EFFECTS OF ENVIRONMENT ON THE SURFACE WAVE
CHARACTERISTICS OF A DIELECTRIC-COATED
CONDUCTOR* PART I
By (MISS) GLORY JOHN AND S. K. CHATTERJEE
(Indian Institute of Science, Bangalore-560012)
Manuscript received on 12th September 1973
1. ABSTRACT
The surface ware characteristics, such os guide wavelength, radial propagation
corn/on! (11 2), etc., of a surface ware (E) excited dieketric (el) coated conductor as
function of the dielectric constant (e2 of the environment in which the structure is
immersed are studied. Results show (i) that surface ware solution exists as long
E2 < Et (ii) existence of maximum of u 2
€2 curves for a particular whit of E l
and shift of the maximum as E 1 is varied; and WO longitudinal power flow in the
environmental medium decreases with increasing E 2 and the rate of decrease
depends upon the value of E l . It is concluded that the dielectric constant of the
environmental medium has significant influence on the characteristics of a
surface wave structure.
)
Key words: Surface wave characteristics. Dielectric coated aerials.
2. INTRODUCTION
Several authors [1-19] have studied surface wave characteristics of
electromagnetic surface wave structures immersed in air. But there seems
to be no information in available published literature on the surface wave
characteristics of electromagnetic structures surrounded by a medium other
than air. In view of the importance of subsurface communication it has
been considered worthwhile to study the effects of dielectric constant. loss
tangent and other properties of the environmental medium on the surface
wave properties of e.in. structures, beginning with the dielectric-coated conductor. The present report is concerned with the study of variation of the
surface wave characteristics of a dielectric-coated conductor immersed in
an infinitely extended lossless medium, as its dielectric constant is varied.
The effects of a lossy medium will be reported later. Further work when
£2 is a tensor is also under progress. It is intended to correlate the results
* The project is supported by PL-480, Contract No. E-262-69(N), dated 5th June, 1969,
Effects of Environment on the Swface Wave Characteristics--Part I
89
of these investigations with the propagation characteristics of surface wave
structures immersed in natural environments such as jungle, snow or inside
the earth.
MED.3
C.2 itto
0
Flo. I. Dielectric coated conductor surrounded by a medium of
dielectric constant E.,
3. FIELD COMPONENTS
The field components for a conductor (a = co) coated with a lossless
dielectric (€1, tto, a = 0) immersed in a medium (€2, /t o , a = 0) and excited
in E4 mode are (Fig. 1) in different media:
Medium 1:0<p<a
Ez,
= AJ3 (u op) e 3 1t_
Ep i = 1 A. I I (" up) eitut---yz
U0
--k 2
H4 i = j q AJ
1(U„p) Staten
(1440110
Medium
2: a < p < b
Ez2 = [BA ( 141P)
C Y 0 (up)] ejtet -six
Ept>, --= ?-1- [B. 11 (uip) + CY (u 1p)1 ei0t-12
(1)
(MISS) GLORY JOHN AND S. K. CHATTERJEE
90
Ho2
k12
= J
wiL0 111
Medium 3:
[Wi(iiip)
C (Yip)] eiwt-tz
(2)
p>
Ez3 = DIU" (jue) e244-7 z
(ju 2p)
Ep 3 = 7 hi
U2
k 2
.
wit 4U2
114,3
(ju 2 p) ejcoe-7i
(3)
where, the radial propagation constants 00 in media I, 2 and 3 respectively
are related to the axial propagation constant y as follows:
110 2
y 2 + ko2
211 2 = y 2 +
1c1. 2
6,2
U1 2
k2 2)
(4)
where
k o2 = jaw on
ki 2 = (02 1.10 E1
k23 —
—CO 2
E
and the axial propagation constant is
4. EXCITATION CONSTANTS
Using appropriate boundary conditions and field components in different media (2 and 3) the following relations between the excitation constants
are obtained :
C =-- B
30
(u1a)
(5)
Yo
u k 2
B=D . . 2 .
u2
111")
Yo (1410
(u11) Yo (u ia) —
(no) Y1 -(iiihn .
(6)
Hence,
2
2
14E,
.
Yo
(ul
a)
Ki(u2b)
BB* = DD* [1ru261 iii(u 1b) Yo(u la)
1 0(141a) Yi (th b ) I •
(6 a)
Effects of Environment on the Surface Wave Characteristics —Part I
5.
