1
Abstract—The growth of the wireless technology has
exploded in the last 10 years, being one of the most common and used standard without any debate. More and more engineers have concentrated their attention on this technology, trying to develop higher data rates for long distances with minimal costs. Due to the limitation of the free licensed frequency band used by IEEE 802.11 standard, the electromagnetic spectrum has become very crowded so, as a result, a lot of interferences appeared. Taking into account these disadvantages, engineers have focused their attention on the antennas, trying to develop small, efficient and directive products in order to properly work in different environments. In this paper a number of three independent antennas that are radiating under three different angles are analyzed in order to obtain an angle of approximately 60 degrees. The development of the antennas that radiate under different angles (10, 30 and 50 degrees) has been achieved using the substrate integrated waveguide (SIW) technology.
Index Terms—Leaky-wave antenna; Substrate Integrated
Waveguide.
I. INTRODUCTION
Different types of antennas have been developed over the years trying to cover a wide range of purposes and applications. For the indoor wireless systems the favorite antennas mainly focused on were the leaky-wave type due to its narrow bandwidth and simplicity in terms of construction. The leaky-wave antennas, known as travelling-wave antennas, are based on the leakage energy along a transmission line. One main characteristic of this type of antennas is the frequency scanning. The dependence between frequency and directivity will be easily observed in the following sections and also, both of them have a major impact over the radiation angle. This phenomenon of scanning the frequency is called beam squint. The radiation patterns of these antennas depend on frequency and they can be perfectly described by the following equation:
(
k= −β jω)
, (1)which represents also the complex propagation constant.
V. N. Petrescu is with the Military Technical Academy, Communications Department, 39-49 George Coşbuc Street, Sector 5, 050141, Bucharest, Romania (e-mail: [email protected]).
A. Aloman is with the Military Technical Academy, Communications Department, 39-49 George Coşbuc Street, Sector 5, 050141, Bucharest, Romania (e-mail: [email protected]).
I. Nicolaescu is with the Military Technical Academy, Communications Department, 39-49 George Coşbuc Street, Sector 5, 050141, Bucharest, Romania (e-mail: [email protected]).
J. L. Gomez-Tornero is with the Technical University of Cartagena, Information and Communication Department, Cartagena, Spain (e-mail: [email protected]).
II. PROPOSED METHOD
In this paper the theoretical facts involved in substrate integrated waveguide technology combined with the leaky wave principles will be demonstrated.
The basic purpose of this project was to build cheap antennas by using very low price materials, such as FR4, a very lossy material with a low relative permittivity.
An aspect to be spelled out is that the antennas have been tested without the loss index of the material. The proposed structures have been developed similar to the usual microstrip technology by using a half-mode microstrip line drilled with periodic metallic posts. This way the width of the microstrip was reduced by half.
The thickened line on the left side in Figure 1 represents the metallic posts and acts like a perfect electric conductor (PEC) wall. In the same figure the electric field distribution of the half-mode described above is represented with blue lines [1].
Figure 1. Half-mode Microstrip Leaky-Wave Antenna [1]
By using the half-mode, the complicated feeding mechanisms are no longer used, so that antenna excitement will be made easier. To have an overview of the antenna and to easily observe the main geometric components for HMLWA, a longitudinal image is shown in Figure 2.
Figure 2. Longitudinal view of HMLWA [2]
Leaky-Wave Antennas Designs for Wi-Fi Band
in Substrate Integrated Waveguide Technology
Victor N. PETRESCU, Alexandru ALOMAN, Ioan NICOLAESCU, and José L. GOMEZ-TORNERO
With regard to the way that the radiation is produced, in Figure 3 is presented the distribution of the electric field on the x-y plane. It can be seen that the electric field lines are coupled into free space in the upward direction and they form a half-sine field pattern of the TE mode. 10
Figure 3. Electric field at the cross section of the antenna
The technology of the stripline has emerged from lack of bandwidth, complexity and also adaptability of the waveguide. In this manner, the coaxial cable has been transformed from a circular shape to a flat one and further the metallic walls have been removed. The structure is made of two layers of metal surfaces, ground and microstrip lines, and a dielectric material.The main characteristic of this type of lines was the open nature that introduced the concept of surface modes and after that the leakage modes [3].
