design of a continuous resistively loaded monopole antenna
TRANSCRIPT
NPSEC-93-011
NAVAL POSTGRADUATE SCHOOL
Monterey, California
Design of a Continuous ResistivelyLoaded Monopole Antenna
by
Darwish Abd El Aziz Mohamed
Ramakrishna Janaswamy
May 1, 1993
Approved for public release; distribution unlimited.
FedDocsD 208.1M/2NPS-EC-93-011
brought to you by COREView metadata, citation and similar papers at core.ac.uk
provided by Calhoun, Institutional Archive of the Naval Postgraduate School
Naval Postgraduate SchoolMonterey, California 93943-5000
Rear Admiral T. A. Mercer H. Schull
Superintendent Provost
This report was prepared for and funded by the U. S. Army Communications and
Electronics Command.
Reproduction of all or part of this report is authorized.
This report was prepared by:
REPORT DOCUMENTATION PAGEForm Approved
OMB No 0704-0188
Public reporting burden for this collection of information is estimated to average l nour per response, including the time for reviewing instructions, searching emsting data sources
gathering and maintaining the data needed, and completing and reviewing the collection of information Send comments regarding this burden estimate or any other aspect of this
collection of information, including suggestions 'or reducing this burden to Washington Headauarters Services. Directorate for information Operations and Reports. 12 15 Jefferson
Oavis Highway, Suite 1204. Arlington. VA 22202-4302 and to the Office of Management and Budget. Paperwork Reduction Proiect (0704-0188). Washington. DC 20503
1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE
1 May 1993
3. REPORT TYPE AND DATES COVERED
Interim Report 1 Jan 93-1 May 93
4. TITLE AND SUBTITLE
Design of a Continuous Resistively Loaded Monopole
Antenna
5. FUNDING NUMBERS
6. AUTHOR(S)
Darwish Abd El Aziz Mohamed and Ramakrishna Janaswamy
7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)
Naval Postgraduate School
Monterey, CA 93943-5000
8. PERFORMING ORGANIZATIONREPORT NUMBER
NPSEC-93-011
9. SPONSORING /MONITORING AGENCY NAME(S) AND ADDRESS(ES)
U.S. Army CECOMCenter for C3 Systems
Fort Monmouth, NJ 07703
10. SPONSORING /MONITORINGAGENCY REPORT NUMBER
11. SUPPLEMENTARY NOTES
The views expressed in this report are those of the authors and do not reflect the
official policy or position of the Department of Defense or the United States Government.12a. DISTRIBUTION /AVAILABILITY STATEMENT
Approved for public release;
distribution unlimited.
12b. DISTRIBUTION CODE
13. ABSTRACT (Maximum 200 words)
Hallen's integral equation with continuous resistive loading is used to design a broadband
monopole antenna. The resistive profile is different from that of the well known Wu-King profile
and results in a higher efficiency compared to the latter. An optimization function for determining
the optimal continuous resistive load of the monopole antenna in order to satisfy the broadband
property is constructed. Simplex method is used to perform the optimization. The integral equa-
tion is solved by the moment method to determine the current distribution, the efficiency, and the
radiation pattern of the monople.
14. SUBJECT TERMS 15. NUMBER OF PAGES
3016. PRICE CODE
17. SECURITY CLASSIFICATIONOF REPORT
UNCLASSIFIED
18. SECURITY CLASSIFICATIONOF THIS PAGE
UNCLASSIFIED
19. SECURITY CLASSIFICATIONOF ABSTRACT
UNCLASSIFIED
20. LIMITATION OF ABSTRACT
SARIMSN 7540-01 -280-5500 St.
Pre
sndard Form 298 (Rev 2-89)scribed by ANSI Std Z39-'8
4 3S3
r*
ABSTRACT
Hallen's integral equation with continuous resistive loading is
used to design a broadband monopole antenna. The resistiveprofile is different from that of the well known Vu - King profileand results in a higher efficiency compared to the latter. An
optimization function for determining the optimal continuousresistive load of the monopole antenna in order to satisfy thebroadband property is constructed. Simplex method is used toperform the optimization. The integral equation is solved by the
the moment method to determine the current distribution, theefficiency and the radiation pattern of the monopole.
