# A 2.4 GHz Cross Rhombic Antenna for a Cube Satellite Application

Authors: Jorge Sosa-Pedroza; Sergio Peña Ruiz; Fabiola Martínez-Zúñiga
Journal: International Journal of Antennas and Propagation
 (2014)

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## Abstract

We present design and construction results of a 2.4 Ghz cross rhombic antenna to be used in a cubesat. Computational design agrees with experimental results after its construction. cross rhombic antenna is a novel planar structure of our own design, presenting circular polarization and medium gain; it is built over a RF60A substrate withεr=6.15, decreasing its size to fit the required dimensions of satellite. A special characteristic of this design is the enhancing of operational bandwidth using a technique we have been studying, related to softening the structures with sharp edges. Results show applicability and success of our technique.


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## Body

## 1. Introduction

A cube satellite is a very small spacecraft, usually having an area as much as 10 cm2 and no much longer than 30 cm; its weight should be less than 1 Kg. Most of these small satellites use commercial electronic components. California Polytechnic State University and Stanford University issued the CubeSat specifications in 1999, helping universities to develop the science and space exploration; these specifications are followed by amateur radio satellite builders. It is easy to imagine that the 10 cm2 satellite area requires an antenna to fit those dimensions. We have been working with planar antennas for long time, developing, designing and constructing our own structures [1]. Some of them have been proposed to be used in different applications. We present in this paper a study of one of those structures: the Cross Rhombic Antenna (CRA). Actually, there are many kinds of planar antennas having different forms. Planar antennas are very popular considering their small dimensions and low cost making them ideal for many applications where small dimensions are needed, as in airplanes, spacecraft, and fixed terrestrial communications taking a great importance in last generation of these systems. Some characteristics to be considered for the antenna design are the following:(i)
high reliability;(ii)
small size;(iii)
low weight;(iv)
high efficiency;(v)
low cost.The cubesat dimensions impose as well antenna dimensions, keeping the best behavior. As we show in Section3, analysis was done in order to get the best behavior for a 10 cm2 of satellite face. CRA is proposed to be used in Sensat, a cube satellite, working at 2.4 GHz. Sensat is a small educational satellite projected with optical and microwave payloads, developed by several Mexican universities.


## 2. The Cross Rhombic Antenna

CRA belongs to the family of traveling wave antennas, with circular polarization, medium gain, and a directional field pattern. Antenna is fed in one end and loaded in the other one, to meet expected behavior. The parametric analysis we present takes in account different characteristics of the antenna such as: microstrip width, load impedance, type of substrate and substrate thickness as well as softening of sharp corners. Antenna behavior is related to its gain, field pattern, axial ratio, and50Ω input coupling; frequency design was 2.4 GHz and we use antenna, Computer Simulation Technology (CST) simulator. Modifying structure characteristics using a RF60A substrate with εr=6.15, we select the best one to construct an antenna prototype to compare it with simulation results. CRA is an evolution of the antenna proposed by Roederer in 1990 [2]. Antenna is a rhomb shape microstrip over a ground plane as shown in Figure 1. Circular right or left polarization depends on feed and load position. Load impedance could be any value but we have noticed that the best results are obtained using short circuit, open circuit or 50 Ω.Figure 1
Cross rhombic antenna.


## 3. Parametric Analysis Using RF60A Substrate

In this section, simulation results are presented, modifying physical characteristics of the RF60A substrate structure havingεr=6.15 and λ=0.0504m at 2.4 GHz. At this frequency, substrate width is h=λ/11. Original design considers the maximum dimension (Figure 1) as 1.67λ or 8.4 cm, matching the 10 cm2 area of cube satellite. Physical parameters considered were as follows: microstrip width, load impedance, substrate thickness, and softening of sharp corners.


