min and Voltage Mode V max ) have linear dependence with a high enough slope to be measurable by modern voltage measuring devices. All data compare well to the graphs given by

PAGE 69

59 Capture CIS Lite Edition from the OrCA D Family 9.2. These graphs are shown below in Figure 24 and Figure 25 and correspond to the slope of the voltage output expected for the Voltage Mode and for the modified Wien O s cillator respectively. The slope of the voltage output is taken as a function of the expected values of the current generated by the sensor between 0 100 o C (0 1 micro ampere). It could be expected to see a slope of 1 m V / o C for th e voltage mode and a slope of 2 m V / o C for the modified Wien Oscillator. The total change in voltage output for the temperature range should be ~ 94 m V for the Voltage Mode and ~ 188 m V for the modified Wien Oscillator. Both these values are comparable to the V 99 V 5 for both the Voltage Mode ( 0.5864 0.4923= 94.1 m V ) and the modified Wien Oscillator (1.6203 1.4182= 202.1 m V for V max and 1.3704 1.1875= 182.9 m V for V min ) Figure 24 The expected slope of the voltage output using the Voltage Mode amplifying circuit generated with OrCAD 9.2 Capture CIS Lite Edition and PSpice

PAGE 70

60 Figure 25 The expected slope of the voltage output using the modified Wien Oscillator amplifying circuit generated with OrCAD 9.2 Capture CIS Lite Edition and PSpice

PAGE 71

61 CHAPTER 5: CONCLUSION AND SUGGETIONS In t his thesis a study of the thermal response of lithium tantalate for temperature measurement purposes was presented The pyroelectric sensor containing the lithium tantalate material was subjected to temperatures between 5 99 o C and the voltage response was measured at sixteen different temperatures within that range. Four different amplifying circuits were used for signal amplification since the current output of su ch a sensor is in the order of nano m icro amperes. Ten meas urements were taken at steady state at a certain temperature for each different amplifying circuit. The maximum and minimum voltages were measured for each circuit using an oscilloscope. The average and standard deviation of these ten points were calculate d using Microsoft Excel 2007. The averages were then plotted against temperature to identify correlation s Three modes showed linear relationships ( maximum and minimum voltage for modified Wien Oscillator and maximum voltage for Voltage M ode). The rest did not show any correlation. Both modes using the modified Wien Oscillator displayed a near ly perfect linear dependence with a resolution of approximately 2.1 m V / o C. The voltage mode showed similar results for linear dependence but the reso lution was half that of the modified Wien Oscillator. Moreover, all three modes had standard deviations between 0 5 and 1 m V It could be said that the modified Wien Oscillator mode is more appropriat e for temperature measurement for this temperature range.

PAGE 72

62 The experimental results compare well with the theoretical results computed using OrCAD 9.2 Capture CIS Lite Edition. For the temperature range which was studied, both the experimental and theoretical data display an increasing slope of about 2m V / o C for t he modified Wien Oscillator and 1 m V / o C for the Voltage Mode. Because their linear dependence is almost perfect and their resolutions are measurable with devices we have today, it is reasonable to assume that the measurement of temperatures between freezing and boiling points of water is possible The resolution of the data could be improved using different values for the components of the amplifying circuits. Different values give different outputs and thus there are values which optimize the resolution. Moreover, the standard deviation of the data could be improved by reducing the input voltage to the electrical b readboard and by eliminating fluctuations of the frequency at which the heating and cooling devices are running. In addition, better test equip ment would improve the overall data collection process and eliminate any other errors which may occur along the way. The modified Wien Oscillator amplifying circuit has not been used in any previous work concerning the amplification of pyroelectric signals Future studies are possible using such a circuit for amplification of pyroelectric signals for different applications.