- 1 -
1- INTRODUCTION
A straight wire antenna of fixed length is narrowband due to the
rapid variations in its input impedance, and to a lesser degree,
in its radiation pattern. A wire antenna is however, light weight,
easy to fabricate and simple to mount on any platform. Travelingwave antennas are desirable for purposes of broadband and
directional communication. A traveling wave antenna may be
obtained by introducing dissipative elements into the antennasystem. The introduction of lossy elements will cause a decrease
in the efficiency. Altshuler [1] found that a traveling wavecould be maintained along a part of a thin cylindrical monopole,
if a resistive loading of appropriate magnitude is inserted 1/4
wavelength from the monopole end. Wu. and King [23 found that if
the antenna is made of resistive material so that the internalimpedance per unit length, is a particular function of the
position along the antenna, a pure outward traveling wave can
exist on an antenna of finite length. An attempt had been made by
Janaswamy [3] to design a broadband monopole antenna by using thecontinuous resistive profile proposed by Wu-King. However theWu-King profile results in a low radiation efficiency. In orderto design a monopole wire antenna that has a broadband propertyand has at the same time higher radiation efficiency than thatobtained using the Wu-King profile, we consider a modified Wu-Kingprofile and incorporate it into Hallen's integral equation [43.
The solution of the integral equation will depend upon the loadingimpedance. We construct a real function which assumes a minimumvalue when the broadband property is reached. FORTRAN programsare developed for solving the integral equation of the antenna as
well as for determining the optimized load impedance. A comparisonis made between the performance of the monopole lo»i»tfo<:l with
Wu-King profile and that of the monopole loaded with the optimumprofile.
2- FORMULATION OF THE PROBLEM
For thin monopole wire antenna, the current distribution wasassumed to be of sinusoidal form. For a finite diameter wire,
the sinusoidal current distribution is not exact. To find thecurrent distribution for a cylindrical antenna, an integralequation can be derived [53. All other antenna properties can be
deduced once the current distribution along the wire antenna has
been determined. We present a brief outline of the integralequation below.
- 2 -
Consider a thin, cylindrical monopole of radius a and length h,
center driven by a delta -function generator of voltage V^ at the
angular frequency o. Let the monopole be situated in vacuum, have
an internal impedance per unit length Z , which could be a
function of position along the monopole. The notation used is as
follows
E Cz) : the tangential component of E at a point z on thez
antenna surface.
I Cz) the current intensity at the same point.
Z Cz) : the internal impedance per unit length of the antenna.
Ve then have
E Cz) = Z Cz) I Cz) c 1 3Z I
Also, E Cz) can be expressed in terms of the vector magnetic
potential A* which has only, a z - component A_ , as
E Cz) = -jo 1 + — A Cz) c 2 :
L k2 dz 2
J
Equating CI) and C2), we obtain on the antenna surface that
^2 • .2
A Cz) + k 2 A Cz) = Z Cz) I Cz) c 3 3
dz 2 r 2gj
where, k = o _/ u co o
The particular solution of equation C3), is
kAip Cz> = J —
JZ Cz ) I Cz ) sin kCz—z ) dz c a 3
The homogeneous solution of equation C3) and corresponding to thecondition A^C-z) = A Cz) and to a driving voltage V, is
A u Cz) =Z n
-J k
oD cos kz + —— sin k|z| c 5 3
where D is a constant to be determined. Combining the particularand homogeneous solutions, the solution of the differentialequation C3) is obtained as
- 3 -
A Cz) = A u Cz) + A Cz)Z Z h 2 p
^[° cos kz + si n k|z|j
kr—I
z,Cz ) I Cz) sin kCz-SD dz
C 6 3
If the antenna considered is thin, i.e. if h » a, the vectorpotential, A Cz) can be expressed in terms of I Cz) as [5]
A Cz) =4 n
I Cz)
-jkR -jkR.
dz C 7 3
where
.-[
R =
K2
=
C z - z )2
C z + z )2 + a
2
1/2
1/2C 8 D
Combining equations C6) and C7), an integral equation for the
current I Cz) is obtained, where
I Cz)
-jkR -jkR.
dz
J r Cz ) I Cz ) sin kCz-z ) dz
o o
+ C cos kz = - J2 r
sin k |z|
C 9 3
where, K, = / fJQ / c is the intrinsic impedance of vacuum and C
is a new constant. equation C9) is the Hallen's integral equationfor the current distribution of the loaded monopole antenna.
