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For Reference 


NOT TO BE TAKEN FROM THIS ROOM 


THE UNIVERSITY OF ALBERTA 


A LINEAR TEMPERATURE CONTROLLER FOR DESORPTION 
SPECTRUM STUDIES 


by 


(c) OPAS CHUTATAPE 


A THESIS 
SUBMITTED TO THE FACULTY OF GRADUATE STUDIES AND RESEARCH 
IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE 
OF MASTER OF SCIENCE 


DEPARTMENT OF ELECTRICAL ENGINEERING 


EDMONTON, ALBERTA 
SPRING, 1973 


~ 


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ATRAIRIA 30 YTI2AIVIMU SHI 


Ha TASsH 
¥ — . a ; 


! , 


THE UNIVERSITY OF ALBERTA 
FACULTY OF GRADUATE STUDIES AND RESEARCH 


The undersigned certify that they have read, and 
recommend to the Faculty of Graduate Studies and Research, for 
acceptance, a thesis entitled A LINEAR TEMPERATURE CONTROLLER FOR 
DESORPTION SPECTRUM STUDIES submitted by OPAS CHUTATAPE, in 
partial fulfilment of the requirements for the degree of Master 


of Science. 


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ABSTRACT 


The processes governing the sierra of an energetic particle 
when it collides with and penetrates a solid surface are exceedingly 
complex. Parameters such as particle type, energy, target material and 
orientation can be well specified and yet it is still extremely difficult 
to accurately predict target behaviour under any given bombardment 
condition. Much, however, can be learned about bombardment processes by 
Studying the behaviour of the trapped particles as they re-evolve from 
the target material at elevated temperatures and a well-defined temp- 
erature-time profile can considerably facilitate evaluation of particle- 


Solid interaction. 


This thesis describes the design and construction of a control 
system for linearly varying the temperature of a solid target as a function 
of time. First, the characteristics of the heating process and of the 
System were investigated. Then the mathematical model of the process was 
derived and used to describe the system behaviour, leading to the design 
and construction of an electro-mechanical controller. The whole system 
was analysed by a frequency response method which indicated that compensation 
was necessary. The compensated system was finally tested and its 


specifications were compared with those previously set. 


The controller was tested by generating post-bombardment de- 
sorption spectra from a stainless steel target which had been previously 


inactivated with both argon and helium ions. In comparing the activation 


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energies for desorption from stainless steel with earlier work, 
discrepancies arise, particularly at the higher temperatures. Deficiencies 
in adequately controlling the target temperature in these earlier 

Studies and different target configurations may account for these 


differences. 


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ACKNOWLEDGEMENTS 
The author wishes to thank his supervisors, Dr. R.P.W. Lawson 
and Dr. J.F. Vaneldik, for their teaching and guidance during the 


course of this work and throughout the writing of this thesis. 


The staff and students of the Electrical Engineering Depart- 
ment are to be praised for making the author's stay in the Department 
both enjoyable and stimulating. The author is particularly indebted 
to Dr. P. Bryce and Mr. R. Schmaus of the High Vacuum Laboratory for 


many helpful discussions. 


The financial support received from the Canadian International 


Development Agency is gratefully acknowledged. 


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CHAPTER 


CHAPTER 


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1.2 
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2.4 


2.5 
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vi 


TABLE OF CONTENTS 


INTRODUCTION 
Preliminary Remarks 
Mathematical Analysis Background 


Objective and Scope of the Thesis 


HEATING PROCEDURE AND DETERMINATION 
OF PROCESS TRANSFER FUNCTION 
Introduction 

Heating Procedure and Background 
Information 

Previous Work Reviewed 

Thermal System Configurations 

2.4.1 Ultra-high vacuum chamber 

2.4.2 Filament and target arrangement 
Thermocouple Accuracy Considerations 
Final Thermocouple 

Mathematical Modelling of the Heating 
Process 

2.7.1 Energy balance equations and the 


behaviour of the process 


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320 


vii 
2.7.2 Linearization and representation of 
the process 


2.7.3 Approximation of the transfer 


function of the process 


CONSTRUCTION OF CONTROL SYSTEM 

Introduction 

Schematic Diagram of the Control System 

Type of Controller 

Circuit Details 

3.4.1 Ramp function generator 

3.4.2 Comparator 

3.4.3 The proportional plus integral 
controller 

3.4.4 Trigger and triac circuits 

Form of the Transfer Function of Each 

Block 

3.5.1 Comparator 

3.5.2 Controller 

3.5.3 Trigger and triac circuits 

Block Diagram Representation of the 


Control System 


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34 


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CHAPTER IV 


CHAPTER 


CHAPTER 


VI 

6.1 
G.2 
o.3 
6.4 


viii 
ANALYSIS AND DESIGN 
Introduction 
Determination of the Frequency Response 
4.2.1 Experimental procedure 
4.2.2 Results 
Adjustment of Controller Gains 
Phase Lead Compensation Network 


Pole Shifting 


RESULTS OF TEMPERATURE CONTROL 
Introduction 

Step Response 

Ramp Response 

Accuracy and Errors in the Measurement 


of Temperature 


THE STUDY OF DESORPTION SPECTRA 
Introduction 

Apparatus 

Experimental Method 

Results 

6.4.1 Desorption spectra 

6.4.2 The determination of activation 


energies 


101 
101 
101 
103 


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Fel 
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BIBLIOGRAPHY 


ix 


6.4.3 Comparison to previous results by 


Burch® 


CONCLUSIONS 
Summary 


Suggestions for Further Work 


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Figure 2.4 


Figure 2.5 


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Figure 2.7 


Figure 2.8 


Figure 2.9 
Figure 2.10 


Figure 2.1] 


LIST OF FIGURES 


Diode plate current as a function of filament 
current. | 

Cross section of the UHV chamber showing the 
thermal system configurations. | 
Temperature-emf characteristic curve of type 

R thermocouple. 

Thermistor bridge circuit. 

Block diagram of the heating process. 
Electrical analog network of the heating 
process. 

Transient responses of the thermal system to 
step filament currents. 

Plotted curves for the determination of poles 
of the system: 

Curve I, plot of loalc(t)-c(~)|/|c(0)-c(~)|vs. t, 
Curve II, asymptote of curve I, 

Curve III, average of rog( She - (142,207 099%) 4 
VScat) 

Plot of curves I, II, and III in linear scale. 
Electrical analog for cooling process of the 
target. 


Cooling curve of the target. 


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Log-Log plot between Veplts) and I,. 

Curves between Vip (tg) and I. 

Block diagram representing the thermal 

system. 

Schematic diagram of temperature control 

system. 

Simplified diagram of control system. 

Ramp function generator. 

Comparing bridge circuit. 

Instrument set up for measuring and 

attenuating thermocouple emf. 

Input network of the recorder. 

Simulation of the transfer function 

“ie pe 
i 


Low drift dc. amplifier of inverted gain Ky. 


K 


Low drift dc amplifier of non inverted gain 
Ko. 
Integrator. 

Summing amplifier. 

Trigger and triac circuits for controlling of 
filament current. 


Turn on characteristics of SCR and triac. 


Load voltage waveform. 


Block diagram of the electrometer and recorder. 


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Figure 3.16 Block diagram of the control circuit. 76 
Figure 3.17 Curve plotted between I, and Vee 78 
Figure 3.18 Block diagram representing the trigger and 

triac circuits. 79 
Figure 3.19 Block diagram of the linearized system. 80 
Figure 4.1 Instrument set up for frequency response test. 84 
Figure 4.2 Bode diagram of the recorder and electrometer. 85 
Figure 4.3 Bode diagram of trigger and triac circuits. 87 
Figure 4.4 Block diagram of the control system with 

calculated transfer functions. 89 
Figure 4.5 Total response of elements from the trigger 

circuit forward to the recorder. 90 
Figure 4.6 Bode diagram of the open loop transfer function 

for Ko=l (solid lines) and that of the compen- 

sated system (dotted lines). 94 
Figure 4.7 Insertion of compensation network. 97 
Figure 4.8 Root locus of the system. 99 
Figure 5.1 Step response of the compensated system. 102 
Figure 5.2 Ramp function responses Of the compensated 

System at various ramp speeds. 104-109 
Figure 5.3 Ramp function response of the compensated 


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Error signal (V-) for a ramp input. 
Filament current (I,) for a ramp input. 
Bombarding electron current for a ramp 
input. 

Thermistor bridge calibration curve. 
Differentiating circuit. 

Helium desorption spectra for incident 
ion energies of 100 to 500 ev, at 


14 


constant dose 1x10 ions/cm, heating rate 


6503-0/5eC, 
Helium desorption spectra for incident ion 


energies of 600-800 ev, at constant dose 


14 


1x10 ions/cm“, heating rate 7.12°C/Sec. 


Argon desorption spectra for incident ion 


energies of 200, 500 ev, at constant 


14 


dose 1x10 ions/cmé and heating rate 5.25°C/Sec. 


Argon desorption spectra for incident ion 


energies of 800 ev, at constant dose 


14 2 


1x10" ions/cm” and heating rate 6.7°C/Sec. 


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CHAPTER I 
INTRODUCTION 
1.1 Preliminary Remarks 


In the study of outgassing and surface properties of metals 
and semiconductors an inert gas ion such as helium at different doses and 
energies may be used to bombard the surface producing defects to its atomic 
lattice. The gas atom finally either becomes trapped within the metal 
Or escapes through the surface with reduced kinetic energy |. Post 
bombardment heating of the target” is a useful technique for studying 
the trapping mechanism and location of injected ions. Heating causes 
escape from the trapping configuration, migration to the surface and 
effusion from the target. The desorbed gas pressure measured in the 


system when plotted with time is referred to as a "desorption spectrum". 


Mathematical analysis of the desorption spectra is of a 
reasonably tractable nature, when the surface temperature is a specified 


function of time. The information obtained from the analysis includes:* 


a) the number of the various desorbing phases and the 


population of the individual phases; 


b) the activation energy of desorption of the various 
phases and 

c) the order of the desorption reaction 

Four temperature functions that were used to analyze the 


desorption spectra are’ 


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if a - 


a) a step function temperature HS a, 


b) a linear temperature increase 


with time (T=T tbt) 


c) a reciprocal temperature decrease 


with time ( += + - bt) 


d) a series of step functions of 


gradually increasing temperature 
[T=T +7 {u(t)-u(t-at) HTo{u(t-at)-u(t-2at) } Macnee 


4 T,fu(t-(n-1)at)} ] 


Generally speaking, thermal inertia associated with the surface 
produces an exponential function of time [T=T,+1'(1-e-*/*)) rather than a 
step function temperature increase. Then analysis of the desorption 


becomes complex and this temperature function is rarely used. 


The linear and reciprocal temperature functions are the most 
widely used functions which will considerably simplify most of the analysis. 
The fourth temperature function is also of some importance and a temperature 
displacement schedule approximating to this function has been employed by 


and Kelly’. It was also used to analyze the desorption 


Burtt et al. 
from a continuum of heterogeneous sites of different desorption energies 
where the linear and reciprocal temperature/time function lead to a 


quantitatively intractable evaluation’. 


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1.2 Mathematical Analysis Background 


P.A. Redhead® has given a detailed analysis of methods for 
determining the activation energy, rate constant and order of reaction 
from the desorption experiments using two heating schedules, i.e. a linear 
and a reciprocal time/temperature variation. In addition G. Carter’ 
describes fully the generality of the numerical technique for the analysis 
of continuous energy spectra and its application to various other 
investigations involving a variety of surface temperature/time schedules. 


Some important results will be quoted here to show the advantages of a 


linear temperature/time function. 


The Maximum Desorption Rate 


The rate of desorption from a unit surface area is 


N(t) = - $2 =v, o” exp (- fr) (1.1) 


desorption rate (molecules /cm-/sec) 


where N = 
O = number of molecules desorbed (molecules/cm*) 
n = the order of the desorption reaction 
Va oe rate constant 
E = the activation energy of desorption (K cal/mole) 
R = gas constant (1.986x1079 K cal/mole °K) 


T = absolute temperature (°K) 


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For a linear change of sample temperature with time (T=T tbt) 
and assuming that E is independent of o, the above equation is solved 
to find the temperature (T,) at which the desorption rate is maximum. 


Then : 


E/RT = (v4/b) exp(-E/R tT) For n = 1 (1.2) 
= (20 v,/b) exp(-E/RT (1.3a) 
pe ie p? bOVneoss 
O.V 
= R= exp(-£/RT,) (1.3b) 


where c= initial surface coverage 


o,= coverage at T 


p p 


For a first order desorption process in which the desorption 
rate depends linearly upon o, i.e. there is no interaction between adsorbed 
molecules in the desorption process, the relation between E and Ty is very 


13 


nearly linear and, for 10 ~ > v4/o > 10° (oK7!), is given to + 1.5% by 


Vv 
E/RT, = tn ba Bag oe GA (1.4) 


taking the first order rate constant v, = 10!3 secu!, 


Carter derives the temperature at the maximum rate as : 


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In order to obtain the initial site population o,, equation A ed EE 
integrated to give 


iF 


. E 
ASG expl -v, {| exp{ - prt dt] (1.6) 
0 


This is eventually solved as : 


o bE 
dEcombleeey 7 
p Te 


Thus the initial site population Oy can be deduced from the 


maximum rate itself. 


For the second order reaction the rate equation becomes : 
r E (1.8) 
dt ~~ ¥2o expt- pF} ; 


The approximate expression for the maximum desorption rate is 


given as 


It can be seen that the complicated expressions are solved 
and approximated by simpler ones to obtain the required information 
when an appropriate temperature/time function is assumed. It is therefore 


desirable to have a linear temperature/time relation for simplifying the 


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analysis of desorption spectra. Furthermore, the linear temperature/time 
relation will clearly distinguish different peaks on a desorption spectrum 
which will help determine the order of the reaction simply by visual 


akamination >: 


1.3 Objective and Scope of the Thesis 

This thesis describes the design of a controller capable of 
heating a stainless steel sample at a linear rate from room temperature 
(25°C) to the sample melting point with due regard to simplicity and 


economy. The prime requirements are: 


1) Linearity in the temperature range of interest from 


25°C up to 1200°C. 
2) Variable heating rate from 5°C/sec to 25°C/sec. 


The required specifications of the controller may be separated 


into two parts as follows: 
a) Transient response requirements 


In general it is desirable that the transient response be 
sufficiently fast and be sufficiently damped. For a step response from 


25°C up to approximately 1200°C the following quantities are required: 


1) Rise time (t.): The time required for the response to rise 


from 10 to 90% of its final value should be less than 5 sec. 


2) Settling time (t.): The time required for the response to 
decrease to and stay within 2% of its final value should 


be less than 15 sec. 


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3) Maximum overshoot (M,): Maximum overshoot should be less 
than 5% of the input amplitude, i.e., less than 60°C 
which corresponds to a damping ratio of between 0.7 and 


Oe 
b) Steady state response 


The output ramp response of the system should exactly 
follow various input ramp speeds but with constant steady state error 
in temperature. Although no stringent limit on this error is required, 


it should be kept small. 


After designing of the controller, its stability and per- 
formance are investigated, and final specifications are determined. The 
final system is later compensated to obtain the required stable per- 
formance. Results are then presented in the form of linear temperature 
versus time curves. Some desorption spectra obtained by use of these 
linear temperature/time functions are shown to demonstrate the capability 
of the controller. The results are compared with those obtained 


previously. 


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CHAPTER II 


HEATING PROCEDURE AND DETERMINATION OF 
PROCESS TRANSFER FUNCTION 


2.1 Introduction 


In this chapter a suitable heating method is chosen. There- 
after the "plant" is arranged according to this method and the actual 
transfer function of the thermal system is determined. The outline of 


this chapter is as follows: 


Section 2.2 describes the heating procedure together with 


some background information. 


Section 2.3 reviews the previous heating method and the 


results obtained by Burch® 


Section 2.4 describes the ultra high vacuum chamber and shows 


the arrangement of the thermal plant components. 


Section 2.5 considers thermocouple accuracy and choice of 


thermocouple. 


The actual thermocouple used is described in the concluding 
portion of section 2.6 and in the last section (2.7), the actual transfer 


function of the thermal system is determined. 


2.2 Heating Procedure and Background Information 


An electron beam is selected as the heat source to heat the 


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target because of its being almost contamination free and because of its 
extremely high temperature capabilities. Thermionic emission is the 
source of electrons. In principle, energy is imparted to free electrons 
in a thoriated tungsten filament by heating the filament. An increase 
in filament temperature increases electron activity and average velocity 
and enables the electrons to overcome the restraining forces at the 
filament surface and thus escape from the filaments. The emission 

from the filament would therefore depend upon its temperature and its 
work function. The thermionic emission current per unit area of 


emitting surface is given by the Richardson-Dushman equation: 


W b 
J = AT? exp (-,2) = AT® exp (-72) (2.1) 
where J = current density in amperes/cm, 

A = aconstant. For tungsten A = 60.2 amp/cem*-deg. ©, 

uN) = absolute temperature (°K), 

Sanaa work function at absolute zero. For tungsten 

Oe 4.5 ev, 
k = Boltzmann's gas constant = 1,381x107!® erg/°K. 


