Half truncated icosahedral passive electromagnetic deflector
for the 60 GHz band
Citation for published version (APA):
Kazim, M. I., Herben, M. H. A. J., & Huang, M. D. (2010). Half truncated icosahedral passive electromagnetic deflector for the 60 GHz band. In Proceedings of the 4th European Conference on Antennas and Propagation (EuCAP 2010), 12-16 April 2010, Barcelona, Spain (pp. 1-5). Institution of Engineering and Technology (IET).
Document status and date: Published: 01/01/2010
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Half Truncated Icosahedral Passive Electromagnetic
Deflector for the 60 GHz Band
M. I. Kazim
#1, M. H. A. J. Herben
#2, M. D. Huang
#3#Electromagnetics and Wireless (EMW), Department of Electrical Engineering
Technische Universiteit Eindhoven (TU/e), P.O. Box 513, 5600 MB Eindhoven, The Netherlands
1m.i.kazim@tue.nl 2m.h.a.j.herben@tue.nl 3m.huang@tue.nl
Abstract—A possible low-cost alternative to a multifaceted
active antenna array configuration for wide angular coverage is proposed. It consists of a single planar antenna array and a passive electromagnetic half truncated icosahedral deflector, comprising multiple facets with different deflecting behavior. A generalized formulation for the simple set-up of the proposed configuration is simulated in MATLAB and a comparison is made with CST MWS simulation. An important aspect of this configuration is the determination of the deflector’s transmission coefficient; the measurement shows an acceptable performance with a transmission loss of (0.63-1.5 dB) and (2.72-3.12 dB) for the 0◦and 34◦ deflectors, respectively, in the 57-63 GHz frequency band.
I. INTRODUCTION
The 60 GHz frequency band has the potential to realize next-generation wireless broadband communication systems. The unlicensed bandwidth of around 7 GHz supports data rates of multiple gigabits-per-second needed for the transport of multiple media streams with sufficient quality-of-service. The 60 GHz band has inspired a multitude of suggested application areas, including wireless gigabit ethernet, wireless HDTV, telecom backhaul, etc. However, to utilize the potential of this frequency band, low-cost antenna solutions with wide angular coverage are desired for the above-mentioned applications. Planar antenna arrays for the 60 GHz frequency band are found in literature. The beam of these antenna arrays, however, cannot usually be steered more than±30◦; the limitation is due to increase in SLL (SLL> -10 dB) [1]. The angular coverage
of substrate lens antennas for millimeter-wave applications is restricted to ±20◦ [2], [3].
The wide angular coverage is made possible by the use of 3D-multifaceted antenna arrays [4], [5]. In multifaceted antenna arrays, an increase in angular coverage is achieved by different spatial orientations of the planar facets, each comprising an active planar antenna array.
A possible low-cost alternative to the multifaceted active an-tenna array configuration is presented in this paper. It consists of a single planar antenna array and a passive electromagnetic deflector (Fig. 1) [6].
Section II presents the proposed half truncated icosahedral passive deflector for the 60 GHz band. MATLAB simulations, based on a generalized formulation, and CST MWS simulation of the basic configuration are also described in this section. Section III highlights the measurement set-up and results for
deflector element
patch/reflector layer 2 patch/reflector layer 1 aperture layer
transm. line layer
-120◦ 0◦ 120◦
Fig. 1: Passive electromagnetic deflector for the 60 GHz band
the deflector’s transmission coefficient. Finally, the conclu-sions are drawn in Section IV.