PAGE 73

63 REFERENCES Batra, A. K., Aggarwal, M. D., Edwards, M. E., & Bhalla, A. (2008). Present Status of Polymer: Ceramic Composites for Pyroelectric Infrared Detectors. Ferroelectrics 84 121. Batra, A. K., Guggilla, P., Currie, J. R., Aggarwal, M. D., & Alim, M. A. (2006). Pyroelectric Ceramics for Infrared Detection A pplications. Ma terials Letters 1937 1942. Chirtoc, M., Bentefour, E. H., Antoniow, J. S., Glorieux, C., Thoen, J., Delenclos, S., et al. (2003). CUrrent Mode Versus Voltage Mode Measurement of Signals From Pyroelectric Sensors. Review of Sc ientific Instruments 648 650. Chung, W. Y., Sun, T. P., & Kao, Y. L. (1996). Design of Pyroelectric IR Readout Circuit B ased on LiTaO 3 D etectors. 1996 IEEE International Symposium on Circuits and Systems. Circuits and Systems Connecting the World 225 228. Chvatal, M., Sedlakova, V., & Majzner, J. (2009). Noise Analysis of Infrared Detectors. 2009 32nd International Spring Seminar on Electronics Technology. Hetero System Integration, the Path to New Solutionsin the Modern Electronics (p. 3). Cua dras, A., Gasulla, M., & Ferrari, V. (2010). Thermal Energy Harvesting Through Pyroelectricity Sensors and Actuators, A: Physical 132 139. DeWitt, D. P., & Nutter, G. D. (1988). Theory and Practice of Radiation Thermometry. New York: J. Wiley & Sons. D ietze, M., Krause, J., Solterbeck, C. H., & Es Souni, M. (2007). Thick Film Polymer Ceramic Composites for Pyroelectric Applications. Journal of Applied Physics 54113 1 7. Epstein, R. I., & Malloy, K. J. (2009). El ectrocaloric Devices Based on Th in Film Heat Switches. Journal of Applied Physics 064509 7. Fedosov, S. N., & Von Seggern, H. (2008). Pyroelectricity in Polyvinylidene Fluoride: Influence of Polarization and Charge. Journal of Applied Physics 014105 1 8. Fukada, E. (1989). Introduction: Early Studies in Piezoelectricity, Pyroelectricity, and Ferroelectricity in Polymers Phase Transitions 135 141.

PAGE 74

64 Guyomar, D., Sebald, G., Pruvost, S., & Lallart, M. (2009). Energy Harves ting From Ambient Vibrations and Heat. Journal of Intelligent Material Systems and Structures 609 624. Jacob, M. V., Hartnett, J. G., Mazierska, J., Giordano, V., Krupta, J., & Tobar, M. E. (2004). Temperature Dependence of Permittivity and Loss Tangent of Lithium Tantalate at Microwave Frequencies. IEEE Transaction on Micr owave Theory and Techniques 536 541. Kao, K. C. (2004). Dielectric Phenomena in Solids. Academic Press. Kinzie, P. A. (1973). Thermocouple Temperature Measurement. New York: J. Wiley. Kohli, C. H., Schmid, P. E., & & Levy, F. (1998). Electrical and Pyroelectric Properties of Lithium Tantalate Thin Films Ferroelectrics 471 482. Lang, S. B. (2004). A 2400 Year History of Pyroelectricity: From Ancient Greece to Expl o ration of the Solar System. British Ce r amic Transac tions 65 70. Lang, S. B. (1981). Bibliography on Piezoelectricity and Pyroelectricity of Polymers. Ferroelectrics 191 245. Lang, S. B. (2005). Pyroelectricity: From Ancient Curiosity to Modern Imaging Tool. Physics Today 31 36. Lang, S. B. (1974). Sourcebook of Pyroelectricity. New York: Gordon and Breach Science Publishers. Lang, S. B. (1999). The History of Pyroelectricity: From Ancient Greece to Space Missions. Ferroelectrics 99 108. Lang, S. B., Shaw, S. A., Rice, L. H., & Tim merhaus, K. D. (1969). Pyroelectric T hermometer for Use at Low Tempera tures. The Review of Scientific Instruments 274 284. Lau, S. T., Cheng, C. H., Choy, S. H., & Lin, D. M. (2008). Lead Free Ceramics for Pyroelectri c Applications. Journal of Applied Physics 014105 1 4. Li, S., Wu, X., Zhang, L., & Yao, X. (2008). Study of Poling Method s for Multilayer Pyroelectric Th in Film for Infrared Detectors. Journal of El e ctroceramics 520 523. Lovinger, A. J. (1983). Ferroelectric Polymers. Science 1115 1121. Ma lhame, R. P. (2002). Elementa r y Amplitude and Distortion Evaluation in Wien and Phase Shift O scillators. ICM 2002. 14th International Conference on Microelectronics 140 143.

