Half Truncated Icosahedral Passive Electromagnetic Deflector for the 60 GHz Band

Transcription

1 Half Truncated Icosahedral Passive Electromagnetic Deflector for the 6 GHz Band M. I. Kazim #1,M.H.A.J.Herben #,M.D.Huang #3 # Electromagnetics and Wireless (EMW), Department of Electrical Engineering Technische Universiteit Eindhoven (TU/e), P.O. Box 513, 56 MB Eindhoven, The Netherlands 1 m.i.kazim@tue.nl m.h.a.j.herben@tue.nl 3 m.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 ( db) and ( db) for the and 34 deflectors, respectively, in the GHz frequency band. I. INTRODUCTION The 6 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 6 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 6 GHz frequency band are found in literature. The beam of these antenna arrays, however, cannot usually be steered more than ±3 ; the limitation is due to increase in SLL (SLL > - db) [1]. The angular coverage of substrate lens antennas for millimeter-wave applications is restricted to ± [], [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 antenna 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 6 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 1 aperture layer patch/reflector layer transm. line layer - Fig. 1: Passive electromagnetic deflector for the 6 GHz band the deflector s transmission coefficient. Finally, the conclusions are drawn in Section IV. II. HALF TRUNCATED ICOSAHEDRAL DEFLECTOR The proposed half truncated icosahedral passive electromagnetic deflector for the 6 GHz band is shown in Fig.. Multiple deflectors are used to form a half truncated icosahedron configuration. The design details of a planar source antenna array ( 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 -,, and + for the 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

2 the facet discontinuities. The directivity of each antenna element i of the source antenna array D i (θ, φ) is defined as D i (θ, φ) =(m +1)cos m θ (1) where m, θ 9 and φ 36.The antenna element of the source antenna array presented in [1] has D i (θ, φ) =6cos θ, for the case of m =. The power pattern or the radiation intensity of the antenna element can be calculated by Fig. : Half truncated icosahedral deflector deflector comprises 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 3 facets in total with 1 regular pentagons and regular hexagons. The dihedral angles are and 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 parametric 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 (18 - α = ), 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 the φ =9 plane) and also the phase delay introduced due to path length difference from the source antenna array located at the origin O to each deflector element kr xyz. The simulations provide a basic understanding for icosahedral deflector design, in terms of deflecting behaviour 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 P i (θ, φ) = P rad,i 4π D i(θ, φ) () where P rad,i is the radiated power of an antenna element i of the source antenna array and is taken to be 4π. The amplitude of the electric field intensity of each antenna element at the far-field distance r is given by η P rad,i D i (θ, φ) 1η E i (r, θ, φ) = 4πr = cos θ (3) r The far-field electric field of the source antenna array is expressed as N E source (r, θ, φ) = E i (r, θ, φ) e (j[βsource+kˆr ri]) (4) where k = π λ is the free-space phase constant, ˆr = sin θ cos φˆx + sinθ sin φŷ + cos θẑ is a unit vector in the direction of the rays, r i is a position vector from the origin O to the i th element of N-element source antenna array and β source is the phase shift applied by each element to steer the beam. The directivity of the source antenna array can be calculated as E source(r,θ,φ) D source (θ, φ) =r η P source (5) 4π where P source is the total radiated power of the source antenna array and is equal to 4πN. The available power P rxyz of each deflector element in xyz-space can be written in terms of the power flow density S(r xyz,θ xyz,φ xyz ) of the incident plane wave towards the direction of the deflecting element and the area of the deflecting element A. Hence, i=1 P rxyz = S(r xyz,θ xyz,φ xyz )A cos θ sa (6) S(r xyz,θ xyz,φ xyz )= E source(r xyz,θ xyz,φ xyz ) (7) η where θ sa 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.5λ, the area of each deflector element A is takentobe(.5λ ). The deflector elements are considered to be isotropic sources with no transmission losses. Since the deflector elements are radiating in the upper half-space only, the directivity

3 of each deflector element D d(xyz) (θ, φ) is equal to (from eq. (1) with m = ). The amplitude of the electric-field intensity of the deflector elements E d(xyz) (r, θ, φ) at the farfield distance r is expressed as η P rxyz E d(xyz) (r, θ, φ) = D d(xyz)(θ, φ) 4πr (8) The far-field electric field of the whole deflector E def (r, θ, φ) containing T deflecting elements is given by E def (r, θ, φ) = T xyz=1 E d(xyz) (r, θ, φ) e (j[βxyz+krxyz+kˆr rxyz]) (9) The phase shift β xyz is adjusted to provide the desired deflecting angle in the φ =9 plane and to compensate kr xyz. The directivity of the whole deflector can be calculated as E def (r,θ,φ) D def (θ, φ) =r η P def () 4π where P def 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 θ source will have its scan angle changed by K d θ source. 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 angle θ dn = n K dθ source 3 (in the φ =9 Trow 1 plane) over the whole deflector, as shown in Fig. 3; T row and T col 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 having T row = T col = and d =.5λ.The height h between the center of the broadside facet and the source antenna array center (at the origin O) is taken to be 8λ. The phase shifts of the deflecting elements are set to meet the criteria of K d =.67, when the source antenna array is steered to θ source =3. Fig. 4 shows the simulation results of the scenario example. The maximum values of directivity for the source and deflector are found to be db (θ =3 ) and 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 deflector Z I θ d1 θ d θ d3 h ˆn d θ def = K d θ source θ source Z ˆr θ O Y φ O X source antenna array Y α II α θ def 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 kr xyz and phase due to geometrical orientation of the skewed facet I II 5 5 III Fig. 4: Scenario example: Comparison of directivity (db) of source (left) and deflector (right) simulated in MATLAB for the φ =9 plane B. MATLAB and CST MWS Simulations - A Comparison CST MWS simulations have been carried out for the 6 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 III