II. HALFTRUNCATEDICOSAHEDRALDEFLECTOR
The proposed half truncated icosahedral passive electromag-netic deflector for the 60 GHz band is shown in Fig. 2. Mul-tiple deflectors are used to form a half truncated icosahedron configuration. The design details of a planar source antenna array (57.5-65.0 GHz) and a passive deflector (57-63 GHz) are reported in [1] and [6], respectively. The source antenna array focuses power on each face of a multifaceted passive deflector which bends this electromagnetic wave towards directions that are out of reach of the source itself. Each deflector face consists of a group of elements with a phase-shift among them. Fig. 1 shows a passive deflector constructed by placing multiple deflector elements in a regular pattern. The design of three different elements, which realize a phase shift of -120◦, 0◦, and +120◦for the 57-63 GHz frequency band, is described in [6]. The three elements are placed in an alternating order along one direction with identical elements along the other direction, thereby deflecting an incident wave by 34◦. The
Fig. 2: Half truncated icosahedral deflector
0◦ deflector comprises 0◦ phase shifting elements along both directions. The above-mentioned deflectors are designed so that the polarization of the emitted wave is orthogonal to the polarization of the incident wave.
A truncated icosahedron is a perfect geometrical shape created by truncating the tips of the icosahedron one third of the way into each edge. It comprises 32 facets in total with 12 regular pentagons and 20 regular hexagons. The dihedral angles are 138◦11’ and 142◦37’ for the hex-hex angle and the hex-pent angle, respectively. A half truncated icosahedral deflector geometry offers a possible advantage over the pyramidal deflector [6], in terms of utilization of more deflecting facets.
A. Generalized MATLAB Formulation
A generalized MATLAB formulation for the simple para-metric geometry of the proposed configuration, delineated in Fig. 3, is presented in this section. The MALTAB code, however, can be extended for the half truncated icosahedral deflector. The two facets of the half truncated icosahedral deflector (broadside and skewed), having a dihedral angle of (180◦ - α = 142◦37’), are excited by the steerable source antenna array. The basic design principle requires that the phase shifts for the deflector elements take into consideration the required deflecting angle (in theφ = 90◦plane) and also the phase delay introduced due to path length difference from the source antenna array located at the originO to each deflector
elementkrxyz. The simulations provide a basic understanding
for icosahedral deflector design, in terms of deflecting be-haviour and angular coverage. It does not include formulation of aspects, such as the associated mutual coupling, deflector’s transmission loss, polarization mismatch and diffraction from
the facet discontinuities.
The directivity of each antenna element i of the source
antenna array Di(θ, φ) is defined as
Di(θ, φ) = 2(m + 1) cosmθ (1)
where m ≥ 0, 0◦ ≤ θ ≤ 90◦ and 0◦ ≤ φ ≤ 360◦. The antenna element of the source antenna array presented in [1] has Di(θ, φ) = 6 cos2θ, for the case of m = 2. The power
pattern or the radiation intensity of the antenna element can be calculated by
Pi(θ, φ) = Prad,i4π Di(θ, φ) (2)
where Prad,i is the radiated power of an antenna elementi of
the source antenna array and is taken to be4π. The amplitude of the electric field intensity of each antenna element at the far-field distance r is given by
|Ei(r, θ, φ)| = 2η0Prad,iDi(θ, φ) 4πr2 = √ 12η0 r cos θ (3)
The far-field electric field of the source antenna array is expressed as Esource(r, θ, φ) = |Ei(r, θ, φ)| N i=1 e(j[βsource+kˆr·ri]) (4) where k = 2πλ0 is the free-space phase constant, ˆr = sin θ cos φˆx + sin θ sin φˆy + cos θˆz is a unit vector in the direction of the rays, ri is a position vector from the origin
O to the ith element of N -element source antenna array and
βsource is the phase shift applied by each element to steer
the beam. The directivity of the source antenna array can be calculated as Dsource(θ, φ) = r2 |Esource(r,θ,φ)|2 2η0 Psource 4π (5) wherePsourceis the total radiated power of the source antenna
array and is equal to 4πN.
The available power Prxyz of each deflector element in
xyz-space can be written in terms of the power flow density S(rxyz, θxyz, φxyz) of the incident plane wave towards the
di-rection of the deflecting element and the area of the deflecting element A. Hence,
Prxyz = S(rxyz, θxyz, φxyz)A cos θsa (6)
S(rxyz, θxyz, φxyz) =
|Esource(rxyz, θxyz, φxyz)|2
2η0 (7)
where θsa is the angle between the ˆr-component of the
incident power flow density and ˆn normal component of the deflecting element. Since the spacing between the deflector elements d is 0.5λ0, the area of each deflector element A is taken to be (0.5λ0)2.