91
CHARACTERISTIC EQUATION
The transverse impedances at p = b being equal, i.e.,
£22
1102
EZ3 I
HIT; I b
the characteristic equation is
r4
5 u2 Ko (u2b)
Ib
E2 141
K1 (u2b)
1.44
o (uha}Y0 (4)1 = 0
Yo (ula) — Jo (u,a) Y 1 (41b)j
yo (IAA
(iiib)
(7)
which is obtained by writing H ow (ju2b) and 1/1(1) (ju 2b) in terms of Ku (u2!,)
and Ic (u2b) respectively.
By using the following relation
u2 2
E2)
u1 2 = (0 2 pet,
(8)
which is obtained from eq. (4), and solving the characteristic equation (7)
the radial propagation constants u / and u2 are determined.
The guide wavelength Ag; = 2701 and the phase velocity up = co/f3 are
determined from the following relation between the axial and radial propagation constants when the media are assumed to be lossless.
y = jp = (U22 k22)1"2.
(9)
POWER FLOW IN MEDIA 2 AND 3
6.
The longitudinal power flow in media 2 (Pza and 3
by using the relations
(Pza)
is calculated
ir b
Re
PZ2 =-*
f
(so
pall
Ep21102 * pdpd9 4
(10)
Ep31103 * pdpd#
(11)
er 00
If
Pia = 4 Re
ØaO
p=o
and using the functional relations (equations 5, 6) for the excitation
constants.
Pzo
743(.0€ 1
BB * [G
Y0 2 (ha)
G (a)]
where
G (r) =
(u1 r) Y0 ( 1a) — Jo (ha) Y 1 (u1r)P
0 (u1r)
Y (u ia)
(uia) Yo (u1r)j2
(10 a)
02
(Min) GLORY JOHN AND S. K. CHATTERJEE
2
-
(uir) Iro (ula) — Jo (alp) Y 1 (u ir)]
x Vo (u10 Y1 (ita) — 4 (ula) Yo 0 40]
(10 b)
where, r = (a. b)
12 DD* b 2 [K 02 (u
P; = 2132b) — K 12 (u2b)
77U2
2
Ko(u2b)
K1(u2b)].
u-2b
(11 a)
In deriving the expressions for Pz2 and Pz3, the following relations have
been used appropriately.
J01 (41p)
=-- 4
1
(u)p)
alp
(1410 = Yo 040
1
uip
( ju
(uip)
(1410
110 ") (ju —• 14" ) (ju 2p)
110 ") (j112b)
IT
fK0 (u2b)
(u2b).
(ju 2b)
The total power now in the longitudinal direction (z) is
PT =
PZ2 PZ3.
Hence, the percentage of powerflow in media 2 and 3 are respectively.
2 X 100
P270 =
9
73. x 100.
7.
(12)
CONSTANT PERCENTAGE POWER CONTOUR
The radius pp of the constant percentage power (p) contour is determined from the relation
F (Pp)i
F (pb)
(13)
Effects of Environment on the Surface Wave Characteristics— Part I
93
where
F (pp) = P p .' [K0 2
(u2pp)
F (pb) = Pb 2 [K02 0219
n 2Ppi
-- K1 2 (112b)
•
2
V
2 („
A al k
11 1Pp
no (U2Pp)
4- u21b Ko (u2b)
( 1-1 2,p)]
004
80.0
80-0
b = 0-0004m
60 .0
60.0
40.0 'is
40.0
20.0 -
20.0
2.0
0L
0
6.0
4-0
2.0
80.0
80.0
b 0-0003m
60-0
4.0.0
4-0.0
40.0
6.0
4.0 5. 13
3.0
20.0
20.0
2-0
0
i
2.0
4-0
6.0
I
0
€2
112 - RADIAL PROPAGATION CONSTANT (PER METRE)
t 1 E2 - DIELECTRIC CONSTANTS OF IT
III MEDIUM
III MEDIA RESPECTIVELY
- INNER CONDUCTOR RADIUS = 0.001
b
IN THE
COATING THICKNESS
no. 2. Variation of U s with Es
(fl u)
94
(Miss) GLORY JOHN AND S.
K.