As it is described in [3] the LWA are based on the propagation of leaky waves that only appear on open transmission lines. In Figure 4 the electric field distribution of the stripline and microstrip line, respectively is illustrated.
a) b)
Figure 4. Electric field distribution for a) Stripline and b) Microstrip line [3] The surface waves are propagation waves that travel through a dielectric or a substrate and do not lose energy by radiation. The name comes from the way that the waves are traveling the dielectric on his full length as shown in Figure 5. Also in this figure it is shown how the field decreases as it moves away from the source.
Figure 5. Surface waves into dielectric [3]
Due to the fact that the propagation direction is oriented toward the y-axis, the propagation constant is consistent with the following expression:
.
y y
k =β (2)
The following equation best describes and characterizes the transmission line. As it can be seen, being a complex
equation, the propagation constant is composed of two important parameters (phase constant and attenuation constant) that can be extracted from theory and simulation environment:
.
y y y
k =β − jα (3)
In Figure 6 an open transmission line is illustrated. Assuming that the radiation on the x-axis has a null value
(
kx =0)
, the propagation constant on the z-axis is described by the equation below:2 2 2 2 2
0 0 .
z y x y z z
k = k −k −k = k −k =β + jα (4)
Figure 6. Leakage wave in dielectric guide [3]
As a conclusion, the radiation properties of leaky-wave antennas are perfectly described by the complex propagation constant of the leaky mode travelling along the antenna. These types of antennas are part of the group of progressive antennas (TWA – Traveling Wave Antennas) [3].
The radiation pattern depends on frequency. Based on the value for the phase constant β the wave can be classified as follows: fast wave
(
β k0<1)
and slow wave(
β k0 >1)
.Expression (3) describes the following phenomenon: the magnetic currents created at the microstrip lateral edge act as a line source in z-plane, determining the directivity in the H-plane, while in the E-plane (x-y plane) a typical fan beam is achieved [1]. Nevertheless, this type of technology that uses microstrip has one major drawback: the leakage rate α and phase constant β cannot be independently controlled [1]. Figure 1 shows that any modification of the width (W) has an effect on the leaky-mode radiated angle θRAD and the
leakage rate. Both parameters mentioned above, phase constant – β and leakage rate – α have an influence on the pointing angle θRAD and the beamwidth ∆θ , best described
by the following two expressions:
0 sin RAD k ≈ β θ , (5) 0 1 cos A RAD L ∆ ≈θ θ λ , (6)
where k0 and λ represent the free-space wave number and 0
the free-space wavelength. As can be seen in (6), the beamwidth and the efficiency of the radiation are related to the total length of the antenna. Thus, the amount of radiated power depends directly on the LWA length LA
0 0 4 2 1 1 . A A L k L RAD e e α π λ α η = − − = − − (7) For the two parameters that describe the radiation, namely α and β , the measurement units nep m/ and rad m / were used. Taking into account the details presented above, this section is orientated to determine the width of the antenna and also the height of the substrate. Thus, two techniques to determine these parameters, namely transverse resonance equation (TRE) and transverse equation network (TRN), were used. Therefore, each antenna has been designed with a series of values noted in Table I.
TABLE I.LWADESIGN PARAMETERS
Angles W (mm) h (mm) 10 RAD= θ 14.735 0.25 30 RAD= θ 14.6 1 50 RAD= θ 14.71 2
These values have been determined by taking into account the analysis described in [2], where it has been concluded that both width and height have an effect on the cut-off frequency. It is desirable to use a thin substrate in order to achieve a low value for the cut-off condition and therefore an initial scanning angle closer to broadside. Also another parameter that has great effect on the cut-off frequency is the relative permittivity, which for the FR4 material is 4.6. Using the commercial software Matlab and the values from the table above, different simulations have been made to calculate the phase constant and the leakage rate and to determine the band of frequencies used by the antennas (2.4–2.5 GHz).
The values of the two parameters are denoted in Table II for three different designs; also in Figure 7 the corresponded graphs are illustrated.
