Optimal Eccentricity of a Low Permittivity Integrated Lens for a High-Gain Beam-Steering Antenna

Transcription

1 EuCAP Convened Papes Optimal Eccenticity of a Low Pemittivity Integated Lens fo a High-Gain Beam-Steeing Antenna Aki Kattunen #, Juha Ala-Lauinaho #, Ronan Sauleau +, Antti V. Räisänen # # Aalto Univesity School of Electical Engineeing, Dept. of Radio Science and Engineeing, SMARAD/MilliLab, P. O. Box 13000, FI AALTO, Finland, aki.kattunen@aalto.fi, juha.ala-lauinaho@aalto.fi, antti.aisanen@aalto.fi + Goupe Antennes et Hypeféquences, Institut d Electonique et de Télécommunications de Rennes (IETR), UMR CNRS 6164, Univesité de Rennes 1, Rennes Cedex, Fance, onan.sauleau@univ-ennes1.f Abstact In this pape, the eccenticity of a lage integated lens antenna is optimised fo a high-gain beam-steeing antenna. With low pemittivity lens mateials, conventional integated lens types, namely the extended hemispheical and the elliptical ones, have diffeent chaacteistics when used in beam-steeing applications. An optimal eccenticity is found that combines the advantages of the conventional lens types. The lenses ae analysed with ay-tacing simulations using a simplified feed adiation patten. I. INTRODUCTION Integated lens antennas with a feed aay can be used fo beam-steeing applications [1]-[8]. The plana feed aay is integated at the bottom of a dielectic lens and beam-steeing is achieved by switching between the feed elements. Extended hemispheical [1]-[6], elliptical [6]-[7], and shaped [8] lenses have been studied. In this pape, it is poposed fo the fist time that the eccenticity of the shaped collimating suface of the integated lens can be optimised to impove the beam-steeing popeties. The conventional integated lens types ae the extended hemispheical [1]-[6] and the elliptical lens [6]-[7]. The elliptical lens has an eccenticity of e 1 and its extension length L equals ea, whee a is the semimajo axis of the ellipse. The eccenticity of an ellipse is defined as: e 2 1 ( b a), (1) whee b is the semimino axis of the ellipse, i.e., the adius of the lens. The extension length of an extended hemispheical (e = 0) lens can be optimised to achieve maximum diectivity [4]. In this pape, the lens eccenticity is vaied between 0 and e 1 and the extension length is optimised fo each lens. The lens pofiles of extended hemispheical (extension lengths optimised based on maximum diectivity without feed offset [4]) and elliptical lenses ae shown in Fig. 2. II. DESCRIPTION OF THE LENSES In a beam-steeing integated lens antenna, a plana feed aay is placed at the bottom of the dielectic lens, as illustated in Fig. 1. Beam-steeing is done by switching between the feed elements. Fig. 2 Lens pofiles of extended hemispheical (solid) and elliptical (dash) lenses. Lens mateials: Teflon (ε = 2.1, blue), Rexolite (ε = 2.53, geen), quatz (ε = 3.8, ed), and silicon (ε = 11.7, black). Fig. 1 Illustation of the beam-steeing pinciple III. ANALYSIS METHOD The lenses ae analysed with ay-tacing simulations. Fist, the fields outside the lens ae solved with ay-tacing. Raytacing is based on geometical optics (GO) and uses the Snell s law on the lens suface and the powe consevation law inside the ay tubes. Secondly, the equivalent electic and 3678

2 magnetic suface cuents ae calculated fom the field solved with ay-tacing, and then the fa-field is computed fom the equivalent cuents. This simulation method is commonly used to analyse lage lens antennas. Examples of ay illustations of Rexolite lenses with diffeent eccenticities ae shown in Fig. 3. In this pape, the equivalent cuents ae calculated on a suface that is othogonal to the ays so that the GO-field (locally planewave) is tangential to the integation suface, and thus, it is not necessay to appoximate the tangential field by pojection. In Fig. 3, total eflections ae shown with yellow ays. angles, an elliptical lens should be chosen, while fo lage scan angles the extended hemispheical lens shows the highest diectivities. It can also be seen fom [6] that