CHATTERJEE
8. NUMERICAL EVALUATION
8.1. Effect of f 2 on the Radial Propagation Constant u2
The radial, propagation constant zi2 is determined from the solution of
the characteristic equation and its variation with a, b, E1 and E 2 is shown
graphically in Figs. 2 and 2 a.
8.2.
Effect of
E2
on the Guide Wavelength Ag
The variation of Ag Wi th E2 is determined from equation (9) and the
relation Ag between and /3 and is shown in Fig. 3.
30-Or
30.0
0 = 0.003 m
20.0
20.0
10.0
10.0
6,7-4.0
0
2.0
4.0
2.0
4.0
(3.0
30.0
3 30.0
0.0 05m
20.0
20.0-
4.0
5.0
10.0 -
10.0
4.0
3.0
2.o
Er: 1.0
0
€i=1.0
2
0
4.0
0L
0
6.
€
U2
-
2 —o-
RADIAL PFtOPAGATIOLI CONSTANT (PER METRE) t THE III NEDIUM
C I ,C 3 DtELECTRIC CONSTANTS Or II i III MEDIA RESPECTIVELY
Q - INNER CONDUCTOR RADIUS
b COATING THICKNESS
0 00005
Ho, 2 a, Variation of as with
es
6.0
Effects of Environment on the Surface Wave Characteristics PartI
95
I
0.071
•
0.050
0.025
•
1
1
1
i
i
a
a
t
i
t
I
t
4-0
2.0
t
t
II
1
6-0
E2
Ai - GuiDE WAVELENGTH ON METRES)
La - DIELECTRIC CONSTANT OF III MEDIUM
FIG. 3.
8.3.
Effect of
E2
yr, vs
ci
on Constant Percentage Power Contour
The variation of the constant percentage power contour with
determined from eq. (13) and is shown in Fig. 4.
8.4.
62
is
Effect of E 2 on P3%
The percentage of powerflow in medium 3 (P 3%) with respect to the
total powerflow PT is calculated as a function of E2 for different values of
El and a by using eq. (12) and is shown in Fig. 5.
8.5.
Radial Field Spread
The values of the u 2 for different a, 6 1 and E2 obtained from the
solution of characteristic equation enable the determination of radial field
spread of components Ez and Er Figure 6 shows the field decay in the
radial direction for E l =60 and E2 = 3•0 for different values of a.
Is 1. Sc.-4
S. K. CHATTER) EE
• (Miss) GLORY JOHN AND
96
0.4
0 a
••■■••
lin.M.
Paga
a
3g
o.00i m
0-4
0.2
0
"'A
0-1
0.08
0.06
75%
0
0.02
10
1
St
2.0
4•0
0
6-0
2.0
6-0
4-0
0.6
ic 0 - 005 m
0•4
1 99 %
0.2
90%
FIG. 4 PERCENTAGE POWER
CONTOUR Vs E2
r
0-08
75 % I
0-06
507.
0.02
0.01L
0
C I 1 E2 - DIELECTRIC CONSTANTS OF
MEDIA RESPECTIVELY
II *
a
04:4
2.0
4.0
£2 —IP-
I
.0
Fzo. 4
RADIUS ON METRES) wiTHiN wi-HCH
POWER IS CONCENTRATED
-
INNER
CONDUCTOR
RADILIS
b
COATING THICKNESS IL 0.00005 rfl
ci
6•0
Effects
of Environment on the Surface Wave Characteristics—Part i
97
100
130
99
19
to•if
a gr 0•001
4.
2-0
6.
3 m
9B
RIG. S
P7 • OuiSiOE
TwE ST RuCT uf tE
vs E 2
,
Pz Y. - PERCENTAGE POWER CLOW 9.4 THE
Z DIRECTtON OUTSIDE THE srauctuRE
99
DIELECTRIC CONSTANTS Or THE
Cir )(2
II le fli MEDIA RESPECTIVEL“
Q — INNER CONDUCTOR RADIUS.
b - COATING THICKNESS 0.00005 in •
€2
Pio. 5
9.
CONCLUSIONS
The analysis leads to the following conclusions regarding the effect of
the dielectric constant of the environmental medium on the surface wave
characteristics of a dielectric-coated conductor excited in E 0-mode.
(i) Surface wave solutions exist as long as
E2
<
(MISS) GLORY JOIN AND S.
98
K.
