Reduced Size Fractal Rectangular Curve Patch Antenna G. Tsachtsiris, C. Soras, M. Karaboikis and V. Makios Laboratory of Electromagnetics, Department of Electrical and Computer Engineering, University of Patras, 26500 Rio-Patras, Greece e-mail:
[email protected],
[email protected],
[email protected],
[email protected] four more rectangles of a quarter of the area of FRC0 and placing them at the four corners of the initiator as depicted in Fig. 1b, the pre-fractal FRC1 is obtained. Repeating this adding procedure one more time at each rectangle placed at the four corners, results in the pre-fractal FRC2 (Fig.1c). The ideal fractal curve would be obtained by applying this iterative procedure an infinite number of times. However, for antenna applications a few iterations would suffice [5].
Abstract: A novel fractal rectangular curve microstrip antenna is investigated as an efficient scheme of miniaturization. Based on simulation results the element possesses good size reduction ability without compromising significantly on the antenna’s bandwidth and efficiency. The radiation patterns between the conventional quarter wavelength patch and the shorted fractal element are similar, concluding that the latter can be used to replace the former. Moreover, the novel geometry has several degrees of freedom that can be used to either reduce further the size of the antenna or keep the bandwidth to a satisfactory level. The novel geometry was also considered for production of circular polarization and exhibited very good results.
y x
D2
D1
D0
D3
W0
Keywords: Microstrip Antennas, Fractals, Fractal Rectangular Curve, Circular Polarization.
L0
a) b) c) d) Figure 1. Construction of the Fractal Rectangular Curve (FRC), a) FRC0 (Initiator), b) FRC1, c) FRC2, d) FRC3.
Introduction The advantages of microstrip antennas such as the low profile, the ease of fabrication and the low cost have made this element very popular and attracted the scientific research for many years. Although the above-mentioned merits would be expected to project the patch as a good candidate for many applications, its large physical size render it improper where the antenna space availability is a limitation. For this, several methods have been considered to reduce the antenna size such as the use of shorting pins [1], material loading and geometry optimization [2]. Although it is interesting to notice that attempts to increase the conductive path of the antenna have been endeavored by introducing slots and notches [2, 3], it was not until recently with the introduction of fractals in antenna engineering that this could be done in a most efficient and sophisticated way [4,5]. Fractal shapes have proved to possess higher dimensionality than the Euclidean ones, in other words they can exploit more efficiently a finite area or volume.
The dimensions of the initiator are W0 by L0, the semi-diagonal D0, the perimeter Π0 and the enclosing area A0. In every iteration the semi-diagonal, the perimeter and the rectangular area enclosing the figure increase respectively. The semi-diagonal at the n-th iteration is found to be: n
Dn =
∑ i =0
1 W0 2 + L0 2 or D n = 2D0 2i +1
n
∑ i =0
1 2i +1
(1)
while the perimeter and the enclosing area are given by: 2
⎛ 2n +1 − 1 ⎞ and A n = ⎜⎜ (2) n ⎟⎟ A 0 ⎝ 2 ⎠ Theoretically as n goes to infinity the semi-diagonal of the FRC is doubled, the perimeter goes to infinity, while the enclosing area increases four times. The ability of the rectangular curve to double its perimeter at every iteration was found very triggering for examining its size reduction capability as a microstrip antenna.
Π n = 2n Π 0
In this paper a novel Fractal Rectangular Curve (FRC) is analyzed and examined as a patch antenna candidate. Based on simulation results the FRC exhibited very good miniaturization ability owing to its space filling properties, without reducing significantly the bandwidth and the efficiency of the antenna. It was also found that as the iteration number increases the radiation pattern remains similar to that of a normal shorted rectangular patch with a slight increment of the cross-polar component. The FRC’s geometry possesses several degrees of freedom more than a conventional rectangular shorted patch that can be exploited to achieve further size reduction or keep the bandwidth to a satisfactory level. Furthermore, due to its compact size and favorable characteristics the proposed geometry was also considered for production of circular polarization for mobile satellite communications. The fractal microstrip antenna exhibited very good results with the axial ratio being below 3 dB in the bandwidth of operation, while the difference between RHCP and LHCP components is greater than 15 dB for large elevation angles for both E-plane and H-plane cuts.
Due to the symmetry of the pre-fractals of Fig. 1 a short can be introduced along the y-axis in order to reduce their size to the half. This results in the shorted antenna elements depicted in Fig. 2 that were finally investigated. Shorted edge
Probe Feed
d W2
W1
W
L/2
L1/2
L2/2
W3
L3/2
a) b) c) d) e) Figure 2. Geometry of the Simulated Shorted Elements, a) SFRC0, b) S-FRC1, c) S-FRC2, d) S-FRC3 and e) Modified SFRC3 (MS-FRC3).