the diffeence in diectivities ae elatively small (in the cases compaed in [6], less than 1 db). The diffeence between the extended hemispheical and elliptical lenses is so small that thee is no eason to conside intemediate lens eccenticities. As can be seen fom Fig. 2, the diffeence is elatively small also geometically. V. LOW PERMITTIVITY LENSES Lenses with diffeent eccenticities ae compaed to find the optimal eccenticity fo a low pemittivity lens mateial Rexolite (ε = 2.53). With low pemittivity lens mateial, the diffeence between extended hemispheical and elliptical lens is appaent, and eccenticities between 0 and e 1 ae studied. In the simulations, the feed adiation patten is consideed to be an ideal point souce with amplitude patten: N E (, ) cos ( ), 0 90, (4) Fig. 3 Ray illustations; extended hemispheical a)-b), optimised eccenticity c)-d), and elliptical e)-f) Rexolite lenses. Without feed offset (lhs) and with 25 mm offset (hs). Yellow ays ae totally eflected. The ed line outside the lens is the suface on which the equivalent cuents ae calculated. The eflected fields ae not calculated in these simulations. Reflection loss is calculated in each case: L efl = 10 log( P tot /(P tot P efl ) ), (2) whee P efl is the total eflected powe and P tot is the total powe adiated fom the feed into the lens. The field leakage fom the extension can be significant and it is included in the simulations. The field leaking out fom the extension mainly affects the side-lobe level and theefoe it can be consideed as a spillove loss: at the main polaisation of Ludwig s second definition of polaisation [9]. The simulations ae done fo a 100 mm ( 25.7 λ 0 ) diamete Rexolite (ε = 2.53) lens at 77 GHz (λ mm). Ludwig s second definition of polaisation [9] is also used fo the fa-field esults. Low diectivity feed elements ae used with N = 0.2 in (4). Fist, the extension lengths ae chosen based on diectivity as a function of the extension length shown in Fig. 4. The diectivities in Fig. 4 ae calculated without feed offset and the field leaking out fom the extension is included. Also diectivity without the field leaking out fom the extension is taken into account in selecting the extension lengths (not shown hee). L spill = 10 log( P tot /(P tot P spill ) ), (3) whee P spill is the total powe leaking out fom the extension pat. The desied popeties ae consideed to be high diectivity and low eflection loss with lage beam-steeing angle ange. In addition, constant diectivity as a function of the beamsteeing angle is desiable. Beam-steeing popeties ae evaluated by simulations with feed offsets. IV. HIGH PERMITTIVITY LENSES Alumina (ε = 9.8) and GaAs (ε = 12.8) extended hemispheical and elliptical lenses ae compaed in [6]; it is concluded that, to obtain good pefomance fo small scan Fig. 4 Diectivity as a function of the extension length. Rexolite lenses with diffeent eccenticities (line colous) without feed offset. Feed element diectivity is 4.5 db (N=0.2 in (4)). 3679

3 TABLE I OPTIMISED EXTENSION LENGTHS OF REXOLITE LENSES WITH DIFFERENT ECCENTRICITIES. LENS DIAMETER IS 100 MM. Eccenticity Extension length L 1 / e a 40.4 mm 0.9/ 46 mm 0.84/ 49 mm 0.78/ 53 mm 0.75/ 53 mm 0.5/ 60 mm 0 70 mm The optimised extension lengths ae listed in Table I. The elliptical lens has an eccenticity of e 1 and the extended hemisphee has an eccenticity of e = 0. The eccenticities between those ae chosen to epesent the lens sizes and diectivities between those of the elliptical and the extended hemispheical lenses. The beam-steeing popeties ae studied with simulations with diffeent feed offsets. The simulated offsets ae 0, 2 mm, 5 mm, 10 mm, 15 mm, etc. in x-diection, esulting in beamsteeing in the H-plane. The feed offset, i.e., the distance fom the feed focal point to the otational symmety axis, as a function of the diection of the maximum of the main beam is pesented in Fig. 5. The diffeences in Fig. 5 ae due to the diffeent total heights of the lenses with diffeent eccenticities and extension lengths. The