CRATT:ERJEE
1. 0
f.0
03
1.0
E (Er OR Li) vs r
FIG. 6.
E (Er oft Ez) -
NORMALISED ELECIRIC
FIELDS (RADIAL AND AXIAL)
0.5
r-
RADIAL DISTANCE ( 11.4 METRES)
rROM THE STRuCTURE
E,
— DIELECTRIC CONSTANTS of
It & Ill MEDIA RESPECTIVELY
- INNER CONDUCTOR RADIUS
b
COATING THICKNESS
E s = G.04,
r
E2 = 3 0 •
o.0000s m
-s-
(ii) The radial propagation constant uo first increases, attains a maximum value and then decreases to a low value with increasing E2 for a particular value of e l . The magnitude of maximum u 2 increases and shifts with
increase of Ei.
Effects of Environment on the Surface Wave Characteristics Part I
511. L)
7 1•••%.1
b=000lm
b = O. 0000S rn
3.8
2.4
p1.8
10
20-0
20.0
ar
ife
1.0
3-8
2.6
1.8
0.6
tao
104
10.0
0.6
•
t.2 t 0 . 2
6.0
4.0
2-0
0L
0
CI
•
6)
1.0
--
2.
4-0
••■■•■00P•
Uz V$ Ei
T1•0
b= 0.001 rn
E i = 6-0
0.5
C2 d: 0.2 & 5-8
1.0 & 5-0
3.0
CL
0
0
0.04
0.02
0.06
r
(IIY E Vs
•J
st
u 2 - RADIAL PROPAGATION CONSTANT (IN METRES) iN THE III MEDIUM
.E. 1 ,e2 - DIELECTRIC CONSTANTS OF It It 1.11 MEDIA RESPECTWELY
a -
INNER CONDUCTOR RADIUS
b -
COATING THICKNESS
0. 003 ri .
E - NORMALISED ELECTRIC FIELDS - Er it Ez
—
r
.
r - RADIAL -DISTANCE (IN MtTRES) FROM /HE STRuCIVRi
s 441tREVONOS 19 NARMS GOUCIAU LINE
-
A. •
•
• 4.
I
FIg •
I
.
99
(MISS) GLORY JOHN AND S. K. CHAITERJEE
100
0075
0.030
0.025
E
As
• GUIDE WAVELENGTH IN METRES.
E2 - DIELECTRIC CONSTANTS OF II it III MEDIA RESPECTivELY •
a-
INNER CONDUCTOR RADtuS = 0.00f
b
COATING THICKNESS = 0.00005 M.
FPO. S.
m
As v..,
S.
(iii) The magnitude of u 2 decreases with increasing values of a, but it
increases with increasing values of b, for any particular value of t i, and es
(Fig. 9).
(iv) The radial field decay differs significantly from Harms-Goubau
line (t, r-t.- I) when Es > 1.
(v) The surface wave field becomes more strongly bound than the
Harms-Goubau line (t 2
I) when E2 is in the range (I < es < ti a 1)
and becomes more loosely bound when t o is in the rally (1> t o > to a 1)1
Effects of Environment on the Surface Wave Characteristics—Part I
te0.0
.-
e
e
ady
e
e
ae
I
e
,••
el
...,
47%
4-
...-
10.
.....
so
a-
.--
.•••
e
c.......,°-<
4 '
ts.' 4.4 0
:At-
.0
e
....
e
,e;
..
re
e
n _ 0.
40
e
de
4-
...
e.
.1
..•
00
.0
e
.•
.0
00
....,
-e
101
..0
.0
60
es•
I
se
ge
or
e
....
0 ,.. . • 00
k
4-
...
e
4.
00
.0
e
so
e
6.0
5.0
f0.0
4-0
30
2-0
( 1 7.. 1-0
-_--
U2 ma x
vs b
U2 MCI*
VS (X
0
10 -3
10-4
10
a, b
o
b
- INNER
-
CONDUCTOR RADIUS (IN METRES)
COATING THICKNESS (iNmETRES)
C 1 €2 - DIELECTRIC CONSTANTS OF 11 Ix, III MEDIA RESPECTIVELY
E2 z E I /2 FOR U2 MCI:-
Fro. 9
This is evident from Figs. 2, 2a, 5 and 7. The attachment of the surface
wave field to the structure is independent of t i for all E2 within the range
specified (Fig. 8).