The deflector elements are considered to be isotropic sources with no transmission losses. Since the deflector ele-ments are radiating in the upper half-space only, the directivity
of each deflector element Dd(xyz)(θ, φ) is equal to 2 (from
eq. (1) with m = 0). The amplitude of the electric-field
intensity of the deflector elements|Ed(xyz)(r, θ, φ)| at the far-field distancer is expressed as
|Ed(xyz)(r, θ, φ)| =
2η0PrxyzDd(xyz)(θ, φ)
4πr2 (8)
The far-field electric field of the whole deflector
Edef(r, θ, φ) containing T deflecting elements is given by
Edef(r, θ, φ) = T
xyz=1
|Ed(xyz)(r, θ, φ)|e(j[βxyz+krxyz+kˆr·rxyz])
(9) The phase shift βxyz is adjusted to provide the desired
deflecting angle in theφ = 90◦plane and to compensatekrxyz.
The directivity of the whole deflector can be calculated as
Ddef(θ, φ) = r2 |Edef(r,θ,φ)|2 2η0 Pdef 4π (10) wherePdef is the total power radiated by the whole deflector
and is determined from individual power contribution of each deflector element.
A scenario is simulated in MATLAB, in which the fixed phase shifts of each deflector element alter the phase front of the incident field by imparting a phase gradient, thereby causing a change in the direction of propagation. Thus, a source antenna array scanned to an angle θsource will have
its scan angle changed by Kdθsource. In order to satisfy this
criteria, the two consecutive deflecting elements (starting from the center element of the broadside facet to the last deflector element on the right skewed facet) are introducing a certain incremental deflecting angleθdn= nK3dθsource
2Trow−1 (in theφ = 90
◦
plane) over the whole deflector, as shown in Fig. 3;Trow and
Tcol represent the number of deflecting elements along the
rows and the columns of each deflecting facet. An example of the scenario has been simulated using the above approach for the case of two deflector facets (broadside and skewed), with each facet havingTrow = Tcol = 10 and d = 0.5λ0. The height h between the center of the broadside facet and the
source antenna array center (at the origin O) is taken to be
8λ0. The phase shifts of the deflecting elements are set to meet the criteria of Kd = 2.67, when the source antenna array is
steered toθsource = 30◦. Fig. 4 shows the simulation results
of the scenario example. The maximum values of directivity for the source and deflector are found to be 16.94 dB (θ
= 30◦) and 17.88 dB (ripple at θ = 57◦), respectively. The deflected beam provides an extended angular coverage at the cost of beam broadening as compared to the source beam. The ripples in the deflected beam are possibly linked to the melting of the side lobes in the main beam, which can be explained as an introduction of both integer and fractional multiples of phase delays among the deflector elements for each deflecting angle, thereby providing the beam maximum at the point where similar phase delays are superimposing. The ripples become smoother when a large number of deflecting
θ O O X φ h d ˆn ˆr deflector Z Z I II III α α θdef θsource θdef = Kdθsource
source antenna array
Y Y θd1θd2θd3
Fig. 3: MATLAB scenario
elements are used but this results in an increase of the size of the deflector. Moreover, the design of a wide range of phase shifters is required for this scenario, which should provide the required incremental deflecting angle among consecutive deflector elements and compensate both krxyz and phase due
to geometrical orientation of the skewed facet.