PAGE 75

65 McGee, T. D. (1988). Principles and Methods of Temperature Measu rement. New York: J. Wiley & Sons. Michalski, L., Eckersdorf, K., Kucharski, J., & McGhee, J. (2001). Temperature Measurement. New York: J. Wiley. Mischenko, A. S., Zhang, Q., Scott, J. F., & Whatm o re, R. W. (2008). A New Approach to Interconversion of The rmal and Electrical Energy. 2006 8Th International Conference on Solid State and Integrated Circuit Technology (pp. 1 4). Nalwa, H. S. (1995). Ferroelectric Polymers: Chemistry, Physics, and Applications. New York: Marcel Dekker. Norkus, V., Schulze, A., Querner, Y., & Gerlach, G. (2010). The r mal Effects to Enhance the Responsivity of Pyroelectric Infrared Detectors. Procedia Engineering 5 944 947. Nougaret, L., Combette, P., & Pascal Delannoy, F. (2009). Growth of Lithium Tantalate Thin Films by Radio F requency Magnetron Sputtering With Lithium Enriched Target. Thin Solid Films 1784 1789. Plumb, H. H. (1972). Temperature: Its Measurement and Control in Science and Industry (Vol. 4). Pittsburgh: American Institute of Physics. Qiu L in, T., Wen Dong, Z., Chen Yang, X., & Ji J un, X. (2009). Design, Fabrication and Characterization of Pyroelectric Thin Film and Its Appication for Infrared Gas Sensors. Microelec tronics Journal 58 62. Quinn, T. J. (1990). Temperature. New York: Academic Press. Ramos, P., DeAndres, A., & Lopez, S. (2007). Effect of Thermal Losses on the Specific Detectivity of Pyroelectric Infrared Detectors. Integrated Ferroelectrics 147 159. Safari, A., Panda, R. K., & Janas, V. F. (1996). Ferroelectricity: Materials, Charact eristics & Applications. Key Engineering Materials 35 70. Satapathy, S., Verma, P., Gupta, P. K., Mukherjee, C., Sathe, V. G., & Varma, K. B. (2011). Structural, Dielectric and Ferroelectric Propertie s of Multilayer Lithium Tantalate Thin Films Prepared by Sol Gel Technique. Thin Solid Films 1803 1808. Shaldin, Y. V., Matyjasik, S., Rabadanov, M. K., & Gabrielyan, V. T. (2007). Py roelectric Properties of Re al LiNbO 3 S ingle Crystals. Doklady Physics 579 582. Shaw, C. P., Whatmore, R. W., & Alcock, J. R. (2007). Porous, Functionally Gradient Pyroelectric Materials Journal of the American Ceramic Society 138 142.

PAGE 76

66 Smith, B., & Amon, C. (2007). Simultaneous Electrothermal Test Method for Pyroelectric Microsensors. Journal of Electronic Packa ging 504 511. Sokoll, T., Norkus, V., & Gerlach, G. (1997). Ion Beam Etching of Lithium Tantalate and Its Applications for Pyroelectric Linear Arrays. Surface and Coatings Technology 469 474. Touayar, O., Mellouiki, I., Sifi, N., & Yakoub i, N (2006). Determination of the Nonequivalence Source Between Electrical and Radiative Heating in a Pyroelectric Sensor Using E xperimenta l Voltage Response and Heat Wave Propagation Theoretical M odel. Sensors and Actuators 572 580. Uchino, K. (2000). Ferroelectric Devices. New York: Marcel Dekker. Vanderpool, D., Yoon, J. H., & Pilon, L. (2008). Simulations of a Prototypical Device Using Pyroelectric Materials for Harvesting Waste Heat. International Jounral of Heat and Mass Transfer 5052 5062. Whatmore, R. W. (1986). Pyroelectric Devices and Materials. Report on Progress in Physics 1335 1386. Wong, C. P. (1993). Polymers for Electronic and Photonic Applications. Boston: Academic Press. Xiao, D., & Lang, S. B. (1988). Measurement Applications Based on Pyroelectric Properties of Ferroelectric Polymers. IEEE Transactions on Electrical Insulation 503 516. Yan, W., Zhang, R., Xiu, X., Xie, Z., Han, P., Jiang, R., et al. (2007). Temperature Dependence of the Pyroelectric Coefficient a nd the Spontaneous Polarization of AIN. Applied Physics Letters 212102 1 3. Zhang, Z. M., Tsai, B. K., & Machin, G. (2010). Radiometric Temeprature Measurements. II. Applications. Boston: Academic Press. Zhang, Z. M., Tsai, B. K., & Machin, G. (2010). Ra diometric Temperature Me a surements. I. Fundamentals. Boston: Academic Press. Zheng, D., Da Gui, H., & De Yin, Z. (2008). Thermal Analysis of the Microscale Pyroelectric Thin Film Infrared Detectors. 2 008 IEEE International Co nference on Mechatronics and Automation (pp. 49 54).