When a target at a high positive voltage is placed near to 
the filament the potential gradient between the target and the filament 
causes the electrons to move and be accelerated toward the target. The 
target surface will be struck by electrons of high kinetic energy. Most 


electrons will come to rest within the target and most of their kinetic 


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energy will be converted to heat. Secondary emission is also caused 

by the bombardment of electrons. When this happens, the striking 
electrons may knock one or more electrons out of the target material, 
giving rise to a reverse component of current which, in effect, causes 

a part of the kinetic energy of the primary electrons to be lost. 

Thus the heat energy delivered to the target will be reduced. The 
velocity of secondary electrons is for the most part very low and they 
may be attracted back to the target or to nearby materials. All 

metals have a low secondary emission at low primary electron potentials. 
The secondary emission yield (cs) of any material is defined as the 

ratio of the total number of secondaries per primary electron; & reaches 
a maximum value at a certain primary electron potential ED (max)? 
usually perween 200 and 400 voits for most of the metals. Beyond 

ED (max) secondary emission decreases slowly and becomes constant at a 
value between 50 and 95 percent of the maximum value’. For type 304 


Stainless steel (clean) after degassing 6 uo aitsty as 


ae P(max) ~ 500 volts 
i 


and at ED = 1300 volts, 6= 1. At the maximum of secondary emission 

it is believed that the majority of the secondary electrons are liberated 
from a depth of several atoms into the metal. Beyond this potential 

the primaries penetrate still farther into the metal, and the probability 
that electrons knocked out of the atoms at this depth will reach the 
surface decreases, with the result that the secondary emission decreases .° 
Thus it is apparent that high positive target voltage has advantages 


in that it reduces energy loss by secondary emission making target heating 


more efficient. 


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By increasing the filament heating current the number of 
electrons liberated from it may be increased. More total kinetic 
energy is then delivered to the target and its temperature will rise 
accordingly. Therefore,it appears possible to control the temperature 


of the target by varying of the filament current. 


The configuration between the filament and target is like 
that of cathode and plate in the diode vacuum tube. For two parallel 
plane electrodes the space charge saturation current density is given 


by® 


2.335x107° Ere 


J = oy ee Ss Ampere /cmé (252) 
X 


where Ep is potential between electrodes (volts), 


x is distance between electrodes (cm). 


This equation constitutes the Child-Langmuir space charge law. 
When the cathode is a filament instead of a solid cathode, a number of 
effects contribute to making the behaviour different from that with a 
solid cathode. The most important effect is the voltage drop along the 
filament, which may cause considerable divergence from the simple three 
halves power law of plate current versus voltage as expressed by equation 
(2.2). Several correction factors have to be added to this expression® 


to take account of the elongated filament effect. 


For every constant value of cathode to plate voltage there is a 
certain value of cathode temperature (corresponding to a particular 


filament current) beyond which the plate current will remain virtually 


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constant as the cathode temperature is increased further. Under this 
condition the emission is said to be space-charge-limited. The nature 


of this saturation is shown in Fig. 2.1. 


EDA 
a3 
f= 
- 
= p3 
— 
oO 
eB) 
~ 
= b4 


filament current 


Fig. 2.1 Diode plate current as a function of filament current. 


In a small region between zero filament current and that 
corresponding to point A (fig. 2.1) no electrons are emitted by the filament. 
Hence if the plate or target current is to be controlled by varying of 
the filament current, the proper operating region must be the region 
between point A and point B, i.e. in the unsaturated region. In this 


region target electron current is given by® 


Ip =b- e WI (2.3) 


where b,g are constants, 


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I. = filament current. 


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Another expression which fairly accurately agrees with the experimental 
results over a portion of the range of I, is 


m 
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where c,m are constants that depend upon the surface area of the emitter. 


This equation is preferred because of its simpler form. 


In heating the target it is more desirable to use filament 
current control rather than target high voltage control because 

a) the quantity of emitted electrons may be controlled more 
directly and easily by only small changes in filament power. The 
effective gain of this process is usually much higher. 

b) The amount of heat delivered can be made high by setting 
the target voltage at a sufficiently high value. The target temperature 
can be controlled from room temperature up to the desired level if 
filament control is used. This is impossible if only the target high 
voltage is varied. 

c) There are many other limitations in varying high voltage, 
7.@., narrow variable range available from the power supply, breakdown, 


danger in operating near high voltage and the complexity in varying and 


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14 
incorporating the high voltage power supply into the control system. 


2.3 Previous Work Review" 


It was determined previously that the specimen heating rate, 
produced by applying a high current directly to the filament and with 1500 
volts applied between filament and target, was approximately linear and 


given by 


Tbs peed ot] 00 (225) 


A deviation from linearity of less than 5% over the temperature 
range 100 to 500°C was assumed. The entire temperature curve was said 
to be more accurately described by 


3 


T' = 1.179x1075t'3-0.388t '24+32.8t'-55 (2.6) 


where t' = t-5 sec , 


T° "= T=30°C. 


The main disadvantages of this procedure are: 

a) the linear temperature-time function derived in equation 
(2.5): is only an approximation for the initial part of the exponential 
temperature rise. The equation (2.6) is not a linear temperature-time 
function and is too complicated. 

b) the heating rate as obtained depends solely on the thermal 


inertias of the filament and the target, on the rate of heat loss from 


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15 


target and filament and on filament radiation to the target. These 

characteristics cannot be varied. It, therefore, becomes more difficult 

to fully analyse desorption spectra for a range of specimens and temperatures. 
c) the temperature-time linearity over the whole temperature 


interval of interest cannot be maintained. 


2.4 Thermal System Configurations 


2.4.1 Ultra-high vacuum chamber 


The design and construction of the ultra-high vacuum system 


and its associated parts have been described in detail earlier’. The 


system was designed for pressures of 1x10 19 torr. The essential part 
is the bakeable type 304 stainless steel experimental chamber six inches 
in diameter by twelve inches long. It incorporates ports at various 
positions to be used for mounting of gauges, mass spectrometer, pumps 
and other temporary instrumentation. Some of the ports are used to 
insert components into the chamber. The volume of the main chamber was 


found to be 8.85 litres. Figure 2.2 represents its cross section 


Showing target, filament, and ion gun arrangement. 


2.4.2 Filament and target arrangement 


The filament was made from fifteen turns of 0.010 inch 
thoriated tungsten wire wound into a coil of about 1.6 mm diameter and 
enclosed in a stainless steel box of width 1.8 cm per side. One open 
Side faced the target and was approximately 1 cm away from it. The 


reason for using thick wire is to enable it to withstand the erosion 


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caused by evaporation and by positive ion bombardment at energies 
corresponding to the high target potential. The positive ions referred 
to have their origin in residual gases in the chamber and from the 
target itself. Another advantage is that a thicker filament would be 
less likely to fracture through brittleness caused by crystallization 
at high temperatures. Outside the box each tungsten wire was wound 
together with a heavy stranded copper wire protected by ceramic tubes 


and passed through a hole made in the bottom side of the box. 


The wires were extended and clamped to a two-lead, high 

current feedthrough. The aforementioned structure was supported by a 
Stainless steel rod of approximately 0.15 cm in diameter as shown in 
Fig. 2.2. The box was electrically connected to a copper feedthrough 
by means of a stainless steel supporting rod and placed-parallel to the 
back of the target. This arrangement fixed the stainless steel box 
essentially at the same potential as the enclosed filament. Hence, the 
electron beam could be more uniformly focused towards the target and 


the temperature gradient across the target could be minimized. 


The target used was a square plate of type 304 stainless 
steel approximately 1.5 cm x 1.5 cm x 0.056 cm. A 0.2 cm diameter stain- 
less steel supporting rod was carefully spot welded to the edge of the 
target to minimize heat conduction losses while the other end of the 
Supporting rod was attached to a Kovar feedthrough. This target support 
system also acted as a ground return lead for the electron bombardment 


beam. 


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2.5 Thermocouple Accuracy Considerations 


The only practical and possible way to measure the target 
surface temperature is to use a thermocouple. This method has the 
disadvantage that with the target and sensor at high voltage some portion 
of the instrumentation associated with the sensor must be at high 


voltage. Breakdown, leakage, safety and convenience become problems. 


Two types of thermocouple material were considered for the 
application, type R-Platinum/13% Rhodium (+) versus Platinum (-) and 
type K-Chromel (+) Alumel (-). It was found that at a pressure of 


10° 


torr,a type R thermocouple made of fine wire (.002 inch in diameter) 
could not be used because at temperatures greater than 500°C the 
thermocouple emf would drift negatively followed by mechanical failure 
of the platinum wire at a point near the target where the temperature 


gradient was highest. 


At this high vacuum, the high temperatures caused excessive 
grain growth? which rendered the platinum susceptible to contamination 
thus causing negative drifts in calibration and also resulted in 
mechanical failure of the platinum element. Negative calibration shifts 
may also be caused by diffusion of rhodium from the alloy wire into the 
platinum, or by volatilization of rhodium from the alloy. A type K 
thermocouple (0.025 inch in diameter) gave satisfactory results at the 
pressure range of 107° torr but the heat loss to the thermocouple was 


high and its larger diameter reduced the sensitivity and accuracy. 


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Neither thermocouple is recommended for long term use in a vacuum because 
of preferential volatilization of the constituent metals in the 
thermocouple and diffusion of impurities from the sample and insulators 


9,10 


near the thermocouple Thermal cycling is also one potential cause 


of errors 9, The trouble was traced to precipitated impurities in the 
wire. Yet another possible cause of error is the presence of inhomogeneities 
in the wire !? in a region where there is a temperature gradient. The 
inhomogeneities may be present in the wire as received, or may result from 
contamination of the couple by sample or electrode material when 

welding, by diffusion of the sample material into the couple at high 
temperatures, or by cold work in bending or stretching. In general it 
would be expected that a fine thermocouple wire would be more susceptible 
to errors from inhomogeneities than a larger diameter wire because for 

a given size impurities will occupy a larger proportion of the cross 
sectional area of the wire and there is a lowered probability of averaging 
by pure metal that bridges the impurity 2, A second disadvantage of 

fine wire, particularly in the absence of a thermocouple protection tube, 
is that its high surface to volume ratio results in a very sharp 
temperature gradient due to radiation from the wire at the worst possible 
place near the weld. The high temperature gradient of the fine wire 


can lead to the mechanical failure of the wire. 


Due to the complicated structure of the vacuum chamber and 
the requirement that the system must be vacuum tight the reference junction 
of the thermocouple had to be left at a point inside the stainless steel 


chamber distant from, and much cooler than the target. The junction temp- 


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erature was determined from a thermistor bridge reading. Actual 
calibration of the thermocouple under the conditions of use was found 


to be impractical. 


On the basis of the preceding facts, one can see that it is 
not possible to claim any high accuracy with this type of temperature 
measurement, Since its accuracy always becomes degraded by conditions 
of use. Since no other suitable method of temperature measurement is 
available, a thermocouple must be used. To obtain reasonable accuracy 
despite the disadvantages mentioned, measuring instruments must be 
carefully aligned, leads must be carefully dressed, and manufacturer's 


emf data must be used. 


2.6 Final Thermocouple 


Despite the disadvantages of fine thermocouple wire it is 
desirable to use aS small a wire diameter as possible in this application 
to minimize heat loss. Such losses cause nonuniformity of temperature 
across the target and slow transient response. At the same time the Pt. 
wire should be thick enough to avoid the aforementioned mechanical 
failure and withstand small leakage currents passing through it accidentally. 
For the same reason, no thermocouple insulator tubes should touch the 


sample in the immediate vicinity of the spot measured. 


The final system incorporated a Pt/Pt-13% Rh (type R) thermo- 
couple with manufacturer's characteristic as shown in Fig. 2.3. Each 
side was made of five 0.002 inch wires wound together and welded near to the 


centre of the rear of the target, i.e. facing the ion gun. The ceramic 


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re niin a ee ey ee, e 4 aati ‘ Sas ‘ 4 + hk ae acl 
Aendem Sapors heme tort fy Ove OF ipuons ASE oo 27 0¢ 


: ; - 4 vis wi od mr * aw - ews sy . st an: * + bb bees ta 
tSsnsHbiToos < MpuUONNS e260 2tHS YU SPAABS! flame baésensiiw DAB 
=! 
ls. sakdut “ater \ oe Pee ‘ie 
vote esdud totsluent siquogamishs on ,Nors2) shee 


$9\ 29» £ batsrogroont sneer Ne font? oT 


of a Tian | woerene 2! nanos ones tm 
a _ a ae 


. Ne 


1700 


1600 


1500 
1400 
1300 
1200 
1100 
1000 


900 


degree (°C) > 


800 
700 
600 


500 


0 2 4 6 8 10 12 14 16 18 20 


Thermocouple emf (mV) 
Riges2;3 


Temperature-emf characteristic curve of type R thermocouple. 


2] 


$4} —— 4+ — + + + + 
aa 
or 


a a 


aeaucs (.ck> 


22 


tubes attached to the supporting rod of the target were used to protect 
and carry the wires to an 8-pin Kovar feedthrough where the reference 
junction was formed. This Kovar feedthrough conducted the thermocouple 


emf out of the chamber. 


The temperature of the reference junction was measured by 
placing a small glass coated Fenwal thermistor GASIL3 specially designed 
for precision temperature measurement, near to the junction, and connected 
to the outside bridge circuit by two Kovar feedthroughs. The resistance 


bridge circuit is shown in Fig. 2.4 


QV 


thermistor GA51L3 
1O00K+1% @ 25°C 


Fig. 2.4 Thermistor bridge circuit. 


if ot borlostts 2edut- 


see BAN tink tas we nf 
att Fo Hor prigvoqque ons 


. bs2y ovew top . 
- « 4 5 q | : 
7 ies A { ‘ yoy A S97 16¥ o ¥ FG 4 iG Id STEW ony tas ” 
‘ . " “ia a ese 2 A t? 
pat i ; 7 ; ubHd> Ap tibe | a3 thoke , 4 KY | af aq Pp oi TOT 26Ww nottonut, J 


« 


Sed en 


+n 4 
ra JUG 


+ 


Ft So VSPISI 


23 


2.7 Mathematical Modelling of the Heating Process 
2.7.1 Energy balance equations and the behaviour of the process 


The target is heated by the transformed kinetic energy of 
electrons striking its surface and by radiation heat directly from 
the filament. Heat is lost from the target by conduction through the 
target supporting system, and by radiant energy loss from its surface 
to the enclosed chamber. Because the target temperature is much lower 
than the filament temperature no heat is radiated from the target back 


to the filament. 


Consider the target supporting system as a homogeneous material 
with uniform cross sectional area A and length x. The temperature 
difference between both ends is ale) where T is the target temperature, 


At is the ambient temperature. The heat loss by conduction through 


this rod is 
= 2 a Sat 

q. = G(T Teh) k ; Gh te) (2.7) 
where 

Oks heat flow rate in watts 

G. = thermal conductance of the supporting system in 

watts/°C, 
k = thermal conductivity of the material in watts/cm°C. 


For type 304 stainless steel k = .1627, 


t 
£7 
re 


attiw nf stay welt geen = 


nl mpteye gnisvoqque sit to sonstavbnos tsmvant = 2” 
4d \eavew e 


ae | 


a | vs ¥ ‘ { 
pe YS pia a} 
2 . * 


of Stefan-Boltzmann law 


where 


24 


ht are in degrees Kelvin. 


Radiant heat loss from the target surface is expressed by use 


eke aoe 


50 radiant energy loss from the target in watts, 


o = universal constant = 5 73e10 8 watt/(cm*.° K*) 

A. = emitting area of the target in cm’, 

F,_(= Shape factor between the target and the chamber 
surfaces, 


te, = emissivity of the target because the target is 


completely enclosed and small compared with the enclosing chamber. 


For type 304 stainless steel ore 0.44, 


where 


Ut are the temperatures in degrees Kelvin. 


The energy balance of the target is given by the equation 

4 _4 d 
+ ge = G.(T-T,) +o Aye, (T-T2) + mc F . (2.9) 
dp = the radiated heat from the filament, 


dp = the kinetic energy converted to heat by electron 


bombardment, 


«Sree 1% pAs mort fast pedetber sag = : 


i 


3) - : ee ny! 
teen | ad sriavno3. p1aaa oe ent = 


25 


M,C = mass and specific heat of the target respectively. 


If the filament carries a current of I, amperes creating a 


voltage drop of Ve volts, the power input is Vele. This will cause the 


temperature of the filament to increase until equilibrium is reached 


and the heat generated becomes equal to the heat lost. Because the 


filament is a slender wire, little heat is conducted away by the leads 


and because of the high vacuum, negligible heat convection is possible. 


Most of the energy loss is by radiation. 


The energy radiated per unit time depends only on the 


filament absolute temperature and is expressed by the Stefan-Boltzmann 


1 


where 


ates te. 


4 4, 4 
P = Vel = oA ce cl ¢ (2.10) 
As = emitting area of the filament 


the total radiation emissivity. For pure tungsten 
at the normal operating temperature range of 2000-2500°K, 
ies 0.260 - 0.301 respectively. 