(vi) Radii for different constant percentage power contour first decreases,
then remains fairly constant and finally increases with increasing e t . This
corresponds to the surface wave field being more and more strongly bound
with increasing e3, then remaining practically independent of Eit within a
certain range and finally becoming more and more loosely bound with further
increase of is. This is consistent with the observations made in (ii) and (Hi),
(Miss) GLORY JOHN AND S. K. CHATTERJEE
102
(vii) Comparison of the characteristics of the surface wave line when
1)
€2 > 1 but remains less than E 1 with that of Harms-Goubau line (€2
(Figs. 7 and 8) shows that the former can be said to guide more strongly
bound surface wave than the latter.
It may therefore be said that by a proper selection of the combination
of a, ci and € 0. the surface wave energy can be mostly concentrated in medium
2 and hence permitting long distance communication by surface wave, if
the medium (2) is of very low loss.
Further work on the effect of lossy environment is under progress and
the results will be reported later.
REFERENCES
j1 Goubau, G.
.. Surface waves and their application to transmission lines.
Journal of Applied Physics, 1950, 21, 1119-1128.
Radio Surface Waves, Chapters 1 and 2, Clarendon Press, 1962.
[2] Barlow, H. H. and
Brown, J.
[31 Wait, J. R.
.. Electromagnetic nurface waves, Advances in Radio Research,
Academic Press, 1964, 4, 157-217.
[4]
.. Excitation of surface waves on conducting stratified, dielectric
clad and corrugated surfaces. Journal of Research of the
National Bureau of Standards, 1957, 59, 365-377.
[5]
---
-
--
Guiding of electromagnetic waves by uniformly rough surfaces.
I.R.E. Transactions on Antennas and Preparation, Special
Supplement, 1959, AP-7, S154-S168.
••
j6j Chatterjee, S. K. and
Madhavan, P.
Propagation of microwaves on a single wire—Part I.
Journal of the Indian Institute of Science, 1933, 37, 200-223.
[7] Contractor, S. N. and
Chatterjee, S. K.
Propagation of microwaves on a single wire—Part 11. Journal
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[8[ Zachariah, K. P. and
Chatterjee, S. K.
Study of the Q factor of a surface wave resonator.
and Electronic Engineer, 1968, 36, 111-131.
Girija, H. M. and
Chatterjee, S. K.
Investigations on corrugated surface wave tine.
Journal of
the Indian Institute of Science, 1969, 51, 38-45.
[I0] Chattedee, S. K. and
Chatterjee, R.
1114
iner■ow ■Ini■ill
Radio.
Propagation of microwaves along a solid conductor embedded
in three coaxial dielectrics—Part 1. Journal of the Indian
Institute of Science, 1956, 38, 157-171.
■=1
9
Microwave resonator. Journal of the Indian Institute of Science,
1968, 50, 345-363.
Effects of Environment on the Surface Wave Characteristics Part I
[12]
103
Study of the surface wave and radiation characteristics of
cylindrical metallic, corrugated structures. Journal of the
Indian Institute of Science, 1972, 54, 1-25.
Girija, H. M. and
Chatterjee, S. K.
[13)
•.
Theoretical study of the fax field of a corrugated circular
metal rod excited in the E 0 mode. Indian Journal of Pure
and Applied Physic; 1972, 10, 794-802.
(141
..
Surface wave characttristics of a cylindrical metallic corrugated structure excited in the E 0 mode. Journal of the
Indian Institute of Science, 1971, 53, 269-326.
[15] Prabhavathi, A. S. and
Chatterjee, S. K.
Theory of open microwave resonator with an axial corrugated
metal rod. Journal of the Indian Institute of Science, 1971,
53, 333-354.
[16] Glory John and
Chatterjee, S. K.
Surface wave decay coefficient of circular cylindrical corrugated metal rod. Proceedings of the IEEE-IERE (India),
1972, 10, 68-78.
[171
Surface wave and radiation characteristics of uniformly
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Shankara, K. N. and
Chatterjee, S. K.
[18]
[19] Chatterjee, S. K. and
Chat terjee, R.
..
Corrugated and uniform dielectric rod aerial excited in E r
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1972,
54, 146-180.
-•
Propagation of microwaves along a solid conductor embedded
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