ARRAY ANTENNA DIAGNOSTICS WITH THE 3D RECONSTRUCTION ALGORITHM

Transcription

1 ARRAY ANTENNA DIAGNOSTICS WITH THE 3D RECONSTRUCTION ALGORITHM Cecilia Cappellin 1, Peter Meincke 1, Sergey Pinenko 2, Erik Jørgensen 1 1 TICRA, Læderstræde 34, DK-1201 Copenhagen, Denmark 2 DTU Elektro, Technical Uniersity of Denmark, Ørsteds Plads, Bilding 348, 2800 Kgs. Lyngby, Denmark ABSTRACT The 3D reconstrction algorithm is applied to a slotted waegide array measred at the DTU-ESA Spherical Near-Field Antenna Test Facility. One slot of the array is coered by condctie tape and an error is present in the array excitation. Reslts show the accracy obtainable by the 3D reconstrction algorithm. Considerations on the measrement sampling, the obtainable spatial resoltion, and the possibility of taking fll adantage of the reconstrction geometry are proided. Keywords: Array, Diagnostics, Resoltion, Spherical Wae Expansion, Inerse Method of Moments 1. Introdction Accrate and general antenna diagnostics techniqes to identify, from the radiated measred field, the electrical and mechanical errors affecting the antenna nder test are of high importance for the antenna measrements commnity. Microwae holography, based on the wellestablished relation between the antenna far-field and the isible region of the plane wae spectrm [1], has been widely sed for this prpose. The algorithm is general, simple and comptationally ery fast bt has a limit in the spatial resoltion of the compted extreme near-field, since the inisible region of the plane wae spectrm is always neglected. The techniqe presented in [2] allows the reconstrction of part of the inisible region of the plane wae spectrm, ths proiding higher resoltion in the compted extreme near-field, bt shows some limitation when dealing with large antennas and typical measrement noise. To oercome these limits, a new class of antenna diagnostics algorithm has been introdced in the last decade. These new methods are based on the discretization of integral eqations, see [3]-[9], which are deried by placing nknown eqialent electric and magnetic crrents on a srface conformal to the antenna and reqiring that the crrents radiate the measred field otside the srface and zero field inside the srface. A discrete set of eqations are obtained by sing a standard Method of Moments discretization, e.g., RWG fnctions on flat trianglar facets [5], or higher-order basis fnctions on cred srfaces [8]. The latter choice has shown to proide better accracy and lower memory reqirements [8]. Althogh more demanding in terms of memory sage and comptation time as compared to microwae holography, these new methods allow reconstrcting the field on an arbitrary 3D srface enclosing the antenna. The 3D reconstrction algorithm deeloped by TICRA in [8]-[9] is implemented in the commercial software DIATOOL. The identification of array element failre is of particlar interest for antenna diagnostics, and mainly docmented in the literatre throgh experimental reslts, see for example [13]. Diagnostics of array failre, howeer, focses often on reslts achieed by microwae holography, which is intrinsically limited in accracy. Thogh noticeable improements were recently achieed by [14], all proposed techniqes assme the knowledge of the array element factor, either from a dedicated measrement or a software simlation. To or knowledge, the enhanced capabilities of the 3D reconstrction algorithm on array diagnostics hae not been stdied in detail yet. The prpose of this work is ths to stdy the accracy achieable by the 3D reconstrction algorithm when dealing with a slotted waegide array of which measred data are aailable. Considerations on the measrement sampling, the obtainable spatial resoltion, and the possibility of taking fll adantage of the reconstrction geometry will be proided. The paper is organized as follows: Section 2 smmarizes the main featres of the 3D reconstrction algorithm implemented in DIATOOL, Section 3 describes the inestigations performed on a slotted waegide array measred at the DTU-ESA Spherical Near-Field Facility, while conclsions are drawn in Section The 3D Reconstrction Algorithm The higher-order inerse Method of Moments algorithm, [8]-[9], was introdced as an extension of preiosly aailable integral-eqation based reconstrction techniqes. The method comptes the tangential electric and magnetic fields EH, on the reconstrction srface S enclosing an antenna, based on the field measred at discrete points otside the srface.