optimal eccenticity lens is chosen based on diectivity and eflection loss as function of the beam-steeing angle, i.e., the main-beam diection, as shown in Figs 6-7. The spillove losses ae also shown in Fig. 7. The spillove losses ae nealy equal because the lenses ae identical below the angle of total eflection (see Fig. 3), and the diffeences ae due to the diffeences in Fig. 5. Fig. 5 Feed offset as a function of the main-beam diection. Rexolite lenses with diffeent eccenticities (line colous). Feed element diectivity is 4.5 db (N=0.2 in (4)). Fig. 6 Diectivity as a function of the main-beam diection. Rexolite lenses with diffeent eccenticities (line colous). Feed element diectivity is 4.5 db (N=0.2 in (4)). Fig. 7 Reflection loss (solid lines) and spillove loss (dash lines) as a function of the main-beam diection. Rexolite lenses with diffeent eccenticities (line colous). Feed element diectivity is 4.5 db (N=0.2 in (4)). An intemediate eccenticity lens (e.g., e 0.75 o e 0.78 ) has highe diectivity and lowe eflection losses than the extended hemispheical lens. Compaed to the elliptical lens, the diectivity emains high and nealy constant also with lage beam-steeing angles. Such intemediate eccenticity is concluded to be optimal fo a low pemittivity integated lens fo a high-gain beam-steeing antenna. The half-powe beam-width (HPBW) as a function of the main-beam diection is shown in Fig. 8. With an intemediate eccenticity lens the beam width is nealy constant as a function of the beam-steeing angle. The beam width of the elliptical lens ( e 1 ) inceases as a function of the beamsteeing angle. That is the main eason why the diectivity of the elliptical lens deceases as a function of the beam-steeing angle (see Fig. 10). The spillove losses, i.e., the field leaking out fom the extension, ae included in the diectivities in Fig. 6, but the 3680

4 eflection losses, i.e., the eflected fields, ae not included. Diectivities, without the field leaking out fom the extension, ae shown in Fig. 9. The diffeences between Fig. 6 and Fig. 9 ae due to the field leaking out fom the extension. Spillove losses (see Figs 7 and 12) incease the sidelobe levels (see Figs 10 and 13) and thus decease diectivity (see Figs 6, 9 and 11). Fig. 8 Half-powe beam-width (HPBW) as a function of the main-beam diection. Rexolite lenses with diffeent eccenticities (line colous). Feed element diectivity is 4.5 db (N=0.2 in (4)). Fig. 10 H-plane diectivity pattens without feed offset (solid lines) and with 20 mm offset (dash lines). Rexolite lenses with diffeent eccenticities (line colous). Feed element diectivity is 4.5 db (N=0.2 in (4)). The simulation esults in Figs 4-10 ae calculated with lowdiectivity (4.5 db, N=0.2 in (4)) feed elements. With low pemittivity integated lenses, eflection losses ae in geneal lowe with low-diectivity feed elements because moe powe goes to the total eflections (see Fig. 3). In Figs 11-12, the diectivity and losses of an intemediate eccenticity lens ( e 0.78 ) ae shown with low- (4.5 db, N=0.2), medium- (7.8 db, N=1), and high- (11.5 db, N=3) diectivity feed element adiation pattens. As Fig. 11 shows the diectivity is nealy constant also with highe diectivity feed elements. The H-plane diectivity pattens of the intemediate eccenticity lenses with diffeent feed element diectivities ae shown in Fig. 13. Fig. 9 Diectivity as a function of the main-beam diection without the field leaking fom the extension. Rexolite lenses with diffeent eccenticities (line colous). Feed element diectivity is 4.5 db (N=0.2 in (4)). The H-plane diectivity pattens of extended hemispheical, an intemediate eccenticity lens ( e 0.78 ), and elliptical lens ae shown in Fig. 10. Fig. 11 Diectivity as a function of the main-beam diection with (solid lines) and without the field leaking fom the extension (dash lines). Rexolite lens with intemediate eccenticity. Feed element diectivities: 4.5 db (N=0.2, black), 7.8 db (N=1, ed), 11.5 db (N=3, blue). 3681

