* Department of Electronic Engineering, City University of Hong Kong Hong Kong SAR, China
Abstract- The input impedance and radiation characteristics of
spaceborne helix antenna using in the LEO microsatellite formation flying are studied theoretically by the method of moments (MoM) in this paper. A helix antenna model with finite ground plane is simulated by the MoM based on the Rao-Wilton
Glisson (RWG) basis function. The effects of several design parameters, including turn number, pitch, and helix radius, on the current distribution, input impedance, and radiation pattern are studied. In addition, the edge effect of ground plane is
analyzed in detailed.
I. INTRODUCTION
In recent years, micro satellite has developed rapidly due to having desirable properties such as cost saving, small package and low power consumption. The evolving of satellite formation flying concept has raised the thinking of those seeking different approaches to new space programs, the low earth orbit (LEO) microsatellite formation flying for some special applications in both Earth and Space science has been paid great attention. The resurgence of interest in small satellites is primarily due to the increasing demands for timely and affordable access to space [1]. In order to effectively combine the resources of autonomous, formation-flying constellations of smaller satellites, the satellites must have the ability to communicate with each other [2], and spaceborne helix antenna usually has been used for inter-satellite and satellite-ground communications. As a smaller and lighter helix antenna is desired, Safavi-Naeini and Ramahi [3] modified the structure to reduce the antenna size dramatically without corresponding reductions in performance. In the Space Technology 5 (ST5) Project, which is part of the National Aeronautics and Space Administration (NASA)'s New Millennium Program (NMP), an evolved antenna [4] is designed by the genetic algorithm to achieve high gain across a wider range of elevation angles and more uniform coverage.
The characteristic of axial mode helix antenna is studied in [5], but the parametric effects of helix antenna have not been discussed. In this paper, the input impedance and radiation characteristics of spaceborne helix antenna using in the LEO microsatellite formation flying are studied theoretically by the method of moments (MoM) based on the Rao-Wilton-Glisson
(RWG) basis function [6]. A helix antenna model with fmite ground plane is modeled and simulated by the MoM code. The results are compared with that of FEKO. And then, parametric studies are performed to provide insights on how these design parameters, including tum number, pitch and helix radius, affect the current distribution, input impedance, and radiation pattern. Finally, the edge effect of ground plane, including shape and size, is discussed in detail.
II. METHOD OF MOMENT BASED ON RWG BASIS FUNCTION
RWG basis function is a kind of vector basis function, and is defmed as two triangular patches attached to each other by an interior edge. After the surface of helix antenna modeled by triangular patches, each two adjacent triangles (r and r) construct a RWG triangular patch model, and the surface current density J can be approximately in terms of the fm as [7]
where
{(!mI2A;;,)P: (r), r in r
fm = (ImI2A�)p� (r), r in r
o , otherwise
(1)
(2)
where 1m is unknown constants, M is the number of interior edges, fm is the vector basis function associated with mth
interior edge, 1m is the length of the edge, and A; is the area
of triangle T± . Position vector p; points from free vertex of
triangle r to the observation point, and p� points from the
observation point toward free vertex of triangle r . The solution I for the impedance equations can be written in matrix form as
ZxI= V (3) where V = {Vm} are antenna excitation voltage column vectors
of length M, and each element of V represents excitation
voltage of each edge element. Z = {Zmn} represents the
mutual impedance matrix of different edge elements, and impedance elements can be given as
It can be seen from Fig. 2 that the results of developed MoM code agree with that of FEKO very well. And then the effects of turn number, pitch and helix radius are discussed. Both surface current and radiation pattern are given at f=2.3GHz.
where p�± is the vector between midpoint and free vertex of A. Turn Number triangle and p�+ , p�- are towards and away from the free
vertex, respectively. The input impedance ZA is
ZA =�= �n • (5) In In In In Using method described in [7], the above matrix is solved
and the constants 1m can be obtained.
III. PARAMETERIC STUDY
In this section, the effects of helix antenna design parameter, including turn number, pitch, radius, on the surface current, input impedance and radiation pattern are discussed by the MoM code. Fig.l shows the mesh of helix antenna model with square ground generated in the Matlab.
Fig, 1 Mesh of helix antenna model with square ground
The size of square ground is 150mm x 150mm, including 21 x21 square meshes. The height and width of connect part is 9mm and Imm, respectively. Helix antenna radius and pitch is 0.22m and O.035m, respectively. The turn number is 3. Each square mesh is divided into 2 triangles, as shown in Fig. 1. The following simulation is based on this model.
In order to demonstrate the accuracy of the developed MoM code, surface current obtained by the MoM is compared that of FEKO, as shown in Fig. 2.
2.5 ,--,----,---.---,---,---,----,---.---,
� 2.0 E 'iii ai 1.5 "0 C � ::J 1.0 u Q) u � ::J 0.5 (f)
w � � � 100 1W 1� 1� 1�
Number of triangles
Fig, 2 Comparison of surface currents
194
We simulate the helix antenna by choosing the tum number as 3, 8, 13, 18, and 23, respectively. Fig. 3 shows the simulated surface current density, input impedance and radiation pattern for different tum numbers.
Fig. 3 Simulated results for different turn numbers (a)surface current density (b )input impedance (c )radiation pattern
It can be seen from Fig. 3(a) that the maximum current appears at the bottom of helix antenna where it is close to the feeding edge, while the minimum current appears at the top of helix antenna where it is the open circuit. When the tum number becomes larger, the standing wave shifts to the right, then the current enters a period of approximately steady rate fluctuation after decrement of tum number, and finally enters divergent fluctuation.
