# A Stacked Microstrip Antenna Array with Fractal Patches

Authors: Xueyao Ren; Xing Chen; Yufeng Liu; Wei Jin; Kama Huang
Journal: International Journal of Antennas and Propagation
 (2014)

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## Abstract

A novel microstrip antenna array, which utilizes Giuseppe Peano fractal shaped patches as its radiation elements and adopts a two-layer stacked structure for achieving both wideband and high-gain properties, is proposed. Parametric study estimates that the proposed antenna’s size can be arbitrarily adjusted by changing the fractal proportion while high aperture efficiency is maintained. Two prototypes with 2 × 2 and 4 × 4 fractal patches, respectively, on each layer are designed, fabricated, and measured. Both simulation and measurement results demonstrate that the proposed antenna possesses encouraging performances of wideband, high directivity, and high aperture efficiency simultaneously; for example, for the two prototypes, theirS
11
<
-
10 dB impedance bandwidths are 23.49% and 18.49%, respectively; at the working frequency of 5.8 GHz, their directivities are 12.2 dBi and 18.2 dBi, and their corresponding aperture efficiencies are up to 91.0% and 90.5%, respectively.


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## Body

## 1. Introduction

Directional antennas with high radiation gain are key devices in many practical applications such as the remote wireless communication. Due to their attractive features like low weight, low profile, small size, and being easy to manufacture, employing microstrip antennas to form array is a widely adopted method to design directional antennas with high gain. However, it is well known that microstrip antennas have an intrinsically narrow bandwidth [1], typically a small percent of the center frequency. In view of the explosive growth of the wireless system and the booming demand for a variety of new wireless applications, it is important to design directional antennas with both wideband and high gain to cover a wide frequency range. Indeed, there are countless researches proposed in the literature to design microstrip antennas with high gain or wide bandwidth, but few of them are for both properties together.To tackle the narrow bandwidth problem of microstrip antennas, various techniques have been proposed. Among them is stacking one or several parasitic layers on a microstrip antenna [2], and various methods have been widely used. For example, the 8-layer stacked patch unit assembly allows for great bandwidth which is more than 50% of the center frequency [3] and the use of high dielectric constant substrate for the driven layer and low dielectric constant substrate for the superstrate can offer more than 25% on bandwidth [4, 5]. The intrinsic properties of fractal geometries are conducive to the miniaturization of antenna size and realization of multiband or broadband characteristics [6, 7]; L-shape slot loaded broadband patch antenna for enhancing the gain without affecting the broadband impedance matching characteristics [8]; the artificial magnetic conductor structures are employed as the antenna magnetic ground plane for bandwidth enhancement and radiation gain improvement of patch antenna [9]. A dipole antenna with a double electromagnetic band gap (EBG) reflector is presented for wide operating bandwidth and high gain [10]. However, there are some defects in the designs. Some of them have high profile; some of them require special materials and increase the production costs; some of them have complex structures, which increase the difficulty in manufacture. More details are shown in Table 1.Table 1
Detailed data of the antennas mentioned previously.
Literature number
Number of layer
Number of array elements
Gain (dBi)
Bandwidth
Profile
Manufacture difficulty
Cost
[3]
8
1
7.4
52%
High
Hard
High
[4]
2
4
12.4
25.6%
Low
Easy
High
[5]
2
1
—
35%
Low
Easy
High
[8]
2
1
8.3
20%
Low
Easy
Low
[9]
4
4
15.95
20.45%
High
Hard
High
[10]
4
1
8.5
44.4%
High
Easy
LowIn this work, a novel microstrip antenna array, which employs a two-layer stacked structure and Giuseppe Peano fractal shaped patches for realizing both wideband and high gain properties, is proposed, analyzed, and measured. The remainder of the paper is organized as follows. Section2 introduces the configuration of the proposed antenna array. A parametric study is presented in Section 3. Simulated and measured properties of two prototypes with 2
×
2 and 4
×
4 fractal patches, respectively, on each layer are given in Section 4. Conclusions are stated in Section 5.


