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Perforated Reflect-Array Antennas Mojtaba Moeini-Fard and Mohammad Khalaj-Amirhosseini Abstract— A new reflectarray antenna structure is proposed. This structure utilizes a perforated dielectric layer as a reflecting surface with the lattice of different holes. The effective permittivity of the dielectric substrate is altered by drilling holes with different diameter and spacing, which simulate an inhomogeneous dielectric layer. This inhomogeneous dielectric layer can be controlled by these holes to collimate the reflected waves in the special direction. Absence of resonator elements in this structure will reduce the dielectric and conductor losses, which are the main losses in reflectarray antennas at resonance frequency. The reflection properties of the perforated substrate versus their holes diameter and spacing between them are calculated by using the method of Finite Difference Time Domain (FDTD), in which an infinite periodic model was employed to obtain the reflected phase curves. Some proposed antennas are designed at millimeter wave frequency and simulated by fullwave analyzer; CST Microwave Studio software. Index Terms— Perforated Dielectric Substrate, Reflect-Array Antennas

——————————  ——————————

1 INTRODUCTION

A

Reflect-Array Antenna is an array of resonator elements illuminated by a feed antenna placed at a particular point. These type of antennas transform the field radiated by the feed into a phase-coherent beam in a specified direction. The focusing effect can be obtained by slightly modifying the shape or size of resonator elements, so that the phase of the reflection coefficient locally changes. Typically, only one relevant geometrical dimension is modified. Therefore, a basic step in the design of reflectarray antennas is the calculation of the phase diagram, which is the plot of the phase of the reflection coefficient versus the relevant geometrical dimension of the element. Due to the quasi-periodicity of the structure, the phase diagram can be calculated under the hypothesis of an infinite periodic array. For a good design of reflectarray antennas, the phase diagram of the selected element should cover a wide phase range, since the focusing effect could require any phase of the reflection coefficient. Microstrip patch antenna is one of the candidates, which used widely as resonator element in the reflectarray antennas. This element has given several configurations of reflectarray, in which, the required phase diagrams are obtained by varying the shape and size of etched resonant conducting elements [1]–[5]. However, at millimeter waves, the mutual coupling between microstrip elements printed on standard substrates becomes significant; in addition, the conductor and surface wave loss are severe. To overcome these limitations, other candidate, dielectric resonator antennas (DRA) have been introduced due to their low loss, relatively wide bandwidth, high radiation efficiency and low mutual coupling [6]-[8]. However, these antennas have other shortcomings such as compli-

cated mechanical processes to form the desired shape of the DRA or critical bonding processes to locate the DRA element at exact location at millimeter wave. In this paper, we present a new approach to reduce all mentioned short comes. The idea is based to drill a series of very closely holes on substrate to control the reflected phase with the choice of the diameter and spacing of the holes. One of the distinct advantages of perforated reflectarry antenna when compared with other reflectarray antennas is the simplicity in designing and manufacturing of them. The Finite Difference Time Domain (FDTD) method is employed to calculate the phase shift diagrams. At first, the equivalent unit cell of an infinite perforated substrate is modeled and analyzed by FDTD method. The phase response of this unit cell versus the variation of holes diameter and spacing are plotted. Then, by implementing these phase curves the proper holes diameter and spacing of each element are calculated. Finally, the usefulness of the proposed structure and its performance are verified by a comprehensive example and using the CST Microwave Studio TM package, which utilizes the finite integration technique for electromagnetic computation [9].

2 ANALYSIS OF PERFORATED SUBSTRATE

The geometry of a uniform perforated substrate and the corresponding unit cell are shown in Fig. 1. The critical feature of perforated reflectarray implementation is how the individual elements are made to scatter with the desired phases. Perforated substrate with variable holes distribution is used to control the reflection phase. There is two degree of freedom to control the reflection phase of perforated substrate: the holes diameter (d) and spacing ———————————————— Mohammad Khalaj-Amirhosseini is with Iran University of Science and (g) between adjacent holes. It must be noted that, the inTechnology, Tehran, Iran. homogeneity of the reflectarray‖s surface is not accounted Mojtaba Moeini-Fard is with Iran University of Science and Technology, in the analysis of elements. This assumption would not Tehran, Iran. involve a significant error at the final results because of © 2010 JOT http://sites.google.com/site/journaloftelecommunications/