PAGE 77

67 APPENDICES

PAGE 78

68 Appendix A : Collected Data for the Voltage Mode (V.M.) and the Modified Wien Oscillator (W.O). T( o C) Measurement V.M. V max (V) W.O. V max (V) W.O. V m in (V) 5 1 0.492 1.418 1.187 2 0.493 1.418 1.187 3 0.493 1.418 1.188 4 0.492 1.419 1.188 5 0.492 1.42 1.189 6 0.494 1.418 1.186 7 0.491 1.418 1.187 8 0.492 1.418 1.188 9 0.492 1.417 1.187 10 0.492 1.418 1.188 Mean 0.4923 1.4182 1.1875 St. Deviation 0.000823273 0.000788811 0.000849837 10 1 0.495 1.429 1.198 2 0.496 1.43 1.199 3 0.495 1.43 1.197 4 0.494 1.431 1.198 5 0.496 1.431 1.198 6 0.495 1.43 1.198 7 0.494 1.429 1.197 8 0.496 1.429 1.198 9 0.495 1.429 1.199 10 0.495 1.429 1.199 Mean 0.4951 1.4297 1.1981 St. Deviation 0.000737865 0.000823273 0.000737865 15 1 0.502 1.442 1.21 2 0.503 1.442 1.21 3 0.502 1.443 1.211 4 0.502 1.443 1.21 5 0.503 1.442 1.21 6 0.502 1.442 1.21 7 0.503 1.442 1.21 8 0.503 1.444 1.211 9 0.503 1.442 1.21 10 0.503 1.442 1.209 Mean 0.5026 1.4424 1.2101 St. Deviation 0.000516398 0.000699206 0.000567646

PAGE 79

69 Appendix A : ( Continued ) 23 1 0.509 1.462 1.223 2 0.509 1.463 1.222 3 0.507 1.462 1.222 4 0.508 1.462 1.221 5 0.509 1.462 1.222 6 0.508 1.461 1.221 7 0.508 1.463 1.223 8 0.508 1.462 1.221 9 0.507 1.464 1.222 10 0.508 1.462 1.221 Mean 0.5081 1.4623 1.2218 St. Deviation 0.000737865 0.000823273 0.000788811 31 1 0.514 1.483 1.247 2 0.516 1.483 1.247 3 0.515 1.483 1.246 4 0.515 1.483 1.248 5 0.515 1.482 1.248 6 0.514 1.482 1.249 7 0.516 1.483 1.247 8 0.515 1.484 1.247 9 0.515 1.483 1.248 10 0.514 1.482 1.248 Mean 0.5149 1.4828 1.2475 St. Deviation 0.000737865 0.000632456 0.000849837 36 1 0.521 1.503 1.261 2 0.522 1.504 1.262 3 0.521 1.505 1.262 4 0.52 1.503 1.26 5 0.52 1.503 1.26 6 0.521 1.503 1.26 7 0.52 1.504 1.26 8 0.522 1.502 1.26 9 0.521 1.504 1.261 10 0.521 1.503 1.26 Mean 0.5209 1.5034 1.2606 St. Deviation 0.000737865 0.000843274 0.000843274