### 3.1. Microstrip Line Width

First case of analysis was the microstrip line widths. Table1 shows the relationship between gain and line width, for the three selected load impedances, while Figures 2, 3, and 4 show the related microstrip line width to return loss parameter for each load.Table 1
Line width analysis (RF60A).
Width
Width
Gain open
Gain 50Ω
Gain short
(mm)
(λ)
(dBi)
(dBi)
(dBi)
a
1
=
1.3
0.025λ
8.8
5.8
8.8
a
2
=
1.5
0.029λ
8.8
5.8
8.7
a
3
=
1.7
0.033λ
8.9
5.7
8.7
a
4
=
1.9
0.037λ
8.8
6.5
8.6
a
5
=
2.1
0.041λ
8.8
6.1
8.5
a
6
=
2.3
0.045λ
8.6
6.0
8.4
a
7
=
2.5
0.049λ
8.3
5.6
8.0Figure 2
Return losses (open load line analysis).Figure 3
Return losses (50Ω load line analysis).Figure 4
Return losses (short load line analysis).As seen in Table1, the best gain results are obtained for a3=0.033λ=1.7 mm with open circuit load, but we choose a5=0.041λ=2.1 mm, considering the better coupling results of Figure 7; however, as seen in Figure 17, there is a better coupling for a6 and a7 but at higher frequencies. Figure 3 shows a better coupling with thicker lines for the 50Ω load, but the gain is lower, as seen in Table 1. For short circuit load, gain is similar to that of open circuit load and better coupling but at higher frequency; to reduce coupling frequency is necessary to increase antenna dimensions which is not desirable. Considering these results, we choose 2.1 mm for microstrip line width and open circuit load. Figure 5 shows field patterns (ϕ=90° and ϕ=180°) and we can see similarity between all of them, and then they are not a parameter to be used for comparison.Field patterns. (a) Open, (b) 50Ω, and (c) short.
(a)
(b)
(c)


## 3.1. Microstrip Line Width

First case of analysis was the microstrip line widths. Table1 shows the relationship between gain and line width, for the three selected load impedances, while Figures 2, 3, and 4 show the related microstrip line width to return loss parameter for each load.Table 1
Line width analysis (RF60A).
Width
Width
Gain open
Gain 50Ω
Gain short
(mm)
(λ)
(dBi)
(dBi)
(dBi)
a
1
=
1.3
0.025λ
8.8
5.8
8.8
a
2
=
1.5
0.029λ
8.8
5.8
8.7
a
3
=
1.7
0.033λ
8.9
5.7
8.7
a
4
=
1.9
0.037λ
8.8
6.5
8.6
a
5
=
2.1
0.041λ
8.8
6.1
8.5
a
6
=
2.3
0.045λ
8.6
6.0
8.4
a
7
=
2.5
0.049λ
8.3
5.6
8.0Figure 2
Return losses (open load line analysis).Figure 3
Return losses (50Ω load line analysis).Figure 4
Return losses (short load line analysis).As seen in Table1, the best gain results are obtained for a3=0.033λ=1.7 mm with open circuit load, but we choose a5=0.041λ=2.1 mm, considering the better coupling results of Figure 7; however, as seen in Figure 17, there is a better coupling for a6 and a7 but at higher frequencies. Figure 3 shows a better coupling with thicker lines for the 50Ω load, but the gain is lower, as seen in Table 1. For short circuit load, gain is similar to that of open circuit load and better coupling but at higher frequency; to reduce coupling frequency is necessary to increase antenna dimensions which is not desirable. Considering these results, we choose 2.1 mm for microstrip line width and open circuit load. Figure 5 shows field patterns (ϕ=90° and ϕ=180°) and we can see similarity between all of them, and then they are not a parameter to be used for comparison.Field patterns. (a) Open, (b) 50Ω, and (c) short.
(a)
(b)
(c)