- 4 -
3- METHOD OF SOLUTION
Moment method techniques [4] will be used to solve the integral
equation C9). The current I_ is expanded in terms of N piecewiselinear subdomain basis functions, as
N
2 +- n nn = l
- Z n-1
G Cz')n
Z Zn n-1
Z — Zn + i
Z — Zn + 1 n
z < z < zn-1 n
< z < zn + 1
C lOtO
elsewhere
Also, the internal impedance per unit length Z is assumed to be
of the form
A MC 1 1 DZ Cz) =
h - z
2 m-1Z C z • h )
m = l
In comparison the Wu-King profile is of the formwk R
Z Cz) = 2
h - z
where R depends on ka and kh. Substituting CIO) and Cll) intoC9) yields
N
I I.
n = l
G (Z )n
L 4 » Ri
-jkR.
4 rc R.dz
N 2 M
"JX p X
o n = 1 O m=
1
2 J-1
CZ ) Cz /h) G (z ) sin kCz-z 5 dz
+ C cos kz2 <
sin k |z|
(12)
which can be written in a simple form as
- 5 -
N N M
T I A Cz) +2 1 I, z™ B Cz) + c cos kz = -j —£- sink|z|
n = l n = 1 m = 1 ^o
where,
C 13)
A Cz) =n
G (z )n
-jkR
4 n R
-,kR.
4 tt R.dz C 14}
B Cz)r J h - zo O
m-1Cz /h) G (z ) sin kCz-z ) dz
c is:
To determine the coefficients I , n = 1.2,...,N and the unknown C,
we will use the point matching method which will result in CN+1)
linear equations of the form
N M
5 I A Cz ) +5 Z B Cz )fc rilnp *- mnmpn = 1 m= 1
+ C cos kz = -j —— sin klzplp 2 t;
P = 1.2, 3, , N+lC 16)
Solution of this system of equations can be considered as functionof the M parameters Z .
4- THE OPTIMIZATION FUNCTION
A broadband monopole antenna in admittance can be synthesized by
minimizing a convenient optimization function. An optimization
function is constructed which includes the current distributionparameters I , and which is minimized by varying the values of
the impedance parameters Z . The proposed optimization functionincludes values of both the admittance as well as of the radiationefficiency weighted differently. Ve construct the optimizationfunction as:
F< Zl ,Z2,.. Zm>
= V.Yi n Sir c f ) - Y
c r efV, I I
«f > - K cr el
C 17 j
where,
n. is a number of spotfrequency range
frequencies in the desired
- 6 -
n
y Cf ) is the input, admit,Lance of the monopole antenna atl n n
frequency f , and it is equal to
Y Cf ) = 2 I (f ) / V, cisDt n n In o
^Cf^) is the radiation efficiency at frequency f^, and
it is equal to
£Cf ) = 1 - P, / P .where^ n Loes l n
P. (f ) = -4- II (f )|2 R „Cf ), (19)
in n ^Z in t n n
P, Cf ) = -i- Cz ) lICz )|2 dz
lose ) = -1- Z (z ) lICz )
I
n ^ J v I
C 20J
Y is the reference admittance in the desiredcrsl
frequency range, which we take as the average of
Y Cf ) over f .
i. n n n
? , is the reference efficiency in the desiredcrel
frequency range, which we take as the average of
^ Cf ) over f .
n n
V and W* are the weights for the admittance and efficiencyi v n C,
respectively.
The Simplex method of optimization C5] is used for determining the
coefficients C Z ) of the internal impedance by minimizing theIT)
optimization function given in C17). The Simplex Cbody in multi-
dimentional space) optimization method computes the values of the
optimization function at the vertices of a simplex in the
parameter space, and on the bases of these values chooses a new,
presumably smaller simplex within which an optimum should be
situated. The number of the vertices of the simplex is equal to
the number of parameters plus 1. Here we chose M = 4 thus,
resulting in five vertices CX„, X,, X . X' , X ), where X. is a
vector of the impedance coefficients CZ , Z , Z , Z ). We haveused coefficients corresponding to the Vu - King profile as one of
the starting vectors needed to accomplish the optimization.