4 results for the case when a 34 deflector plate (T col = 5, T row = 9, d =.6λ, h = 4.5λ ) 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 db (θ = ) and db (θ = 4-45 ), respectively, for MAT- LAB simulations. CST MWS gives the maximum values of directivity for the source and the deflector as db (θ = ) and 14.6 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 Fig. 5: Comparison of directivity (db) of source (left) and deflector (right) simulated in MATLAB (solid) and CST MWS (dash) for the φ =9 plane III. MEASUREMENT OF DEFLECTOR S TRANSMISSION COEFFICIENT An important aspect of the proposed 6 GHz antenna configuration 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 (L a ) 19 mm (L b )have been used. The 3 db half power beam-width (HPBW) in E- plane and H-plane, calculated using the empirical expressions ψ E = 5.6 λ L a and ψ H = 68.8 λ L b, is ψ E = and ψ H =18., respectively [7]. The two standard gain horn (SGH) antennas, are located in each other s far-field r ff,at a distance of d 1 (d 1 = d = 77 mm; r ff = 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 surface I on the deflector plate can be estimated on the basis of the HPBW of the horn antenna as equal to d 1 tan ψ E/H in both the E-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 3 rd 3λd Fresnel zone radius 1d d 1+d, 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 significant variations in the amplitude (<. db) and phase (< ±1 ) values of the deflector s transmission coefficient S 1. The set-up has been tailored to determine the transmission properties of both the and 34 deflectors, as depicted in Fig. 6. The S 1 has been measured for three PCB samples of each of the deflectors. The effect of angle of incidence on the deflector has also been measured. The measured S 1 for the and 34 deflectors at angle of incidence is plotted in Fig. 8. The transmission loss for the and 34 deflectors is found to be ( db; repeatability error: db) and ( db; repeatability error: ±.45 db), respectively, in the GHz frequency band. The effect of angle of incidence ( to ) on transmission loss of the deflector is observed to be ± 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 S 1 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 and 34 deflectors shown in Fig. 9, highlight the misalignment of the different PCB samples. IV. CONCLUSIONS A half truncated icosahedral passive electromagnetic deflector for the 6 GHz frequency band is presented in this paper. A generalized MATLAB formulation for the simple parametric geometry of the proposed configuration is described. 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 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

5 deflector plate standard gain horn (SGH) antennas deflector ψ/ d 1 d turn table rf absorbers 34 deflector I transmission coefficient S frequency (GHz) Fig. 8: Measured deflector s transmission coefficient for angle of incidence; without deflector (solid), with deflector (dash), with 34 deflector (dash-dot) deflector ( deflecting element) 34 deflector (- deflecting element) Fig. 6: Measurement set-up for deflector s transmission coefficient determination standard gain horn (SGH) antennas deflector rf absorbers blue foam material Fig. 7: Anechoic chamber measurement set-up PCB Sample 1 PCB Sample 1 in measurements as well as NXP Semiconductors, Nijmegen for X-ray photographs of the deflectors. REFERENCES [1] J. Akkermans and M. Herben, Planar beam-forming array for broadband communication in the 6 GHz band, in European Conf. Antennas and Propagat. (EuCAP7), Edinburgh, UK, November 7. [] X. Wu, G. V. Eleftheriades, and T. E. van Deventer-Perkins, Design and characterization of single- and multiple-beam mm-wave circularly polarized substrate lens antennas for wireless communications, IEEE Trans. Microwave Theory Tech., vol. 49, pp , March 1. [3] N. T. Nguyen, R. Sauleau, and L. L. Coq, Lens antennas with flattop radiation patterns: benchmark of beam shaping techniques at the feed array level and lens shape level, in European Conf. Antennas and Propagat. (EuCAP9), Berlin, Germany, March 9. [4] L. Josefsson and P. Persson, Conformal Array Antenna Theory and Design. New Jersey: Wiley, 6. [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 , September 9. [6] M. Kastelijn and J. Akkermans, Planar passive electromagnetic deflector for millimeter-wave frequencies, IEEE Antennas Wirel. Propag. Lett., vol. 7, pp. 5 7, 8. PCB Sample PCB Sample Fig. 9: X-ray photographs of PCB samples of the (left) and 34 (right) deflectors [7] C. A. Balanis, Antenna Theory: Analysis and Design, nd ed. John Wiley & Sons, 1997.