PAGE 80

70 Appendix A : ( Continued ) 41 1 0.524 1.52 1.271 2 0.524 1.521 1.272 3 0.524 1.521 1.272 4 0.523 1.521 1.271 5 0.523 1.523 1.273 6 0.524 1.52 1.273 7 0.524 1.52 1.273 8 0.523 1.52 1.271 9 0.524 1.521 1.271 10 0.523 1.521 1.271 Mean 0.5236 1.5208 1.2718 St. Deviation 0.000516398 0.000918937 0.000918937 47 1 0.528 1.532 1.281 2 0.527 1.533 1.281 3 0.527 1.534 1.282 4 0.527 1.532 1.283 5 0.527 1.532 1.281 6 0.529 1.532 1.281 7 0.528 1.533 1.282 8 0.529 1.533 1.283 9 0.528 1.534 1.281 10 0.529 1.534 1.282 Mean 0.5279 1.5329 1.2817 St. Deviation 0.000875595 0.000875595 0.000823273 53 1 0.535 1.54 1.292 2 0.535 1.542 1.291 3 0.534 1.54 1.293 4 0.535 1.54 1.292 5 0.535 1.541 1.292 6 0.535 1.542 1.291 7 0.534 1.54 1.29 8 0.536 1.542 1.292 9 0.535 1.54 1.292 10 0.533 1.541 1.293 Mean 0.5347 1.5408 1.2918 St. Deviation 0.000823273 0.000918937 0.000918937

PAGE 81

71 Appendix A : ( Continued ) 60 1 0.541 1.553 1.3 2 0.542 1.553 1.299 3 0.541 1.553 1.3 4 0.543 1.552 1.301 5 0.543 1.552 1.3 6 0.541 1.552 1.3 7 0.541 1.553 1.299 8 0.541 1.552 1.301 9 0.541 1.552 1.3 10 0.541 1.55 1.3 Mean 0.5415 1.5522 1.3 St. Deviation 0.000849837 0.000918937 0.000632456 67 1 0.55 1.562 1.315 2 0.549 1.561 1.316 3 0.551 1.562 1.316 4 0.55 1.563 1.316 5 0.551 1.562 1.315 6 0.549 1.562 1.317 7 0.551 1.563 1.316 8 0.55 1.562 1.316 9 0.549 1.562 1.318 10 0.549 1.562 1.316 Mean 0.5499 1.5621 1.3161 St. Deviation 0.000875595 0.000567646 0.000875595 73 1 0.558 1.575 1.329 2 0.556 1.576 1.329 3 0.558 1.577 1.328 4 0.559 1.574 1.329 5 0.558 1.575 1.329 6 0.558 1.575 1.33 7 0.559 1.575 1.329 8 0.557 1.575 1.329 9 0.558 1.576 1.329 10 0.558 1.575 1.3 Mean 0.5579 1.5753 1.3261 St. Deviation 0.000875595 0.000823273 0.0005

PAGE 82

72 Appendix A : ( Continued ) 80 1 0.565 1.587 1.341 2 0.566 1.588 1.34 3 0.565 1.587 1.34 4 0.566 1.587 1.342 5 0.567 1.588 1.341 6 0.568 1.587 1.341 7 0.565 1.587 1.342 8 0.566 1.587 1.341 9 0.566 1.586 1.341 10 0.566 1.588 1.341 Mean 0.566 1.5872 1.341 St. Deviation 0.000942809 0.000632456 0.000666667 87 1 0.572 1.598 1.354 2 0.573 1.599 1.354 3 0.572 1.6 1.355 4 0.572 1.598 1.355 5 0.573 1.598 1.356 6 0.571 1.598 1.354 7 0.571 1.597 1.353 8 0.571 1.597 1.354 9 0.572 1.598 1.354 10 0.572 1.598 1.354 Mean 0.5719 1.5981 1.3543 St. Deviation 0.000737865 0.000875595 0.000823273 94 1 0.579 1.611 1.361 2 0.579 1.61 1.363 3 0.58 1.609 1.362 4 0.58 1.61 1.36 5 0.578 1.611 1.362 6 0.579 1.609 1.362 7 0.579 1.61 1.362 8 0.579 1.61 1.361 9 0.579 1.61 1.361 10 0.578 1.61 1.362 Mean 0.579 1.61 1.3616 St. Deviation 0.000666667 0.000666667 0.000843274

PAGE 83

73 Appendix A : ( Continued ) 99 1 0.586 1.62 1.37 2 0.587 1.621 1.371 3 0.586 1.619 1.37 4 0.586 1.62 1.371 5 0.587 1.62 1.369 6 0.587 1.621 1.371 7 0.586 1.621 1.37 8 0.586 1.62 1.37 9 0.586 1.621 1.371 10 0.587 1.62 1.371 Mean 0.5864 1.6203 1.3704 St. Deviation 0.000516398 0.000674949 0.000699206