JOURNAL OF TELECOMMUNICATIONS, VOLUME 3, ISSUE 2, JULY 2010 18

the smooth variation of the holes distribution in comparison with wavelength. An infinite periodic model using the Finite Difference Time Domain (FDTD) was employed to analyze the reflection phase characteristics of the perforated substrate, as shown in Fig. 2. In the model used to calculate the reflection phase of incident plane wave, a perfectly matched layer (PML) was positioned at the top of model to simulate the infinite radiation boundary [10]. The total/scattered field plane (TF/SF plane) was set below the PML layer to realize the plane wave source [10]. By using the PEC and PMC walls, the periodic boundary condition is modeled. Then, a TEM plane wave excitation was introduced for this model and the reflected fields phase diagram determined at any point between PML layer and TF/SF plane. The scattered electric fields are calculated in time domain and then transformed to frequency domain by discrete Fourier‖s transform. For confirming computational accuracy of the fine-grid FDTD, the results of the finite integration technique (FIT) under sufficient fine-grid resolution are calculated by using the CST Microwave studio.

g

d/2

d

(d+g )

2(d

+g )s

in ( 60

)

h

Figure 1. Geometry of a uniform perforated substrate and the corresponding unit cell

PML layer

In this paper, the perforated substrates in all cases are formed by holes drilled into the dielectric material Arlon AR1000 with the dielectric constant 10, dissipation factor 0.003 and thickness 3.125 mm at operating frequency 30 GHz. The incident field is a plane wave coming from the normal direction and the linearly polarized along the yaxis. Fig. 3 shows the reflection phase of different unit cells, corresponding to different holes diameter, as a function of the hole‖s spacing. The figures show first, that the FDTD calculation results agree well with the results obtained by CST simulation, which assures the validity of the fine-grid FDTD results. Second, all the phase reflection curves correspond to different holes diameter cover the 360o phase shift. Third, increasing the holes diameter minimizes the slope of the curves, which reduces the sensitivity of reflectarray to fabrication tolerance. Moreover, the slope of the phase curves is a measure of the bandwidth of the reflectarray, as a curve with a smaller slope will lead to less phase error and more bandwidth. In all cells discussed above, the cross polarization levels (TEMy on TEMx mode or TEMx on TEMy mode) are very low (below -40 dB). This factor is important in the case of dual-linear or circular polarization. Finally, it must be noted that, the unit cell with smaller holes diameter (d), which cover 360o phase shifts, is of interest, because of decreasing the size of the reflectarray elements.

3 DESIGN ELEMENT

OF

PEFORATED

REFLECTARRAY

The key technique in the design of a perforated reflectarray is how to select the individual elements so that they scatter the incident wave with proper phase compensation to produce a beam toward a specific direction. Perforated reflectarray is formed by subdividing the perforated substrate into square segments with different holes distribution. Selecting the proper holes diameters and holes spacing at each element will compensate the required reflected phase. The configuration of a perforated reflectarray is shown in Fig. 4. The reradiated field from the perforated surface in desired main-beam pointing direction, uˆ 0 , will be in the form of

TF/SF plane

(1)

PEC (front & back)

PMC (left & right)

where F is the feed pattern function,

is the reflection

coefficient at the mn-th element position. Terms

and

are the position vectors of the mn-th element and the Perforated Substrate Ground plane

Figure 2. An infinite periodic model based on FDTD used to calculate the reflection phase of a normal incident plane wave

feed horn antenna, respectively. Phase is the required phase of the scattered field from the mn-th element. The condition for an array aperture distribution to be cophase in the desired direction, uˆ 0 , is given by (2) Where Rmn is the distance from the feed source to the mn-

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

th array element, i.e., Rmn | rmn

 r f | . According to the

different phase curves shown in Fig. 3, the proper holes diameter and spacing for the mn-th element is determined to produce a phase shift,

, in the scattered field.

Figure 3. Reflection phase of perforated substrate versus hole spacing (g) for different hole diameters (d=0.5, 1, 1.5 and 2 mm)

To design perforated reflectarray element, there is a factor worthy of mention. The element dimensions d x d y : in the above relations the required phase of mn-th element is determined at the center of the element. This causes a significant phase error, which will increase the output side lobe levels. In order to avoid this phase error, the elements size must be reduced. But there is a mechanical restriction by the holes diameter and spacing. Simulation of different element sizes shows that selecting dx dy / 2 is the best choice in constructing perforated reflectarray at operating frequency 30 GHz.