Te = filament temperature in °K. 


If the filament is considered as a radiant heat source having 


very small area and spherically radiating heat with constant intensity 


in all directions, then, from the filament and target configurations 


described earlier, the target area will roughly subtend a solid angle 


onfved sowor steel tnsrbsy 5 25 bstspfenod af Tee Ls 


yathenstat SRRPEROD iti Jeon ov ritsibes el isatvedge brs 5975 tha 


9 Ase st bos anamafit?) ily ments ont , snotdoottt Le: 
a 


LF wh 5 tournd yt 18 bed 


7 7, ' 
’ . 


26 


a steradian or less. This solid angle is equal to z of the solid 


angle subtended by a sphere, measured at the center. Because ede: no 
heat is reflected from the target to the filament. Therefore, the 


mean value of radiated heat absorbed on the target surface is 


Ve I, or less (2.11) 


o|— 


seb 


At higher target temperatures, the filament is operated 


at I, = 3 amperes, Ve = 8 volts. Therefore, 
] % 
p = G x 24 = 4 watts. 


The amount of electron bombardment heat is 


Qe > ED Ip watts (Zale) 


where ED high voltage applied between the filament and target. 
A suitable value for ED is 1800 volts. 


Ip = electron bombarding current. 


The value of I, corresponding to the previous value of I. is 


approximately 45 mA, therefore, 


1800x45x1072 


We 


81 watts. 


at 


(ft sit neswied bollqgs spayiay: horn aa 


f 17 \ oF “ As Kite 7 y 
sfov OOST 2f .5 Ot sulev Sfagsirve A 


feuca 2+ afpne Btfo2 att .eeof yo netbetas2 
gis: A+ 45 bayienon , 9° 2 6 VG obnoetdve sfpns 
jneme!?t aft os s4pxeF ont wort bstoetrsy 2 

"5a 7 io beard. 1s 4 ‘i bote That TO outsv 


= i 
sal ag 7 4 
ces iv } J P. i’ 
‘ - 


4 fy 3 


tS | 7? iz ’ oe §,] b is) 08 iS ed faa Fe 1ORQi n tt 7 
' 
1 
; 


-sorova| los hove = a ¥ ¢ cOTSgaes c " i 


: _ 


- 
a it : be rm 
man p . ar 
‘ , yr 
’ 4 pare pl A © mv cy: - ~ = 
H Ife ' L 7O4 roy : rt ae) ru ar mi 
= : 
+ ~ ~ 
2 NIBW 4 3 ‘ 
a4 gq q~- 37 


t 


onibyedwed rorfosie”= 


notesatt chm SD yor 


i ‘ 


aritxe 


= 


27 


Hence dp = 20 qp at I, = 3 amperes. 


The radiant heat occurs immediately when power is applied 
to the filament and before the electron bombarding heat begins. It is 
likely that this effect helps eliminate the insensitive region before 
point A as shown in Fig. 2.1. The amount of heat radiated depends on 
the power input to the filament which is rather low and constant. This 
can be explained by looking at the emission equation (2.1). The 
exponential term accounts for most of the variation of emission with 
temperature. In the case of tungsten at 2500°K a 1% change in temperature 
changes the 7 term by 2% but changes the exponential term by 20%. 
This causes the emission-temperature function to be a very rapidly varying 
function. The power applied to the filament is therefore changed 


only slightly for a large change in electron emission current. 


At a target temperature of T = 1300°K the radiant heat loss 


can be estimated from equation (2.8) 


[Re 8 


Gq, = 5.73x10 °° x2x2.25x0.44x(28561-81)x10 


I 


32.4 watts. 


By estimating the effective dimensions of the supporting 


cm, the thermal conductance is 


Zz 
rod as being 2 = 5cm, A = n(Pet) 


2 


6. = 0.16270 (924) ‘ 57 1.47x107 


3 watt/°C 


. : 
y ; 
v 
. +e ° vat ; 
sta HB Oo 9) Ie «fa f ~ 4} ian 
; 
1 ’ " ln iT 
1s; : ‘ : 7 oom Ot} 7 OT : 2i4 i 
‘ « nt 
. 7 bn nome le? € “ot 
5 atbysanod rovtoele sfd avoTsda DAS TAOMBIT) ort ot 
: j 
15 
a3 b'} Ce en ae ee. oe ee ee es met , 
; : ¥} ot O07 Sfyrn 1S rae IQ8TTe ¢€fhs gPitd foatt 
4 * 
. - ~ i= * \ bi 
uh: » TCHS i] Jf era nt fwotd 26 A satoq 


J ~~ 2a 
ft : eat ari 1 3 re moO} Va HIT Ei GX 
“f 2 > aA +* oe vis 1 we fk 
: Af t wild  ¢ roth ie 6 JT Vai UM ? 5 
‘ ‘ Ia ' ¢ 
i by IGS» sh | : +¢ 26D ng i . Sot 
J j & 4 . > a 
WOR I J is } iry3a j itd 
7 ; he - L yo yoy Aor + we 
: - A Ct : + Biat) iat Q7 J 4 i ij — )7 nd < mao Ong - 
: ” 4 r -~ 
| rier: racing {t+ add ot bathdas swag on 
”~ ” , a F 
P rmtus NOFEEThHys Ao a it IPD OSS, fa Ea & WT y 
~ r r : : + Me i 
: is mei / ; YW SW Gio J ee a : 
Di , s a ‘ 
i > +> » oo ; ‘ > ra Fes e ie hal - 
Lo.) MOTTPSEVPS Moy hota tes ad ie: 
2 ; ay. ¢ eo . a 
Onp fre aIGC} Os Auto a rie 2 
t 21 fae » Lec Ne 4 GI ot —= “P 
¢ 


=" 4a. A ro 
eI BW FLAG 


oransmth svisjzetta oad pattemizes ya 


j2 ond To 


en 


iu ii : , . . S : h ; a : : - Me 
: _&. Sb . eds we met 
a: sit add i ( 3 By = A dod = 8 ontod ae bo 
| -_ hile ae tal a 2 


7 : 7 


28 


Hence the conduction heat loss is 


3 


1.47x10 ~x1000 


te) 
i} 


1.47 watts 


which is only 4.35% of the total heat loss. 


If this conduction heat loss is neglected the thermal 


energy balance equation (2.9) is reduced to 


pene 4 _4 dT 
Qptde = oA,e,(T -T,) + MC ae (2eis) 


At steady state & is zero and the temperature of the target 


is 


4 
F OptaptoA,e,T 1/4 


u (2.14) 
h oA e, 
During the cooling period the thermal energy balance is 
4 4 dT 
Ae], = oA,e,T + MC at (215) 


Equilibrium temperature is 


r F 
_ 
: ; ; pay 
’ S i es eat ry 
| e70! tesf nattoaupaos Sony sonSsn 
ike Be i F 
\/} }T* ' Vred = owl 
« 
siypouw VTR4 
of 4eo¢ tas ont 7 ac hk viao 
Oj 6351 ; ts i 
P P . 
nt bejoslpan, 2p zeal teat qorTowHneS 2 ri 
“ ' Tv. te he io ¢} mor tT + 
Os i? boo" i~ athe J Diehl 
= 
as - b % A. < r 
a : ' : : V) a ape ) —4 rab 
7 & Ls J od 3 
iy ? 5 OFS5 2 FF Sic Yt S306 JA 
< ba ; A, oy 
’ : | ore gf ts a 4 
{ he? * , 4 4 hd 
et | 
‘ Au fj 


i grid bOFISG 'S 


Ne 


f 


iffooo sit ontyud 


a 


- 


29 
oALe 1" 1/4 


2 t*tia s 
Ly i. oA,e, ) es (2.16) 


Equation (2.13) can be rearranged as 


eee Ce ee ST (2.17) 
an(1~ att rh) 
A Ay 

where Q) = QptactoA,e,T.. (2.18) 


Equation (2.17) is integrated from ambient temperature Ls 


up to any temperature T as follows: 


MC 
si Sg po ata tl Al (2.19) 
| aeey 4 


The right hand side integrand can be evaluated by a conventional 


method and the exact result is 


MC 1, T: ath aki 
t = ——--,- T. (are tam - arc tan—2 ) + =" (an wah gn h a) 
q h T T 2 eet T,-T 
26A.¢é.1 h h h hoa 
Grverh 
(2.20) 


A simplified form of this solution obtained by knowing the 


nature of this problem is!! 


a 
i] 
’ 
=, a 
> ; Ar - 
} 
i 
L\ f > 
: \ r Ay 
63° vie 
; | = ome i eer 
6 ‘. PNA a 
41 4 : 
: te en rn i 
Hh DSRib HS" Si) tt \ -a) TOrsm = 


banrstdo aorszutée 2efn: anot bervtlante A 


_ 


iv et me Fdovq afad to 
Aes" i 


| s 
: 


30 


i 8 ) e (2.21) 


In the same manner the simplified expression for the cooling 


process iS 


“t/t, 
De ee ee. = (2e72) 
A 3 
where ee MC/40A,€,T), (eige) 
IMCS AGR eT? (2.24) 
Cc tetra : 


The temperature at the beginning of the cooling 


process. 


It is obvious that the time constant of the heating process 
as defined by equation (2.23) is inversely proportional to the final 
temperature, or in other words, to the amount of heat input. Either the 
heating or the cooling process cannot actually be described by single 


time constants. 


For the purpose of design, all processes have to be linearized 
so that linear analysis can be applied. In the final design, adjustment 
of system parameters is necessary because the system cannot be described 


accurately in linear terms. 


2.7.2 Linearization and representation of the process. 


Equation (2.13) is expanded as 


i - 
ii ( 
: — 
 ¢ 
r\3- 
A?’ 
\ - y 
qa (. Te ,T} = ae ==9 
Lh 
| ; IT TOTES 1QXS: Osi rie fe ony YSnnsm SMbe Shy ? 
. at 
ov 4 
> 
3 “ oa r . Y 
a) { ~1 } : ' 
“A & 5 
; : 
‘ as és 
4) 49 Not wi a 
Tiny Ay ; . 
soc 3 
J i SETI ‘al oft t ’ abi sy ot j 1 r 
i 
an c } {j 4 
: ‘> tnetent wart , wt oO rydo 21 
a f tc : 7 JOTY OC 
9 
ra 
: en , ; +; ee Se 
iBNOrsyouod Vise ravi ef (€$.8) vorysul So VO baniteb & 
¥ ; Te ae eer er ee 
Sj nic: oon 3 Bofl TO JNhOMs Sn OF .éByuW ano Tl YO «8 vis oqmed 
= ‘ anil y 
sipnie vo 6 Py 26 Ts y{ i suga6 tonnes 22390%0 pit foao, en TS ont tsar 
: in 
s OW rBjeNGD 
y =) 
a Ps } . ¢ se c , a fi 
baxfyseni!) 4d oF svar asoo19 [ls ,.fotesb to seaqtuq ant 707 + Le 


rs 


+ 4 “oo . 6 5 ; Lat s : = a * ae 
- Sosnbeyibs .agtzeb fant? add ml .batiqgs sd nso_eteyiane sent! Tend a 


_ =. = ry : : 7 aie : ; 7 a : 
sdtiszsh od Jong) mateye edt s2uscod yisee2gnert et eigtamsTeq. matey | 

ap? CBr = a <i " he : : 

7 (i : [is . 


3] 


e Bae, dT 
Onde = Apes (T +7, )(T+T,)(T-T,) + MC oe (2.25) 
Let 
Pee tPTo Niet.) = -.G.(T) 
Cet a a t 
Assume a mean value of T = T which is constant. Then, 
G(T) = G, is constant. Also let Q = Gptde = heat flow input. Hence 
- &(T- dT 
2 its SL Ug AL (2.26) 


Rearranging and Laplace transforming this equation yields 


ThG eee Ls = 0 + GT 
t G tea 
t 
7 
] a 
T=Q . 
Gece) le ae 
c iG 
t t 
Ly 
G 1s 
eG tSt] ‘ tSt] (2.27) 
where. 7. = es a time constant. 
G 
LE 


Both Qp and dp are functions of power input to the filament 


(12R,) and vary in the same direction. Each amount may be approximated 


to be directly proportional to I, within its operating range. Therefore, 


Suish 
eC er! 


ent "Sawod to 2 
Dita 


i ™ vita sth a 


a 


and 


B 


T,S*] 


eto) 


Ge iF 
where A,B are linearized gains at steady state, 
Te is the heating time constant of the filament. 


From the previous discussions it is clear that Op is rather 


constant and less than qe: Then A < B. 


The linearized heating process as described by equations (2.27), 


(2.28) and (2.29) can now be represented by the block diagram in Fig. 2.5 


Fig. 2.5 Block diagram of the heating process 


a3 


This figure also includes a transport delay "a" resulting 
from the physical separation between the heated surface and the thermo- 


couple junction. The electrical analog network !2 is shown in Fig. 2.6 


transport 
delay 


R / 1/G 


Fig. 2.6 Electrical analog network of the heating process. 


From the behaviour of the thermal system, it was found that 
heating of the target required a considerably longer time than heating 


of the filament. Therefore from Fig. 2.6 


- ~ 
{ 
' ; , 4 “ } a phys] ‘ oy" i et 
~ 4 - ; 
t j ; . oral — ‘ g : a {er} 
i SRS qg iM ) ? ue as 
| 
wy nolens ~y * ora | - f } , « 
i i ny WOT BITS 2: +) ° 
| 
\ 
: * * 
fOGCRS TT 
r % 
: i red a 
} -. 
- ‘ SS n / ieee ; 
. 7 : q t 
: ‘ , 7 j i] - 
a : i 
' =a < fi 
. - ’ 
a i % » 4 
; ¥y f 4 ~— j 
8 - i : i. ‘ a 
' : 
j j A Nene cecinoreniiar 5 
7 
H > , } ; 
ee a ene ee ae mw = 
, 
si = tan wA 7. rs «TZ a ¢ 
iJ mh 6 Wy Myi BIS [éo7 ID ia Gea 


mateye Ssoadt oft to qwotveted ahd mort 

: + — s . ” F "6, pee y a : 

enisser nsds omiy vsprol yldarsbfenoo 6 berhipey deprar oa3 Yo Entsaam 
: Ni 

pha mot svotevedT .tnamel tt 


34 


The dominant time constant of the thermal system is there- 
fore RC, and the response to a step input will be largely affected by 


this time constant. 


2.7.3 Approximation of the transfer function of the process 
a) Heating 


The transfer function of the process was estimated from a 
step response curve obtained by applying a step of input current to the 
filament and then recording the thermocouple emf output versus time by 
means of a Moseley Autograf Model 2D X-Y recorder. The responses for 
step filament current inputs between 3 - 4 amperes are shown in Fig. 2.7. 


The high voltage ED was set at 1800 volts. 


For the purpose of analysis of the step response curve, the 
filament current in the operating region was found to lie in the range 
between 2 - 3.5 amperes and mostly at 3-3.4 amperes. The step response 
for I. at 3.4 amperes was selected as the most representative one in 


the whole controlled temperature range. 