TABLE II.PHASE CONSTANT AND LEAKAGE RATE
Angles α k0 β k0 10 RAD θ = 0.0468 0.1765 30 RAD= θ 0.0517 0.4992 50 RAD= θ 0.037 0.7658 a) b) c)
Figure 7. Phase constant, leakage rate and radiation angle: a) 10º, b) 30º, c) 50º From Figure 7 it can be noticed that the radiation angle
RAD
θ varies with the frequency.
Figure 8. Radiation angle with respect to frequency III. THEORETICAL RESULTS
In this section the results obtained in the previous one were used and processed by using MATLAB in order to obtain the radiation pattern, the beamwidth and the efficiency of the antenna. By using a basic relation between frequency and wavelength, for a central frequency of 2.45 GHz, it has been determined that the wavelength has the value of 122.449 mm: 0 . c f = λ (8)
As is described in [2], using a longer antenna can achieve greater radiation efficiency. For this design a length of 3λ (LA=367.347 mm) was chosen. Another important aspect, that is considered in this section is related to the distance between posts and the diameter of them, namely d and s.
For these parameters to be well obtained, the following condition must be satisfied:
2 .
s≤ d (9)
To meet the above condition, the following values were chosen: d= , 2 s= . 4
Using the values noted in Table II it was possible to obtain the desired parameters, as is shown in Table III.
TABLE III.LWADESIGNS WITH POSTS A
L α/ k0 β k0 ∆θ−3dB θRAD η
3λ 0.0468 0.1765 17.64 10.08 83
3λ 0.0517 0.4992 20.34 29.88 86
3λ 0.037 0.7658 28.26 50.04 76
From Table III it can be observed that the desired angles and beamwidth were obtained. For all of these 3 antennas the efficiency should be above 80%. As it can be observed, the first two antennas (for 10º and 30º) comply with this minimum threshold, unlike the third one (for 50º), which has an efficiency of 75%. Although it does not meet the requirements, this value is an explanatory one due to the fact that the energy has to reach the end of the structure in order to obtain a high scanning angle. Efficiency can only be increased if the length of the antenna changes, but this is not allowed by DIN A3 standard. In Figure 9 the three radiation patterns for the three antennas are illustrated.
Figure 9. Radiation Pattern for 10º, 30º, 50º
The software that was used to determine the radiation patterns for the three designs had the capability to plot the theoretical H-fields that the designs should radiate. It is very important to extract also these plots in order to have a reference of how the antennas should work in the simulation environment. The fields are illustrated in Figure 10.
Figure 10. H-fields generated in MATLAB
IV. ANALYSIS OF SIWLWA
As it was mentioned before, the simulations were carried out in HFSS, a commercial software that is very efficient in simulating tridimensional models. This first section analyzes the results for the reference model. In Table IV, the values for the parameters used in HFSS for the three designs were used.
TABLE IV.DESIGN PARAMETERS FOR HMLWA WITHOUT ADAPTATION
A first analysis was related to the used mode. Thus, for the three designs it was checked if the proper propagation with the half-mode TE10 were well chosen. In Figure 11 are illustrated for the three designs the TE10 mode.
Figure 11. E-field for the three designs: 10º, 30º, and 50º
It can be observed that it was obtained the proper mode; also the fields are traveling a longer distance for thinner substrates but also the number of fields increases with the thickness of the substrate. It is a very important observation because as it could be seen in Figure 9, the antenna designed for 50 degrees is not so directive in H-plane. This happens due to the thicker substrate of the model, so a small amount of energy reaches the end of the antenna.
Another important aspect essential to this first analysis is related to the radiation pattern, which is represented in the following figure (Cartesian coordinates).
Figure 12. Radiation pattern in Cartesian coordinates for 10º, 30º, and 50º From Figure 12 it can be illustrated that the radiation patterns are similar to those obtained in MATLAB, but it can be noticed that the radiation angles are different. For
Design Height Length W0 Wguard Wfree P0 Diam.