5- DESIGN OF THE MATCHING NETWORK
Once a resistive profile has been determined, we design a matchingnetwork to make the antenna even more broadband. We have designeda matching network using the EESOF C ESYN / TOUCHSTONE ) circuitdesign code [73. The matching network is a 2-port device insertedbetween the source with 50 ohm source resistance and the designedmonopole antenna. First a matching network was synthesized and
- 7 -
optimized using the program ESYN with lossless lumped elements.Then the synthesized matching network was simulated and furtheroptimized using TOUCHSTONE program but with lossy elements with Q-
factor equal to 75. Two matching networks are then synthesized.
Two matching networks have also been designed for the monopoleloaded with Vu - King profile.
d- RESULTS
For a monopole of length h = 1.5 m and radius a = 0.5 cm operating
over the frequency range 30 - 90 MHz, a FORTRAN program was
developed in order to solve the integral equation C16) subjectto minimize the optimization function C17) with respect to the
coefficients Z of the resistive loading impedance. The number of
the coefficients Z was taken as M =4 and the current distributionwas expanded using N = 10 basis functions. Different optimalloadings were determined for different permissible values of the
optimization function C17), where the broadband property wassatisfied. A flat input impedance can be obtained at the expenseof the radiation efficiency and vice versa. the optimizedresistive load is the one which satisfies the good broadbandproperty and at the same time gives a high antenna radiationefficiency. The optimum load was found with equal weights
V = Vx = 1 ) to be
42 m-i
Z Cz) = J Z C z / h ) C2ijh — z m=i
where,
Zx
= 6.41
Z3
= -13.49y Z
2= 2. 95,
y 2. = 6 81
h = 1
.
5 m, a =0.5 cm ), Vu -
the geometric mean frequencyFor the considered monopole C
profile was calculated at the geometric mean frequency of
51.96 MHz. It is
vk 564.64 -j 148.67
Z Cz) = ohm/m C22Ji. h - z
For implementation we use only the resistive part. Fig. 1 showsthe variation of the resistive loading of the optimum load
compared with that for Vu - King profile. It is clear from the
figure that the internal resistance R per unit length for the
Vu-King profile is higher compared to the optimum loading.
Table CI) shows the variation of the input impedance of the
- 8 -
monopole loaded with the optimum load compared with that of
the monopole loaded with Vu and King profile [33. It can be seen
from Fig. 2 that the input resistance R for the monopole with the
Vu - King profile is quite flat whereas the one using the optimumload varies from 54.4 ohm at 30 MHz to 343.9 ohm at 90 MHz. Also
from Fig. 3, it is clear that the input reactance is capacitive
for the Vu-King profile over the entire frequency range and has a
little change while for the case of the optimum load there is a
resonsance at 52.7 MHz. Fig. 4 shows the main disadvantage of
using Vu - King profile : lower value of the radiation efficiency
£. It can be seen that the maximum value of £; for the monopoleloaded with Vu - King profile is 11.85 fc C at 90 MHz ) which is
less than the minimum value of < for the monopole loaded with
optimum load, where < changes from 15.83 v. at 30 MHz to 39.74v. at 90 MHz. Table C2> shows the variation of the efficiencywith the frequency for the optimum load compared with that for Vu
- King load. The VIRE software program 161 has been used to
determine the radiation pattern of the designed monopole using
lumped equivalent loading. Fig. 5 shows the radiation pattern at
frequency 70 MHz for the case of the optimum load. Table.
3
summarizes the scattering parameters of the designed matchingnetworks using lossless lumped elements for the two impedanceprofiles. Fig. 6 shows the S parameter variation across the
frequency range and Fig. 7 shows that the VSVR for the optimumprofile is less than 2 all over the operating frequency. Also it
is clear from Fig. 8 that the gain CS21> is greater than 0.94
across the frequency band. The overall efficiency of the monopoleC < x 1^21 I
^ ^or ^ne t'wo cases OI " loading is shown in Fig. 9.