With C(t) as the exponential output response of the thermal 
system, the logarithm of |C(t)-C(~)| / |C(0)-C(~)| was plotted versus t 


the resulting plot (curve I of Fig. 2.8) behaves 


as shown in Fig. 2.8 
asymptotically as the straight line II with slope = .0438 and ordinate 
2.2 at the origin. The nonlinearity in the first time interval shows 
that this thermal system is not a simple first order one but chat it 


can be considered as such to a first approximation. 


ony jave femvedd odt To Jnetaheo om hisnineb ofT 
= : : dn : cVoett : i\ INS TANOD anirt s mniwy © 


~~ wt 


a) 
i betootis vfepas! od Il tw duqnt gate @ oF s2nogeey odd bos .0,f S107, 


} | -tnasenos anit atay 


* : * -" ss o f\  . 
nitomt vyarensat of! To Horse irxovagA a 


—- ht 


259019 any to. NorgongeT Vateney erT 


¥ 


a ~ 4 nt Fo -noofe é onivfaosn vd heate +h oyrrys senogeoy 


. \ i} . ‘ ra oll 
i | xy = - H i } if as i ae | a‘) 
_ © 7 4 = 
16 - ; G ' FARIS TS 
~ . _ r 
' t — ay 
it if 2 a5 ’ 765 ' 
+4 
» | 
* _ c _ 
‘ c= ho. 7 3 [ I < ) eit, iO” 
t * i ee -~ : ie P i, eos fh eed 
> ofl i ti ay Pa Mur Hy FaSTwWS Jen 
. os 
~ i aw B=) vs oe) += _ 
Sh ; c Sh . 5 *,.c- ' | Oe co yn ‘J »\ a 
c s - 
+ + ‘ : wy t ; 
; " \ : ah O8)Se iaté } -% a6 } 


‘ ; weit 7 F be Pass 
a i 1 Siwss 1 dai tu tJ ALS: 


+ evevev bettofa zaw jfe)9-(O791 \ |()9-(F9SP mete rege! sk mea ls 


@ovetiad (8.8 .pf4 to I sviuo) tefg ontefves onf .° Bs i nt one 


agote ddtw Li ontl tdphesta” ort er Tsarsosqmyes 


bo bas BED. 


rsa ta is mt. 
i tes 


FON i ita _ 0 ’ 


ha) 


08 


OL 


"SjUauAND JUsWeL Ly dazs 07 wWayshs LeuMay. aYyZ JO Sasuodsau yUaLsUeu] /*2 “BL4 


(spuodas) awLy 
09 0S Ov O€ O¢ OL 


OL 


LL 


(Aw) jwa afdnodowiay | 


N - 


( ZH) Kouanboss 


ies 
| 


ie Neel EES Eee la hel ks, 


SS 


' j t 
H 1 
SS Se te + 
ies 
' ‘ 


Sates za teetaters Sy al senate toe lessee ra 1 20a ea ed 
i f { i 
“ { t - ; t = { rot as { uel | 4 
Sas 5 a4 . Sun pincer - = ® | 3 el! awe { -- eae : ae 
' 7 H 
mi RES > . > pas Seen Pare | HSE oh Fees a zi bone = . a ap es t- 
Sloot = See tee Ee =A\s Sabato sets esas |B ote cies, a EI NEE = Sree ; pone 
Shi Srp “ a oe 2 eS SE aS a v= ee cee dnjooe nog | a : : = i 
cee i SBE Sioa : aS GueS meloaiel as = See ae aie at —— Gl ESA Wa ees ere) he SS eS Eee 
7 7 = + —— = ~--4 se - es oe Pasonil = : = i i t HN 
--4 am papes mere pb =. na en Ree ey St ees ees a ; SS S| eee 8 2S) PSRs Se rei es ; wot r 
--—+. ~ : : + = i 
am REISS, EH i +-f-——— ES) SEkSS Peet GS SeSt RSS Pe DN ee aes [ai PSS SES | } { tia 
~ po = Sas - SoS8 (SSeS Heese Fee ees : ft -« = Se SE (Pe ae es Tee fsa a Re = j oy { - 4 
ot Woes eee > aS Sas —p— 4 ~~~ -—— Bee Ses ae ee Se Ss ere See eed eees bee ee = 1 - ' } 
i EL eee HE ‘ a oe eee OSes eee aS! bee IC ier Seyi ie = Fed ET ae eS i aemecat 
eons ‘ . = = 
PR at es SSE } sk PEST iced Fo ae FS Tay Ee SEES OS KF RATES aan Is t sas = a as Ae ' ; er: 
fae SSE = Se SST es A cee: Be Be car ae ER : 2 4 rel 


- Time (seconds) 
2.8 Plotted curves for the determination of poles of the system. 


104 


F 


- a ee ee ee 
. ) pot. 


ht 
1° a-—4 4 
a re es be ; 
aa T ' } 
H } b 


le A I I mm 


2 ee ee ee ee ee ee ee eee eee Lot cnet 


For a first order system the transfer function is 


(- HE) 


37 


(2.34) 


(2.34) 


This is the equation of the straight line II. This yields’ 


~ 09 © - signe = - .0438. 


“~ 


nofjonut vst2eneud afd mateye vebyvo TeyhT 6 104 . 


38 


Normalized response % 


0 10 20 30 40 50 60 
Time (seconds) 


Figen 43 


Plot of curves I, II, III in linear scale. 


39 


This means that the function C(t) behaves asymptotically as 


2.2 t/10.1 . 2.207 099t | 
The chosen normalized step response = c(t) was redrawn 
in Fig. 2.9 together with the variation of the function 1 Bye oe 


which was asymptotic to normalized c(t). 


Next the logarithm of the difference between curves I and II 
| 


[ 
or log Chey - (1-2.2e EEANY 


curve through those points was approximated as a straight line as shown 


was plotted against time. The average 


by curve III in Fig. 2.8. The deviation of points from the straight 
line may be caused by the nonlineariy of the system itself, or by in- 
accuracy in the procedure which relies entirely on the accuracy and the 


measurement of the step response C(t). 


Curve III has an ordinate at 1.2 which corresponds to a time 


constant of 5.5 secs. The straight line then represents the exponential 


function 1.20 7t/9-5 = 1.297: 182t_ 


Hence the approximate expression for the unit step response 


OR 
C(t) = K(1-2.20 7° 999% + 1,297 182t) (2.35) 
wey laentee ie 
and that for C(s) = K(< - S+.099 * sta ? 


_ K(-.00014s + .018 
; See ae tet (2.36) 


ez 


as vi faotdodquyes. dovared Ole nottonut sdv tent ensom etaT ma a 
ea 
Fe80.- a Oe 
iS 
fe eat | eenogzey qote hast feamon nazora tT ope 
PS as sf nottonu? odd to notteryay ait dttw vadtspos @.S at nt 


Ad)> best lemon of of tosqmes 260 dot 


pwevbsy 26 


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ansyave afl .omrt tenieps baddelq 2a (20, “gS, S<f) - L322" gor 
nwote 26 rf! ddprevte $926 peFearxorgds Os 2intag sors Aquos | 

fiprait2 oat mort atefoq to notisived sAT B.S FT oF rit ov5u9 NY 
-nt vd vo .tisetr msteve sat to virsenhiron 6td yd Beewee od yen 
bose vosyweos ofS no Visattas 2o¢7a7 icy plo srubss67q arts nt 
.(4)9 s2ndgestt Gai? add to trem 


uit a ot 2baoqesiyes Astdw S.0 ts atentbio neveed TTT ayiud AG 


(etinsnoays odt etnaszovaet nsay sant taptsyre eft .asse 2.2 to trey 
ar ‘y ” , a 
TS8Y. gh, f = @ 2\2 sf aoe P 


senones: cote ttnw sit vot norezsiqxs siemrxongge @at Gone, — 


~ 


+ $00O.- 96 cory = (x9 -\ 


40 


The negative numerator coefficient of s corresponds to a 
positive zero in the s plane; it should be neglected because its co- 
efficient is much smaller than .018 and it is unlikely that this thermal 
system will have an unstable zero. This term, again, might arise 


from the inaccuracy in the procedure. 


Thus the approximate normalized transfer function becomes: 


G(s) _ __.018 
k (s¥.099) (s+. 182) (2.37) 


Once more it should be recalled that the position of the 
first pole is the more reliable one while that of the second pole is 
just an approximation of the combined effects of nonlinearities and the 


other pole contributed by the filament. 


Theoretically the method so far described is applicable to 
a periodic system of any order but its use becomes inaccurate and unwieldy 
for higher order systems. In this thermal system the previous method 
cannot be relied upon to give more accurate results if additional poles 


are extracted from the step response. 


b) Cooling 
The equivalent eiectrical analog for cooling of the target 


can be drawn as in Fig. 2.10. Since the heat source is absent, the 


od zbnocaer1o9. 2 to tnatolPhaoo wsteiseur svidapan on 


e nit . rn ie : 7 * 
vistifnw 2t tt bags 8f0. ned? vellome dowm ef Inefo ‘Ms 
-” ~ | rf ¥ 
| re fe ‘ : rae + ty * | 1k POT 4 as: att, re ov 5 j itw 
| oy shy cary ZY (i ont at Yost . aft & 
co tResS lv Sr 4 Y§ wk 7 
! . P “fT " eon ~mine tae sadT 
go ff OMA J eMsw bSsss) siya STsemexowGGs Sas cue! . 
: q 
i 
: _ . Wn 
xi igi}? 
eee Yara > rae 
\ 1, TEP YEE, Te] “ 
nae F r “ ‘ . » s ™ 
} PAT ae 5 bi, t 3 OBR tis) h rf aT FTV 
| ‘a tent al tdw r ha vos ae oe 
Jd o iw SiO Sy H a SYOn att } fog 
nF F, Lb ” ° 5 dite tea — 
} ; J at > 1D Stig JOCS SNE XO TGGQ¢ t 
Wa, 
Snamof ht} ott vd-bésudiviads si fog * 
- t,o r S29 ¥ : f t f ayy edt y 14 a) is QartT 
1 6neB 83 yey MHOD 49 ; Oo Von FO ine eve oFbot 
4 ’ 4 sid. 
' j tous Tamra rey bs me | joni to Sa , LY 
i" i mateve femreds ett nl .2mpteye asbio yvenprA 
9 . tb t effuesy stewwo0s svom evip oF noqp barley ods 


i genogeay qste_ ant movt bedos 


4) 


Fig. 2.10 


Electrical analog for cooling process of the target. 


current source Q must be disconnected and the previously charged C, will 
discharge through Re only. The linearized expression for cooling is 


simply an exponential decay asymptotic to the final temperature: 


rs * -t/t 
T= Of is + if (2.38) 
where A is the initial temperature at t = 0 
iP = final (ambient) temperature 


T time constant 


The time constant t can be determined directly from the recorded 


cooling curve by drawing a tangent line at t = 0. 


This line will intersect the ambient temperature line at t = T 
as shown in Fig. 2.11. From measurement the average T is 12.38 sec. 
The dominant pole therefore is at s = -.081 in the complex plane. This 
value shows close agreement(within the experimental error)with the value 


of the first pole in equation 2.37 . The most probable value was chosen 


+ sft to 2daotivg pntfoto sot oolsns feofydosTs 


} \ F ‘ 
eo Th nig YS DOIG RoOQ¢ TH aa ' \} Sa two 
lado ; aeraodat 
OT Ze WA M51 V6 fifa Sit) Ne 0 71 Provo st 
—, 3 
‘ 
f ¥ 4 . me de thn ps on fr 4 —e 
J > Via Hi" 3 Y8098) By Pity 3 
a, 
y é \ Fm , - - 
i ja \ i i | = 
» ie) iw 
: : : ar «a — 7. 
eo vee A) bod od oo ee a8 “4 | 


uteyeqiot (Jnotdmsp fantt = 7 


saptanoy aart ma iPy ins 


bebyo0s) 91 “ut vitoavib bantanagsh od ss + tnptEnoa) omit GAT ti 


q 


.O= 2% 36 9ntl Jnsened & — vd svt ne . 


hig 


anil aNviseqnies .tnatdns arts Pte. g2't9 ont tite ani baetaT 


— 4 


Rik gat Wwe woe 2 


meets, T49 spe aed Hey Sasi som hai 


42 


To 
Temperatur 
Y, 
0 12:38 = 7 Time 
Eigseccul 
Cooling curve of the target 
(arbitrary scale). 

as s = -.09. 


c) Steady state gain 


To find the steady state gain between the unit step input 
current I. and the output temperature T, Fig. 2.5 is analysed. If 


I, = ] ampere is applied to the filament, the steady state temperature 


will be 
Releange 
: A+B G ] 
T(te-) = T. + lim s. ——-.. — = (2.39) 
Be t,St] 1 +1 S 
= T_ + (A+B) R (2.40) 


where R. = 1/G,. 


43 


Therefore the steady state gain (AtB)R, = T(t>~)-T.. 


If the final temperature is measured and the ambient temperature is 
T(tos)-T 
known then the steady state gain a5 goer gL any value of I, can 
f 
be calculated. If it is assumed that the thermocouple emf is directly 


proportional to the difference between target and ambient temperatures, 


i.e. 
T(t)-T, = k Vey (t) (2.81) 


where Ve p(t) is thermocouple emf (mV) at time t, 


and k is a constant, 
KV (t+) 
then (A+B)R, = —=——— . (2.42) 
18 I, 


Hence the steady state state gain between Ven and I, can be 


found as: 


th etdag | (2.43) 


This steady state gain can change depending upon I, because 
of the nonlinear relationship between bombarding electron current, radiant 
heat and the filament current. The transfer function of the thermal 


system can be rewritten as 


44 


ee AASB)RE PeOIbDoaces 
Te . s+.09)(st+.18 (2.44) 


To find the steady state gain between the filament current 
in amperes and the thermocouple emf in millivolts, different inputs I, 
were applied to the filament. Ven was then recorded in each case after 
the transients had died out (t>5r). One problem inherent in these 
measurements was that the thermocouple emf dropped down gradually as the time 
increased. This created large errors in measuring the steady state 
temperature. The effect was evident when high filament current was used. 
This phenomenon is likely caused by: 

1) The increase in reference junction temperature due to 
heat radiated and conducted from the process. 


2) Secondary electrons and positive ions being released from 


the target more rapidly at high temperatures. 


The second cause listed above was evident from the gradual 
decrease in electron bombarding current as measured over a long time 
interval. Working at low current and taking data only once in a long 
time could reduce this error especially with respect to the first cause. 


A decrease in the electron current, however seemed unavoidable. 


The relationship between the electron current and the filament 


current as given by equation 2.4 is rewritten as 


i) F 
th 
| = | * 
il 
4l| 
ty 
i 
| 
Wy 
ii 
Hi sina A 
ni || ‘ 7 a : 
iW a cz 7 1“ Ml ‘ 
iI » » Sato | a3 
WI B.S = aiden ane 2 ee 
My of asthe | 
i) (8 ’ = i ,* & % 
| 
| | ~ 
i 
| i a fad ofan ate vbsete aig bak? of 
| ‘ . - fey . ra + on 
| } ra , ‘ f J Tj it, fi iia 9 rt we writ 3 3A3 eg 9G 
| t ie ~ é -_- 
; c moosy maddy 26H 4 od TYSRE ff ait OF beria 
4 : to (4 
—_ - aoe he oo) , oar , + nal on 
ron’ mgldoyva and +. (rds TUO BSID Hem eFASTeAs 
+ 
“ s 
poy ou! WA : ho tm Nya sri} Fani 2bhw 
we ar 4 ‘ Tw ~ - > hye + ~ ir rr rT 
p ; SIT? APT NShw ishive 26m Josette st 
2 _ - t r ate 
icy ve ba2uea Yiowel af x 
™~, 
- 
| oe . r 
i J = 3 t a \. Fi me tar y 'y Ste boi if or f 
— a Sed 
peageny of ot teatoubribo bre © 
¢ ' er : " ra a enn’ fe 
1 et ng 52.8) i f te ie ; 34978 ViaEbpnooed (os 
P 
Sywis dprd Je yvibtass atom 
’ } a“ ~ . 4 ‘ 
‘> 26w ovids bagel! Seuso bnooee’ git 
=. 
= a 
t by 4 > a rye © of aa a A 
} o bevu2sam 2% iD bY scinod nOysaSts had ss A139 
vy 
z 
| ino stab gntass bas inertia wot d5 per \ies _ 


| orth. aid asubar bine 


Peet i 


SUD ssaaiedaa fe ett ft (Bee 


45 
leant Bi (2.4) 


If each electron that comes to rest in the target delivers 
equal energy to the target and all its kinetic energy is completely 
converted to heat, then the power converted to heat equals: 


n 
d= lEply = aEp! (2.45) 


Pot 
An equilibrium state will be established when the rate of 
heat input equals the rate of heat loss. Let Se be the net amount of 
heat (in joules) delivered to the target to raise its temperature from 


Ty to le at steady state. Thus, the increase in temperature is 


Q b(aE,I,") t 
- Eran a Hee S 0 
where b < 1 because of heat loss, 


t. = settling time which is assumed to be constant, 


M,C = mass and specific heat of the target. 


Equation 2.46 can be reduced to 
n 
AT = a E,I (2.47) 


where a = eer a constant. 


| P é 
. 
oe 
4) 
fi 
y 
= 
l : 
iT 
| 
Hi 
\\| 
{ -“ le 3 
| ij nt teeny ot eonwsd tend nondosts oss Tt! 
! ‘ 
" 
a wi | iy oh a, tern 2 rt: 5 7, 
} t + JISSRTA 237 [ 15 {yi Q JSO Ho at VJ of 
1 
; j _ Pm 
} 1 ot hasdyvevnos tswot ent nent ,ysen o3 
7 } : r “4en 
, A ged © boa a 
‘ ’ 7 
th). te kk : ers, ee. er eee ae 6, 
“iw bederldstes od lifw eiate-gurid bi fupe An 
a= 4 : ithe ies - 
; ’ I th Ge 2 i Beh 5, SG5% Sh 2+ hus 
=. 
P 4 ' a 4 ht = or 
, ey BY 02 4aj o3 Devevrisp (2a1 uo! 
4 We eet 43%. e ba 4 
FeYaONS aE! 1c HE ee | ewitt od Rhee oe Yossie a 
~—, 
, 5 * \ ~ 
5 | Yate 2 Y 
5 = 2) 
{ - ; i _ by is — a 
a : _ = -—-T- © et “ Phat = id 
aif eT « 


3frtrogge bné zebm = 0,7 


46 


Equation 2.41 is rewritten as 


If Ep is kept constant, then the thermocouple emf (Vi) and 


the filament current (I,) are related in a simple manner by 


(2.48) 


en(te) is in mV, 


I. is in amperes, 


where V 


8 iS a constant. 