## 2. Antenna Configuration

Fractals are geometrical shapes, which are self-similar, repeating themselves at different scales. With the development of the fractal theory, the nature of fractal geometries has been exploited in many fields of engineering and science, including antenna design. The utilization of fractal geometries in antenna design has led to the evolution of a new class of antennas called fractal shaped antennas.The Giuseppe Peano fractal is a class of fractal geometries. Its recursive procedure is shown in Figure1. A Giuseppe Peano starts from a segment with length f
2 and allows its central part with length f
1 to break into two zigzag sections; it is constructed iteratively by growing new zigzag sections that have a specific length ratio n
=
f
2
/
f
1 with respect to their parent section.Figure 1
The recursive procedure of the Giuseppe Peano fractal.As depicted in Figure2, when the Giuseppe Peano fractal is applied to the edges of the square patch, this fractal patch with different sections resonates at different frequencies which together to form a wide working frequency band.Figure 2
The Giuseppe Peano fractal patch.The configuration of the proposed microstrip antenna array is illustrated in Figure3. This antenna utilizes a two-layer stacked structure, containing a radiation layer and a parasitic layer. Each layer is printed on a PCB (printed circuit board) with relative permittivity ε
r
=
2.55 and thickness h
=
1 mm. The two layers are separated by air with distance of h
z
=
3.2 mm.Configuration of the proposed microstrip antenna array.
(a)
The cross-section diagram
(b)
The radiation layer
(c)
The parasitic layerOn the top surface of the radiation layer, some Giuseppe Peano fractal shaped patches are etched periodically. They act as radiators and are connected to a microstrip corporate feeding network to form an array. On the bottom surface of the parasitic layer, the same patches as that on the radiation layer are also etched. Those patches are parasitic elements for enhancing the bandwidth and gain of the antenna array.This antenna is fed from a 50Ω coaxial connector. The microstrip corporate feeding network consists of a serial of T-junctions to deliver electromagnetic energy uniformly and multiple-section quarter-wavelength impedance transformers to achieve impedance match and is used to provide equal amplitude and in-phase excitation to all fractal shaped patches.From Figure3, we can see that L
s
=
2
×
(
D
+
L
), X
=
(
D
-
L
0
-
W
1
)
/
2
L
t
=
(
D
+
L
-
W
2
)
/
2, and L
3
=
(
D
+
L
)
-
2
×
(
L
1
+
L
2
)
-
W
1. Finally, the structural parameters of this antenna are optimized by Genetic Algorithm (GA) [11, 12] as follows: D
=
16.46 mm, L
=
14.71 mm, L
r
=
16.06 mm, W
1
=
2.27 mm, W
2
=
2.07 mm, W
3
=
1.77 mm, L
0
=
1.38 mm, L
1
=
3.66 mm, L
2
=
8.20 mm, and h
z
=
3.19 mm. The total area of the antenna is 62.34
×
62.34 mm2.


## 3.  Parametric Study

Here, we investigate the effect of the antenna’s parameters on its performance characteristics. In this section, the proposed antenna works at 5.8 GHz, has2
×
2 and fractal 4
×
4 patches on the radiation and parasitic layers, respectively, and adopts second iteration Giuseppe Peano fractal patches.