PAGE 84

74 Appendix B: Collected Data for the Current Mode (C.M.) and the Double Current Mode (D.C.M.). T ( o C) Measurement C.M. V max (V) D.C.M. V max (V) 5 1 0.488 0.976 2 0.487 0.974 3 0.486 0.972 4 0.486 0.972 5 0.488 0.976 6 0.487 0.974 7 0.487 0.974 8 0.486 0.972 9 0.486 0.972 10 0.488 0.976 Mean 0.4869 0.9738 St. Deviation 0.000875595 0.00175119 10 1 0.487 0.974 2 0.488 0.976 3 0.488 0.976 4 0.488 0.976 5 0.486 0.972 6 0.486 0.972 7 0.487 0.974 8 0.487 0.974 9 0.487 0.974 10 0.486 0.972 Mean 0.487 0.974 St. Deviation 0.000816497 0.001632993 15 1 0.488 0.976 2 0.489 0.978 3 0.488 0.976 4 0.487 0.974 5 0.487 0.974 6 0.488 0.976 7 0.489 0.978 8 0.489 0.978 9 0.489 0.978 10 0.487 0.974 Mean 0.4881 0.9762 St. Deviation 0.000875595 0.00175119

PAGE 85

75 Appendix B : (Continued) 23 1 0.487 0.974 2 0.487 0.974 3 0.488 0.976 4 0.487 0.974 5 0.486 0.972 6 0.486 0.972 7 0.488 0.976 8 0.488 0.976 9 0.487 0.974 10 0.486 0.972 Mean 0.487 0.974 St. Deviation 0.000816497 0.001632993 31 1 0.488 0.976 2 0.489 0.978 3 0.489 0.978 4 0.487 0.974 5 0.487 0.974 6 0.487 0.974 7 0.489 0.978 8 0.487 0.974 9 0.487 0.974 10 0.488 0.976 Mean 0.4878 0.9756 St. Deviation 0.000918937 0.001837873 36 1 0.489 0.978 2 0.488 0.976 3 0.487 0.974 4 0.487 0.974 5 0.488 0.976 6 0.487 0.974 7 0.487 0.974 8 0.488 0.976 9 0.486 0.972 10 0.487 0.974 Mean 0.4874 0.9748 St. Deviation 0.000843274 0.001686548

PAGE 86

76 Appendix B : (Continued) 41 1 0.486 0.972 2 0.487 0.974 3 0.487 0.974 4 0.486 0.972 5 0.488 0.976 6 0.486 0.972 7 0.486 0.972 8 0.486 0.972 9 0.488 0.976 10 0.488 0.976 Mean 0.4868 0.9736 St. Deviation 0.000918937 0.001837873 47 1 0.486 0.972 2 0.486 0.972 3 0.486 0.972 4 0.486 0.972 5 0.486 0.972 6 0.485 0.97 7 0.486 0.972 8 0.487 0.974 9 0.486 0.972 10 0.486 0.972 Mean 0.486 0.972 St. Deviation 0.000471405 0.000942809 53 1 0.486 0.972 2 0.487 0.974 3 0.487 0.974 4 0.485 0.97 5 0.487 0.974 6 0.486 0.972 7 0.485 0.97 8 0.486 0.972 9 0.488 0.976 10 0.486 0.972 Mean 0.4863 0.9726 St. Deviation 0.000948683 0.001897367

PAGE 87

77 Appendix B : (Continued) 60 1 0.486 0.972 2 0.486 0.972 3 0.486 0.972 4 0.487 0.974 5 0.485 0.97 6 0.486 0.972 7 0.486 0.972 8 0.486 0.972 9 0.487 0.974 10 0.488 0.976 Mean 0.4863 0.9726 St. Deviation 0.000823273 0.001646545 67 1 0.488 0.976 2 0.487 0.974 3 0.486 0.972 4 0.485 0.97 5 0.485 0.97 6 0.486 0.972 7 0.486 0.972 8 0.486 0.972 9 0.485 0.97 10 0.486 0.972 Mean 0.486 0.972 St. Deviation 0.000942809 0.001885618 73 1 0.486 0.972 2 0.486 0.972 3 0.485 0.97 4 0.485 0.97 5 0.487 0.974 6 0.486 0.972 7 0.486 0.972 8 0.487 0.974 9 0.488 0.976 10 0.485 0.97 Mean 0.4861 0.9722 St. Deviation 0.000994429 0.001988858

