Journal of the Indian Institute o f Science, Bangalore 560012, India
[ Section A : Engineering and Technology ]
Scp~atnber 1980
Volume 62
Number 9
CONTENTS
Page
ORIGINAL PAPERS
Mievo wave Engineering
G ~ o QJohn
~
159
D. H. L. Prasad
171
AN OSCILLATOR CIRCUIT WIT14 A 1 INCAR RELATION BETWEEN FREQUENCY AND
TEMPERATURE
S. Chaudhuri
179
Q-BANDBBAM
WAVEGUIDE
Chemical Enginceving
ESTIMATION
OF
SUWACE ENSION OF P U R E LIQUIDS
SHORT COMMIJNICATION
Instrumcatation
j.
Indian Inst. Sci. 62 (A), Sept., 1980, Pp. 159-170.
,G Indian Institute or Science, Printed in India.
Qband beam waveguide
GLORY JOHN*
Communication Engineering Deparfment,.Indian Institulc of Sci+~c~,
Bangsforc 560 012.
U&cal
Receiyed on August 23, 1980.
A report of the design, development ana periom~ancecharacteristics of a Q-band (8 nim) confoal.
mned, aielectric lens beam waveguide is presented.
Key words: Beam transmission, bean1 waveguide, millimeter waw transmission
The pioneering work of Goubau, followed by several other investigatorsl-?%on h a m
waveguides using iris, confocal mirrors and lenses, and guides -using gas focusing
system, including the study of the presence of higher ordcr modes and their effect on
the transmission characteristics of beam modes, stability of modes, phenonxnon o l
mode conversion due to misalignment of phase transformers and the problem of launching a Gaussian beam onto the beam waveguide, has led to the evolution of a new
method of free-space guided wave long distance communication by millimeter, submillimeter and optical waves with very low dispersion loss, which is du: to the utilisation
of the principle of reiteration of wave beams at regular intervals.
The object of this work is to study the free space millimeter wave propagation
~haracteristicsfor long distance communications and, as a first step, a 25-feet long guided
wave test bench using dielectric zoned lenses has been designed and developed to work
at 8 mm wavelength.
As far a s can be gathered from available published literature, smooth surface lens
has been used by the earlier investigators for the construction of beam waveguide. In
order to reduce the (i) weight and (ii) absorption loss in the material, it has been thought
worthwhile to use zoned dielectric lenses. It js also the object ofthis work to &termin$
whether efficient reiteration of wave beams can be achieved a t regular inter5alr by using
z~Lt&, instead of smooth, surface lens.
' hrseat address :
Dept. of Matheitlatin, Unijcrsity of Dundoe, DUlKee DD1 4HN,
UK.
159
GLORY JOHN
-
0
.'
25
7 15
-d
: ILrn
ib,
1
FIG.1. Plot of axial field variation (theoretical).
The paper presents a report containing the design details of the beam waveguide and
rasults of measurement of its performance characteristics.
2. Numerical computation of axial and radial fields
The mathematical formulation of the principle of propagation of wayes guided by beam
waveguides is based on elzctro~nagnetic wave beams of the type which exists in thi
Fresnel region of highly directiunal antennas and whose field distribution can be reconstituted at periodic intervals. Sincz the electromagnetic e n e r a in the Fresnel region is
essentially confined to a cylil~drlcalspace and the free space loss is insignificantly small,
the reconstitution of th; Frrsnel chxracter of the field by beam waveguide provides a
method for long distance communication at inilliineter wavelengths. The expressiio
for ths transverse electric field in terms or elementary waves4 is
where 7 is the mode parameter
G,, (x) = p L: (xz)
Q-BANI) BEAM WA\'~GUID);
?,i
1 ;
10
0
5
70 i m
5
2
1010
P
FIG.2. Plot of
,?
5
0
:100
irn
5
10
(cm )
r a d ~ a lfield variat~on(thcoret!cal).
are the Lagiwrrc-Gaussian functions and
LZZ (.+)
-
e" x-"' d"
=
re
= .cnr"'l
are the g e ~ l e r a h dLaguerre poiynomials.
The beam modes satisfy the following orthogonal relations
27
@=0
wl~cre
I
iC
p=o
Em,,Em~~,pd/~cl~=&mn~dn~,
..=em;..
nz# n
(4)
(3
The axial ( 2 ) field distributions for the fundamental mode E,,, and the transverse ((0
field distributions for E,,,, as well as some higher modes, computed using eqn. (1) with
162
GLORY JOHN
FLG.3. Experimental set-up of the Q-band bedm waveguide
the help of DEC-10 computer are presented respectively in Figs. 1 and 2. These figures
exhibit a decay of the E,, mode in the sdirection and a. Gaussian form in its crosssectional field distribution at different axial di$tances from the source. This is the desired
property of a beam waveguide.