Feed Horn

z

Beam Direction (u0 )

Rmn L rf

dx

rmn

o

Perforated Substrate y

dy

Ground plane x

Figure 4. Total view of the elements arrangement and coordinate system for the perforated reflectarray antenna

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4 EXAMPLES AND RESULTS

tarray with a broadside feed and a broadside main beam. As mentioned before we use the Arlon AR1000 substrate with dielectric constant r 10 , loss tangent of 0.0037 and

150

100

Reflection phase [deg]

In this section, the performance of perforated reflectarray antenna is verified through presenting some examples at frequency 30 GHz. As the total structures of antennas are very large, simulation with FDTD method requires a huge amount of memory (requiring a very fine mesh to model the holes), which make it difficult. As a consequence, the antennas were modeled and simulated only by CST Microwave Studio (MWS). For the first example, we consider a L 10 0 100 mm square perforated reflec-

Fig. 6(a) shows the required phase shift ( ) of each element and the corresponding hole spacing (g [mm]) obtained from the Fig. 3. Also, the perforated substrate is shown in Fig. 6(b); it consists of 5904 holes which are drilled on the substrate. Each hole simply consists of removal of the dielectric material down to the ground. So, the dielectric mass covers only 53% of the perforated substrate, which equals to a solid substrate with the same surface and 1.67 mm thickness. This reduction of dielectric mass causes the lower dielectric loss, which is more significant at millimeter wave frequencies [12]. Simulated structure beside the E-plane pattern of this antenna is shown in Fig. 7. Note that the beam is broadside, and it achieves a maximum directivity of 26.76 dB, while the sidelobes are below 9.89 dB. The H-plane pattern is shown in Fig. 8 with sidelobe levels 11.48 dB. The directivity of the reflectarray is defined as the ratio of the scattered intensity in the main beam direction from the reflectarray to the scattered intensity averaged over all directions. Fig. 9 shows the simulated directivity against frequency. The 1-dB directivity bandwidth of the perforated reflectarray is about 16.7%. To avoid the horn blockage, the reflected beam must be directed out of broadside. So, another example with the 30o off broadside beam direction was designed. This reflectarray consist of a square perforated substrate with dimension L 10 0 100 mm . The substrate is Arlon AR1000 with dielectric constant r 10 , loss tangent of 0.0037 and thickness 3.125 mm. It is subdivided into 400

31 GHz

0

45.3 deg

-50

30 GHz

-100

43.8 deg

-200

-250

0

0.5

1

1.5

2

2.5

g [mm]

Figure 5. Curves of the reflection phases at different frequencies, to evaluate the element bandwidth mn

- g

g

mn

2

289.523

0.3

4

Element in y-direction

of Fig. 3, the holes with diameters d = 1 mm are chosen in this example. It is interesting to know how much the phase diagram changes when varying the frequency. Actually, more frequency bandwidth occurs for reflectarray antenna when the phase curves have small variation toward the central frequency ( 45 ) [11]. Fig. 5 shows the variation of phase curves for different frequencies centered at 30 GHz. Based on this plot, bandwidth of the reflectarray element is estimated to be about 6.6%.

29 GHz

50

-150

thickness 3.125 mm. The substrate is subdivided into 400 elements of equal size of d x d y / 2 5 mm arranged in a lattice of 20 20 elements. A linearly polarized pyramidal horn is used for a feed antenna, with its phase center located at r f L 100 mm . Considering the curves

d=1 mm

200

241.61

6

0.5 0.7

8

193.697 0.9

10

145.784

12 14

97.8709

1.1 1.3

16

49.9579

18 20 5

10

15

20

Element in x-direction (a)

(b) Figure 6. The design processes of broadside perforated reflectarray (a) The required phase shifts of elements and corresponding g values with d=1 mm. (b) The geometry of the designed perforated substrate

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E-plane

mn

30

&g

mn

2

0.3 307.914

4

20

Element in y-direction

Radiation Pattern [dB]

g

358.541

10

0

-10

0.5

6

257.287

8

206.659

10 12

156.032

14

105.405

16

0.9 1.1 1.3

54.7779

18

-20

0.7

20 5

-30 -100

-80

-60

-40

-20

0

20

40

60

80

100

[deg]

10

15

20

Element in x-direction (a)

