Progress In Electromagnetics Research Symposium Proceedings, Marrakesh, Morocco, Mar. 20–23, 2011 1875
Matching Technique Design for Multi-fed Full Wave Dipole Antenna
Yahya S. H. Khraisat1, 2 , Khedher A. Hmood3 , and A. Anwar3
1
Electrical and Electronics Department, Al-Huson University College, Al-Balqa Applied University, Jordan
2
Hijjawi Faculty for Engineering Technology, Telecommunications Engineering Department
Yarmouk University, P. O. Box 1375, Irbed 21110, Jordan
3
School of Electrical and Electronic Engineering, Engineering Campus
Universiti Sains Malaysia, Seri Ampangan, Nibong Tebal 14300, Penang, Malaysia
Abstract— This paper is focused on the derivation of equations for a full-wave dipole antenna
based on feeding techniques. The current distribution was measured, followed by the measurement of parameters of antenna like gain, radiation patterns and input impedance. Based on these
observations four equations for current distribution were eventually formulated. These equations
were then used to compute the values of the same parameters of the antenna. Finally, the values
of parameters obtained practically and theoretically were compared to analyse the validity of the
developed equations.
1. INTRODUCTION
In this paper, it was found that the full-wave antenna offers a high gain by devising the feeding and
applying multi feeding instead of one. Novel design methodologies and implementation techniques
for full wave antennas with dual and triple feeding are studied.
For a true harmonic operation, it is necessary that power is to be fed into the antenna is at an
appropriate point. A full wave dipole antenna was to be fed by various methods. These methods
can be classified into three categories; namely, symmetrical dual feeding, asymmetrical dual feeding
and symmetrical trouble feeding. The analysis of the parameters of asymmetrical dual feeding full
wave dipole antenna was discussed at Microwave Radar and Remote Sensing conference MRRS
2008 [1].
The current distributions were measured using a shielded loop [2] and [3] protruding through
a slit in the antenna surface along its axis that gave exact and accurate measurement rather than
sinusoidal distribution. The sinusoidal distributions of current and voltage are approximations
rather than exact descriptions [4] and [5].
Next, the current distributions were modeled and formulated whose parameters were deduced
from the measured current distribution by applying the current distribution data in models as
derived by IEEE standard. According to [6], it is difficult to apply directly measured data in the
forms derived by same authors.
2. DEVELOPMENT OF EQUATION FOR CURRENT DISTRIBUTION
This section presents results from an experimental investigation of current distribution test. This
investigation serves to experimentally find the current distribution wave form, and to obtain formulas by using curve fitting and trial and error methods. The relative magnitude of the current
distribution along the antennas was measured and normalized with respect to maximum amplitude.
The measurements were conducted on half-wave dipole which is well known in its characteristics,
on center-tap full-wave and on off-center full-wave dipole. Figure 1 shows the current distribution
for Symmetrical dual feeding in-phase.
Curve fitting, trial and error were used to obtain formulated four equations that expressed in
the following sections. Equations (1), (2), (3) and (4) represent the mathematical expression of the
current distribution for Symmetrical dual feeding in-phase, Symmetrical dual feeding out-of-phase,
asymmetrical dual feeding in-phase, and asymmetrical dual feeding out-of-phase respectively.
¶
µ
L
− /z/
(1)
I(z) = sin β
2
PIERS Proceedings, Marrakesh, MOROCCO, March 20–23, 2011
1876
Current distribution vs Antenna length
Current distribution
nomalized
1
0.8
0.6
0.4
0.2
0
-0.2
0
20
40
60
80
100
-0.4
-0.6
-0.8
-1
Antenna Length CM
Figure 1: Measured current distribution for symmetrical dual feeding in-phase.
3. DERIVATION OF EQUATIONS FOR RADIATION PATTERN, GAIN, AND
RADIATION RESISTANCE
According to the thin wire approximation and Maxwell Equations, the z-component of the radiated
electric field for infinitesimal dipole is shown in Figure 2 and depicted in Equation (5) [7].
r
dEθ =
j60πejω(t− c ) I(z) sin θejk(z cos θ)
dz
λr
(2)
In the pervious section the current distribution model obtained is presented in Equation (1). This
Equations is used to derive the radiation pattern of antenna.
Referring to pervious section, the predicated Equation for the current distribution is:
¶
µ
L
− /z/
I(z) = Imax sin β
2
where β = 2π/λ . Expressions of the current distribution are as given below:
µ
¶
L
I = Imax sin β
−z , z ≥0
2
µ
¶
L
I = Imax sin β
+z , z ≤0
2
(3)
(4)
Substituting Equations (3) and (4) in Equation (2), yields
Z0
Eθ =
−l
2
1
· µ
¶¸
¶¸
· µ
Z2
l
l
jkz cos θ
+z e
dz + sin k
− z ejkz cos θ dz
sin k
2
2
(5)
0
Using Equation (6) to solve the Equation (5) gives Equation (7) [7]
Z
eαx
[α sin(βx + γ) − β cos(βx + γ)]
eαx sin(βx + γ)dx = 2
α + β2
³
´
³ ´