5 the optimal eccenticity lens intoduced in this pape, the design in [7] has clealy lowe losses but the diectivity popeties ae not as good. Fig. 12 Reflection loss (solid lines) and spillove loss (dash lines) as a function of the main-beam diection. Rexolite lens with intemediate eccenticity. Feed element diectivities: 4.5 db (N=0.2, black), 7.8 db (N=1, ed), 11.5 db (N=3, blue). Fig. 13 H-plane diectivity pattens without feed offset (solid lines) and with 20 mm offset (dash lines). Rexolite lens with intemediate eccenticity. Feed element diectivities: 4.5 db (N=0.2, black), 7.8 db (N=1, ed), 11.5 db (N=3, blue). VI. DISCUSSION One of the design goals in this pape is to have constant diectivity as a function of the beam-steeing angle. The extended hemispheical lens has (nealy) constant diectivity as a function of the beam-steeing angle, e.g., [4], [6]. The lens eccenticity optimisation is intoduced as a new method to achieve this goal with bette diectivity popeties. In [7], an elliptical Rexolite lens is designed with a conventional eccenticity that has smalle extension length than the conventional elliptical lens. Compaed to the conventional elliptical lens, constant diectivity as a function of the beam-steeing angle (up to about ) is achieved with lowe diectivity and lowe losses [7]. As compaed to VII. CONCLUSIONS The optimal eccenticity of a low pemittivity integated lens fo a high-gain beam-steeing antenna is found to be an intemediate value between those of the conventional integated lens types, namely the extended hemispheical and the elliptical lens. An intemediate eccenticity lens has a elatively high diectivity that is constant ove a wide ange of beam-steeing angles. Rexolite (ε = 2.53) lenses with diffeent eccenticities ae simulated with a ay-tacing simulation method. The extension length is optimised fo each eccenticity and the beam-steeing popeties ae compaed with simulations with feed offsets. A lens with eccenticity of about e 0.78 is found to be optimal to achieve good diectivity as a function of the beamsteeing angle. ACKNOWLEDGMENT This wok was suppoted in pat by COST IC0603 (ASSIST), the Academy of Finland though the Cente of- Excellence pogam (SMARAD), and Tekes though BRAWE poject. REFERENCES [1] D. F. Filipovic, S. S. Geahat, and G. M. Rebeiz, Double-slot antennas on extended hemispheical and elliptical silicon dielectic lenses, IEEE Tansactions on Micowave Theoy and Techniques, vol. 41, no. 10, pp , [2] D. F. Filipovic and G. M. Rebeiz, Double slot antennas on extended hemispheical and elliptical quatz dielectic lenses, Intenational Jounal of lnfaed and Millimete Waves, vol. 14, no. 10, pp , [3] D. F. Filipovic, G. P. Gauthie, S. Raman, and G. M. Rebeiz, Off-axis popeties of silicon and quatz dielectic lens antennas, IEEE Tansaction on Antennas and Popagation, vol. 45, no. 5, pp , [4] A. Kattunen, J. Ala-Lauinaho, R. Sauleau, and A. V. Räisänen, A study of extended hemispheical lenses fo a high-gain beam-steeing antenna, Euopean Confeence on Antennas and Popagation (EuCAP 2010), Bacelona, Spain, Apil, [5] J. Ala-Lauinaho, A. Kattunen, J. Säily, A. Lamminen, R. Sauleau, and A. V. Räisänen, Mm-wave lens antenna with an integated LTCC feed aay fo beam steeing, Euopean Confeence on Antennas and Popagation (EuCAP 2010), Bacelona, Spain, Apil, [6] M. J. M. van de Vost, P. J. I. de Maagt, and M. H. A. J. Heben, Scan-optimized integated lens antennas, in Poceedings of the 27 th Euopean Micowave Confeence, Jeusalem, Isael, 1997, pp [7] X. Wu, G. V. Eleftheiades, and T. E. van Devente-Pekins, Design and chaacteization of single- and multiple-beam mm-wave ciculaly polaized substate lens antennas fo wieless communications, IEEE Tansactions on Micowave Theoy and Techniques, vol. 49, no 3, pp , Mach [8] A. V. Boiskin and R. Sauleau, Synthesis of abitay-shaped lens antennas fo beam-switching applications, Poceedings of the 40 th Euopean Micowave Confeence, Pais, Fance, Sept., 2010, pp [9] A. C. Ludwig, The definition of coss polaization, IEEE Tansactions on Antennas and Popagation, vol. AP-21, no. 1, pp , Jan