−50 0 50 −50 −40 −30 −20 −10 0 10 20 −50 0 50 −50 −40 −30 −20 −10 0 10 20 θ (degrees) θ (degrees) I II III
Fig. 4: Scenario example: Comparison of directivity (dB) of source (left) and deflector (right) simulated in MATLAB for the φ = 90◦ plane
B. MATLAB and CST MWS Simulations - A Comparison
CST MWS simulations have been carried out for the 60 GHz source antenna array and different spatial orientations of the passive deflector facets. Although the simulation takes into account most of the electromagnetic effects, however, it is computationally very intensive and requires more than 13 million mesh cells, for the simple set-up of a broadside deflector facet and a single source antenna array. The CST simulated designs of the 34◦ deflector (shown in Fig. 1) and source antenna array, presented in [6] and [1], respectively, have been used to set-up the simulation, which can deflect the incident beam to 34◦, when excited from the broadside direction. Fig. 5 shows CST MWS and MATLAB simulated
results for the case when a 34◦ deflector plate (Tcol = 5,
Trow = 9, d = 0.6λ0, h = 4.5λ0) is excited by the
6-element hexagonal source antenna array from the broadside direction. The maximum values of directivity for the source and the deflected beam are found to be 14.88 dB (θ = 0◦) and 13.36-13.45 dB (θ = 24◦-45◦), respectively, for MAT-LAB simulations. CST MWS gives the maximum values of directivity for the source and the deflector as 13.56 dB (θ =
0◦) and 14.06 dB (θ = 33◦), respectively. The results between MATLAB and CST MWS agree in terms of the deflecting behaviour of the beam. The isotropic source assumption of deflector elements in MATLAB explains almost the constant broadening of the deflected beam. Moreover, the deflected beam pattern is sensitive to parameter h, as observed from
MATLAB siumlations. The MATLAB approach provides a useful and efficient tool to set-up different deflector scenarios. The parametric model can be easily extended to investigate the trade-off among directivity, angular coverage and geometrical dimensions of the icosahedral deflector.
−50 0 50 −25 −20 −15 −10 −5 0 5 10 15 −20 0 20 40 60 80 −25 −20 −15 −10 −5 0 5 10 15 θ (degrees) θ (degrees)
Fig. 5: Comparison of directivity (dB) of source (left) and deflector (right) simulated in MATLAB (solid) and CST MWS (dash) for the φ = 90◦ plane
III. MEASUREMENT OFDEFLECTOR’STRANSMISSION
COEFFICIENT
An important aspect of the proposed 60 GHz antenna con-figuration is the determination of its transmission properties for the entire band of operation (57-63 GHz). The measurement set-up is shown in Fig. 6. The two standard gain horn (SGH) antennas with an aperture of 13 mm (La)× 19 mm (Lb) have
been used. The 3 dB half power beam-width (HPBW) in
E-plane andH-plane, calculated using the empirical expressions ψE = 50.6 ◦λ La and ψH = 68.8◦λ Lb , is ψE = 19.46 ◦ and
ψH = 18.10◦, respectively [7]. The two standard gain horn
(SGH) antennas, are located in each other’s far-field rf f, at
a distance of 2d1 (d1 = d2 = 277 mm; rf f = 144.4 mm);
the deflector plate (95 mm × 95 mm), is then positioned at half of the distance between the transmitting (Tx) and the receiving (Rx) horns. The polarization of the emitted wave by the deflector plate is orthogonal to the polarization of the incident wave [6]. The illuminated surfaceI on the deflector
plate can be estimated on the basis of the HPBW of the horn antenna as equal to2d1tanψE/H2 in both theE-plane and the H-plane. The effective illuminated area of the deflector, after
taking into consideration the polarization change, is calculated to be 88 mm × 88 mm. The measurement set-up meets the 3rd Fresnel zone radius3λd1d2
d1+d2, which is equal to 45.5 mm
from the center of the deflector plate. Therefore, most of the power of the Tx is confined within the boundaries of the deflector plate, ensuring the edge diffraction effects on the measurements less critical.