Taking the logarithm of both sides of (2.48) gives 
log Ven (tg) = log 8 + n log I, (2.49) 


It is expected that a log - log plot between Ve p(t) and I ¢ 
Should be a straight line with slope n and ordinate 8. However, the 
nonlinear effects from radiant heat and from the electron bombarding 
process itself will cause deviation from the linear relationship as obtained 
by (2.49). The resulting plots of data presented in Fig. 2.12 show that 


this nonlinearity is large for low values of I,. All points have to be 


A 


ein 


rb bas | ny sno 12 IW) 3 ort iiiptenre & 


tay 


- 


wissen nortasle and may bing seat snetbecaint esagTtts ees ri 
| styabos 283 kite tiaedt 2 


inci ool a as 


a 


\/ Aq 
“ane 
snus 


47 


ne 


a (ee Ss 
H i 
el ERE | 

Se i t 


4 
tat 

—p-- 
; 


{ 


“ft 
' 


ES 


et 


Satter 
aa tian ae 


a 


(Au) jwa a,dnoosowway) 


filament current (amp) 


EiGecete 


Log-Log plot between Viplt,) and Ip. 


ed 


~~ : ‘ ; ¥ a 7 _— 
. & Te - 4 . ~ ».. - ~~ 
— a z. ~~ Seer mcnentioeneme arte ntegme = = a ager a fhe eee hie 
’ ] : a - re —. a 
i | : yg = ! a a 7 “ =: 
Pad een a 


: — = ee ae 4 ws - ey Sees epee | 
5 a ig i 
e i 
= a 
“ 
‘ ! 
ss ~ = : ‘ — 
a ea: é 
- : 
er ua ; ; Ps 
7 —,5 = 
2 
Z wt a 
ae 4 al 
PP aie 7 
- af “ i 
- Pa 
’ a f * 
a ae fang; pet oe oa gee = ae — - oo wane 
- 
= 5 
- _ 4 ~- — ~ - - - _—— — -~ - > - ~ 
an ~ - 
= — a ee a Os — ee = a = oo 
- 


pe gp npr “en - ~~ ee ‘ ~— - . — | : 
3 

} é 
j 
A eet 

: ; 
cs <= - ie ss 

y 
~ - = ~ ma 


Steady state thermocouple emf (mV) > 


approximated 
straight line 


! 
I 
calculated —— 


curve i 
u 


experimental 
curve I 


] 2 3 4 
; filament current (amp) 
Fig.2,13 Curves between Vin ltg) and Ip. 


| 

7 

; 

' i 
& 
x 

; 3 

‘ ~ r 9 

, a 
 » 


——— a 
; 
"y 
> 


—eee meee —— oP : 


49 


averaged by the straight line I. 


The other set of data obtained from repeating the same procedure 
as discussed above was plotted as the straight line II to show the effect 
of deteriorated emissivity of the filament. This is because thorium can 
be completely evaporated from the tungsten filament after a few heating 


cycles at currents of more than 3.5 amperes over extended periods of time. 


The straight line I has an ordinate at .25 and a slope of 


tan 72.3° = 3.72. Hence, from equation 2.48 
GO Ua eae (2.50) 


where V,, is in millivolts and I, is in amperes. 


th 
The initial data of Vi pt)» I, and those calculated from 
equation 2.50 were plotted in Fig. 2.13. These two curves show good 


agreement between measured and calculated values. 


The block diagram representing the thermal system can be 


drawn as in Fig. 2.14. 


As mentioned earlier, the nominal operating values of I, lie 
between 2-3.5 amperes. This region of the curve shown in Fig. 2.13 can 
be approximated as a straight line having slope rise = eee = 6.53 


mV/amp. Therefore, the transfer function can be simplified to 


th _ .106'e °° 
Tp (st.09)(s#.18) (2.51) 


= 


gVAUO 


Ronan 2. ‘gate, anh 3 sit 
a 


ie 
€ 
4 : 
“Ae - : 
7 
: Po 
i‘ 
4 
, 
1 ° OP 
7 re * AD ran+ aay va hg BOVE 7 
‘ Oy t iets se Dil Yo w Q iy 
* ~ * . At tre 
] ‘ ta (4 5 wa i4n or r 
HH) BOBD > F9e Wns 
26 betjola 26w svads baceNse! 
>  & rurk » re hats 4 
F a ‘ ‘ ’ tae Was © Vv 1 Fw 


. * 7 2 hi’ ~ 
SAS Wot PSISTOGHVS ajal om 
a. fs ,; 1 4 ’ + 
3 ay son TO ern rw 6 2 
i 2 ¥ — 
ent fi Mipie se of 
4 oc xf = Ge x 
4 ' oat prt ' > 7% r. 
? at a i 
: * 
~ .. S ‘ a “4 4% 
ate f aa. & Po bes b «tt 4 
1 6 es1OviP Lim At et ae’ 
: a 
be a ae 
‘ dS BRS pe fH THT Birt 


at batsofe pyew Ge.S fe of; 


Vad ow 


inlss bee be tTeesom neews 


2970S" npyes th iota ‘ont 


a 
-~ 


6 ~ 


‘e, 


c v “a 


norger < aka, - RS 2.£-$ o 


tense 6 6) ‘ia 


prs prt nf 26 


venorsnsm ah 


“4 
at) 


a, 


ad jpoMostwesS 


ro 


50 


th 
mV 


Fig. 2.14 


The time delay “a" mentioned previously is also inserted in 


the final equation (2.51) to complete the transfer function but cannot 


be determined by the previous method. The frequency response method, 


which includes this effect, will be used to analyse the system as 


discussed in Chapter IV. 


_ 
1 
) 
i : 
an fe eer ree en eet at ett me em 
i ~¥ ; 
: i : - \ i 
| PSYNG sao ri’ + 
: Les + J 3 X th ; ait 7 
rN oad a “ t : a a 
' ‘~ ' » badd 
; > ; 
i — é : 
oF Pore | aie. 


“a. a 
t 
: pid 
~ 
' , ae? Ps 
y PysS t 4<¢ we tt Pots ¥ 4 ceft T 


PMH Sh. OFSi0N09 Gs, \ ICs yy 06 FabyPS ant? 
; ‘ Pon, 4 - 
snaypoNt? adT .bortem.avohisya sdf Wd Denterrersa ae 
Hi 4 
seylens od bgeu od [iw ,598%%s effd 2abeiont Aoi 


. Wl y33gs99 4 


5] 


CHAPTER III 
CONSTRUCTION OF CONTROL SYSTEM 
3.1 Introduction 


This chapter will describe the proposed electron bombardment 
control system. Details of control circuits and other system components 
are given. The transfer function of the control circuits are estimated 


and later the block diagram of the complete system is drawn. 


Section 3.2 presents the schematic diagram of the proposed 


control system. 


Section 3.3 determines the type of the required controller for 


the application. 
Section 3.4 describes the control circuit details. 


Section 3.5 estimates the form of the transfer function of 


the control circuits. 


In section 3.6, the block diagram form of the complete control 


System is given. 


3.2 Schematic Diagram of the Control System 


A control system was constructed to control the filament current 
for the purpose of heating the target in a linear manner as required. 


The simplified schematic diagram is shown in Fig. 3.1. 


Serie corel 


/ 


ie 
— 


fordaos oF betauitenoo : 


, 


dad To. wns te 9 >t3 


& 
ie 


mine forts foo A” 


" : 


mn As vc aie 


es e 
Le Ft ab 


® oe 5 
7 q 


- 7 
NWOT 


2 ae 


“wayshS [O4}UOD aANzeUaduia? Jo WeubeLp ILzZeWaYydS LE oo a ie | 


o2 


punoub 


daqueyo wnndea ybLy euz[n 


29648} 


<= 


quale | L 


PLotys 


FLNOALD DELAY 4abb Lu} 


AQE207L AaUUos 


-Sueu} JUaWe| LY ADWUAOJSUCU 


asind 


VAOZL VADEL 


ADWAOJSURUZ UOLZLLOSL 


Aa | |OU}U0D 


uy %EL-4+d/"d 


A0zeUuedwod 


Jozeuauab uoLzoun, dues 


oa 


SS HT ome 


- 2 


Bit? At ™ 
Sites sa = ft W | ‘wi 
SOT 5 

H 
: 
4 
: re 
i enews 
» > : 
C4 f | 

— | Fd 1 

i | 

} wate 

eI 

} — 

\ » 

| - (ested 

‘ Disarfte 

7 ~”A 

; 

| insmei ft ~~ 

: ‘ 

' 

‘i. I a —~ ea <> 


ye 2 ee 
Lahde Ges aottsfoet 


7 


on | 


“4 7. a 
a 
ell 


se TSisp AOtsom? Cmsy 
Sis 


oe | 
. . —— 
oe binning: 


= ee 


— 
a a 
es wer 
J VUls5 TP } 
_— 
: 
_ 
+ ~~ 
ae 
es . — 
45 <hr§ 
sie ~—aJ Zine me 
5 
. 
iP > “2 
ra 
i 


53 


The potential difference between the target and the filament 
must be maintained at about 2 KV. Since the control system must supply 
AC power to the filament in response to thermocouple measurement of 
target temperature, high voltage isolation of parts of the control 
system is required. To eliminate the difficulties of floating the entire 
control system, the positive side of the high voltage supply was 
grounded and the filament power supply at the negative side was floated. 
This offers potential advantages as follows: 

a) Safety and convenience of using and adjusting the control 
system. 

b) Elimination of inaccuracy and difficulties resulting from 
electrical breakdown or leakage. 

c) A reduction in the number of interfaces between high and 


low voltage elements. 


3.3 Type of Controller 


The transfer function of the thermal system as determined can 
: b e -as 
be written as et OO; (et. 12 where a and b are constants. The control 


System may also be simplified and redrawn as in Fig. 3.2. 


If the controller is a proportional controller having gain K, 
the steady state error of the output temperature with a unit ramp input 


is given by 


e.. = lim : lie (3.1) 
SS 1+G(s)H(s) 5° : 


s>0 


| “ 


i ; ; 4 ae eee pa 
we foun moteve fortnos sdf somite .¥Y S tuods Js bantainism sa eum 
_ 
ripe 3} quooornaens oF semeaee, A Frees rf? off oF Tawag . P 
od 2 


2 _ 
phe taaw® ae i, mn red ene nt tris . 
OT 3 mt Ge i gp we uy f wif é StsT6 jaqmss 9p" Pie 


| i iy 23 169 rH 9p 
| - 
- 
a 
; ‘ a Poh bin » wid a ae he cae “ay oF + . 
Oti t 7eet | ‘ae 20h Tl usteerh Sy 8Tanimris @ QStITwost ci maz. ta 
. S 
3 _ 7 
sae i *. ~ Th fo ar we? 5% ne 
fov Ape gig to sbte swivheoa afd yumsteye fomwned 
ie bes 
9 
5 ie : — 
. 4 { { pULie Hi, Je 7 SH2 DAS DO : 
a tah iad 4c ruongulkie Tete nat sy Qh hry - 7 
‘aworfod 2s. esoetrpvbe [stinetey zyart Hh 
; | a 
_ 
Ie pArey Yo ‘sonstneviou-bns YSotHe (8 
a, 
: ++ ’ t rag F Perit 
i Dy ptt j oh oO SOLS 
~ ossseal 90 
=~, 
Ww ost IeINT to Yedmwn srt Ae 
fea r er iam Oil : aa 
& iio ¥ Louris = 3 iO Anordonut i } 
Te on iF 
1) _ > of 
} M ; ‘ ; 
f pe ; _ 4 a i 9 d ” . 7. . 
siden “ OD STE © PN bh SYaiW 4 ye +o nt aot 26 nasst w > 
Ola re min top ;, > ae 
: ae > 
- — he bye ee b mat ns 
t .2 nr. 25 ipeybey bag HOTT? quire 9do2ts bo mS ey 
fi - ~ 


«A NPHG enrval weal losfnos [snbts1oqoriq 6 af yo T Pog neo gag FI” 
, *., ‘ ‘ - ~~ 


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a is le ye 


Simplified diagram of control system. 


which becomes infinite when the time increases. Generally speaking, 

if the controller does not include a free integrator to contribute at 

least one pole at the origin, the output temperature of the element will 

not change linearly with time but will gradually deviate from the ramp 

function input. The controller must, therefore, contain a free integrator 
] 


with transfer function 5 50 that the system will be at least type one 


and its output can follow a ramp input with a finite error. In this 


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thermal system a Straight integral controller only is not applicable 
because the system will become unstable even at very low gains. The 
S-plane locations of the closed-loop poles of this system with an 
integral controller included are very close to the imaginary axis. 

Their locations change depending on the value of the loop gain K. By 
Slightly increasing gain K, two closed loop poles of the system will move 
into the right half s plane and the transient response to a constant 
magnitude input will increase monotonically or oscillate with increasing 
amplitude. Such a system is unstable. The stability of a linear system 
is a property of the system itself and does not depend on the input or 


driving function of the system. 


To increase the stability and improve the response of 
the system it is desirable to modify the controller to a proportional 
plus integral type having the transfer function Kp (1+ = where Kp and 
7 are gain constants called proportional gain and Picentat gain re- 
sa ci¢ey) This controller will create a negative real axis zero 
having a position determined by the value of Ts. The presence of a 
negative real axis zero will pull the locus of the poles towards itself; 
hence, the system will be more stable over a wide range of gains Kp. 
However, the actual system may be more complex and have additional poles 
from other components in the control loop. To obtain enough stability 
the loop gain may have to be carefully adjusted. If the system per- 


formance is not satisfactory after the adjustment of gains, compensation 


networks or derivative gain may have to be included. 


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The following section will deal with the details of the 
control circuits to obtain the proportional plus integral control action 
of the filament current as outlined in Fig. 3.1. Approximate transfer 


functions of various parts are also given. 
3.4 Circuit Details 


Economy, simplicity and reliability were guiding considerations 


in the construction of this control system. 


3.4.1 Ramp function generator 


Several dc amplifier circuits comprising a typical operational 
amplifier yA709 modified with a FET differential input stage using two 
FET's 2N3819 which had very similar characteristics were built and used 
as an integrator with a gain of 1/RCs of about .02/s.The results were 
not satisfactory however, because the gate bias current was very high 
producing high rate drifts which were non-adjustable. This also made 
the circuit insensitive to small inputs. To avoid these drift problems, 
a mechanical integrator was built by connecting a 10 turn Helipot 
precision potentiometer (having a resistance of 10K + 3% and a linearity 
tolerance of only 0.250%) across a low voltage source and rotating this 
potentiometer by means of a small Rustrak synchronous motor at a constant 


speed of 2 rpm. The complete circuit is shown in Fig. 3.3. 


3.4.2 Comparator 


Many problems may be eliminated if the comparator is a 


bridge circuit having the prescribed ramp voltage generator as one side 


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57 


upper limit adjust 


output ramp 
function 


lower limit adjust 


FIGws.3 

Ramp function generator. 
of a bridge circuit and a linear precision potentiometer rotating precisely 
according to the output signal as the other side. The error voltage can 
then be taken from the two sliders of the potentiometers. An available 
Electronik 16 Lab Recorder from Honeywell had an accuracy of + ie of full 
scale, a dead band of 0.1% of span and a travel speed of only 0.2 sec for 
full scale deflection. The above metioned scheme was implemented satisfactoril) 


by attaching a 1 turn, 10K Helipot precision potentiometer (having linear 


tolerance of .150% and resistance tolerance of 1%) to the rotating pen 


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Shaft of the recorder and by connecting the two potentiometers together 


as shown in Fig. 3.4. 


reference output 
: Signal by 

Input y d 
R recorder 


-V- error 
Signal 


ll G..ce3.24, 


Comparing bridge rent. 

A self contained precision bridge circuit capable of comparing 
the input ramp function with the desired output signal was thus formed. 
The position of the slider of the right arm of the bridge was determined 
by the controlled temperature of the target when the input to the recorder 
was the thermocouple emf. The full scale input of the recorder was about 
3.4 mV and a potentiometer had to be used to attenuate the maximum 
thermocouple emf down to this value. By varying this attenuation the 


maximum controlled temperature and the speed of temperature sweep could 


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also be varied. The speed of the temperature sweep, however, could only 


be increased, i.e., the sweeping period would be 5 minutes or less. 


This procedure is shown in Fig. 3.5. 


20K, 10 turn Helipot 
recorder 


thermocouple 
electrometer 


digital voltmeter 


Fag. 3:5 


Instrument setup for measuring and attenuating thermocouple emf. 


The Keithley Model 600B Electrometer has excellent zero stability 
and was used as both a thermocouple emf indicator and as a unity gain 
buffer amplifier. Its zero drift was less than 2 millvolts per 24 hours, 
less than 200 microvolts per °C, after 30 minutes warm up. The input 


impedance was greater than 10/4 ohms and the output impedance was 910 ohms. 


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Thus, the electrometer could be used as an isolation amplifier to isolate 
the thermocouple from the rest of the circuit. A 20K _ 10 turn Helipot 
potentiometer was placed in series with the recorder to attenuate the 
thermocouple emf down to less than 3.4 millivolts at the input of the 
recorder. A digital multimeter, DANA Model 3800 was also connected 
across the output of the electrometer to facilitate reading of the 


thermocouple emf. 