Fractal Rectangular Curve Patch Antenna The shape of the proposed configuration is a generalization of the “Squares Curve” [6], using a rectangular initiator instead of a square one and named after this as a Fractal Rectangular Curve (FRC). The FRC is constructed by applying a geometric transformation on the rectangle FRC0 of Fig. 1a. By producing
The traditional quarter-wavelength patch antenna (S-FRC0) has been used for comparison purposes. Its width W and length L/2 for operation at the 2.4 GHz are respectively 49.4 and 20.67 mm [7].
1
reduction. Along with the scaled S-FRC3 a modified geometry (MS-FRC3) has been simulated, which stems from the former by merely adding a metal patch as shown in Fig.2e. This simple modification has proven to enhance the bandwidth by a factor of 13.5 %. Therefore it can be concluded that the fractal rectangular curve not only has very good miniaturization ability, but also respects in a good extent the bandwidth of the antenna.
The corresponding ratio a = W/L is 1.195. The widths Wn and the lengths Ln of the other shorted FRC elements (Fig. 2b,c,d) were calculated from equation (1) so as their rectangular enclosing area to be the same with the S-FRC0. In this way the inherent area increment characteristic of the fractal rectangular curve can be circumvented. The corresponding ratio an = Wn/Ln of the prefractals was initially chosen to be equal to a. This, however, is not obligatory and the effect of the ratio an on the characteristics of the antenna will be examined in a later section. Each shorted element is mounted on a 1.5748 mm-thick substrate, with relative permittivity εr = 2.2 and loss tangent, tanδ = 0.0004. The thickness of the antenna copper layer is 35 µm and the copper’s conductivity is σ = 5.8xe7 S/m. The ground plane, which is mounted at the bottom of the dielectric slab, is infinite. The configurations of Fig.2 were simulated using the IE3D Method of Moments based electromagnetic field solver [8].
5 0 -5
S11 (dB)
-10
Results
-20 -25
The computed input return losses (S11 in dB) of the S-FRC0, SFRC1, S-FRC2 and S-FRC3 patches are shown in Fig.3. The detailed behavior of these elements at resonance, i.e. central frequency (fn), bandwidth (BWn), achieved reduction and efficiency (n) are depicted in Table1. At the third iteration a reduction of 28 % has been achieved, which corresponds to a 50 % area reduction relative to the S-FRC0 microstrip antenna. It can also be seen that as the number of iterations increases the size reduction capability of the element decreases making thus the pursuit of a higher number of iterations unneeded. This saturation can be attributed to the fact that the current flowing along the perimeter of the element cannot follow the small details of the geometry and prefers, instead, a smoother path [5].
-35 -40 2.0
2.2
2.4
2.6
2.8
3.0
Frequency (GHz)
Figure 4. Simulated Input Return Losses of the Scaled SFRCs TABLE 2. EFFECT OF SIZE REDUCTION ON BANDWIDTH
-5
Antenna
fn (GHz)
BW (%)
BW Reduction (%)
S-FRC0 Scaled S- FRC3 Scaled MSFRC3
2.381
2.9
--
2.377
1.85
36.2
2.430
2.1
27.6
Fig. 5 illustrates the E-plane and H-plane radiation patterns of the scaled MS-FRC3 and the S-FRC0. It can be seen that the patterns of the two elements are similar with the cross-polar of the H-plane pattern not increasing substantially. As far as the directivity is concerned, for the quarter wavelength patch is 5 dBi while for the MS-FRC3 4.4 dBi. So the latter can be used to replace the conventional rectangular patch without compromising on the pattern characteristics.
-10
-15
S-FRC0 S-FRC1 S-FRC2 S-FRC3
-20
S-FRC0 Scaled S-FRC3 Scaled MS-FRC3
-30
0
S11 (dB)
-15
-25
-30 1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
Frequency (GHz)
S-FRC0
MS-FRC3
0 330
Figure 3. Simulated input return losses (S11) of the S-FRCs.