3. Experimental &-up
Figure 3 shows the experimental set u p of the beam waveguide which has been desigcd
and developed. It consists of uniformly spaced phase transformers (zoned dielectric
lenses) which represent the actua.1 guiding structure a.nd terminations for launching and
receiving the desired bea.m mode. The transm.itting horn, which is a pyramidalhorn
with a ga,in of 22 db, is excited by a Reflex Klystron R5146. The receiving horn is
similar to the transmitting horn, and the power output is taken through a bolomersr
to a power bridge.
4. Design of lens
The phase transformers are designed to adwnce the phese in the outer portion of the
beam relative to the centre, according to the relation
Q-BAND BEAM WAVEGUIDE
FIG. 4. Zoned dielectric lens R = 15 cnl ; f = 135 cm.
where # is the phase advance at a radius p, D is the spacing of the phase transformers
and k = 2nli. The diffraction loss L, of a phase transformer, caused by the crosssectional 1imita.tion of the beam, is rehted to the maximum phase shift ,.#,
= kRiD,
'vhere R is the radius of the phase transformer6Ju. It has been shown by Christian
and Goubaus that for the fundamental mode this loss drops below 0.01 db per iteration,
if dm,,, approaches 2 ~ .Hence in the present work, the maximum phase shift for the
fundamental mode has been fixed to a value of 2n, and, by fixing a suitable value for
D. the aperture radius R has been determined. This value of R givas the minimum
diTraction loss per iteration.
1.3. Zoned dfelectvic lenses
h p l e hyperboloid contour dielectric lenses of large diameter are quite heavy, and have
sign~ficantattenuation loss. These disadvantages can be reduced by employing the
'stepped ' or ' zoned ' construction. In a stepped lens, the maximum change in the
optical path length which has to be introduced by the lens material is one wavelength.
Hence the thickness of a pIanoconvex lens need never exceed u = ?.i(n - I) (where ?.is
Table I
Design dimensions of zoned lenses
Range of P (cnl)
Thickness of lens (cn?)
These values agree well with the actual path length calculations
the wavelength and n is the refractive index of the material), irrespective of the aperture
size. The zoned lenses of focal length Dl2 have been constructed by machining ann~ia~
steps of appropriate widths and depth into the surface of the dielectric sheet of
refractive index n. The lenses were made in such a way that the pha.se change across
the successive zones is 45" (n/8radians), the depth of the steps being 48. The thco.
retical efficiency of such a lens is very nea.rly equal t o that of a n ideal phase correctine
lens".
Figure 4 shows the zoned, dielectric lens with a radius R = 15 cm and focal length
Table I gives the design dimensions of the lenses used for the
construction of the beam waveguide. The dielectric constant of the lens material is
2.56.
,f (= Di2) = 135 cm.
Flo. 5. Axial variation of the field: ( a ) without the lens (experi~~rn~tal);
(@wit11one lens (experirnsntali.
Q-BAND BEAM WAVBGUIDC
2 1
20 crn
FIG 6 . Fundamentdl m o d e combined with Ihe higher order modes (experimental)
5. Measurements
The results of measurements to explore the axial and cross-sectional field distributions
with and without phase transformers are rep~rtedin Figs. 5-9. The normalised power
patterns instead of field patterns are plotted. It is obscrved that:
(i) The axial field (the outer envelope of the field has been plotted for simplicity)
is oscillatory very near the source (Fig. 5 a, without lens) and the oscillation
persists for about 25 em away from the sourco. The oscillation may be ascribed
to the presence of higher order modes superposed on the fundamental mode.
FfQ.7. Cross-sectional varlatlon of the field
without the lens (experimental)
GLORY JOBN
FIG. 8.
CroPr-sectional vn~ialion of tho Beid with one lens (cxperimmtal)
(xi) The oscillation disappears alter one lens is used (Fig. 5 b).
(ii) The higher order mode> having higher ratc of attenuation die out fastzr than
the fundamental mode. This is evident from a comparison of the two mres
in Fig. 6. which presents the cross-sectional field distributions very close to the
source (Fig. 6 a) and 20 cm away (Fig. 6 b) from the previous location of the
measurement.
(iv)
The introductio~lof a phase trancformer does llot changc the heam mode.
(v)The beam cross-section broadcns considerably in the =-direction without any
lens (Fig. 7).