It can be seen from this figure that the overall efficiencyof our design has improved significantly compared to the Vu -Kingprofile. To be the matching networks realizable, the previouslydesigned networks are further optimized using TOUCHSTONE code bymaking the inductors and capacitors lossy with a Q factor valueof 75. Table. 4 summarizes the scattering parameters of thedesigned matching networks obtained using lossy lumped elements.Figs. 10. 11 show the variation of the S - parameters across thefrequency range for the lossy matching network case. Figs. 12 and13 show the VSVR and the overall efficiency for the lossy matchingnetworks. It is seen that even with lossy elements the presentdesign yields an input VSVR < 2 while still maintaining a highoverall efficiency compared to the Vu - King case. Fig. 14 showsthe topology and element values of the matching network for theoptimum loading, while Fig. 15 shows the circuit diagram for the
- 9 -
matching network which corresponds to The Wu - King profile.
7- CONCLUSION
It was shown that efficient optimization of wire-antenna
admittance can be performed by varying distributed loadings alongits length. Depending upon specific requirements on the wire -
antennas, it is possible to construct many optimization functions
by changing the values of the weights V and W~. The choice
of the values of V and W* depends upon the specificrequirements of whether a broadband input admittance or overall
efficiency is desired. The decision on terminating the optim-ization procedure depends on the goal of the antenna synthesisprocess. This report has introduced a new loading to improve the
efficiency of a broadband monopole. A matching network was
synthesized in order to maintain good impedance matching such thatthe VSVR is less than 2 across the required frequency band.
REFERENCES
[1] Altshuler,E. E., "The Traveling-Vave Linear Antenna, ' IRE. Trans.
Ant. Prop. AP-9, No. 4, pp. 324-329, 1961.
[2] Vu,T.T and R. V.P.King, '"The Cylindrical Antenna Vith Non
Reflecting Resistive Loading, " IEEE Trans. Ant. Prop. AP-13,
No. 3, pp. 369-373, 1965.
[3] Janaswamy , R. , "Videbanding Techniques For VHF Antennas-I,"Naval Postgraduate School, Monterey, Report # NPS-EC 010,1992.
[4] Balanis, C. A. , Antenna Theory Analysis And Design, Harper and
Row, Inc. , 1982.
[53 B.D.Popovic, M.B. Dragovic and A. R. Djordjevic, Analysis and
Synthesisof Wire Antennas, Research Studies Press, England ,
1982.
[6D Davis, V. A. , VIRE Program, Virginia Polytechnic Institute and
State Univ. , 1980.
E7] EESOF, Inc., Touchstone User's Manual, 1986.
- 10 -
TABLE 1. THE INPUT IMPEDANCE OF LOADED MONOPOLE
FREQUENCY INPUT IMPEDANCE INPUT IMPEDANCE INPUT IMPEDANCE
MHz UNLOADED OPTIMUM LOAD VU-KING LOAD
30 9. 47-J196. 03 54. 65-
j
203. 37 252.85-j 305.60
40 20.16-j 80.47 75.98-j 96.28 254.51-j 241.49
50 40.76+j 17.53 112. 19-j 18.23 253.09-j 209.85
60 84.49+J120.62 171. 58+
j
36. 96 248. 56-j 188.14
70 193.44+J242.89 256. 88+
j
51.89 241.91-j 174.81
80 502.85+J310.63 336. 08-
j
02.04 234.43-j 164.34
90 789.49-jl96.58 343.98-j 98.20 227.13-j 155.28
h = 15 id a = 0.5 cm
TABLE 2. SCATTERING PARAMETERS OF THE LOADED MONOPOLE
WITH LOSSLESS MATCHING NETWORK
FREQUENCY
MHz
OPTIMUM LOAD VU - KING LOAD
|S11| |S21| |S11| |S21|
30 0. 335 0.942 0.036 0.99940 0.299 0.954 0.019 1.00050 0. 273 0.962 0.019 1.00060 0.217 0. 976 0.029 1.00070 0.210 0. 978 0.014 1.00080 0.169 0.986 0.034 0.99990 0.184 0. 983 0.033 0.999
h = 1.5 m . a = 0.5 c m
- 11 -
TABLE 3. SCATTERING PARAMETERS OF THE LOADED MONOPOLE
WITH LOSSY MATCHING NETWORK
FREQUENCY
MHz
OPTIMUM LOAD VU - KING LOAD
|S11| |S21| |S11| |S21|
30 0.259 0.882 0.133 0.918
40 0.265 0.918 0.116 0.93950 0.243 0.930 0.058 0.94760 0.193 0. 941 0.038 0.94670 0.187 0.937 0.066 0.93880 0.153 0.935 0.058 0.932
90 0.201 0.913 0.071 0.922
h = 1.5 m a = 0. 5 c m
- 12 -
"X
eu
\S)
sII
IB
•c TJ
e J Jin
©> £
»H c 3._> fc
II *1
X 3 a
1
~ Xi
\
-*—s s s S s CDs s s s s sG in 6 in s inm N CM vH «H
IT
CO
s
f-
s
s
\
ocr*
£
0)m
c
•c
>•H
a?