The attenuating potentiometer inserted in the position as 
shown was found to be the simplest and most efficient method of 
attenuating when the arrangement of the recorder input network is 


considered (Fig. 3.6). 


Constant 
Voltage 
Circuit 


input 


of circuit 


Fig. 3.6 


Input network of the recorder. 


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3.4.3 The proportional plus integral controller 


The integral gain may be varied manually by changing 7 to 
K i 


= where K is a variable gain. The required transfer function of the 


i K 
controller is then changed to =. + Ko. This was simulated as shown 
j 
5 Pee a eas a 


PVG oS o7 


K 
Simulation of the transfer function ot K,. 
j 
The circuit details of each function are as follows. 


a) Amplifiers of gains - K, and K, 


These are two temperature controlled differential dc amplifiers 


15, 16 


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monolithic transistor pair (wA726) is stabilized at a temperature above 
ambient by an integrated circuit heater. As the ambient temperature 
changes, the power fed to the heater is changed to maintain the temp- 
erature of the differential pair at a constant level. Since the temp- 
erature of the differential pair does not change appreciably the effective 
input voltage drift is considerably reduced. Because the device is 
constructed on a single silicon chip with only small mass involved the 
chip temperature stabilizes within a few seconds. When stabilized, 

the input offset voltage drift is only about 0.2 uV/°C, and the input 
offset current drift is reduced to about 10 pA/°C. The long term drift 
is about 5.0 uV/week. 


Figs.3.8 and 3.9 are the schematics of the inverting amplifier 
of gain Ky and the noninverting amplifier of gain K, respectively. The 


16317 


design of these circuits can be summarized as follows. 


The differential stages were designed to be operated at low 
collector current levels to minimize input bias current, input offset 
current and their drifts. The collector current was set at 100 uA per 
transistor. For this collector current, hee was 400. Since the two 
transistors are matched, the power supply must deliver the total current 
of 200 uA to both transistors, assuming that r e I. A constant current 
source comprising a matched pair transistor 2N2060A was used in the 
emitter circuit; this significantly improved the common mode rejection 


ratio (CMMR) which is proportional to the high output resistance Ro of 


the current source. 


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error signal _ y 
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75K 


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Low drift dc amplifier of non inverted 


gain Ko. 


65 


For the circuit of the constant current source as shown, the 
bases of both transistors Qa and Qp are at the same potential. When 
the transistors are located very close together on the same chip (matched 
pair), their properties will be very similar and their collector currents 


will tend to be equal regardless of temperature. 


The QB collector current may be calculated by 


Ue ra tees 5 all be g1AAz9 
75K TSK 75 
« 200 uA as required. 
The Quip collector current is largely independent of temperature and there- 


fore so is the collector current of Qin: 


Once the collector current levels were chosen, load resistances 
determined voltage biases. Collector resistors were chosen to provide 
the desired gain and output dc level within the bias limits for common 


mode voltage swing. The chosen value of collector resistor (R.) was 


R 
25K2. Common mode gain which can be approximated by - Se (where Ro = 
fo) 


output resistance of the current source) therefore should be very low. 
The desired bias was achieved by using a zener diode IN757A to reduce 
the power supply from +15 volts to +6 volts. For simplicity, the 
temperature controlling circuits and pin connections to the integrated 


circuits are not shown. 


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66 


The input voltage offsets due to unequal base-emitter volt- 
ages in the input transistor pair remained finite for these two circuits 
and could not be tolerated in the experiments. A normal method of 
balancing these dc offsets by using a small trimming potentiometer with 
a resistor network is shown in each figure. The drift from variation 
in the voltage offset due to temperature variation was successfully 


minimized and that due to the supply variation could not be noticed. 
b) Integrator 


The integrator circuit built from a single operational ampli- 
fier MC1439G is shown in Fig. 3.10. The RESET switch was used to set 
the initial condition of the capacitor equal to zero (V=0 at t= 0). 
Adjusting of the dc balancing potentiometer to obtain minimum drift 
when applying zero error input signal to the control circuit would give 


the optimum performance. 


When considering the dc offset and bias current of the 
operational amplifier the output of the integrator consists of two 


components; !/ the integrated signal term and a group of error terms, j.e., 


5 


, 
efhile Ldn i 


where Vie is the input offset voltage, 


Ip is the input bias current. 


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67 


In this equation only Lis and I, are considered as causes 


S B 
of integrator error. The maximum voltage drift rate due to these 


offsets can be found by differentiating the above equation, 


(3.4) 


For the MC1439G operational amplifier!® the typical values 


of ie and I, at Lo = 25°C are 2.0 mV and 0.2 uA respectively. Therefore 


the typical maximum error is 


(| = 20.029 mV/sec (3.6) 
max 


which is very high. Under actual operating conditions there is the 
possibility that ye and I, will be greater than the typical values 
indicated due to other parameter variations such as temperature and 
component aging. The error component due to bias current was minimized 
by increasttaethe capacitance of the feedback element. The capacitor 


used in the circuit was a mylar 10 uf capacitor 100 WV. 


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68 


2K 


RESET 


V. 
i 


from the output of 
amplifier K 


MC1439G 


100K 10k 100K 


+15 -15 


Fig. 3.10 
Integrator. 
The long time constant and the desired accuracy required many 
changes in the circuit. The dielectric of the feedback capacitor should 
be polystyrene or teflon which has low leakage current compared to the 


Le The circuit may be modified by employing a matched 


input bias current. 
pair of insulated gate FET's as a differential input stage followed by 
another operational amplifier with higher performance. 


c) Summing amplifier. '/ 


The outputs of the integrator and the K, amplifier were 
finally connected to the input of a summing amplifier. The summing amp- 


lifier consisted of a single MC1741CP internally compensated operational 


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69 


amplifier!” set at unity gain. The circuit is shown in Fig. 3.11. 


from 
integrator K 
71 


K. amplifier MC1741CP 


offset adjust 


Pigvad at 
Summing amplifier. 


3.4.4 Trigger and triac circuits’? 


The basic function of the trigger circuit is to generate the 
pulse signal to trigger the thyristor (SCR or triac) from the off-state 
to the on-state. The position of the pulse signal on a half cycle of 
the supply load voltage depends on the magnitude of the input control 
Signal to the trigger circuit. Once triggered, the thyristor will remain 


conducting for the rest of that half cycle. The average power to the load 


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can thus be controlled efficiently by controlling the conduction period 
of the ac wave. 
The trigger circuit used in this application utilized a 
2N2646 unijunction transistor (UJT) operated as a relaxation oscillator. <2 
The ramp and pedestral contro1<2 was later adapted to the circuit. 
The required thyristor type was determined by the current requirement for 


filament heating. The circuit that was built used a GESC46B triac 


capable of delivering 10 amperes of maximum current. 


The complete circuit is shown in Fig. 3.12. 


The characteristics of the trigger and triac circuits 


In the phase control (conduction period control) process there 
is a time delay in turning on the SCR (or triac) and the percent anode 
to cathode voltage is descreased as a function of time following the 


application of the trigger signal. The delay time ty is shown in Fig.3.13¢" 


100 
90 
Be Pid. 3. tS 
o Turn on characteristics of SCR and triac. 
8. 
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> 
(8) 
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72 


and defined as the time between the 10% point of the leading edge of 
the gate current pulse and the 10% point of the anode voltage waveform. 
The delay time decreases as the amplitude of the gate current pulse is 
increased, but approaches a minimum value of 0.2 to 0.5 u sec. Rise 
time t. is defined as the time required for the anode voltage to drop 
from 90% of the initial value to 10%. Total turn on time is defined 


as ea = ty + th and a typical value is 3 u sec. 


In the present case the transformer contributes an inductive 
component to the load. This inductance may affect the shape of the 
current waveforms, delay characteristics and commutation (turn off 


process) interval. As in the L R circuit the transient current is 


(ine conee!) (3.7) 


z~|=< 


i= 


Higher = t will slow the load current rise time, depress the peak 
currents and widen the conduction interval. The last effect is the re- 
sult of inductive voltage in the load circuit. As the delay angle is 
increased the inductive voltage increases. This additional voltage 
allows the thyristor to conduct longer than the corresponding thyristor 


in a resistive circuit. 


A small time delay also exists in the phase control process 


itself. This is the time required for the capacitor in the UJT circuit 


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73 


to be charged up to the triggering voltage of the UJT emitter. This 
time delay is governed by the time constant = RC in the UJT circuit 


and the magnitude of the control signal. 


The most significant time delay occurring in the control 
process is from the trigger process. This is explained by the waveform 


ape lOees. |e. 


Fig. 3.14 


Load voltage waveform. 


Suppose that the first half cycle has not been turned on. 
If at time t, a pulse is applied to the gate of the triac, the latter 
turns on after a finite time as previously described. Suppose now that 
half cycle has then been partially turned on as shown. Then a next 
trigger signal originating at ty has to wait at least 5° ty seconds to 
turn on the next half cycle, corresponding to the position of the 


trigger signal. This time delay is not constant but it will vary between 


5 19dt8 nO 2 


cer nad nartt 2 


ised t io. en te ~ inte 
Rs! nian e 19. * 


om 


74 


0 and og or =~ 8 milli seconds where f is the power line frequency. 


This time delay is large enough to create instability or 
severe nonlinearity in the control system with a quickly-responding 


controlled quantity. 


Furthermore, once the triac is turned on, it stays on for 
the rest of that half cycle, and the system becomes unregulated for 
that time period. However, the controlled quantity in this case is temp- 
erature, which has a long time constant when compared to the switching 
frequency of the triac. As a result of the long thermal time constant, 
the system may still be approximated by a linear continuous model suit- 


able for the regulation of target temperature. 


3.5 Form of the transfer function of each block 


3.5.1 Comparator 


The behaviour of the comparator is governed by the transfer 
function of the electrometer, of the potentiometer attenuator and by 


the transfer function of the recorder including the bridge circuit. 


In normal operation the attenuator potentiometer was adjusted 
to display 13 mV thermocouple emf, corresponding to the maximum temp- 
erature of about 1200°C, on 60% of full chart. Let the dc gain of the 
recorder combined with the attenuation of the potentiometer be A,. Also 
let the normalized transfer function of the electrometer and the recorder 
be G(s) and G(s) respectively; therefore all elements can be represented 


in block diagram form as shown in Fig. 3.15. The frequency response of G(s) 


é 
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and G(s) will be determined in the next chapter. 


reference R 
input 


error signal to 
controller 


Vib thermocouple emf 


as ly NS ll 


Block diagram of the electrometer and recorder. 


Full chart recording time corresponds to 5 minutes approx- 
imately. This is the time required for the synchronous motor to drive 
the reference potentiometer a full 10 turns. When the control system 
Operates, the slider of the feedback potentiometer (right arm of the 
bridge) has to follow the slider of the reference potentiometer to main- 


tain the bridge output voltage (error signal) near zero. If only 60% 


of full rotation is used the ramp speed will be increased to Any 
: ° sa < Smm 
Tam which corresponds to 1200-25) | When 10 


3 min. 3 min 


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76 


a smaller percentage of full rotation of the recorder potentiometer is 
used, however, the attenuation of the attenuator potentiometer must be 
increased. This will result in the total gain Ar being decreased. 
Compensation must be provided for this by increasing oy and/or amplifier 
gains Ky» Ko. 

3.5.2 Controller 


The transfer function of the controller was previously 
established as : (K, + +): Amplifier gains K, and K. are constant in 
the normal frequency Sis of interest (less than 1 KHz). The block 
diagram of the control circuit including the amplifier offsets is drawn 


in Fig. 3.16 


error signal from the N,(s) Nats) 
bridge 


V 


Aig. 2.16 


Block diagram of the control circuit 


. 
c - 


: A - : 


7 
—* 
is 
. 
a 


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where Ny is the offset at the integrator input, 
No is the offset of the summer and amplifier Ko. 


Both Ny and No are approximated to be constant. 


3.5.3 Trigger and triac circuits 


The gain of the trigger and triac circuits may be expressed as 


-S 
output current (amperes) _ : -@ tb 


f 
input control voltage Ye 


The time delay t in the expression varies between 0 and 8 ms. The 
time constant T represents 5 for the inductive portion of the filament 


transformer load. 


To find the steady state gain of the circuits a variable dc volt- 
age was applied to the circuit. The output filament current was then 
measured. It was found that the circuit had a small insensitive region 
at low input signal eg but this could be minimized by adjusting the 


gain of the circuit which also set the initial output current. 


The data plotted in Fig. 3.17 show a linear relation between Ve 
and Ie. The straight line has slope of 0.521 Amps/Volt. 


The block diagram of both circuits can be shown as in Fig. 3.18. 


3.6 Block Diagram Representation of the Control System 
From the curves of Ven vs. I, and I, vs. es the nonlinearities in 
the normal operating region (I, = 2 to 3.5 amperes) are quite small. 


The system therefore may be linearized so that linear analysis can be 


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filament current I¢ (Amperes )> 


4.0 


a 


WwW 
=) 


ine) 
Oo 


ine) 
—) 


Lo 


10 


0.5 


0 


0 1 2 3 4 
Fig. 3.17 Curve plotted between I, and LA 


78 


5 6 7 
control signal V (volts) = 


79 


control signal 


Pig. 3.18 


Block diagram representing the trigger and triac circuits. 


applied. The slopes of these curves about certain operating points can 
be regarded as constants that were calculated before (Chapter I and 


previous section 3.5). The linearized system is then as shown in Fig.3.19. 


The variable parameters in this system are AR? Ky» T. and K, 
which have to be set to meet the specifications as outlined in the last 


section of Chapter I. 


In the next chapter, frequency response methods will be used to 
obtain all necessary details of the complete system characteristics. In part- 
icular, the system parameters are adjusted by use of Bode plots to obtain 


the desired performance. 


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CHAPTER IV 
ANALYSIS AND DESIGN 
4.1 Introduction 


This chapter will present procedures in the analysis, design and 
compensation of the system to meet the specifications. The approach 
used in this chapter is based on the frequency response method as 
represented by Bode fadrane In this method, the steady state res- 
ponse of the open loop transfer function to a sinusoidal input is repre- 
sented by two separate plots: one is a plot of the logarithm of the 
magnitude of the sinusoidal transfer function, the other is a plot of 
the phase angle; both are plotted against frequency on a logarithmic 
Scale. The system behaviour is determined and the design is carried out 
via frequency domain techniques. The transient response behaviour was 
considered in terms of frequency domain specifications such as phase 
margin, gain margin, resonant peak value and bandwidth. The analysis 
and design in the frequency domain is therefore indirect because the 
system is designed to satisfy the frequency domain specifications rather 
than the desired time domain specifications. However, the frequency 
response plot indicates clearly the manner in which the open loop transfer 
function should be modified or adjusted to obtain the desired transient 
response characteristics. After the open loop transfer function has been 
designed by the frequency response. method, the transient response character- 


istics have to be checked to see whether or not the designed system 


. 
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82 


satisfies the requirements in the time domain. If it does not, then the 
design transfer function must be modified and the analysis repeated 
until a satisfactory result is obtained. 


Wal) also be used to show the contributions 


The root locus method 
of each open loop pole or zero to the system behaviour. In this method, 
the locus of roots of the characteristic equation of the closed-loop 
system, as the gain is varied from zero to infinity, is plotted in the 
S plane. The position of the closed loop poles for a specific gain of 
the open loop transfer function may be approximated, and the character- 


istic of the transient response of the closed loop system may, therefore, 


be determined. 


The next section will show the results of the frequency response 
test in which the frequency response of each component in the control 
loop was determined experimentally and finally combined. The 
resulting frequency response indicates the manner in which various 
parameters of the controller should be adjusted to obtain stability and 
meet the required specifications. This is done in section 4.3. Later, 
the system is compensated to maintain the stability at higher values of 
gain as illustrated in section 4.4. The final section(4.5) will discuss 


the effect of the inexact cancellation of one pole of the thermal plant. 


4.2 Determination of the Frequency Response 


The frequency responses of the following components were determined: 


a) Recorder including electrometer and attenuating potentiometer. 


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a) 
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= 


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83 


b) Trigger, triac circuits and the thermal system (filament, 


target and thermocouple). 


4.2.1 Experimental procedure 


A General Radio Type 1305-A low frequency signal generator was 
used to obtain the frequency response of two sets of system components. 
The generator frequency was variable from 0.01 Hz to 1000 Hz. Two 
outputs were available from the generator. The phase of one output 
with respect to another fixed reference output was variable. The phase 
shift adjustment on the generator was calibrated in degrees. To obtain 
the frequency response of a system component, the generator, the 
oscilloscope and the component under test were connected as shown in 


Rigs “414 


In finding the frequency response for both component sets a) and 
b) the sinusoidal signal was superimposed on a dc bias signal at 
Suitable level and then applied to the system components as mentioned. 
The gain and phase shift through the system components were measured 


by means of the oscilloscope as the input frequency was varied. 
4.2.2 Results 


The Bode diagram of the recorder and electrometer with VA set at 
6 volts is plotted as shown in Fig. 4.2. The attenuation from the 
potentiometer setting (= 16.08 db) is to be subtracted from the recorder 
gain. The frequency response of the electrometer at a gain of 1 is 
flat (within 3 db) throughout the frequency range from dc to 50 KHz. 