(vi) With one lens, however, the beam undergoes a change from a broad to a
Mrrow cross-section (near the focal point of the lens) and then the beam diverges,
thus exhibiting the reiteration phenomenon,
la)
FG. 9. Axial wuiation of the iield : (0)with
!dth two lenses.
two lenses ; (b) Crois-scctioiml variation or the field
biii The effect or inserting the second lens on the axial and cross-sectional field
distribution shows further the principle of reiteration (Fig. 9). The asymmetry
(Fig. 9 b) is possibly due to slight tilt of the second lens with respect to the
first lens.
h besn verified that (a) the wave beam is reiterated when confocal, zoned, dielectric
are wed as phase transformers in place of smooth surfaced transformers in a beam
rdwide, (b) properly aligned beam waveguide can be used for long distance communiQfmn at millimeter wave frequencies. Since the loss calculations and the calculations
r r f m t a n lenergy flux contours have already been done for the beam waveguide by the
"tier investigators4,these have not been repeated for the case of zoned dielectric lenses,
168
GLORY JOHN
Acknowledgement
T h e a u t h o r gratefully acknowledges t h e help a n d encouragement received fran
prof. (Mrs.) R. Chatterjee a n d Prof. S. K. Chatterjee for t h e above investigation,
References
Measurements on an iris beam waveguide, Proc. IRE, ]%lV1,
1679-1680.
2. FOX, A. G. AND
Lr, T.
Resonant modes in a maser interferometer, Bell
1961, 40, 453-488.
3. DEGENEORD,
I. E.,
$IRKIS, M. D. AND
STFlW, W. H.
The reflecting beam waveguide, IEEE. Pans. on Micr. 77.,
1964, MTT-12, 445-453.
Sy~t,
On the guided propagation of electromagnetic wave
Pans. Ant. Prop., 1961, AP-9, 248-256.
5. &RIS~'IAN,3. R.
GOUBAU,
G.
AND
I,,
re&.,
,RE
Experimental studies on a beam waveguide for miiiimeter
IRE Trans. Ant. Prop., 1961, AP-9, 256-263.
Optical relations for coherent wave beams, Smp. ~ k ~ t i . ~ ~ ~
theory and antennas, Copenhagen, Pergaman Prers, Oxford, 1962,
907-918.
7. TIEN,P. K., GORDON,
3. P.
AND
WHINNERY,
J. R.
Focussing of a light beam of gaussian field distribution in moti.
nuous and periodic lens-like media, Proc. IEEE, 1965, 53, 129-136,
A lens or light guide using convectively distorted thermal g r a d k
in gases, Bell. Syst. Tech. J . , 1964, 43, 1469-1475.
Reiterative wavebeams of rectangular symmetry, Arch. Lr,El&.
Uber., 1961, 15, 555-564.
Higher modes in guided electromagnetic wavebeam, IRE Tram
Ant. Prop., 1962, AP-10, 349-350.
11. HIRANO,
J. AND
FAKUTSU,Y.
Stability of a light beam in a beam waveguide, Pror. IEEE, 1%.
52, 1284-1292.
Mode conversion loss in a sequential, confocal lens Sysfem,PIN
IEE, 1964, 111, 610-615.
On the theory of randady misaligned beam waveguides,
Trans. Micr. Th. Tech., 1967, MTI-15, 206-215.
Loss measurements with a beam waveguide for long
transmission at optical frequencies, Proc. IEEE, 1964 52, 17%
Loss measurements of the beam waveguide, IEEE Trm.
Th. Tech., 1963, MTT-11, 18-22.
16. CHRSIUN, 1. R.,
Gaue~u,G , AND MINK,J.
Self-aligning optical beam wavegnides, IEEE Catf.
Ehgp. Appaicafinns, Washington D.C., 1967.
169
U-BAND BEAM WAVEGUIDE
1;. GoWAU, G. AND
CKRBMN, J. R.
18.
cwm,
J. R.,
Gous~u,G.AND
MINK, S.
19.
BASKAKOV, S.
E.
A SCHWERING, F.
ZAWLER, A.
AND
I!. CHAPFIN,R. J.
BEYE?, I. B.
AND
Some aspects of bean1 waveguides for long disiance transmission
at optical frequencies, IEEE Truns. Mic,: Th. T~ch., 1964.
MT-12, 212-220.
Further investigations with an optical beam waveguide Tor longdistance transmission, IEEE nuns. Micr. Th. Tech., 1967,
MTT-15, 216-219.
Excilation of beam waveguide, Rudio En$#. Elecrr. PIZTA.(USSR),
(Engl. Trans.), 1964, 9, 492-499.
Beam waveguide excitation by the aperture field of a tubular waveguide, IEEE Tms. Micr. Ti!. Tech., 1967, MTT-15, 191-192.