βl
βl
−jω(t− rc
cos
cos
θ
−
cos
2
2
jπ60I0 e
)

Eθ =
r
sin θ
In this study L = λ = 1. Substituting λ = 1 and simplifying Equation (7), yields
·
¸
r
j60I0 ejω(t− c ) cos(π cos θ) + 1
Eθ =
r
sin θ
¸
jω(t− rc ) ·
j60I0 e
cos(π cos θ) + 1
Hϕ =
2πr
sin θ
(6)
(7)
(8)
(9)
Progress In Electromagnetics Research Symposium Proceedings, Marrakesh, Morocco, Mar. 20–23, 2011 1877
Equations (8) and (9) represent the radiation pattern of Eθ and Hϕ respectively for antenna A1 .
The total radiated power is:
Z 2π Z π
1
Re
Eθ Hϕ∗ r2 sin θdθdϕ
(10)
2
0
0
Eθ
Hϕ =
(11)
ηo
Substituting Equations (8) and (9) in Equation (10), yields
¸
Z 2π ·
cos(π cos ϑ) + 1 2
2
p = 60Io
sin θdθ
sin θ
0
(12)
For numerical analysis and calculation, Matlab and MathCAD software were used to simplify
Equation (12) and the derivation of the gain is
120Io
r
Z
E2
P =
da
120π
Emax =
(13)
(14)
where da = 2πr2 sin θdθ
¸
·
602 Io2 cos(π cos θ) + 1 2
p =
2π · r2 sin θdθ
120πr2
sin θ
0
¸
Z 2π ·
cos(π cos ϑ) + 1 2
2
p = 60Io
sin θdθ
sin θ
0
Z2π
Let cos θ = u, sin2 θ = 1 − u2 , and sin θdθ = du
Z 1
(cos(πu) + 1)2
P = 60Io2
du
1 − u2
−1
¸
Z 1· 2
cos (πu)2 2 cos(πu)
1
2
= 60Io
+
+
du
1 − u2
1 − u2
1 − u2
−1
(15)
(16)
(17)
(18)
0
Let 1 + u = πv , du = dv/π, 1 − u = vπ , du = dv 0 /π
¸
Z 2π · 2
cos (v − π) 2 cos(v − π) 1
2
= 60Io
+
+
dv
v
v
v
0
#
Z 2π " 1
2 cos(v) 1
2
2 (1 + cos 2v)
= 60Io
−
+
dv
v
v
v
0