0 30
0
330
-10
-10
300
60
300
60
-20
TABLE 1. SIMULATED RESONANCE PERFORMANCE Antenna
S-FRC0 S-FRC1 S-FRC2 S-FRC3
fn (GHz)
2.381 2.059 1.858 1.713
BWn (%)
2.90 1.75 1.34 0.93
(fn-f0)/fn(%)
-13.5 22.0 28.0
-20
-30
n (%)
270
-30
90
-40
270
-30
-20
-20 120
240
120
240
-10
210
-10
0
150 180
The compromise for the achieved miniaturization is the bandwidth and efficiency reduction as can be readily observed from Table 1. However, in order to make a proper bandwidth comparison between the S-FRC0 and the S-FRC3 the latter has been scaled down by a factor of 0.72 in order to resonate at the same frequency with the former. The obtained results are illustrated in Fig.4 and Table 2. The bandwidth of the scaled S-FRC3 suffers a 36.2 %
210
E-plane (Eθ) Η-plane (Eφ) Η-plane (Eθ)
Figure 5. E-plane and H-plane Patterns.
2
90
-40
-30
39.4 37.2 33.2 30.0
30
0
0
150 180
Techniques for Further Size Reduction
Circular Polarization Behavior
The two parameters that affect the performance of the antenna are the ratio an = Wn/Ln of the corresponding initiator, and the distance d of Fig. 2d. The former can be chosen within a practical range between 0.8 and 2, making sure from equation (1) that the enclosing area of the pre-fractal is equal to the S-FRC0. Fig. 6 depicts how the ratio a3 of the scaled pre-fractal S-FRC3 affects both the bandwidth and the resonant frequency.
Due to its compact size and favorable characteristics the ability of the FRC to produce circularly polarized fields was also examined. In order to produce a circular polarization a Fractal Square Curve at the second iteration was considered, which stems from the FRC by setting the corresponding ratio a=W/L=1. For the excitation of the element a two-port configuration was used having the same amplitude but in phase quadrature. The location of the feeds (x, y) in mm is (-3.5, 0) and (0, 3.5) respectively with the element centered at the origin (0, 0), while the area enclosing the antenna is 33.3 mm2 as depicted in Fig. 8. The dielectric substrate, its thickness and the metal thickness are the same with the previous configurations.
2.2
2.7
2.1
2.6
BW
2.5
BW (%)
Frequency 1.9
2.4
1.8
2.3
1.7
2.2
1.6
2.1
1.5 0.8
1.0
1.2
1.4
1.6
Frequency (GHz)
2.0
33.3 mm
Port 2 (0,3.5)
2.0 1.8 Port 1 (-3.5,0)
a3
(0,0)
Figure 6. The Effect of the Ratio a3 on the Bandwidth and Resonant Frequency of the Scaled S-FRC3.
It is interesting to notice that for the value of a3 = 0.8 the bandwidth does not change noticeably, whereas the resonant frequency decreases by a factor of 11 % compared to a3 = 1.195. So a frequency reduction of 40 % (68% area reduction) has been achieved without paying any additional price for the bandwidth. For the value of a3 = 1.3 the maximum bandwidth is accomplished with only a 2.4 % resonant shift.
Figure 8. Geometry of the Fractal Square Curve at the Second Iteration and Configuration of the Ports.
The computed S parameters of the Fractal Square Curve patch antenna are shown in Fig. 9. The resonant frequency is 2.396 GHz with 14 MHz bandwidth (0.6 %) and isolation between the two ports below –15 dB at the resonant frequency.
The motivation for altering the parameter d of the antenna originated from the fact that since the current flowing on the perimeter of the antenna element lacks the ability to follow the small details of the geometry, it can be forced to follow a longer path by reducing the parameter d. It becomes clear from Fig. 7 that this parameter can further reduce the size of the patch at the cost, however, of the bandwidth.
0 -5
2,4
1,8
2,3
S Parameters (dB)
-10
2,0
Frequency
BW (%)
1,6
2,2
1,4
2,1
1,2
2,0
1,0
Frequency (GHz)
BW
-20 -25
S11 S12
-30 -35 -40 2.35
1,9
0,8
-15
2.36
2.37
2.38
2.39
2.40
2.41
2.42
2.43
2.44
2.45
Frequency (GHz)
1,8
0
-1
-2
-3
-4
Figure 9. The S Parameters of the Fractal Square Curve Patch Antenna at the Second Iteration.
-5
d Reduction (mm)
The axial ratio and the gain of the antenna as a function of frequency are depicted in Figure 10. It can be seen that the axial ratio in the broadside direction is below 3 dB throughout the antenna’s bandwidth, while the gain is kept above 6 dBi with the maximum being 6.36 dBi.
Figure 7. The Effect of the Distance d on the Bandwidth and Resonant Frequency of the Scaled S-FRC3.