A lowless launcher for beam waveguide, IEEE Tram. Micr. Th.
Tech., 1964, MTT-12, 555.
Quasioptical components
millimeter
and
submillimeter waves,
Ed. by F. A. Benson, Published by Life Books Ltd., London, 1969,
403-450.
J.
Indian Inst. Sci. 62 (A), Sept. 1480, Pp. 171-178.
of Science, Printed in India.
9 Indian Institute
Estimation of surface tension of pure liquids
D. H.L. PRASAD"
Department of Chemical Engineering, Indian Institute of Science, Bangalore 560 012.
Received on August 5, 1980 ; Revised on September 19, 1980.
Based on the theorem of corresponding states, surface tension of liquids is expressed as
g
= [0.4 -k 0.009 R,
+ 0.00108 (411N/r"lBkT,)]
x
PEi3GI3(1 - T ~ ) ~ ~ / ~ .
The equation predicts surface tension of pure polar as well as nun-polar liquids better than other
gcnemlised methods.
Key nor& : Surface tension, corresponding states, polar and non-polar liquids.
Values of surface tension of liquids are needed in connection with several chemical
engineering calculations such as those for interfacial area, plate-spacing, slot-opening,
entrainment rate and liquid-holdup in problems relating to two-phase flow, nucleateboiling heat transfer and the design of distillation columns. A good estimation method
is very useful for design purposes in the absence of experimental data. In view of
thc applications in other fields as well, estimation of surface tension remained a topic
of interest for over a century.
The theoretical aspects of surface tension have beea discussed in several books on
surface chemistry (for example Adamsonl). Surface tension results due to the various
forces acting o n the molecules and is expmsed as dynes/cm. From the theoretical and
axperimental knowledge, it can be stated that the surface tenion of pure liquids in equilibrium with their own vapours (or with air) decreases with increase in pressure and
temprature and becomes zero a t the criticaI point.
* Present address : Properties Group, Design and Engineering Division, Regional R e s w h Laboratory.
Hydenbad 5M 009.
1Lk-2
171
2.
Methods of estimation of surface tension
Even before the time of Van der Waals2, attempts have been made to correlate surfaet
tension of liquids in terms of other known or easily determinable properties.
a
result, several methods for the estimation of surface tension have been proposed,
Important ones among them have been lnentioned heere and their merits and limitations
discussed. Detailed account is given by Partington3 and Reid et a14.
Van der Walls equation"
with K and
as universal constants is the basis for the correlations based on &
theorem of corresponding states. While eqn. (I) does not give accurate results, m&,&
extending the concept give results of engineering accuracy.
Macleod6 found a relation between surface tension y, density of liquid p, and
of vapour pv in the form
Sugden6termed [PI the parachor and found that the parachor can be calculated by
the group contribution method. Equation (2) predicts surface tension reasonably
well (with an error of about 5:4) if experimental values of liquid and vapour dens*
are available at the conditions of interest. Varjations of the method in terms of all the
variables of eqn. (2) are possible. Lennard-Jonei potential parameters have been I!&
to correlate
Liquid and vapoar densities can be determined from one of the
preferred corresponding states correlation^^-^^.
Wrighti2 proposed a variation of Sugden's method while the relationships with viscosity have been used on some o c c a ~ i o n s ~ ~ J ~ .
Most of the methods discussed so far, and others proposed'5-zl, are disadvantageous
as they require some physical properties such as viscosity, liquid density and/or vapour
density, refractive index, etc., at the conditions of interest, in addition to the 0 t h
parameters needed to use the correlations. Corresponding states methods based on
Van der Waals equations overcome this difficulty and are superior as estimation methods.
Brock and Bird"2 developed the ideas given in Van der Waals paper for non-polar
liquids and proposed
where the constant K i n eqn. (1) is expressed as function of the third parameter debd
by Riedels3, as
Hakim ef a P used Pitmr's acentric factor24 and proposed the correlation
r
=
p ~ ~ Q,
q Kl~ -s T~)/0.41"
(4)
ESTIMATION OF SURFACE TENSION OF PURE LIQUIDS
173
ivhere
+ 0,359w - 1 . 7 6 9 ~- 1 3 , 6 9 9 - 0.51 + 11298w,:
+ 0.5385 o - 14.61 x - 32.07 X" 1.656 w"i 22.03 wx
Q, = 0.1574
nz = 1.21
UJ=
- 1.0 -log
,
:= log
jn
(P,,/P,J
P,at
TR=0.7
at T, = 0 . 6
which P,, is the reduced vapour pressure of normal fluid.