## 4. Further Size Reduction

We tried a further size reduction of RCA, moving corners to the antenna center, but with little changes in microstrip lines width, as shown in Figure6. Table 2 shows the final dimensions. To define the new microstrip width, we analyze the effects on gain and coupling; results are shown in Table 3 and Figure 7. Figure 8 depicts the different field patterns for each microstrip width.Table 2
Antenna dimensions (RF60A).
Original
Modified
Maximum length
1.67λ
1.62λ
Interior arm
0.32λ
0.31λ
Exterior arm
0.51λ
0.49λ
Truncated arm
0.46λ
0.45λ
Angle between interior arms (α)
31.42°
31.42°
Angle between exterior arms (β)
69.99°
69.99°
Angle interior-exterior arms (γ)
115.71°
115.71°Table 3
Antenna gain line analysis.
Width (mm)
Gain (dBi)
a
1
=
1.5
8.3
a
2
=
1.6
8.3
a
3
=
1.7
8.3
a
4
=
1.8
8.3
a
5
=
1.9
8.2
a
6
=
2.0
8.2
a
7
=
2.1
8.1Figure 6
CRA modification.Figure 7
Return losses for different line widths.Field patterns versus microstrip line widthsϕ=90°.
(a)
(b)
(c)
(d)
(e)
(f)
(g)


## 5. Substrate Thickness

Although we can make any change in dimensional antenna characteristics in simulation process, a limitation arises if we want to construct it, because commercial substrates have defined thickness dimensions; then we change that dimension in order to know its effects on radiation parameters, taking special attention in results with the materials on hand. Using the best former results, simulation was made for different substrate thicknesses, as Table4, shows with gain results for each one. Figure 9 depicts the coupling results. Figure 9 depicts the coupling results, as seen h=λ/11 has again the best coupling results, but the commercial thickness of substrate we have is h=λ/9=5.6 mm. We keep the analysis of both the thickness substrates, in the following paragraphs, as a way of comparison.Table 4
Antenna gain substrate thickness analysis.
Thickness (mm)
Gain open (dBi)
h
1
(
λ
/
5
)
=
10
5.4
h
2
(
λ
/
6
)
=
8.4
5.7
h
3
(
λ
/
7
)
=
7.2
6.8
h
4
(
λ
/
8
)
=
6.3
7.7
h
5
(
λ
/
9
)
=
5.6
8.1
h
6
(
λ
/
10
)
=
5.04
8.1
h
7
(
λ
/
11
)
=
4.58
8.2
h
8
(
λ
/
12
)
=
4.2
8.3
h
9
(
λ
/
13
)
=
3.8
8.3
h
10
(
λ
/
14
)
=
3.6
8.3Figure 9
Return losses for different substrate thicknesses.


## 6. Softening Sharp Edges to Enhance Bandwidth

It can be noticed inS11 parameters of former figures that curves are very sharp with small bandwidth, making antenna design and construction with a high dependence on frequency; repeatability could be a problem considering high dependency of antenna parameters of structure dimensions. To avoid this problem, we propose to increase bandwidth softening antenna corners, making it less dependent on frequency [3, 4]; to set those changes we selected the best parameters of the analysis, that is, strip line width a=2.0 mm, substrate thickness h=λ/11, and open circuit load; antenna modification is shown in Figure 10.Figure 10
Cross rhombic antenna with softened edges.We noticed a small change in frequency coupling after softening edges; to solve this problem, all dimensions were modified and a new substrate thickness analysis was done in order to get a new optimum value forh at the 2.4 GHz resonant frequency; simulation results are presented in Table 5 and Figure 11. Good coupling for h4=λ/8 and h5=λ/9 is noticed, and the last one is precisely the thickness we have to construct; Figures 12 and 13 show field patterns for those thicknesses.Table 5
Antenna gain substrate thickness analysis.
h
Gain (dBi)
a
=
λ
/
6
6.1
b
=
λ
/
7
7.4
c
=
λ
/
8
7.8
d
=
λ
/
9
8.1
e
=
λ
/
10
8.2
f
=
λ
/
11
8.1
g
=
λ
/
12
8.2Figure 11
Return losses for different substrate thicknesses.Figure 12
Field pattern forh=λ/8.Figure 13
Field pattern forh=λ/9.Final optimized dimensions are presented in Table6. An antenna gain of 8.1 dBi is noticed. Figure 14 depicts the S11 parameter response comparison, with and without softening, for h=λ/9; as it is seen, there are a higher bandwidth and a better response for the optimized antenna. As a way of comparison with other kind of antennas, the rectangular microstrip slot patch presented in [5] has narrower bandwidth and less gain.Table 6
Optimized antenna dimensions.
Optimized
Original
Total diameter
1.66λ
1.62λ
Interior arm
0.32λ
0.31λ
Exterior arm
0.50λ
0.49λ
Truncated arm
0.46λ
0.45λ
Line width (a)
0.042λ
0.039λ
Angle between interior arms (α)
27.19°
31.42°
Angle between exterior arms (β)
69.99°
69.99°
Angle interior-exterior arms (γ)
115.71°
115.71°Figure 14
Comparison between sharp and softened ends antennas.