0)
o
-
>
_(u / who) ayoi aniisisaa
13
£
Lf
GII
*
e
in
i
T '
\ : : 1
\ : I
...k ; :..«/
\ : : /
V • - '
\ : : /
v . : '
V- 1
v I
: s . |
\ /
X: \ :
>v '
V.:.JM: : ) v
:1 v
•
J ^1 V.
:i
^1 ^
}
...2 .V.
j!
i
•\
\1 \
T> T I \| \
\J J /: \
('V."
o> c •**
c 3 : \E ,: \
¥ - \i -)
3 a .: \> j \
\.J:
x + |: :
\1
° |i
|: :
: |: :
|: :
\
\
\
\
1 u i 1 1 y
sa
g
3wPC
GLn
s
u
5
VQ)
-Wc—
*
<C
•H
ftj
>
U
fO
•J
w
w
3ac
•HL.
s g G G G G Gun g Ln G Lfl G inm ro N CM H »H
m
3DNyiSIS3H mdNI
14
£
in
Gii
e
II
i —
r
"1 «r
—t "i "r
: /: :
/ ; i ;
: / : 1 :
/ 1
/ |
/ ; ; ;
"C •o^ :
L...- Uf T
: ne
f
/
J J /
a> E /
c 3 /
_-. &>E 7
i T ; f:"
3 a\ i
* \
I
l :
\:
I
1
1 \;
X 4 \ \:
i
L : i; L"\ V-
\ \:
: \ : V
\ : 1
i
\\
A *? :"
\ :
\ ;
\
\
\ :
\ ;
\
\ : \
\: \^: \
\: \: \
\\
v :
\
\ :
\ :
\ :
Vi i
1 1 fc C
Gen
03
g
C Czu3
u.
G
G
GGm
GGN
GG
GG
GG(S3
I
GGm
i
uc0)
3cr0)
Lu
KD«Pi
(1)
>C
H*i
(D
•H(h
TO
>0)
ucTO
«Ju<c
(D
c
00
u.
aowyioyaa injNi
15
£V
IP
sII
*
e
if.
«-i
n
"W3
3
)
I
I
t 1 i1 —i
1
\
\ i
\ :
\ :
1 :
; ; ki:
1
1
J
1
.i.
t
i
i
-A •
\
\
\
\
\
'I
: \
: \
\
: \
:. . . l
-x-
Wu-King
Load
C •
J
£
£
«j
a
4
o
\
\
\
\
v..
\V
\\\\V.
; \ :
; \
\
\:
\ \
; : i- :—\
:
\\
\
\
\
,
\\\
\
\
\
\ \ \\—^j 1 1—i.
s00
zWCuu.
sin
6
m CD U5 CD 1/5 SV V ro m N N
in in
uc<D
O"ID
Uu.
Cm
oc
•H3uc3
ucCD
CmCmUc
•H
•Hc10
C*
»C
ccCD
«JC<CD
J=
H
•Hu.