10 RAD= θ 0.25 3λ 14.735 1.5 12 4 2 30 RAD = θ 1 3λ 14.6 1.5 6.5 4 2 50 RAD= θ 2 3λ 14.71 1.5 6 4 2
example, for the first design
(
θRAD = 10)
the angle has changed in HFSS to 13 . The difference between theory and simulations can be observed. The radiation patterns are also represented using polar coordinates, illustrated in Figure 13.a) b) c) Figure 13. Radiation pattern in polar coordinates: a) 10º, b) 30º, c) 50º
Having in mind the figures illustrated in the theoretical designs obtained from MATLAB, the next analysis was concerned with the radiation fields. As we observed in Figure 10, the antennas radiate in the H-plane and so in Figure 14 are illustrated the H-planes in polar coordinates for the three designs.
a) b) c) Figure 14. 3D polar coordinates H-plane: a) 10º, b) 30º, c) 50º
Analyzing the two figures, Figure 10 and Figure 14, it can be noticed that the same radiation in the H-plane was obtained also from HFSS simulations.
A very important aspect that is represented in this paper is the capability of scanning the frequency bandwidth as it has been discussed in the previous sections. Having this capability, the three antennas can be used in many applications i.e. Wi-Fi domain, mainly in object tracking. In Figure 15 is illustrated the scanning beamwidth for the three designs.
a) b) c) Figure 15. Scanning beamwidth: a) 10º, b) 30º, c) 50º
In Figure 15 it can be observed that the antennas radiate more directive in H-plane rather than in E-plane. This type of radiation is called “fan beam” and it has an important role in determining the fingerprint for positioning technique.
In this part of the simulations it was also represented the directivity sweep, which means that by increasing the frequency from 2 GHz to 3 GHz it can be seen how the directivity changes, aspect illustrated in Figure 16.
Figure 16. Directivity Sweep for 10º, 30º, and 50º
As it was expected, the antennas are radiating with the highest value in the center of the bandwidth, which is 2.45 GHz. It also can be observed that if three channels are chosen, 2.4 GHz, 2.45 GHz, and 2.5 GHz, representing the edges and the middle for our working band, good values for directivity can be obtained. From Figure 16 it can be noticed that the entire Wi-Fi band is covered.
To better illustrate the theoretical ideas about this type of antenna with respect to radiating angles, Figure 17 was prepared.
Figure 17. E-plane directivity for 10º, 30º, and 50º
These types of antennas offer a radiation of a fan beam shape, very important to applications like radar. This means that they have a greater directivity in the H plane compared to the directivity in the E plane.
Another important aspect that was mentioned in the theoretical section about these designs was concerned with the radiating angle. Considering (5) it can be noticed that the radiating angle is controlled by the phase constant and so in Figure 18 is illustrated this important aspect.
It can be observed that once the frequency has greater values, the radiating angle increases. In this way, the desired radiating angle by controlling the phase constant is obtained.
V. CONCLUSION
This paper had the purpose to design three antennas that are capable to radiate in the Wi-Fi band. Also, the antennas had to comply with the DIN A3 standard, which limited the dimension of them (maximum 297×420 mm) and to be build using FR4 material, known as a very low cost one.
The purpose was to design three independent antennas using the SIW LWA technology, along with the half-mode
10
TE , that can radiate under three different angles, namely 10º, 30º, and 50º providing good coverage of almost 60º.
It was shown that, by using proper simulation environments like Microwave Office and MATLAB, different radiating angles of the antennas were obtained. The
most challenging task was to obtain the same results from both theory and simulation environments.
As a final conclusion, the imposed limitations of size and material of the antennas make these structures unusable in the Wi-Fi band using the technology presented.
REFERENCES
[1] A. J. Martínez Ros, “Analysis and synthesis of leaky-wave devices in
planar technology,” Ph.D. dissertation, UPCT, Cartagena, Spain,
2014.
[2] A. J. Martinez-Ros, J. L. Gómez-Tornero, and G. Goussetisy, “Frequency scanning leaky wave antenna for positioning and
identification of RFID tags,”RFID-Technologies and Applications, IEEE International Conference on RFID-TA, 15-16 Sep. 2011. [3] A. Campillo Soler, “Optimización de antenas leaky-wave en
tecnología de guía integrada en substrato usando simuladores electromagnéticos comerciales,” Dept. Tech. Info. Comm., UPCT,