Therefore the frequency response obtained effectively is that of the 


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variable phase input 
to horizontal axis 


a 


oscilloscope 
displaying Lissajous 


oscillator 


system component 


Fig. 4.1 


Instrument set up for frequency response test 


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recorder only. From these plots the transfer function of these three 


components combined is 


gw 227x(40n)*x140nxe7 “O08 
r SoS e ee 


(4.1) 


15.79x108 x @7 1005s 


(s+125.66)* (s+439.82) 


Parts of the response curves at higher frequencies which could 
not be found experimentally were interpolated and are shown as dotted 
lines. Another Bode diagram for the trigger-triac circuits and the 
thermal system combined is shown in Fig. 4.3. It was found that the 
trigger-triac circuits contribute nothing to the shape of phase response 
curve within the measurable range of frequency response (< 5 Hz). Both 
response curves generally agree with the linearized second order trans- 
fer function as derived in Chapter II, but without time delay effects, 
in the measurable frequency response. The dc gain and the -positions of 
poles, however, are different because a new target and filament had to 
be used for this test. Any change made in these elements will usually 
result in the transfer function of the thermal system also being changed. 
From the frequency response curves the normalized transfer function is 


found to be 


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Pears Fe 2825 S 
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where the suffix P refers to the plant. The dc gain during the experiment 


was found to be approximately ax1073, 
The block diagram of the complete system is shown in Fig. 4.4. 


The frequency response curves from Fig 4.2 and 4.3 are added 
together, yielding the total response of elements from the trigger circuit 
forward to the recorder. The results are shown in Fig. 4.5. The response 
curves have the essential characteristics of the thermal system itself. 
The instability is mainly caused by the presence of the recorder which 
increases the order of the system by two. However, the forward gain 
can be increased up to 53 db (=gain at 446.7) before the system will 
become unstable. The transfer function of the combined curves is found 
to be 


pei ce ee 


G(s) G iki os ce A ee 
(s+.25)(st+1.13) (s+125.66)° (st+439.82) 


r P 


4.3 Adjustment of Controller Gains 


The open loop transfer function of the system is 


x10? xe7 0055, beth Tic 
G(s) G(s) G(s) = 6(s)H(s) = 28310 >e SATA 


3 5 (s+.25) (st1.13) (st125.66)°(s+439. 82) 


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The presence of the pole at the origin from the integrator creates 
the stability problem. By looking at the frequency response in Fig. 
4.5, only a value of gain K. as small as 10 will result in negative 
phase and gain margins if the zero in G(s)H(s) is not properly located. 
This will bring the system to instability even at very low forward gain 
and the system becomes useless. Therefore the zero at s = - zi must 
be carefully placed such that it cancels a pole either at s = 0 or at 
s = -.25. In order to maintain the integrating effect of the controller, 


the pole at s =-.25 should be cancelled; thus 


Ese (4.4) 


The compensated open loop transfer function after cancellation is 


therefore 


5 -.005s 


17.83x10° xe x K 


2 


a = pevdh eae (4.5) 
s(s+1.13)(s+125.66)° (s+439.82) 


G(s)H(s) 
The Bode diagram of the open loop transfer function for Ko =] is 


plotted as solid lines in Fig. 4.6. 


The steady state errors due to the reference input and the amplifier 
offsets are considered as follows. 

a) Steady state positional error to the ramp function input 

If this error is to be kept less than .05 volt per volt/sec (i.e., 


5 #/sec) of the final output velocity, then 


92 


_ output velocity ge 0 

Ky Steady state error ay. (4.6) 
= Sle 20 sec 

05 
and also 

_ lim 

Sas “aq G(s)H(s) (4.7) 

S$. 17 eelO mer oe x K 


s>0 2 ; 
S(s+1.13)(s+125.66)° (st439.82) 


See as 


This implies that .227 K 20S Or K Shei. 


Wee ee 


K 
Therefore — > .25x28.1 or >. 22.03 depending on K,. 
ae 


b) Steady state errors due to amplifier offsets 
From the block diagram in Fig. 4.4, the closed-loop transfer 


function _th in the absence of V,, N. is 
Ny Roane 


Ven(S) | 1:13x107> oe ; 
Nats)or St Ae ae a ee ee ey 
] T,s(s+.25)(s+1.13)+ 17.83x10~ xe (K,+K,T;s) 


(s+125.66)°(s+439.82) 


Hence the steady state error due to a step offset of magnitude Ny 


93 


is 


-3 N 
egg (Ny) = lim s. sae oe ee rm 5 -.0058 = 
s+0 T,S(s+.25) (st+1.13)+ 17.83x10° xe ° (K,+K,T.s) 
2 |="21 
(s+125.66)° (s+439.82) 
Ny 
The steady state output due to offset Ny is then 
te 
Cos = -e., (Ny) = 227K, ° (ae) 
The magnitude of N, is usually less than .2 volt and from this 
equation Ny is uSually minimized by a large gain from the recorder 
( = 227). 
In the same manner, the steady state error due to a step offset 
No can be found as 
* art 1.13x107 Tis No 
4 US) GIRLIE SER sa Seerece Serene =e ee eee en Le bess 
s+0 T,S(s+.25) (st1.13)+17.83%10 e- (K,+K,T,s) 
(4212) 


Thus the steady state error due to offsets of the amplifier having 
gain Ko and of the summing amplifier which do not pass throuch the 


integrator will be zero. In the transient state where these offsets have 


vd basgrmatn 


— A ¢ — 
supeeerenct ia (M29 f 
CAC» Faye ee) . 


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some contribution to the error signal, they are still negligible when 


compared with the error signal due to the reference input (Vp) itself. 


The amplifier drift is not a serious problem because of its 
equivalent rate of rise being small compared to the speed of the ramp in- 


put. 


For a satisfactory transient response performance, the phase margin 
should be between 30° and 60° and the gain margin should be greater than 
6 db.“'From the Bode diagram plotted in Fig. 4.6 the value of gain K, 
at 2 db will give a phase margin equal to 30° but from the requirements 
for steady state error, Ko must be at least 88.1 or 38.9 db. At this 
value of gain Ko the phase and gain margin are approximately -14° and 


-l14db respectively. These indicate that the system is unstable at this 


gain setting. 


In order to meet all the system requirements and to maintain 


Stability, phase lead compensation was introduced. 


4.4 Phase lead compensation network 


The phase lead network was designed?! 


based on the value of Ko of 
100 or 40 db. The desired phase and gain margin are 30° - 60° and 

> 6 db respectively. The transfer function of the network as represented 
by the Bode plots was adjusted to compromise between the desired 
specifications and gain loss by the attenuation of the network. The 


design yields the transfer function of the network as 


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The attenuation is <- or 04. 


The network was inserted into the feedback path between the electro- 


meter and the attenuating potentiometer as shown in Fig. 4.7. 


The gain of the electrometer was set at 100 at which the frequency 
response was 0 - 1 KHz. The bandwidth was still wide such that its 


gain remained constant for the whole operating frequency range (<10 Hz). 


The transfer function of the network is 


¥V_{s) R! R, Cst] 

Se ne (4.14) 
Vals) Ry#RTD * RAR'S s+] 
RHR", 
1 
= ] (4.15) 
s + 
aR, C 

where R's, s Ry // (input resistance of the recorder and resistance 


of the attenuating potentiometer), 


a= RoR ° (4.16) 


C was initially chosen as standard value of 1 uf, 
therefore Ry = —~—— = 79.5K 
10 ~x4n 


and R's = .3.32k. 


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The input resistance of the recorder is approximately 340 2. 
Ro was chosen as IM2. This will allow the adjustment of the attenuating 
potentiometer to be made to obtain the required input signal to the 


recorder. 


The Bode diagram of the compensated system is plotted in dotted 
lines in Fig. 4.6. From the response curves the gain cross over frequency 


is at f = 3.4 Hz, the phase margin is +34° and the gain margin is +12 db. 


4.5 Pole Shifting 


Higher target temperatures will have the effect of reducing the 
time constant t, Of the heating process as expressed by equation C2020)9 
The pole of the thermal plant nearer to the origin will move away from 
the origin, which will result in the cancellation of this pole by the 
zero from the controller becoming inexact. The root locus in this case 
may be shown as in Fig. 4.8 but without the compensation network. In- 


K 
creasing gain Ky of the controller will move the zero at - phe towards 
j 


the origin. The pole at the origin due to the integrator oh be more 
effectively cancelled by this zero. The controller will then behave 

as a proportional controller having gain Ky with only a small integrating 
effect. From the Bode diagram in Fig. 4.5, without the integrator, 


the forward gain can be increased up to 400 before the system becomes 


unstable. Therefore Ko can be increased up to 


400 400 
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Fig. 4.8 


Root locus of the system. 


before instability sets in. Thus the controller has another operating 


condition as follows: 


0< K, < 440, 
Ky 

per. 7.0% 4.17 
KT, ( ) 


j.e., the controller being mainly proportional and only slightly integral. 


If the above condition is satisfied and gain K. is sufficiently 


high then the output will follow a ramp input with a small deviation 


i ae Y 


2 


100 


(depending on K) from linearity in the time interval and temperature 
range of interest. The long time constant of the thermal plant also 


helps to reduce this deviation to a smaller amount. 


With the designed compensation network, the gain Ky can be in- 
creased further to a very high value before the instability starts. 
From the interpolation curve in Fig. 4.5, the marginal value of the 


forward gain is 90 db or 3.163x10" corresponding to Ko of about 3.48x10". 


The next chapter will illustrate typical step and ramp responses 
obtained from the actual system. These results will be compared to the 


specifications as set for the system. 


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CHAPTER V 
RESULTS OF TEMPERATURE CONTROL 
5.1 Introduction 


This chapter will show the results of experiments carried 


out on the designed system, and will compare these against the specifications 


set for the system. Some other relevant characteristics of the control 


sytem will also be discussed. 


5.2 Step Response 


The output temperature change as a function of time in 
response to a step of input voltage was obtained by setting the reference 
potentiometer at a predetermined position corresponding to a required 
output temperature. The power to the control system was then turned 
on and the step response of the compensated system was recorded as 


Shown in Fig. 5.1. 


The transient performance of the controller may now be 


investigated. The temperature rises from room temperature (~25°C) up to 


the final temperature of approximately 1000°C with the following specifications 


a) Delay time, ty : In this case the delay time is the time required 
for the response to reach half the final value. By measurement, ty fe 
lefaSec, 


b) Rise time, th The time required for the response to rise from 10 to 


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90% of its final value is = 3.4 sec. 

c) Settling time, t. : The time required for the response to decrease 

to and stay within 2% of its final value is = 14 sec. 

d) Maximum overshoot, Mp : The maximum overshoot is =~ 5.4% corresponding 


to a damping ratio of — = 0.7. 


According to the required specifications, th < 5 sec and 
Mp < 5%. These requirements conflict with each other. The maximum 
overshoot and the rise time cannot be made smaller simultaneously. 
However, the results obtained are quite acceptable and represent a 


reasonable compromise. 


5.3 Ramp Response 


The linear temperature time curves or the ramp function re- 
sponses of the compensated system are shown in this section together 
with their time functions in the form of T = a+ bt. Fig. 5.2 a) to 
g) show the ramp responses of the system as designed previously. Fig. 
5.3 shows the ramp responses of the system with parameters Kis Ko and 
T. adjusted for the second set of operating condition as described in 
section 4.5. These conditions were Ko = 400, K, = 150, T. = #0 for 
which the controller behaves as a proportional controller with only a 


small integrating effect. 


In Fig. 5.2 the steady state error signal (Ve) is fairly 
constant and less than 2 mV, implying that the thermocouple emf output 
differs from the reference input by less than Soo mW in the steady 


State. This corresponds to the constant positional error in temp- 


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Thermistor bridge calibration curve. 


temperature °C + 


30 «40 60 80 100 120 140. 160 


oo nee Ta 4 a 


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erature of less than 5°. However, at high temperatures near the 

target melting point this error is slightly increased due to the higher 
rate of heat loss. The linearity is also degraded when the input 

ramp speed is higher because the transient response affects a larger 


portion of the curve. 


Figs. 5.4, 5.5, and 5.6 show the error signal, filament 
current and bombarding electron current respectively for a ramp input 
Signal. These curves confirm the validity of the assumptions made in 


the analysis and also show the system performance. 


5.4 Accuracy and Errors in the Measurement of Temperature 


The best accuracy obtained from the thermocouple emf reading 
by means of the digital meter (DANA 3800) is .1lmV which corresponds to 
a temperature difference of about 15°C. This means that the temperature 
reading is qeeirate within + 15°C as far as the digital meter is concerned. 
In addition to the direct thermocouple errors resulting from its own 
limitations in this kind of application, another cause of error is 
the reference junction becoming hotter during the heating period. Close 
to the final temperature this error is quite large. Within the heat- 
ing period of 3 minutes the temperature at the reference junction was 
found to rise up to 45°C as measured by the thermistor bridge circuit. 
The thermistor bridge calibration curve is shown in Fig. 5.7. This temp- 
erature rise corresponds to a thermocouple emf reading of +.136 mV. 
Therefore at the target temperature of 1200°C the thermocouple emf should 
be 13.051 - .136 = 12.915 mV but not considering other errors. The 


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116 


increase in the reference junction temperature depends linearly (to a 
first approximation) on heating time period and the intensity of heat 

at the target and filament. Hence, for a long heating period, this 
error will be sant nee and the temperature-time output for a ramp 

input will not be linear at high temperatures. It is then apparent that 


constant temperature control cannot be obtained over long time periods. 


7 
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117 


CHAPTER VI 
THE STUDY OF DESORPTION SPECTRA 
6.1 Introduction 


This chapter demonstrates some of the desorption spectra obtained 
by using a linear time temperature schedule as described in the previous 
chapter. Some of these results will then be compared with those obtained 


by Burch?. 


6.2 Apparatus 


In the present work the same ion beam generator and the same 
configuration as described by Burch were used to bombard a clean stain- 
less steel target with measured doses of helium and argon ions within 
the energy range of 100 to 800 ev. Following bombardment the chamber 
was evacuated and isolated and the target temperature was raised at a 
known rate. The rate of pressure change caused by the desorption of the 
trapped gas was recorded by differentiation of the output signal from 
an AEI "Minimass" mass spectrometer tuned to the mass number of the inert 


gas. 


The differentiating circuit as shown in Fig. 6.1 consists 
of a noninverting FET dc amplifier set at a gain of 100 followed by a 


low noise differentiator circuit. 


Two matched, general purpose silicon JFET's, type MPF111 


were used in the amplifier. The current source, comprising two 2N3904 


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119 


transistors as shown, delivered about 400 yA. One transistor connected 
as a diode acted as a zener device to partially compensate for variations 


with temperature of the other transistor's base-emitter voltage. 


6.3 Experimental Method 


The bombardment-desorption sequence involved the following 
experimental steps: 

1. The target was cleaned by heating by electron bombardment 
up to 1200°C. 

2. The chamber was evacuated to a background pressure of 
5 x 107° torr. 

3. The chamber was isolated and an inert gas was admitted to 


> ahd:4 107° torre 


the system to a pressure between 1 x 10- 

4. The clean target was bombarded at the selected ion energy 
and the target current recorded in a specified time period. 

5. Following bombardment, the chamber was evacuated to a 
pressure of less than 5 x 10° !9 torr with the mass spectrometer now turned 
on. 

6. The chamber was again isolated, the target heated at a 
linear rate as controlled by the circuits described in this thesis and 


the time derivative of output from the mass spectrometer was recorded 


during the heating period, generating a desorption spectrum. 
6.4 Results 
6.4.1 Desorption Spectra 


The desorption spectra obtained for incident ion energies of 


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124 


100 to 500 eV for helium are shown in Fig. 6.2. The heating rate is 
6.83°K/sec. from room temperature up to 1200°C approximately. Figure 
6.3 shows desorption spectra of the same gas of incident ion energies 


600 - 800 eV but the heating rate is slightly changed to 7.12°C/sec. 


Two desorption spectra for argon at incident ion energies 
of 200, 500 eV with heating rates of 5.25°C/sec are shown in Fig. 6.4. 
Another spectrum at an energy of 800 eV with a heating rate of 6.7°C/sec. 


is shown in Fig. 6.5. 


In all cases, the incident ion current was constant at Packets 


amperes throughout a 5 minute bombarding period. The target area is 


eeeo cm, hence the number of incident ions by measurement is 


-7 : 
1, 5x10 1 
n(meas) = x x 60x5 
SPL waa: 
seirasxi0! — jons/cm@ 


. e J J 2 
However secondary emission reduces this to a value 


n(true) = pimeas) (6.1) 
= 0.8n (meas) (6.2) 


14 


0.8x1.25x10 


1x10!4 


ions/cm. 


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125 


The desorption spectra in Fig. 6.2 contain many distinct 
peaks which show pronounced variation with increasing energies. At low 
energies =~ 200 ev there are 5 individual peaks. For ease of identification 
and comparision with previous work, these peaks are labeled O12 Ap» Ags 
n and g in order of increasing temperature. The first three peaks 
are very wide and the 04 peak is visible only at ion energies of 100, 
200 ev at 150-160°C. The On peak can be noticed up to an ion energy of 
500 ey at 395-405°C. 