A further reduction of the order of 22 % has been achieved, with a corresponding bandwidth of 0.97 %. So a frequency reduction of 50 % (75 % area reduction) is feasible.
3
8
Antennas and Propagation Magazine, Vol. 43, Issue 4, pp. 12-27, Aug. 2001.
6
Gain AR
Gain (dBi)
4
4
2
3
0
2
-2
1
-4 2.34
2.36
2.38
2.40
2.42
[3] Singh, D., Gardner, P. and Hall, P.S., Miniaturised Microstrip Antenna for MMIC Applications, Electronic Letters, Vol. 33, No. 22, pp.1830-1, October 1997.
5
Axial Ratio (dB)
6
[4] Kim, I., et al., “The Koch Island Fractal Microstrip Patch Antenna”, Antennas and Propagation Society, 2001 IEEE International Symposium, Vol. 2, pp. 736-9, 2001. [5] Gianvittorio, John P. and Yahya Rahmat-Samii, Fractal Antennas: A Novel Antenna Miniaturization Technique, and Applications, IEEE Antennas & Propagation Magazine, Vol. 44, No.1, pp. 20-35, February 2002.
0 2.46
2.44
[6]
Frequency (GHz)
[7] Balanis, Constantine A., Antenna Theory Analysis and Design, Second Edition, John Wiley & Sons, Inc., 1997
Figure 10. The Computed Axial Ratio and Gain Versus Frequency.
[8]
The E-plane and H-plane radiation patterns of the Fractal Square Curve for the RHCP and LHCP components are depicted in Figure 11. The configuration of the ports was such as to produce a right hand circular polarization, which is 15 dB greater than the left hand
George Tsachtsiris received his electrical engineering diploma from the University of Patras, Greece, in 1999. His is currently pursuing his Ph.D. working on the areas of printed antennas and antennas of Fractal geometry.
10
0
0
-10
-20
-20
LHCP
-30
-30
LHCP (dB)
10
0
-10
-10
-20
-20
LHCP
-30
RHCP -40 -100
-80
-60
-40
-20
0
20
40
60
RHCP (dB)
H-Plane 10
0
RHCP (dB)
LHCP (dB)
E-Plane 10
Zeland Software Inc., “IE3D”, http://www.zeland.com/
Biographical notes
component for θ = ± 700 in the E-plane and θ = ± 400 in the Hplane.
-10
Marneffe, T., http://users.swing.be/TGMSoft/
-30
RHCP
80
-40 100
-40 -100
-80
-60
Theta
-40
-20
0
20
40
60
80
-40 100
Theta
Constantine Soras is an Assistant Professor in the Department of Electrical and Computer Engineering, University of Patras, Greece. His research interests include computational electromagnetics, printed antennas and indoor radio wave propagation. He is a member of IEEE and ACES.
Figure 11. E-Plane and H-Plane Radiation Cuts for Both RHCP and LHCP Polarization Components.
Conclusion In this paper a fractal rectangular curve microstrip antenna is proposed as a novel scheme for size reduction. As the number of iterations increases the resonant frequency decreases to reach at the third iteration a size reduction of approximately 30 % (50 % area reduction). The radiation characteristics of the fractal patch antenna proved to be similar, while the bandwidth and efficiency did not suffer a great reduction. The geometry exhibits a good degree of versatility since several modifications can be applied in order to accomplish a further reduction in the order of 50% (75 % area reduction) or enhance the bandwidth to a degree of 27 % less than the conventional quarter wavelength patch. Furthermore, the ability of the novel fractal patch element to produce circularly polarized fields was examined, exhibiting an axial ratio below 3dB in the band of operation and a difference between the RHCP and LHCP greater than 15 dB for large elevation angles.
Manos Karaboikis received his diploma in Electrical & Computer Engineering from the University of Patras, Greece in 1999. His is currently pursuing his Ph.D. working on the areas of printed antennas and diversity techniques.
Acknowledgment
Vassilios Makios is a Professor in the Department of Electrical and Computer Engineering, University of Patras, Greece. His research interests include electromagnetics, embedded systems, microwave and optical communications. He is a senior member of IEEE.
The authors would like to thank Vodafone Hellas and the Karatheodory Programme of the University of Patras for supporting this effort.
References [1] Garg, Ramesh, et al., Microstrip Antenna Design Handbook, 2001 Artech House, Inc. [2] Skrivervik, A.K, Zurcher, J.F., Staub, O. and Mosig, J.R., PCS Antenna Design: The Challenge of Miniaturization, IEEE
4