^ ^0W3iDiii3 Kioiiyiawa
16
-90
Patterns - Uertical Cut Oeg
Horizontal - solid : flax : -9.990E+0002 dB
Uertical - dashed : Max : -4.401E+0000 dB
\JBM0 7^0 720 -/10 JO
yy/
Zenith Degrees (Azinuth : 0)
90
Fig. 5 Radiation PatternAt Frequency 70 MHz
Of The Optimum Monopole
17
cu
V.
sII
*
£
II
JC
r.
l
T3 1C '
J
t»
c
i
3
i
i 1 i*
3 : 1
3 • i
D :
'
J : \
i LL... 1
:
: se: co3
: u:
ii ;/
: na : i
l
-i
4„:
1
1
":'Z
"
;z
; 5: c
l : r
i
LOSSLESS
/
;
: i
i
1
I
1
:.A :
1,
•i
i:
:
/
:
/
:
/
1
.±_
j _,
I
!
ri
i
<i—
en
sCO
CD s Smes
ro
>zw
w
N
0>
-c £H
H(n >u. Dr\ *;H ro
iH cw •H\s E
+s (U
c H0)
•H ^u (h
•H(m *v. *J0! 0)
zu
k£c c
•H•H £*> Uu «J 0)
0) n H•H r O<m a0) tn
Cki « cS)
«J ~H r3 Wa Cfi 0)
c O £M -J Hofc
[ITS] 3WU
18
£U
WSII
CO
cc
e
IT.
«H
II
X
. -T_ , —i 1 1 1*
:l
w\1
; ; it v
i
TJ T)
:
: o o.J J
©3
; •: ;/
;/
'}
I
; £
: o> E: C 3: ... E: tt•
i w: 3 a: >
:
I
x +
:i o
"' uZcrr
cc
1:
1!
/:
: 1!
li
'.
A'. ,."' rCOCOuCOCO©
/
;
/:
/
/ ;
':., . J. . , ..'
; /
:
/
:
/
:
/
: i
' 1 1
: / :
: / :
! _J
sCO
cr^
s u5cu.
s
m N in in
83
*
0)
z
c•H
£W
0)
^H(R
KC-J
0)
XHin
u.
>
ac
•H
trnsn
19
cu
wsII
e
w
II
1
ii
1 :
1 =
J
i I T
73 T3
J J
0> £C 3
E
i i i
1I
I
I :
I :
IP1 :
ao3aa
i —
>
3 a>
1
x +i
I :
I :
I
I :
I
i
^t.
r
r
uCt . . . .
! :
I
I
I
I
!
CO
u—
©
I :
i
I
I
\
„..i
I :
\
\
I
I :
ii
—
k—
i
11
0*i
Uru
ucu.
0^ OD n sfi m v ID Ns s tc s s s
[TZS] 3WU
B G s
0)
iHWtfi
_J
0)
aHfc,
u.X
-Hrs *
2
IB
CD
t,
0)
*
c•Hs:u
o rCu
(h
0)
XIto
c«uHCO
W5H
20
£V
IT
SII
to
cce
t! !
i
1 1— 1
\ •
V"i •o •v
\ :
'i
: c1
\ :
' : :
i
J J\ :
t e> E \
'
r cE
....£.:..
\* ..» 1:
i —ji-
\ 3 a i-
*>>
«\
_w jr. . . .
I
Xi
4:\
:* .._U !
at \ :
cr \ ;
'
\
r \
:
\ :
— v \
l
*- \
--c :4 .4.....;
r: \ :
\
to \ \ I
CO \\ •:bi \ :
j \1 :
co \ 1
co -
x° :
V_ _\ X . .
\\\
\\
\:
V
1
...A....*\ -
: \\\ : \
\ : : \
\: \\ :
\ \ \
i
1
1 IV1 h—
en
sCD
>ozu:
crucu.
cLT.
in sm
in S in
.a
*
0)
2:
c•Hx:u
£
W0)
«HKW
J
ucid
•H
u•HOhUU
QJ
>oavie
CX3 ADN3I0UJ3 1TV33A0
21
ev
in
sII
K
z
—II
1 T 1
<
'
' '
i }73 : *
:
\:
i
J Ji
'
o g :
\
C 3 ••- - ....£...
2e
; /
* ° ii
! 1
; \
; \
; i
:
i
; i
; i
-. i
i
/
i
i
i
X_ ..K. .