### 3.1. Effect of the Fractal Proportion

The Fractal proportionn is defined as
(1)
n
=
f
2
f
1
,
which can be seen from Figure 1. The greater the n is, the closer to square patch the Peano fractal radiator is.The2
×
2 square patches antenna array which works at the same frequency of 5.8 GHz is illustrated in Figure 4. Each layer is printed on a PCB with relative permittivity ε
r
=
2.55 and thickness h
=
1 mm, the same as the fractal ones.The configuration of the two-layer square patches2
×
2 antenna array.
(a)
The cross-section diagram
(b)
The radiation layer
(c)
The parasitic layerThe structural parameters of this antenna which is optimized by GA are as follows:D
=
29.50 mm, L
=
15.02 mm, L
r
=
17.30 mm, W
1
=
3.72 mm, W
2
=
2.78 mm, W
3
=
2.18 mm, L
0
=
1.52 mm, L
1
=
3.40 mm, L
2
=
13.27 mm, and h
z
=
3.48 mm. The simulated reflection coefficient and simulated directivity are given by Figures 5 and 6, respectively.Figure 5
The simulated reflection coefficient of the square antenna array.Figure 6
The simulated directivity as a function of frequency for the square patches antenna array.It is obvious that theS
11
<
-
10 dB impedance bandwidth is about 14.02% (from 5.37 GHz to 6.18 GHz). At its working frequency of 5.8 GHz, the antenna has an input reflection coefficient of −22.65 dB, which estimates that a good impedance match has been achieved.Different2
×
2 array antennas of different fractal proportion (n
=
2, n
=
2.5, n
=
3, n
=
3.5, n
=
4, and n
=
4.5) which are also working at 5.8 GHz are optimized by GA. Figure 7 reveals the simulated reflection coefficient of different fractal proportion antenna arrays and Figure 8 reveals the simulated directivity.Figure 7
The simulated reflection coefficient of the different fractal proportion.Figure 8
The simulated directivity as a function of frequency for the different fractal proportion.From Table2, one can observe that the fractal proportion has a great influence on the antenna performance. As fractal proportion n increases, the aperture area of the proposed antenna must increase for maintaining the same working frequency of 5.8 GHz. When the fractal proportion n
=
3.5, the S
11
<
-
10 dB impendence bandwidth reaches 23.49% versus 14.02% of the square antenna array working at the same frequency, the aperture area of proposed antenna is only 49% of the square patches antenna array’s.Table 2
Details of different antennas.
n
f
L (GHz)
f
H (GHz)
f
M (GHz)
f
%
L
s (cm)
2
5.33
6.23
5.78
15.57%
56.68
2.5
5.29
6.27
5.78
16.98%
59.43
3
5.21
6.37
5.79
20.03%
62.12
3.5
5.07
6.42
5.78
23.49%
62.34
4
5.28
6.30
5.79
17.62%
64.90
4.5
5.33
6.25
5.79
15.89%
65.40
Square
5.37
6.18
5.78
14.02%
89Another interesting observation worthwhile pointing out is the attainable aperture efficiency calculated only by the directivity, shown in Figure9. The vast majority of them are more than 85%. The average aperture efficiency (from 5.4 GHz to 6.1 GHz) is shown in Table 3.Table 3
Fractal proportionn
Average aperture efficiency
2
89.53%
2.5
90.86%
3
90.30%
3.5
91%
4
92.18%
4.5
91.32%
Square
88.48%Figure 9
The simulated aperture efficiency of the different fractal proportion antenna array.Table3 demonstrates that the average aperture efficiency of the Peano fractal antenna array is higher than that of the square antenna in the same working band. The maximum value of average aperture efficiency is obtained when the fractal proportion n
=
4.


### 3.2. Effect of Fractal Iteration

First and second iteration are relatively applied to the edges of the square patch. All the parameters of the second iteration antenna array are set to be the same as the first one. The comparison of the reflection coefficient of these two antennas is drawn in Figure10.Figure 10
Comparison of the simulated reflection coefficient of the 1st iteration and 2nd iteration.One can observe that the impedance bandwidth forS
11
<
-
10 dB is 24.18% (from 4.98 GHz to 6.35 GHz), which is much wider than that of square patches antenna array and slightly larger than that achieved in first iteration of the fractal patches antenna array. As the iteration of fractal geometry increases, its resonance frequency decreases, which may lead to an effective antenna miniaturization. However, for iterations higher than the second iteration, the antenna design becomes quite complicated and its fabrication becomes difficult. The comparison of simulated radiation patterns in the E-plane and H-plane of these two antennas is shown in Figure 11.Figure 11
Comparison of the radiation patterns of the fractal iterations, 1st and 2nd.The comparison indicates that the influence of radiation patterns that comes from the fractal iteration is almost negligible.


### 3.3. Effect of Array Elements Number

In this part, a proposed antenna with4
×
4 Giuseppe Peano fractal radiated elements and working at 5.8 GHz is also optimized by GA.Figure12 compares the simulated reflection coefficient of the 2
×
2 square patch antenna and that of the 4
×
4 Giuseppe Peano fractal antenna. As known to all, when the number of array elements increases, the impedance bandwidth of the antenna array decreases because of the mutual coupling between the array elements [13, 14]. Although the element number of fractal antenna array is four times that in the square antenna, the impedance bandwidth for S
11
<
-
10 dB is 18.43% (from 5.32 GHz to 6.40 GHz), which is much wider than that of square patches antenna array introduced previously.Figure 12
Comparison of the simulated reflection coefficient of the2
×
2 square patch antenna and the 4
×
4 Giuseppe Peano fractal antenna.