The population of a3 is much higher than that of On but is 
found to decrease and maintain the same magnitude in spectra taken beyond 


300 ev. This peak occurs at 590-600°C. 


The n peak appears clearly in the 200 ev spectrum at 655-660°C 
but seems to contribute only slightly to the total gas desorption 
spectrum. It gradually decreases in magnitude and disappears in the 


600, 700, 800 ey spectra. 


The 8 peak is the most dominant peak in all desorption spectra 
and is found to shift from 765-775°C to 805-815°C in going from the 100 ev 


to the 500 ev spectra. 


Fig. 6.3 shows the effect of increasing ion energy with only 
a Slight increase in heating rate. Only two distinct peaks Oe and 8 can 
be noticed. It is found again that the positions of the Oe peaks are 
the same at 600-610°C but g peak shifts slightly from 850-860°C to 


870-875°C. These two peaks eventually decrease in amplitudes for higher 


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126 


ion energies as observed in the 800 eV spectra. Higher ion energy gas 
will be trapped more deeply below the surface and will require a higher 
energy for release. It can be seen from Fig. 6.3 that most gas is 
desorbed at higher temperatures. This also corresponds to the temperature 


shift that g exhibits for progressively higher incident ion energies. 


The shape of the desorption spectra can be used to determine 
the order of the desorption reaction’. For a first order case the 


peak shape is expressed by 


N 
InlyP] = RLF - i + oa - expl- RF - me (6.3) 


where No = the rate of desorption at Ty 


= maximum desorption rate. 


This equation shows that for first order reactions ‘the de- 
sorption rate curve is asymmetric about Th: 


For the second order case 


weet cexpt- EL - y+ Dy? expl- St yn? (6.4) 
p p p 
when (L) + 1, then 
p 


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127 


Thus the desorption rate curve is symmetric about the maxi- 


mum at T. f -T : 
at T, for |T p| smal] 


Using appropriate sweep speeds for the linear temperature- 
time schedules,as described in the previous chapter, will give good 
resolution and the symmetry of these peaks may be clearly distinguished 
simply by visual examination. The desorption spectra obtained were 
examined by use of this fact and only theg peak was found to be symmetric. 
The a-group peaks are asymmetric and too wide. The n peak is rather small 
and likely to be symmetric if it is not masked by Og and 8 peaks, 


however the other properties incline to those of the a group. 


From the information discussed so far it can be summarized 
that for a group peaks the activation energies (which are functions of 
tT) are independent of ion energy and their shapes are asymmetric. Those 
for the 8 group appear to increase with incident ion energy and their 
Shapes are symmetric. The n peak behaves midway between the a and 8 
groups. Thus it will be concluded that the a group peaks are first order 
processes and the g peak is a second order process. The processes 
governing the gas desorption in the n peak cannot be characterised by 


visual examination alone. 


6.4.2 The determination of activation energies 


The activation energies for a group peaks may be calculated 


from equation (1.4): 


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128 


Vea 
tet aging!) - 3.64 (1.4) 
RT b 
p 
Walk 
Then E = RTALIn a eran (6.6) 
a 10!3+ | 
= 1,986x10°°>T [In ——?-3.64 ] k cal/mole (6.7) 
or in electron volts : E(eV) = EtKcal emote) (6.8) 
Redhead 3 has shown that 
Oo 
| Chest CLL aie nal (6.9) 
Sm n=I en=2 


where a the coverage at the start of the temperature 
sweep, 


p = the coverage at temperature Th: 


Q 
! 


The initial surface coverage can be obtained by measuring 
the area under the desorbtion rate curves, 7.e., 


oo 


cae ui Ndt (6.10) 
0 


Using basic desorbtion rate equations and the approximation 
io} 
for -. it was shown for the linear sweep case that 
fo) 


al 
“ 
| = 
of % 
ot. ys 
t 
TOT ‘ 
y 7 mw = . ~~ ry 
Fe a F . @ » * TL“ OFfLTAnRO | © 
[p> 67 & Dake ~~ > fl | j " i AGI » t 
“s q 
' Se 


Ww 
~~ 
j 
-— 
sy 
— 
Hl 


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wee eS 


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+7) 
eae ie 
é« 94 ey we 
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; ; 
a ait; os 


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= ' 


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eee it 


129 


2 
eN_RT 
Sache PP TOn na! 
0 
D (onat) 
AN RT 
= 5p eis eh ere 


Therefore at the same Ty and the same peak the activation energy obtained 
from the first order calculation (Ea) and that obtained from the second 


order calculation (Eg) will have the ratio 


Eat 
Ea e 
Fe = * Ea (6.12) 


Hence the activation energies of the 8 peaks can be calculated 
from equations (6.7) and (6.12). If gas desorbtion from the n peak can 
be regarded as a first order reaction process, the activation energy 


can then be found from equation (6.7). 


The results from the calculation are tabulated below: 


Results from Helium Desorption 


Peak qT Activation Energy 
(approximated in°C) (kcal/mole) (ev) 
04 155 26 Lai 
Oo 400 41.3 1.29 
9 595 53.6 2.34 


n 657 O/ 26 2.56 


~ 


= 
2 
a 
7 

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4 


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(Si eet 


Wigin! | Ae 


130 


Peak qh, Activation Energy 
(approximated in °C) kcal/mole eV 
765-815 95.35-99.25 4.14-4.32 (Ion energy 
100-500ev ) 
B 
850-875 103.1-104.9 4.47-4.55 (Ion energy 
600-800 ev) 


In the high temperature region gas is continuously desorbed 
from many sites of different desorption energies. These small peaks with 
no gap between them make the analysis rather difficult and uncertain. 

For higher incident ion energy most gas desorbes from this region and 


the desorption rate will stay high until the target is melted. 


The same phenomenon appears in the argon desorption spectra 
as shown in Fig. 6.4 and 6.5. By carefully examining these three desorption 
Spectra some dominant peaks can be labelled as a‘, a", a'", and g'. 
Only the first two peaks appear in the low ion energy (200 ev) spectrum. 
The next peak (a''') arises in the spectrum for 500 ev ion energy and 
eventually all four peaks appear in the spectrum for 800 ev ion energy. 


Some additional peaks also appear between oa group peaks. 


It is interesting that the a group peaks and g' peaks in the 
argon desorption spectra correspond to those for the helium desorption 
spectra. This agrees with the observation! that the activation energies 
are the same for all gases, suggesting a release mechanism determined 
by the thermal behaviour of the lattice rather than of the trapped 


particle itself. It may be checked here by calculating the activation 


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131 


energies of different peaks when the orders of reaction are known from 
the corresponding helium desorption peaks. The results are tabulated 
below: 


Results from Argon Desorption 
i 


Peak _p Activation Energy 
(approximated in °K) kcal/mole ev 
a! 460 Lone 1.22 
a 639 38.5 Ve67 
a hee 819 Bi ie 
n' 943 58 .6 2.54 


B' 1108 101.5 4.4] 


It can be seen that the calculated activation energies given 
above agree with those obtained from helium desorption spectra within 
experimental error. 


Another distinct peak appears between a" and a'" peaks in 
Fig. 6.4 approximately at 718°K and has the activation energy 44.6 


kcal/mole (1.94 ev). 


It should be noticed that the resolution of the argon de- 
sorption spectra at low ion energy is rather low compared with helium 
and higher ion energy must be used to clarify all peaks. The reason 
for this concerns mass and radius of the trapped gas atom. The helium 


atom, having small radius and mass will have deeper penetration for a 


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132 


given ion energy. 


6.4.3 Comparison to previous results by Burch® 


Most results from this work agree with those obtained by 
Burch. However, more peaks are found both in helium and argon desorption 


Spectra and the activation energies for the g peaks are different. 


Each peak can be compared by the order of the reaction and 


activation energy as follows: 
present peak : Oy [A | og | on B 
peak found by Burch: Oty Seo rad B 


The activation energies for a-group peaks and the n peak are 
in the same range but those for g peaks as calculated by Burch are 
between 2.98 to 3.08 ev while the values from the present work are 
between 4.14 - 4.32 ev for the same range of ion energy (100-500 ev). 
Different methods of calculation and different target configurations 


probably cause differences in activation energies. 


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CHAPTER VII 
CONCLUSIONS 


7.1 Summary 


The work reported in the preceding chapters of this thesis 
can be summarized as follows. A proportional plus integral temperature 
controller was built for the linear control of the temperature rise of 
a Stainless steel target from room temperature up to the melting point. 
Successful attempts were made to limit the number of complicated 
components in the construction of the controller while maintaining its 
efficiency and accuracy as required in this application. The solution 
resorted to some mechanical arrangement of the available potentiometers 
which become the most valuable parts of the controller and simplify all 
delicate work. Thus the design of the controller is electromechanical 
in nature. At least one high performance ramp generator and a summing 


amplifier with inherent drifts and offsets were eliminated. 


The controlled thermal system appeared to be a nonlinear 
system mainly because of the associated radiant heat gain and heat loss 
from the target. The behaviour of the thermal system, as described by 
some complicated expressions, showed that the position of one pole of 
the thermal system depended on the actual target temperature. To avoid 
any difficulty in dealing with these nonlinear solutions, a linearizing 


method was introduced and the thermal system was approximated as a linear 


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134 


second order system. Therefore, the entire system could be analysed 


and designed by using only basically linear techniques. 


Stability of the system was obtained by cancellation of 

an unwanted pole in the transfer function of the system. After doing 
So, the Bode plot showed that the phase and gain margin of the system 
were very small. To keep the steady state error of the target temp- 
erature to a small TERA the controller gain had to be increased, again 
causing the system to be unstable. A phase lead compensation network 
had to be introduced into the feedback path to increase the stability 
and improve the system performance. The results were better linearity 
of the output temperature, no noticeable overshoots, greater overal| 


system stability. 


Many unavoidable errors in the temperature measurements are 
pointed out. These errors were due to the rapid deterioration of the 
thermocouple under the particular conditions of use, and the increase of 
the reference junction temperature during each run. When the control 
system was operated over a normal time period (3 minutes) of one run, 
the error due to the latter cause was small and of the same magnitude 


as the error from the measuring instrument. 


To demonstrate the application of the controller and to study 
the gas adsorption from the surface of stainless steel (type 304) commonly 
used in vacuum system manufacture, some helium and argon ion desorption 


Spectra for different ion energies were obtained. The results revealed 


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135 


that the activation energies obtained from the desorption spectra for 
both trapped gases were in the same range. This shows that the 


activation energies are the properties of the material itself. 


Generally most results agree with those obtained by Burch. 
The a-group peaks are first order reactions, the g peak is a second 
Order reaction process while the n peak falls between the a and 8g 
characteristics. The activation energies for the a and n peaks in both 
this and Burch's work are within the same range but for the g peak the 


present values, as calculated by the method described, are higher. 


7.2 Suggestions for Further Work 


Considering the designed controller, better performance may be 
achieved by replacing all moving parts with electronic circuits specially 
designed for this purpose. The electronic controller will be more 
accurate, have better overall frequency response and be capable of 
controlling a faster rate of temperature rise. The integrator and 
summer should be modified such that the drifts and offsets which create 
additional errors are minimized. The target and filament configurations 
should also be modified so that heat transfer by the electron bombarding 
process is much more effective resulting in the effective gain of the 
thermal system being increased. This may also require another high 
voltage power supply capable of delivering more current at higher voltage. 
To implement the suggested improvements, the ultra high vacuum chamber 


may also have to be modified to prevent breakdown between the filament 


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136 


current supply leads and the chamber. 


Further useful information on surface properties of various 
materials may be obtained by performing different desorption tests 


using the facilities provided by this linear temperature controller. 


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137 


BIBLIOGRAPHY 
Kornelsen, "The Ionic Entrapment and Thermal Desorption of 
Inert Gases in Tungsten for Kinetic Energies of 40 EV to 


SVKEVy Catimeue nopl. Physi, vol. 42," pp. 364-381, “19647 


. Burch, "Low Energy Ion Bombardment of Stainless Steel," 


M.Sc. Thesis, The University of Alberta, Canada, 1971. 
Redhead, "Thermal Desorption of Gases; Vacuum, vol. 12, 


pr 203-211), 41962: 


[4] G. Carter, "Thermal Resolution of Desorption Energy Spectra," 


hap) R.BY 


pe KAR. 
iis WOH: 


HePpl EAR 


Vacuum, vol. 12, pp. 245-254, 1962. 

Burtt, J.Si.Colligon and J.H. Leck, Brit. J. Appl. Phys., 
VOI?! 2 7 (pt 6396),6 1961": 

Spangenberg, "Vacuum Tubes," ch. 4, 8, McGraw-Hill, 1948. 
Kohl, "Handbook of Materials and Techniques for Vacuum 
Devices," p. 570, Reinhold Publishing Corp., New York, 1967. 
Chaffee, "Theory of Thermionic Vacuum Tubes," Ch. 4, 5, 


McGraw-Hill, New York, 1933. 


[9] American Society for Testing and Materials, Committee E-20 on 


PO" RL. 


Temperature Measurement, "Manual on The Use of Thermocouples 

in Temperature Measurement," 1970. 

Forgacs, B.A. Parafin, and E. Eichen, "High Voltage Cathode 
Temperature Measurement," The Review of Scientific Instruments, 


vol. 36, No. 8, pp. 1198-1203, Aug. 1965. 


{ 
a ; 
¥ { 
~ t 
! 
vii 75 y 
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{ _ 
- * ‘ = . 1 
. 7 : ~ 5 ein i ‘ r % Sa i” _—_ 
{i 9T3 | tu Jean nf 29280 tren! 7 
f 
’ oe Prey, | r 1 rf ac’) ti y 74 | 
' ‘ e | v ¢*+¢y ie eo ' ° « ThE «* s 
\\ = 
. ve. » = t " ~» }¢ oO 
risdnieg fol yoy a)": owd .2.M 
— 4 ” ; y & ws “+t aT y 
: FQ At gal mi .oc.4 == 
P : : P , w rs — —: rt 
i : = rm 2) SS 087 AF 
t ; ri PHo _ 
- P \~ fl .a0 
‘i 
: ‘ - bos 2 a ee san malt veins ox : 
; ' TI Se2gy TO tf } tie Se T SETI ST | TSS TBS 2 
, i" 
* 
' L ‘a F ns nee 1 
A, ~PdS-@b$ .aq ,Sf .fov ,muuasy 
n a ia nS ¥ t - : ely 
. s 4 : ’ po = WV : OT f1GdesGut ew We 8.8 
> ° 
* ; \ yf 
* at q e ‘ .~ ov 
j 


° : J 3 : € - ‘ Po u MAUMOG ¥ , P¥ednst OIG * ie AM 


: v Skin ht 1 htadnt 
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ie J 
- : al mT) t ———— an — Lt? + 7 = 4. an am | / 
+ > : Le! HEL | >} THD Vay f ro ( roornT’ ead bad eule 
conor de 4 Mw 
Ae rOY wal ql ftit-wes 
. ‘ 
i a bg" 
Ac. f nore oe ae oe 
M0 OS-3 vodttamod ,2tetratet bine patvest sot qetooz ees 
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aos ‘edramerw2sam wresbort9 aqmeT af 


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y 


[11] 


[12] 


[13] 


[14] 


[15] 


[16] 


[17] 


[18] 


Bea. 


[20] 


[21] 


138 


M. Kutz, "Temperature Control," John Wiley and Sons, Inc., New 
York, 1968. 

B. Gebhart, "Heat Transfer, Ch. 4, 5, Second Edition, McGraw-Hill, 
New York, 1971. 

W.K. Roots, "Fundamental of Temperature Control $ Ch. 3, Academic 
Press, Inc., New York, 1969. 

P. Naslin, "The Dynamics of Linear and Non-Linear Systems," 
pp. 225-228, Blackie and Son Limited, London and Glasgow, 1965. 

G.J. Deboo, C.N. Burrous, "Integrated Circuits and Semiconductor 
Devices - Theory and Application," Chapter 3, McGraw-Hill, 

New York, 1971. 

"Application Note for »A726 Temperature Controlled Differential 
Pair," Fairchild Semiconductor, Mountain View, California, 
1967. | 

J.G. Graeme, G.E. Tobey and L.P. Huelsman, "Operational Amplifiers, 
Design and Applications; McGraw-Hill, New York, 1971. 

"Application Note for MC1439G, MC1539G Operational Amplifiers," 
Motorola Semiconductor Products, Inc., Phoenix, Arizona, 1968. 

"Application Note for MC1741, MC1741C Operational Amplifiers," 
Motorola Semiconductor Products Inc., Phoenix, Arizona, 1969. 

F.W. Gutzwiller, et al., "SCR Manual; 4th Edition, General 
Electronic Company, Syracuse, New York, 1967. 

K. Ogata, "Modern Control Engineering," Prentice-Hall Inc., Engle- 


wood.Gliffss Nule, 1970. 


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