## 7. Construction and Comparison

Two different antennas were constructed, one of them with sharp edges and the other with softened edges. Both antennas are shown in Figure15, using RF60A substrate with εr=6.15 (λ=5 cm at 2.4 GHz) and thicknesses of h5=λ/9.Constructed antennas (a) sharp edges and (b) soft edges.
(a)
(b)Measurements were done with an Anritsu MS4624B Vector Network Measurement System. Figure16 shows S11 comparison between simulation and construction at h5=λ/9 (real) and h7=λ/11 (optimal); as seen, there is very good similarity between them but with a deviation of about 100 MHz over design frequency.Figure 16
Return losses (antenna with sharp edges).Figure 17
Return losses (antenna with softened edges).On the other hand, Figure17 shows comparison of S11 parameters for same antennas but with softened edges; as it is seen, there is a good similitude between all of them. Finally, Figure 18 depicts coupling comparison between simulation and constructed softened edges antennas. We see again a deviation of about 70 MHz between both antennas due to construction problems. Field patterns for constructed and simulation antennas are shown in Figure 19, also with some differences.Figure 18
Measured return losses (CRA with softened edges).Figure 19
Simulation and measured field pattern comparison.Figure20 shows gain comparison of both antennas, and as seen, there are some differences, with a better response for the simulated one. It is clear that we have to improve our construction methods.Figure 20
Gain comparison.To characterize circular polarization, we obtained axial ratio, measuring horizontal and vertical field patterns. Both patterns have almost the same magnitude, except in 30° and 285°, probing circular polarization. Figure21 presents circular polarization measurements; (a) shows measured field patterns and (b) shows axial ratio obtained from subtraction magnitude of both field patterns.Circular polarization (a) field pattern comparison. (b) Axial ratio.
(a)
(b)


## 8. Conclusion

We have presented parametric analysis of CRA with results of gain, field pattern, and return losses. Results shown of comparing simulation and constructed structures using RF60A withεr=6.15 agree with most of measured parameters although with a displacement of about 100 MHz, meaning that error in the design frequency is due to manufacturing inaccuracy.As it is seen from simulation, best configuration is that using open load, getting the best coupling and gain (8.1 dBi in the simulation and 7.9 dBi in measurement). We also analyze the substrate thickness effects on resonant frequency.A better similarity is obtained for the antenna with softening sharp edges considering its less dependence of frequency. We concluded that the best geometry for CRA is the one with soft edges with better performance and higher bandwidth.We have proposed CRA for other applications, as those presented in [6, 7], where we designed and constructed air dielectric antennas for GNSS at 1.5 GHz and also an air dielectric antenna for 2.4 GHz with 14.0 dBi gain and bandwidth around 60 MHz, for both of them, are greater than those of rectangular or circular patches presented in [8, 9].The final dimensions of antenna are10×10×0.56 cm with weight of 157 g, and an excess of 1.6 cm over the 8.4 cm of maximum antenna dimension for the ground plane. Those 10 cm per side perfectly fit in the area of Sensat cube satellite.



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*Source: 268151-2014-02-19.xml*