The extruded polystyrene blue foam material has been used for the measurement set-up, as shown in Fig. 7. It has been observed that the foam material does not introduce any sig-nificant variations in the amplitude (< 0.10 dB) and phase (< ±1◦) values of the deflector’s transmission coefficient |S
21|. The set-up has been tailored to determine the transmission properties of both the 0◦ and 34◦ deflectors, as depicted in Fig. 6. The |S21| has been measured for three PCB samples of each of the deflectors. The effect of angle of incidence on the 0◦ deflector has also been measured. The measured
|S21| for the 0◦ and 34◦ deflectors at 0◦ angle of incidence is plotted in Fig. 8. The transmission loss for the 0◦ and 34◦ deflectors is found to be (0.63-1.5 dB; repeatability error: + 0.1-1 dB) and (2.72-3.12 dB; repeatability error: ± 0.45 dB), respectively, in the 57-63 GHz frequency band. The effect of angle of incidence (0◦ to 20◦) on transmission loss of the 0◦ deflector is observed to be ± 0.13-0.5 dB, in the whole band of operation. The repeatability error and angle of incidence dependency is attributed to misalignment between the horn antennas and manual adjustment of the deflector plate. Moreover, a degradation of |S21| has been observed among different PCB samples, which is possibly linked to the fabrication tolerances and misalignment among different layers of the deflector. The X-ray photographs of the 0◦ and 34◦ deflectors shown in Fig. 9, highlight the misalignment of the different PCB samples.
IV. CONCLUSIONS
A half truncated icosahedral passive electromagnetic de-flector for the 60 GHz frequency band is presented in this paper. A generalized MATLAB formulation for the simple parametric geometry of the proposed configuration is de-scribed. The results from MATLAB formulation and CST MWS simulations agree in terms of deflecting behaviour, however, the latter takes into account more electromagnetic effects. The measurement shows an acceptable performance of the deflector’s transmission coefficient in the 57-63 GHz frequency band. As a future work, it is planned to extend the the MATLAB code for the different scenarios to investigate the trade-off among directivity, angular coverage and geometrical dimensions of the icosahedral deflector.
ACKNOWLEDGMENT
The authors would like to thank A.R. van Dommele and A.C.F. Reniers, EMW Group, TU/e for providing assistance
deflector plate
turn table standard gain horn (SGH) antennas
rf absorbers 17◦ 17◦ 17◦ 0◦ deflector 34◦ deflector d1 d2 I 2 ψ/2
Fig. 6: Measurement set-up for deflector’s transmission coef-ficient determination
deflector
blue foam material
standard gain horn (SGH) antennas
rf absorbers
Fig. 7: Anechoic chamber measurement set-up
in measurements as well as NXP Semiconductors, Nijmegen for X-ray photographs of the deflectors.
REFERENCES
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flat-top radiation patterns: benchmark of beam shaping techniques at the feed array level and lens shape level,” in European Conf. Antennas and Propagat. (EuCAP09), Berlin, Germany, March 2009.
[4] L. Josefsson and P. Persson, Conformal Array Antenna Theory and Design. New Jersey: Wiley, 2006.
[5] I. Khalifa and R. G. Vaughan, “Geometric design and comparison of multifaceted antenna arrays for hemispherical coverage,” IEEE Trans. Antennas Propagat., vol. 57, pp. 2608–2614, September 2009. [6] M. Kastelijn and J. Akkermans, “Planar passive electromagnetic deflector
for millimeter-wave frequencies,” IEEE Antennas Wirel. Propag. Lett., vol. 7, pp. 105–107, 2008. 57 58 59 60 61 62 63 −60 −55 −50 −45 −40 −35 −30 −25 −20 frequency (GHz) transmission coef ficient |S21 |
Fig. 8: Measured deflector’s transmission coefficient for 0◦ angle of incidence; without deflector (solid), with 0◦ deflector (dash), with 34◦ deflector (dash-dot)
0◦ deflector (0◦deflecting element) 34◦ deflector (-120◦deflecting element) PCB Sample 1 PCB Sample 1 PCB Sample 2 PCB Sample 2
Fig. 9: X-ray photographs of PCB samples of the 0◦(left) and 34◦ (right) deflectors
[7] C. A. Balanis, Antenna Theory: Analysis and Design, 2nd ed. John Wiley & Sons, 1997.