From the Fig. 3(b), we observe that real and imaginary parts of input impedance do not change very much from 2 GHz to 2.3 GHz except the 3 tum case.
In Fig. 3(c), the gain becomes larger while the tum number increases. The detailed information, such as gain, side lobe level (SLL) and front-to-back ratio (FBR), is listed in Table l .
TABLE I GAIN, SLL, AND FBR FOR DIFFERENT TURN NUMBER
Turn Radiation Pattern
Number Gain (dB) SLL (dB) FBR (dB)
3 9.8 -17.1 11.5
8 12.1 -21.2 15.0
13 13.6 -21.2 16.3
18 14.8 -25.1 17.0
23 15.6 -24.8 18.0
It can be seen from Table 1 that: l)gam and FBR mcrease with the increment of tum number, while SLL decreases; and ii)less effect of tum number on the radiation performance can be observed as the tum number increases. When the tum number changes from 3 to 8, the gain increases 2.3dB, while SLL decreases 4.ldB.
B. Pitch The pitch is chosen as 20mm, 25mm, 30mm, 35mm, 40mm,
and 45mm, respectively. Input impedance and radiation pattern for different pitches are plotted in Fig. 4.
250 0:----,-----.-----,--,----,--------,
200 ���� E 150 � .<:: o ID 100 U C '" -g 50 0. .s
2.05
--.--;e(S-20mm) --<>-im(S-20mm)
--6--fe(S=25mm) --..-im(S=25mm)
--+-re(S=30mm) --;<--im(S=30mm)
-+--re(S=35mm) --<l>-im(S=35mm)
--..-..e(S=40mm) -4--im(S=40mm)
--+-fe(S=45mm) --+-im(S=45mm)
2.10 2.15 2.20 Frequency(GHz)
(a)
2.25 2.30
195
90
10
-5
-10
-15 180 0
-15
-10
-5
�S=35mm 10 --e--S=40mm 300
-->f-S=45mm 270
(b)
Fig. 4 Input impedance and radiation pattern for different pitches (a)input impedance (b )radiation pattern
As shown in Fig. 4(a), the real part of input impedance decreases first and then increases as the increment of pitch. From Fig. 4(b), we can see that: 1 )the antenna gain for pitch 20mm, 25mm, and 30mm have similar values; 2)the antenna gain decreases and the side lobe increases as the pitch increases continually.
C. Helix Radius The helix radius is set as 20mm, 21mm, 22mm, 23mm, and
24mm, respectively. Input impedance and radiation pattern for different helix radiuses are shown in Fig. 5.
Fig. 5 Input impedance and radiation pattern for different helix radiuses (a) input impedance (b)radiation pattern
Fig. 5(a) shows that the real part of input impedance decreases fIrst and then increases along with the increment of helix radius. From Fig.5 (b), we can see that the antenna gain increases as the helix radius increases, but the direction of maximum radiation changes.
D. Ground Plane The antenna models with the square and round ground are
plotted in Fig. 6.
"I ... '''1 , .. ."
(a) (b)
Fig. 6 Mesh of helix antenna model for different grounds (a)square ground (b )round ground
The size of non-uniform square ground in the Fig. 6(a) is 150mmx150mm, and the mesh is generated by PDE toolbox [7]. The feeding region is meshed by dense non-uniform meshes to improve the computational accuracy. The radius of the round ground is chosen as 75mm, 84mm, and 106mm, respectively. The simulated radiation patterns are shown in Fig. 7.
10
0
·5
·10 180 i
-10
-5
0
10
90
270
----original square ground --{)--found ground with R=84mm --<-round ground with R=75mm ...."...,.ound ground with R=106m --+-non-uniform square ground
300
Fig. 7 Radiation pattern
196
It can be seen from Fig. 7 that the radiation patterns of the non-uniform and uniform square ground agreed quite well to each other, and the gain of round ground with radius of 84mm is mostly consistent with the square ground.
IV. CONCLUSION
In this paper, the effects of helix design parameters, including helix turn number, helix pitch, helix radius, and ground plane, have been investigated in detail by MoM based on the RWG basis function. The presented study is considerably useful for engineering practice .
ACKNOWLEDGMENT
This work was supported in part by the National Natural Science Foundation of China under Grant 60901001 and in part by the National High Technology Research and Development Program of China under Grant 2008AA12A216.
[1]
[2]
[3]
[4]
[5]
[6]
[7]
REFERENCES
G. M. Chen and D. D. McLennan, "A study of learning curve impact on three identical small spacecraft," IEEE Aerospace Conference Proceeding, vol. 6, pp. 3970-3976, 2004. G. Q. Wu, Z. W. Sun, and S. Wu, "Research of direct spread spectrum communication system for formation micro-satellites," Sixth International Conference on Information Technology, pp. 1585-1587, 2009. A. H. Safavi-Naeini and O. Ramahi, "Miniaturizing the axial mode helical antenna", IEEE Second International Conference on Communications and ElectroniCS, pp. 374-379, 2008 C. Carlisle and E. H. Webb, "Space Technology 5 - A Successful Micro-Satellite Constellation Mission," 21St Annual AIAAlUSU Conference on Small Satellites, pp. 1-7, 2007. Q. L. Lu and C. S. Pan, "Research on the characteristic of the axial mode helix antenna and simulation," Transactions of Shengyang LiGong University, vol. 26, pp. 1-4, June 2007. S. M. Rao, D. R. Wilton, and A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Trans. Antennas and Propagation, vol. 30, pp. 409-418, March 1982. S. N. Makarov, Antenna and EM Modeling with Matlab [M]. New York: John Wiley and Sons, 2002, pp. 12-18.
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