## 3.1. Effect of the Fractal Proportion

The Fractal proportionn is defined as
(1)
n
=
f
2
f
1
,
which can be seen from Figure 1. The greater the n is, the closer to square patch the Peano fractal radiator is.The2
×
2 square patches antenna array which works at the same frequency of 5.8 GHz is illustrated in Figure 4. Each layer is printed on a PCB with relative permittivity ε
r
=
2.55 and thickness h
=
1 mm, the same as the fractal ones.The configuration of the two-layer square patches2
×
2 antenna array.
(a)
The cross-section diagram
(b)
The radiation layer
(c)
The parasitic layerThe structural parameters of this antenna which is optimized by GA are as follows:D
=
29.50 mm, L
=
15.02 mm, L
r
=
17.30 mm, W
1
=
3.72 mm, W
2
=
2.78 mm, W
3
=
2.18 mm, L
0
=
1.52 mm, L
1
=
3.40 mm, L
2
=
13.27 mm, and h
z
=
3.48 mm. The simulated reflection coefficient and simulated directivity are given by Figures 5 and 6, respectively.Figure 5
The simulated reflection coefficient of the square antenna array.Figure 6
The simulated directivity as a function of frequency for the square patches antenna array.It is obvious that theS
11
<
-
10 dB impedance bandwidth is about 14.02% (from 5.37 GHz to 6.18 GHz). At its working frequency of 5.8 GHz, the antenna has an input reflection coefficient of −22.65 dB, which estimates that a good impedance match has been achieved.Different2
×
2 array antennas of different fractal proportion (n
=
2, n
=
2.5, n
=
3, n
=
3.5, n
=
4, and n
=
4.5) which are also working at 5.8 GHz are optimized by GA. Figure 7 reveals the simulated reflection coefficient of different fractal proportion antenna arrays and Figure 8 reveals the simulated directivity.Figure 7
The simulated reflection coefficient of the different fractal proportion.Figure 8
The simulated directivity as a function of frequency for the different fractal proportion.From Table2, one can observe that the fractal proportion has a great influence on the antenna performance. As fractal proportion n increases, the aperture area of the proposed antenna must increase for maintaining the same working frequency of 5.8 GHz. When the fractal proportion n
=
3.5, the S
11
<
-
10 dB impendence bandwidth reaches 23.49% versus 14.02% of the square antenna array working at the same frequency, the aperture area of proposed antenna is only 49% of the square patches antenna array’s.Table 2
Details of different antennas.
n
f
L (GHz)
f
H (GHz)
f
M (GHz)
f
%
L
s (cm)
2
5.33
6.23
5.78
15.57%
56.68
2.5
5.29
6.27
5.78
16.98%
59.43
3
5.21
6.37
5.79
20.03%
62.12
3.5
5.07
6.42
5.78
23.49%
62.34
4
5.28
6.30
5.79
17.62%
64.90
4.5
5.33
6.25
5.79
15.89%
65.40
Square
5.37
6.18
5.78
14.02%
89Another interesting observation worthwhile pointing out is the attainable aperture efficiency calculated only by the directivity, shown in Figure9. The vast majority of them are more than 85%. The average aperture efficiency (from 5.4 GHz to 6.1 GHz) is shown in Table 3.Table 3
Fractal proportionn
Average aperture efficiency
2
89.53%
2.5
90.86%
3
90.30%
3.5
91%
4
92.18%
4.5
91.32%
Square
88.48%Figure 9
The simulated aperture efficiency of the different fractal proportion antenna array.Table3 demonstrates that the average aperture efficiency of the Peano fractal antenna array is higher than that of the square antenna in the same working band. The maximum value of average aperture efficiency is obtained when the fractal proportion n
=
4.


## 3.2. Effect of Fractal Iteration

First and second iteration are relatively applied to the edges of the square patch. All the parameters of the second iteration antenna array are set to be the same as the first one. The comparison of the reflection coefficient of these two antennas is drawn in Figure10.Figure 10
Comparison of the simulated reflection coefficient of the 1st iteration and 2nd iteration.One can observe that the impedance bandwidth forS
11
<
-
10 dB is 24.18% (from 4.98 GHz to 6.35 GHz), which is much wider than that of square patches antenna array and slightly larger than that achieved in first iteration of the fractal patches antenna array. As the iteration of fractal geometry increases, its resonance frequency decreases, which may lead to an effective antenna miniaturization. However, for iterations higher than the second iteration, the antenna design becomes quite complicated and its fabrication becomes difficult. The comparison of simulated radiation patterns in the E-plane and H-plane of these two antennas is shown in Figure 11.Figure 11
Comparison of the radiation patterns of the fractal iterations, 1st and 2nd.The comparison indicates that the influence of radiation patterns that comes from the fractal iteration is almost negligible.