The twelve constants appearing in the relations for Q, and nz of the correlstion were
obtained from the experimental da.ta of 16 polar liquids soze of which are only
slightly polar. The values of surface tension ca.lculated using eqn. (4) are sensiti\e to
the values of w and x which in turn depend heavily an the nature of the vapour
pressure curve in the region T, = 0.6 to 0.7.
3. Present work
An easily determinable property satisfying the requirer.ents of chirrecterising all classes
of substances, as pointed out earlier"mo1ar polarization at the critical tempereture,
P,,, defined as
Pnc = R,
+ (4nNu2/9kTJ
(5)
where
R, is the molar refraction, cc/mole
N is the Avogadro's number, molecules/mole
p is the dipole moment, debye units
k is the Boltzmann constant
T,is the critical temperature, " K
h been chosen to explore the possibility of arriving at a good correlation for surface
tension of liquids. The general form of eqn. (I) is retained, and effectively, this work
can be considered as an attempt to relate K of eqn. (I) to easily determinable
properties.
Experimental values of surface tension of ten substances (acetone, benzonitrile, ethylmetcaptan, n-propyl-alcohol, propionic acid, n-hexane, n-octane, toluene, carbontetrachloride and cyclopentane) representing polar as well as non-polar substances are
converted to the reduced units by calculating the values of (y/PZ'BC'3)and TR. The
Educed surface tension of each substance is plotted as a function of (1 - TR)"'D to verify
thE temperature dependence. The slopes of the straight lines through the points on
these graphs give the values of K for each substance. Temperature dependence is found
174
Table I
Summary of comparison of calculated values of surface tension with experimental data
P
No. Of
points
<;
averagz absolute deviatianY*
-
Presenr
method
Brock and
Bird
niethod
.Maceiod and
Sugden
method
Acetic acid (29, 30)
Acetone (29, 30)
Aniline (29, 30)
Benzene (29, 30)
Benzonitrile (29)
Bromobenzene (29)
12-Butane (29)
11-Butylalcohol (30)
Carbondisulphide (29, 30)
Carbontetrachloride (29, 30)
Chlorobenzene (29, 30)
2.3-Dimethylbutane (29)
Ethylacetate (29, 30)
Ethylbenzoate (29)
Ethylmercaptan (29)
n-Heptane (29, 30)
n-Hexane (30)
Isobutyric acid (29)
hlethylalcohol (29, 30)
Methylformare (5, 28)
n-Octane (30)
Phenol (29, 30)
n-Propylalcohol (28, 29)
n-Propylbenzene (29)
Toluene (30)
2,2,3-Trimethylpentane (31)
Overall
4
6
6
7
3
3
3
3
5
8
6
2
8
5
2
7
3
5
6
6
3
5
5
5
3
1
120
* Numbers in parentheses indicate references
** Per cent average absolute deviation =
(Exptl. vaiue - Calc. value)
where N i3 tbe number of data points,
8.2
2.5
4.5
5 7
0.3
4.7
3.8
7.6
3.0
1.5
2.0
2.6
12.4
10.3
2.0
0.6
3.4
8.9
16.8
10.0
0.3
2.1
5.2
2.0
3.1
9.0
5.6
52.6
5.1
6.4
2.3
2,2
0 3
1.1
36.3
2.9
4.4
1 0
0.4
1.4
13.2
2.3
2.0
0.3
54.0
92.2
7.0
0.2
25.8
52.2
0.9
2.0
2.3
15.3
to experimental data.
4.5
2.9
5.2
4.3
3.2
0.9
9.2
2.8
4.5
1.2
1.5
0.8
2.9
5.0
7.9
1.8
0. I
2.4
13.7
9.0
0.1
7.8
2.0
2.5
2.1
3.0
4.0
ESTIMATION OF SURFACE TENSION OF PURE LIQUIDS
175
, be well represented by (1 - TR)~'"
as the surface tension values could be predicted
t o m the graphs with an error of less than or equal to 1%.