1 »
C: 3-
Ed
: Z: W: Z
o-i
Ocz
c
: ; /
/:
: /:
: : / :
: / :
: : [...1.:-
i
i
i
/
i
i
: : : / :
: / :
: / :
: 1
: :I
: I
: : a J.
i
i
i
j
1 : 1
i\ 1
I : /
: | : | :
: : 1 : ' :
'
i i a «—
sen
a* e N «£ IT T" m Ns s CD CSS
ITTS3 9WU
s S
0)
HU
EQw J*
h3c *(1) ^•H flj
N U 2•H
y Cm *Cfc- C
> 0) -H
U c JSz Uu «J~
C (C
eo a•H*5 >su wo> w«H<M J0)
u-P3ac
•Hb.
22
cu
U)
sII
to
c
ii
s
1 11
:\
\
\
\ IX ••:
—i
"0 X6 t
C
J J
tt E
•c
£
i
1
1
I
I
}
i —>
3 a>
1
i
1
.. * +
3fr-
it:
Zcrz
•I
1 cl
^ • v •
'
cz>COtoc
i
I:
/:
/ :
J..:....
p1;
1 :
i
1 ! .
[|
c*l
sCD
G
Cw
u:
S
as
fa
*
0)
z
c•H
u
(0
s:
(0
to
o-j
0)
JCH(h
h.
ac
•Hfa.
IT m IT N Ift
s
H'fi'S'n
23
eL
IT
Cli
t
IT
I!
>c
1/:
1:
1
/;
_...^.j ;
i 1 : 1 :
C 6
J J
Ec a
i
1 :
1 :
1:
!
i :«L . - ..• ;..CS...
a
: 1
X: 1
a
•f
I 1'
: : «
1
L ,4 .
i
i!; s
li sII
•
! Ill:
|1! : :
II •
1 1
=
IP :
1 I:
It : :
1i|
1:\
p* e N s£ IT. r- IT N —s s S S S S
IT2S3 9WU'
S C C
c
c
_ s
&
_ C
e
*
a>
2:
c•HXu
KK
c•HfC
D
a-
c~
oj
u
5KCft
u
fa.
24
EV
IS:
sII
CO
c
£
IS>
1 f
:
/
; /
:/
:/
1
A
; ; i
oo :1
n, c -.i
T
X
\
I
-•§-:*
W : \z
; \
1 1 \
c aE
i w3 a>
I
x +l
:\
':
\
: \
! \
: \
i
: \
\
i
; \
\
j....
>COCO©
\\ ;
\ :
>-...:
\
; \
; \
: \
\
i-
\\
: \\
: \
. . : . . . . \>
i
\
\
! i j
\\ :
\\ : :
Y•\ :
:
: \ :
1 V |
\
I
\
1
\
1
>CJz
O"uccu.
s LT)
ms S in in
J*
o*
nzhic•HJ=
u«•>
ID
£
(0
00
_'
JC
Uca)
•H
u•H(h(hU
num>o
•H
(X) ADN3IDIJJ3 TTVH3AO
25
< 1 /'• m ( J V- /
1 nH _( *- o p—
•-
Dr
< .- <,
Fig. 14 Matching Network For The Monopole Loaded
With The Optimum Load
V / _/ V / ,' _
H t- 575 n
H
-(~
| 500^0 < _c
-< ? 7
1
J ~1
-• •
Fig. 15 Matching Network For The Monopole Loaded
The Vu - King Profile
26
INITIAL DISTRIBUTION LIST
No. Copies
1. Defense Technical Information Center 2
Cameron Station
Alexandria, VA 22304-6145
2. Dudley Knox Library, Code 52 2
Naval Postgraduate School
Monterey, CA 93943-5002
3. Chairman, Code EC 1
Department of Electrical and Computer Engineering
Naval Postgraduate School
Monterey, CA 93943-5000
4. Professor Ramakrishna Janaswamy, Code EC/Js 10
Department of Electrical and Computer Engineering
Naval Postgraduate School
Monterey, CA 93943-5000
5. Professor Richard Adler, Code EC/Ab 1
Department of Electrical and Computer Engineering
Naval Postgraduate School
Monterey, CA 93943-5000
6. Dr. Darwish Abdel Aziz Mohamed 5
Officers Building Home 2BFlat 44
Toson- Abokir- Alexandria, Egypt
27
DUDLEY KNOX LIBRARY
3 2768 00342562