## 3.3. Effect of Array Elements Number

In this part, a proposed antenna with4
×
4 Giuseppe Peano fractal radiated elements and working at 5.8 GHz is also optimized by GA.Figure12 compares the simulated reflection coefficient of the 2
×
2 square patch antenna and that of the 4
×
4 Giuseppe Peano fractal antenna. As known to all, when the number of array elements increases, the impedance bandwidth of the antenna array decreases because of the mutual coupling between the array elements [13, 14]. Although the element number of fractal antenna array is four times that in the square antenna, the impedance bandwidth for S
11
<
-
10 dB is 18.43% (from 5.32 GHz to 6.40 GHz), which is much wider than that of square patches antenna array introduced previously.Figure 12
Comparison of the simulated reflection coefficient of the2
×
2 square patch antenna and the 4
×
4 Giuseppe Peano fractal antenna.


## 4. Experimental Results

Two prototype antennas with2
×
2 and 4
×
4 radiations elements, respectively, have been fabricated and measured, which are shown in Figure 13. Some glass sticks with a diameter of 5 mm are used for propping them up.Figure 13
The both layers of the fabricated prototype antennas.Figure14 is the comparison of the measured and reflection coefficient of the prototype antennas, respectively.Figure 14
The measured and simulated reflection coefficients of the prototype antenna.The measured and simulated results are in good agreement. From the measurement, theS
11
<
-
10 dB impedance bandwidth of the antenna is about 23.49% (from 5.07 GHz to 6.42 GHz) for 2
×
2 fractal array antenna and 18.19% (from 5.34 GHz to 6.41 GHz) for 4
×
4 fractal array antenna, respectively. At its working frequency of 5.8 GHz, the antenna has an input reflection coefficient of −16.95 dB and −18.81 dB, respectively, which estimates that a good impedance match has been achieved. Figures 15 and 16 depict the simulated and the measured radiation patterns at different frequencies within the effective frequency band.Figure 15
Measured and simulated radiation patterns on theE-plane and the H-plane at different frequencies of the 2
×
2 fractal antenna array.Figure 16
Measured and simulated radiation patterns on theE-plane and the H-plane at different frequencies of the 4
×
4 fractal antenna array.


## 5. Conclusion

A novel Giuseppe Peano fractal antenna array is presented. Structural parameters of the proposed antenna are optimized by a parallel GA to achieve both high gain and wideband properties over a desirable frequency band with the center of 5.8 GHz. Two prototype antennas were fabricated and measured. The measurement results and the simulation results agree well and show that the optimized antenna array possess some encouraging properties.By comparing the proposed antenna with the square patches one, the important conclusions resulting from this study are as follows.(1)
The Giuseppe Peano fractal configuration provides extremely high flexibility to achieve broadband performance while maintaining higher average aperture efficiency in the operating frequency band. Fractal proportion can be selected according to design requirements; for example, if the impedance bandwidth is a major consideration in design, the fractal proportionn close to 3.5 is comparatively suitable; if the design requires making full use of the high aperture efficiency to maintain the high directivity over the bandwidth, the value n approximating 4 is more reasonable.
(2)
In the case of the same number of array elements and the working frequency, the Giuseppe Peano fractal antenna array can more effectively reduce the required aperture area (reduce 51%) than the traditional square patches antenna array. As the iteration of fractal geometry increases, its resonance frequency decreases; this may lead to an effective miniaturization of antenna. At the same time, the radiation pattern is essentially unchanged.
(3)
Although the element number of fractal antenna array is four times that in square antenna, the impedance bandwidth forS
11
<
-
10 dB is 18.43% (from 5.32 GHz to 6.40 GHz), which is still much wider than that of square array antennas introduced previously (which is about 14.02% from 5.37 GHz to 6.18 GHz). This clearly showed that the introduction of fractal radiation unit can reduce the mutual coupling between the antenna elements.Given the conclusion above, the merits of wideband and high aperture efficiency make the proposed antenna a good candidate for various applications.



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*Source: 542953-2014-02-09.xml*