¶
¶
Z 2π µ
Z2π µ
(1 − cos v)
1
1 − cos(2v)
P = 60Io2 2
dv −
dv 
v
2
v
0
0


¶
¶
Z 2π µ
Z2π µ
(1 − cos v)
1
1 − cos(2v)
P = 60Io2 2
dv −
dv 
v
2
v
0
0


¶
¶
Z 2π µ
Z4π µ
(1 − cos v)
1
1 − cos(y)
P = 60Io2 2
dv −
dy 
v
2
y
0
0
·
¸
1
2
P = 60Io 2(0.557 + ln(2π) − Ci(2π)) − (0.577 + ln(4π) − Ci(4π))
2
(19)
(20)
(21)
(22)
(23)
(24)
PIERS Proceedings, Marrakesh, MOROCCO, March 20–23, 2011
1878
·
P =
60Io2
¸
1
2(0.557 + 1.837 − 0.023) − (0.577 + 2.531 − 0.006)
2
P = 60Io2 [3.319] = 199.1Io2
P = 199.1Io2 = Io2 Rrad
Rrad = 199.1Ω
(25)
(26)
(27)
(28)
cos θ)+1
To determine Emax , the function [ cos(πsin
] approaches its maximum as θ → π/2 and apθ
proaches zero as θ → 0 and π, thus
"
#
¡
¢
r
j60Io e−jω(t− c ) cos π cos π2 + 1
Emax =
(29)
r
sin π2
·
¸
r
j60Io e−jω(t− c ) 1 + 1
Emax =
(30)
r
1
120Io
Emax =
(31)
r
Equation (32) can be used to calculate the gain [8, 9].
G=
2 r2
Emax
30P
(32)
Substituting Equations (27) and (31) in Equation (32), yields
120Io2 r2
E 2 r2
=
= 2.41
30P
30Io2 199.1
G = 10 log(2.41) = 3.82 dBi
G =
(33)
(34)
Half-power beam width is the angle between two solutions of Equation (8) [10].
·
¸
cos(π cos θ) + 1
1
= √ ; 0≤θ≤π
sin θ
2
Solving Equation (35) for θ and the numerical solution gives θ ≈ 124◦ and 66◦ and the half-power
beam width of 124◦ − 66◦ = 48◦ .
4. CONCLUSIONS
Expressions for the current distribution, gain, and radiation patterns of full-wave dipole antennas
were developed. The relation of the current distribution with the feeding modifications and the
polarity of feeding were numerically and experimentally investigated. The expressions for current
distribution were developed, and validated, and compared with the experimental results.
For symmetrical dual feeding in-phase, the equation of the current distribution is found to be
similar to the conventional full-wave antenna Equation. For symmetrical dual feeding out-of-phase,
the Equation follows the theoretical concept of the full-wave antenna (off-center fed). However, the
Symmetrical feeding in-phase achieved 3.82 dBi gains.
REFERENCES
1. Yahya, S., H. Khraisat, K. A. Hmood, and A. Anwar, “Analysis of the parameters of asymmetrical dual feeding full wave dipole antenna,” Microwave and Remote Sensing Symposium
(MRRS 2008), Kiev, Ukraine, September 22–24, 2008.
2. Edwards, H. N., “The measurement of current distribution in aerials at VHF,” Proc. I.R.E.
Australia, 351–355, 1963.
3. King, R. W. P. and G. S. Smith, Antenna in Matter, MIT Press, Cambridge, MA, 1981.
4. Hassan, S. I. S., “Matching in rhombic and pseudo rhombic antennae,” Ph.D. Thesis, University
of Exeter, 1987.
5. Idris, S. H., C. M. Hadzer, and M. Z. A. Ghgani, “A full-wave dipole antenna for mobile
terminal application,” Technical Journal, Vol. 8, EE-USM, 1999, ISNN 1594-6153.
Progress In Electromagnetics Research Symposium Proceedings, Marrakesh, Morocco, Mar. 20–23, 2011 1879
6. Takamizawa, K., W. A. Davis, and W. L. Stutzman, “Novel techniques for analysis of array
antenna,” UNSNC/URS. National Radio Science Meeting, 176, CDROM, Boston, MA, 2001.
7. Balanis, C. A., Antenna Theory-Analysis and Design, 2nd Edition, John Willy & Sons Inc.,
1997.
8. Irdis, S. S. H., “Antena dan perambatan,” Pust Pengajian Kejuruteraan Elektrik dan Elektronik, Universiti Sains Malaysia, 1997.
9. Miller, E. K. and F. J. Deadrick, Some Computational Aspects of Thin-Wire Modeling, R. Mittra, editor, Springer-Verlag, New York, 1975.
10. Idris, S. H. and C. M. Hadzer, “Analysis of the radiation resistance and gain of full-wave
dipole,” IEEE Antenna and Propagation Magazine, Vol. 36, No. 5, 1994.
11. Idris, S. H., C. M. Hadzer, and M. Z. A. Ghgani, “A full-wave dipole antenna for mobile
terminal application,” Technical Journal, Vol. 8, EE-USM, 1999, ISNN 1594-6153.