Figure 7. E-plane radiation pattern of broadside perforated reflectarray

H-plane

Radiation Patterny [dB]

30

20

10

0

-10

-20 -100

-80

-60

-40

-20

0

20

40

60

80

100

[deg] Figure 8. H-plane radiation pattern of broadside perforated reflectarray

(b)

27

Figure 10. The design processes of 30o off broadside perforated reflectarray (a) The required phase shifts of elements and corresponding g values with d=1 mm. (b) The geometry of the designed perforated substrate

26.8

Directivity [dB]

26.6 26.4

elements of equal size of d x

26.2

/2

5mm arranged

in a lattice of 20 20 elements. A linearly polarized pyramidal horn is used for a feed antenna, with its phase center located at r f L 100 mm . The holes diameter is d

26 25.8 25.6 25.4 25.2 25 28

dy

29

30

31

32

33

34

Frequency [GHz] Figure 9. Directivity variation of broadside perforated reflectarray against frequency

= 1 mm. The required phase shift, hole spacing of elements and the corresponding perforated substrate are shown in Fig. 10. It consists of 6400 holes, which shows that only 49.7% of the perforated substrate is covered by dielectric material. This reduction of the volumetric dielectric mass will reduce the total dielectric loses. Fig. 11 shows the patterns on the H- plane. Note that the beam is 30o off broadside, and it achieves a peak gain of 24.2 dB, while the sidelobes are below 11.45 dB.

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H-plane 25

Radiation Pattern [dB]

20 15 10 5 0 -5 -10 -15 -20 -100

-80

-60

-40 -30 -20

0

20

40

60

80

100

[deg] Figure 11. H-plane radiation pattern of 30o off broadside perforated reflectarray

5 CONCLUSION A new reflectarray antenna was presented in this paper. The presented antenna consists of a perforated substrate with lattice of holes and a feed antenna. Perforated substrate with variable distribution of holes was used to control the reflection phase. Four different sets of holes with different spacing and diameter were introduced for perforations, resulting in a required phase shift ranging from 0 to more than 360 degrees. These results obtained from both Finite Difference Time Domain and CST Microwave studio simulations. There is good agreement between FDTD and CST outcomes. Finally, the performance of perforated reflectarray antenna was verified through presenting two examples at 30 GHz frequency.

REFERENCES [1]

[2]

[3]

[4]

[5]

[6]

May 2008. M. G. Keller, J. Shaker and A. Petosa, A. Ittipiboon, M. Cuhaci, Y. M. M. Antar, ”A Ka-band dielectric resonator antenna reflectarray”, European Microwave Conference 2000, Paris, France, pp. 272-275, Oct. 2000. [8] S. H. Zainud-Deen, Abd-Elhady, A. A. Mitkees and A. A. Kishk, ”Design of dielectric resonator reflectarray using fullwave analysis”, NRCS 2009, Egypt. B10. March 2009. [9] CST- Microwave Studio, User‖s Manual, 4, 2002. [10] A. Taflove, Computational Electrodynamics: The Finite Difference Time-Domain, Boston: Artech House, 1995. [11] M. Bozzi, S. Germani and L. Perregrini, ”Performance comparison of different element shapes used in printed reflectarrays”, IEEE Antennas Wireless Propagat. Lett., vol. 2, pp. 219-222, 2003. [12] D. M. Pozar, S. D. Targonski and H. D. Syrigos, ”Design of millimeter wave microstrip reflectarrays”, IEEE Transactions on Antenna and Propagation, vol. 45, No. 2, pp. 287-295, Feb. 1997. [7]

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Mohammad Khalaj Amirhosseini was born in Tehran, Iran in 1969. He received his B.Sc, M.Sc and Ph.D. degrees from Iran University of Science and Technology (IUST) in 1992, 1994 and 1998 respectively, all in Electrical Engineering. He is currently an Associate Professor at College of Electrical Engineering of IUST. His scientific fields of interest are electromagnetic direct and inverse problems including microwaves, antennas and electromagnetic compatibility. Mojtaba Moeini-Fard was born in Tehran, Iran, in 1981. He received the B.Sc. degree from Guilan University in 2004 and his M.Sc. degree from Iran University of Science and Technology (IUST) in 2006, all in Electrical Engineering. He is currently a graduate student working toward the Ph.D. degree in College of Electrical Engineering of IUST. His research interests include of RF/microwave passive structures and antennas and electromagnetic numerical methods.