Values of K could be related to the constituent? of molar polarization at the critical
temperature-the nan-~olar contribution (R,) and polar contribution (4nNp?/9 kT,).
resulting equation for surface tension is:
ne
y = [0.4 f 0.009 R, f 0.00108 (4nNpv9 kT,)] x P5I3 El5
(1 - TR)ll/*
(6)
4. Resolts and discussion
Values of surface tension of several pure liquids calcuIated using eqn. (6), the Brock
a d Bird method and the Macleod and Sugden method are compared with the experimental data. In view of the difficulties in obtaining accurate values OF co and x, the
Hakim et al method has not been tested for this group of substances. Comparisons
summarised in Table I show that the present method is decidedly snpzrior to the other
~neerlized method of Brock and Bird and is of accuracy comparable to that of
Macleod and Sugden method which requires liquid and vapour density data at the
conditions of interest. Table I1 summarizes the comparison of the calculations for
polar substances using the present method, Hakirn and co-workers method and Brock
and Bird method. Experimental data used for this are those from refs. 28 and 32
(which are also the input data used in the development of the Hakim and co-workers
Table l3
Summary of comparison of surface tension of s o w polar substances
Sobstnnce
No. of
points
compared
Per cent average absolute deviation
Present
method
Hakim and Brock and
coworkers Bird
method
method
176
D. H. L. PRASAD
an overall basis the present method gives considerably superior
correlation).
compared to the other methods and is therefore recommended as a good estimation
method for surface tension in the absence of reliable experimental data.
On
Acknowledgement
The author is grateful to Professor D. S. Viswanath (currently at the unj,itY of
Missouri, Columbia, U.S.A) for the discussions he had on the topic and t o professor
C . N. R. R ~ Ofor his constant encourapment.
References
1. ADAMSON,
A. W.
Pl~ysicalclie~nist~y
of surfores, Interscience, New York, 1960.
2. VANDER WAALS,J. D.
Z. Phys. Chem., 1894, 47, 1558.
3. PARTIVGTON.J. R.
An advanced treatise on physical diemistry, 1950, vol.
VIII(G), 134-162.
n,
The plwpoties of ,cases and iiqiiid.~,Third Edition, McGraw-~&
SHERWOOD,
T. K. New Ycrk, 1977. Ch. 12, 603-612.
4. REID,R. C., PRAUSNITZ.
J.
M.
AND
5. MACLEOD,
D. B.
Trans. Faraday Soc., 1923, 19, 38
6. SUGDEN,
S.
J. Chem. Soc., 1924, 1177.
7. BROCK, J. R. AND
BIRD, R. B.
AIChE JI, 1964, 10, 677.
8.
KIRKWOOD,J. G. AND
J. Chem. Phys., 1949, 17, 338.
BUFF,E. P.
9. LYDERSEN,
A. L.,
R. A.
GREEKORN,
HOUGEN,
0.A.
AND
Generalized fhern7odynarnic properties of pure fluids, University of
Wisconsin, College of Engineering Experiment Station, Report 4.
1955.
10. hTm, K. S.
LIPPMAN,D. Z., CURL,
R. F.,HUGGINS,C. M.
AND PETERSEN, D. E.
J. Am. Chem. Soc., 1955, 77, 3432.
11. PRASAD,D. H. L. AND
Generalized thermodynamic properties of real fluids using maim
polarization at the crirical remperarure as the third paramet6
Report, Department of Chemical Engineering, Indian Institute 0 l
Saence, Bangalore, 1974.
VISWANA~H,
D. S.
J. Appl. Chem., 1961, 11, 193.
J. Phys. Chem., 1938, 42, 1207.
Periodica Polyfech., 1959, 3, 167.
J. Indian Chem. Sac., 1942, 19, 51.
J. Chem. Phys,, 1968, 48, 5364.
ESTIMATION OF SURFACE TBNSION OF PURE LIQUIDS
I:.
MEYER,
J. Phys. Cllew., 1963, 67, 2160.
S. W.
18. SCEIONHORN. H.
J. C l ~ e ~ E
n .I I ~ XDafu,
.
1967, 12, 524.
~ 9 . RAu, M. V., R t V l l Y , K. A.
AND SASTRT,S. R. S.
H~dl~o(.ul~h.
Prowss., 1958, 47 (I), 151.
8.
OIIIMER, D.
JDSEFOWITZ,
F.,
S. AND
Q. F.
SCHMUTZLER,
31. PORTEOUS,W.
22
B n o c K , J. R. A N D
BIRD, R. R .
24.
HAKLM, D
STEENnEnG,
STEIL,
25.
1..
D.
AND
L. I.
P~rzm,K. S.
26. HALM.R. L.
STEEL,L. I.
AND
27.
VISWAX+\TH,
PRMAD, D.
D. S .
H. L.
28.
WASHBURN,
E. W. (Ed.)
AND
Proi.. Piftiz Sjnposiwn on Tl~e~n~ophysical
A-operfies, ASME
Newton, Mass., Sept. 3 0 - 0 c t 2, 1970, 1% 236.
Internarionai o-iticai rabies, Vol. IV, McGraw-Hill, New York,
1929.
Phys. C l i ~ . n Ref.
~ . Data, 1972, 1, 841.