PAGE 88

78 Appendix B : (Continued) 80 1 0.486 0.972 2 0.486 0.972 3 0.486 0.972 4 0.487 0.974 5 0.488 0.976 6 0.486 0.972 7 0.486 0.972 8 0.487 0.974 9 0.486 0.972 10 0.486 0.972 Mean 0.4864 0.9728 St. Deviation 0.000699206 0.001398412 87 1 0.486 0.972 2 0.486 0.972 3 0.485 0.97 4 0.485 0.97 5 0.487 0.974 6 0.486 0.972 7 0.486 0.972 8 0.487 0.974 9 0.488 0.976 10 0.485 0.97 Mean 0.4861 0.9722 St. Deviation 0.000994429 0.001988858 94 1 0.486 0.972 2 0.486 0.972 3 0.485 0.97 4 0.487 0.974 5 0.487 0.974 6 0.486 0.972 7 0.486 0.972 8 0.487 0.974 9 0.488 0.976 10 0.488 0.976 Mean 0.4866 0.9732 St. Deviation 0.000966092 0.001932184

PAGE 89

79 Appendix B : (Continued) 99 1 0.486 0.972 2 0.486 0.972 3 0.486 0.972 4 0.486 0.972 5 0.486 0.972 6 0.487 0.974 7 0.487 0.974 8 0.488 0.976 9 0.488 0.976 10 0.485 0.97 Mean 0.4865 0.973 St. Deviation 0.000971825 0.001943651

PAGE 90

80 Appendix C: 90% and 95% C onfidence I nterval Values for T en V max M easurements at E ach T emperature and E ach A mplifying C ircuit Table 1 5 9 0 % confidence interval values in mV for ten V max measurements at each temperature and each amplifying circuit Wien Oscillator Voltage Mode Current Mode Double Current Mode 0.488901139 0.510260516 0.542689431 1.085378863 0.510260516 0.457325062 0.506060784 1.012120949 0.433364405 0.320060915 0.542689431 1.085378863 0.510258656 0.457325062 0.506060784 1.012120949 0.391993087 0.457325062 0.569552588 1.139104555 0.522657036 0.457325062 0.522657036 1.045314072 0.569552588 0.320060915 0.569552588 1.139104555 0.542689431 0.542689431 0.292174477 0.584348335 0.569552588 0.510260516 0.587989011 1.175978641 0.569552588 0.526724751 0.510260516 1.020520411 0.351824171 0.542689431 0.584348335 1.168696669 0.510260516 0.542689431 0.616342154 1.232684308 0.391993087 0.584348335 0.433364405 0.866728811 0.542689431 0.457325062 0.616342154 1.232684308 0.413196895 0.413196895 0.598779022 1.197558045 0.418330037 0.320060915 0.602332307 1.204665234

PAGE 91

81 Appendix C: (Continued) Table 1 6 95% confidence interval values in mV for ten V max measurements at each temperature and each amplifying circuit Wien Oscillator Voltage Mode Current Mode Double Current Mode 0.559104328 0.583530779 0.620616287 1.241232575 0.583530779 0.52299412 0.578727993 1.157455277 0.495592862 0.366019689 0.620616287 1.241232575 0.583528653 0.52299412 0.578727993 1.157455277 0.448280877 0.52299412 0.651336827 1.302672946 0.597707364 0.52299412 0.597707364 1.195414728 0.651336827 0.366019689 0.651336827 1.302672946 0.620616287 0.620616287 0.334128931 0.668257152 0.651336827 0.583530779 0.672420607 1.344841923 0.651336827 0.602359177 0.583530779 1.16706085 0.402343953 0.620616287 0.668257152 1.336514305 0.583530779 0.620616287 0.704845087 1.409690174 0.448280877 0.668257152 0.495592862 0.991185724 0.620616287 0.52299412 0.704845087 1.409690174 0.472529421 0.472529421 0.684759998 1.369519996 0.478399651 0.366019689 0.688823513 1.377647734