Physirocher~~icdcorrsfanrs of pure orgririic conlyormd?~, msevia,
Amsterdam, 1950.
Chen~.Rev., 1953, 53, 439.
Lon~folf-Bor~rstei?
tablrs, Springcr-Verlng, OHG, Berlin,
Band 11, Teil 3 , 421-430.
1956,
J.
Indian Inst. k i . 62 (A), Scgt. 1980. Pp. 179-185.
Inrtilolc of Sciencc. Prinred in India.
,B Indian
Short Communication
An oscillator circuit with a linear relation between frequency and
temperature
S . CHAUDHURT
Indian Institute of Tropical Meteorology, Punc 411 005, India.
Received on September IS, 1980.
Abstract
A Grnple ins14 ruuenl which measures point temperature in connection wlth the construction o f thcmml
difusion cloud-chamher and ernploys a n oscillator circuit is designed and described. Head thermistor is used as a temperature Fensor. A new procedure is suggested for obtaining a linear functional
&tionship between temperature a n d frequency. Thermocouple is used lo calibrate the insfrun~ent.
The method otlers high accuracy and valid for wide range of temperature measurement.
Key words : Ilhcrmocouplc, thcmistor, monostablc nlultivibrdtor
1. Introduction
Digital measurement of different physical quantities has gained a tremendous i m p < tance with thc development of digital integrated circuit in instrumentation. Of thc
different physical quantitics which are frequently required to be measured tcmperaturc
is a very impoitant one. Different electrical oscillator circuits using thermistor had becn
suggested by different workersL,"here attempts had been made to achieve linear relationhip betwen the frequency or the time period of the oscillator and the tempcraturc.
In all these circuits linearization of thermistor was achieved at a certain fixed opcratiog point to temperatwe-frequency function. But in these circuits error due to nonlinearity increases appreciably as temperature shifts away on either side or the chosen
section point. A new procedure is suggested in this paper in which the linearization
of thermistor is achieved by designing the oscillator circuit in such a way that thc
tine period of oscillation is proportional to the natural logarithm of thermistor resistance. The range of the present instrument is from 15 to 65" C, having an
aa:UTacy of
(0.1 t o 0.7"C).
FIG. 1. The osciUaior circuit.
2. Sensor
Small bead thermistor encapjuleted in a glass tube near its tip is used as temperature
sc3;or. The funclional relationship between resistance and temperature for a thei.
mistor is given by the followi~lgexpression
where R, is the thermistor resistance in ohm at T o Kelvin. A is a oonstdnt (ohm) of
thermistor ; /Ia constant (Degree-Kelvin), typical or material and e is the base of
Napierean Logarithm 2.71 8.
3. Theory of oscillator circuit
The basic oscillator circuit is shown in Fig. 1. Tl~reeFET input operational amplifiers
are used in t h ~ scircuit. This operational amplifier need two supplies i 15V. The
slew rate of this amplifier is 6 V / p sec but the off-set voltage is relatively high of the
order of 30 to 90 mV a t room temperature. - V,,,is a negative d.c., fixed v o l w
(- 4V). R, a 6.8 KQ tempo product thermistor is employed to measure the unknown
ternpcrature. The resistance variation for t h ~ stype of thermistor is 2.4 to 11.25K8
corresponding to a temperature variation of 65 to 15" C (Fig. 2). The gain of the
operational amplifier 01 is always more than that of the operational amplifier 02
at ths maximum desired temperature measurement. The output of the operational
amplifier 01 and 02 are both positive and i s given by
A N ELECTRONIC M E W O D FOR TBMPERATURE MEASUREMENT
181
where R,, R, and R, are shown in Fig. 1.
At the initial instant of time t = 0, voltage across the condenser C is Vc ::= 0 and
,&age across R is
NOW c starts t o charge through
R and the expression for charging current is
As the quantities in the first term are constant.
At
R Y
t = 0 ; V , = 0 and I; = I,, = -
Ro
-Ie'
R
'
At any instant of time the voltage across R
The output of the operational amplifier 03 changes from negative to positive voltage
S t a t e when the two of its input voltages ate equal and the output of nlonostable
multivibrator rises irom 0 to 15 volt momentwily ( 0 . 8 sec)
~
which is determined
by the RC time constant of the mnultivibrator. The monostable multivibrator is constructed with the help of two high speed n-P-n transistor (type 2N2221) as shown in
Fig. 1. Due t o this positive voltage level 3t the output of tlic mcnostable multivibi.s.tor,
the transistor T saturates momq~tarily and enables it to discharge the condenser C
completely. Due to this the input voitages o f the operational amplifier 03 come back
Table I
Chmscteristics of the thermistor used
Thermistor
Tempo
Nominal
resistance
& 15% Rd,
K-ohms
Material constant calculated
from calibration curve
FK
A ohm
6.8
2963.68
0.3853
Time
constant
Dissipation
constant
sec
mwl0c
12
0.43
to its initial condition. The process is repeated and an oscillation in the circuit i
generated. The operational amplifier 03 changes its state when
=
,-f/RC
v2 ,
vc,
2
The time period of oscillation in the circuit of Fig. 1. is given by
t = R
C
I
vo,
~
~
substituting the values of V,, and Vo, from eqns. (2) and (3)
substituting from eqn. (1) the value oC R, in the above equation
The expression for the frequency of oscillation is
f=-
1
--1
Re [constant
+
[I.
Substituting the values of diffwent circuit parameters and also the constants of thermistor (Table I) in the above equation
-
AN ELECTROEIC METHOD FOR TEMPERATURE KEASUREMENT
183
--
FIO. 2. Characteristic of a 6.8 K temao
=paduct thermistor.
FIB.3. A linear calibration of the instrununt.
If the monostable delay t , ( 0 . 8 3 5 ~sec) is considered in eqn. (6) the expression for
temperature is
Equation (8) is employed
the instrument. Figure 3
passing through the origin.
through the origin, is due
amplifiers.
to measure temperature. Equation (7) is used
shows a calibration which indicates straight
The deviation from the ideal case, i.e., straight
to monostable delay and off-set voltage of the
to calibrate
line almost
line passing
operational
4 Calibration
The temperature vs. resistance characteristic of a 6 . 8 KQ thermistor is shown in Fig. 2.
Table I shows the value of constants of the thermistor. The constants of thermistor
are calculated by solving eqn. (1) a t the two en& of the temperature ran@ to be
m u r e d using Fig. 2. The instrument was calibratd using wpper-cons*mtan tkamo"uple in the temperature range 15-65' C. The tbrmistor bead temperature and the
thcrmoeouple temperaturn arc found t o agree within + (0.1 to 0.7" C). The skaight
ha. 4. A two-hour record of room temperaturc fluctuation on July 3. 1980.
line in Fig. 3 shows the linear calibration of the instrument using thermocouple
temperatures as well as conlputed temperatures. The instrument was used to take hvo
hour room temperature record from 1,500 to 1,700 hr I.S.T. on July 3, 1980, s
shown in Fig. 4.
5. Conclusions
This method has shown exceUent linearity in the temperature range 15-65" C. The
sources of error in this instrument are thc off-set voltage or the operational ampIkfs
and the small monostable delay of the multivibrator apart from the drift in the Passive cor~lpnentssuch as resistances and capacitances, etc. The effect of small man@
stable &lay can be made non-cxistent by using I.C. non nos table multivibrator (SN 74121)The off-set error can be reduced by proper off-set voltage adjustment of the cperationd
amplikrs. The modern FET input operational amplifiers having low off-set d t W
will gim better result. Moreover the position of thermistor bead and the hot juEtwn of t ~ r m o c o u p l eare not exactly identical inside the oil bath. This may create an
AN ELECTRONIC METHOD FOR TEMPERATURE MEASUREMENT
185
error in the minPerature measurement. If the circuit parameters in Fig. 1 are selected
in such a way that &A = RoR, and fi = IIRC in eqn. (6) in that case the frequency
oscillation (f) is an exact linear representation of absolute temperature (T). The
latrclment can be used for continuous and precision ineasurenlent of ten~peraturc as
an important physical parameter.
Acknowledgement
The author is very grateful to his fiiend Shri S. M a h a h o b i s , fornlerly attached to the
Institute of Radio Physics and Electronics, Calcutta University, for his very valuable
suggestions in developing the oscillator circuit. He is also very thankful to Dr. A. K.
Kamra, SSO(1) in-charge of Instru~nentDivision of Xhc Indian Institute o r Tropical
Meteorology, for providing necessary facilities for this work.
References
I. LOVBORG, L.
A linear ternporaiure lo frequellcy converter, J. Sci. Insnslmm., 1965,
42, 611-614.
2. IKENCHI,MOTOAKI.,
FURUKAWA,
TRONOZO
AND
MATSUMOTO,
Gono.
A linear remperarure to frequency converter, I.E.E.E.
I~rsfrum.Measurenie~t!, 1975, IM-24 (3), 233-235.
-
-
Trans.
-
Published by T. K. S. Iyengar, Executive Editor, Journal of the Indian Institute of Science,
Bangalore 560 012 and Printed at the Bangalore Press, Bangalore 560 018
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