2 The tangential fields on the reconstrction srface S are obtained by the eqialent electric and magnetic srface crrent densities Js and Ms according to Js nˆ H, (1) Ms nˆ E (2) with ˆn being the otward normal nit ector. These eqialent crrents correspond to Loe s eqialence principle, since they prodce zero field inside S, and are fond by soling the so-called data eqation, which relates the measred data and the nknown srface crrent densities, 3. Slotted Waegide Array The 3D reconstrction was applied to a 6 by 7 slotted waegide array of dimensions 30 cm by 27 cm working at 5.25 GHz, with different row excitations and a condctie tape coering one slot, as shown in Figre 1. E meas 0 LJs K Ms, (3) where 0 is the free space impedance and L and K are integral operators defined in [8]. The a priori information that the fields radiated by the srface crrent densities mst be zero inside S is then enforced as a bondary condition eqation [6] and the correct set of eqialent srface crrent densities is finally fond. The srface of reconstrction is discretized sing crilinear patches of p to forth order. The electric and magnetic srface crrents densities on each patch are expanded in higher order Legendre basis fnctions M M 1 M M 1 X a B a B, (4) m 0 n 0 m 0 n 0 where X [ Js, Ms ], coefficients, M and a and the - and - directions, and a are nknown M are the expansion orders along B and B are the - and -directed higher-order Legendre basis fnctions defined in [8] and [10]. The crrent expansion of Eq. (4) is then inserted in the data eqation of Eq. (3) and the aboe mentioned bondary condition eqation. These copled eqations are finally soled by the iteratie soltion scheme described in [9], which allows one to achiee an accrate soltion by balancing the effects of noise with the reqirement of achieing Loe s crrents. The inerse Method of Moments algorithm in DIATOOL differs from other similar methods [4]-[6] in three important aspects. First, the geometry and nknown crrents are represented by smooth polynomial fnctions. Second, the testing of the bondary condition operator is performed on the actal srface of reconstrction. Third, a new reglarization scheme is employed, in which the data eqation and the bondary condition are treated separately. These differences reslt in improed efficiency, enhanced accracy, and better resoltion properties. Figre 1 The 6 by 7 slotted waegide array in the DTU-ESA Spherical Near-Field Antenna Test Facility. The antenna was measred at the DTU-ESA Spherical Near-Field Antenna Test Facility on a fll sphere, with sampling in t eta and p i eqal to and. respectiely, and a SNR of 70 db. The measrement coordinate system is shown in Figre 1: the origin coincides with the geometrical center of the array, the x- axis is horizontal, the y-axis is ertical and the z-axis points ot of the paper. The distance between slots is 0.67 λ, with λ being the waelength, along the ertical y- axis, and 0.85 λ along the horizontal x-axis. Since the prodct kr o, where k is the waenmber and r o the radis of the antenna minimm sphere, is eqal to 21, one finds that the Spherical Wae Expansion (SWE) of the field radiated by the antenna can be trncated to N=31, according to [12] N kr max 10,3.6 3 o kr o. (5) Once the maximm N is fond, the sampling on the measrement sphere mst at least be eqal to 180 N (6) which becomes Δθ=Δφ=. for N=31. Conseqently, the field measred at the DTU-ESA Facility has an oersampling factor of 2.9 in theta and 1.3 in phi,

3 relatie to the ale of., and proides 7280 field samples distribted oer the measrement sphere. The nmber of measred field samples sets an pper limit for the maximm nmber of nknowns that the 3D reconstrction algorithm can sole. In DIATOOL the maximm nmber of nknowns is approximately eqal to twice the nmber of measrement samples, in the present case arond The nmber of nknowns depends on the nmber of patches sed to mesh the closed srface, on which the crrents are reconstrcted. Moreoer, it depends on the accracy of the polynomial expansion sed to represent the nknown crrents. The polynomial expansion order is atomatically adapted to the electrical size of each patch, leading to the so-called normal accracy. It can, howeer, be increased by an order at a time, by sing en anced, ig or extreme accracy, if necessary. T e normal and en anced settings are in general sfficient when dealing with measred data with 70 db SNR. The maximm dimension of the patches sed in the mesh of the reconstrction is 2 λ. Thogh it is recommended to se as large patches as possible, in order to limit the memory sage and the comptation time, it was fond that the possibility of decreasing the patch dimension plays an important role in the reconstrction capabilities, as it will be discssed in the next paragraph. The reconstrction srface was a box enclosing the slotted waegide array of Figre 1, with sizes 32 cm by 28 cm by 2 cm, with the top face coinciding with the array apertre. First, the maximm dimension of the patches was set to the defalt ale of 2 λ and the en anced accracy was chosen. This gae rise to 30 patches oer the reconstrction box and 4536 nknowns. The amplitde in db of the y-component of the reconstrcted tangential electric field on the top face of the box is shown in Figre 2, together with the sed patches and the location of the coered slot. It is seen that it possible to distingish the 6 by 7 slots and that the radiation on the coered slot location looks different with respect to the rest of the apertre. The length of the patches was then redced to 0.8 λ, which almost coincided with the spacing of the slots along the horizontal axis, and gae rise to 142 patches oer the reconstrction box. By keeping t e en anced accracy the nmber of nknowns became The reslt of the reconstrction is shown in Figre 3. It is seen that the indiidal slots are better resoled when compared to Figre 2, both in the cols and rows, and that the coered slot is now clearly identified. Moreoer, it can be obsered that the slot rows 2 and 3 are strongly excited whereas rows 6 and 7 are ery weak. This is in contradiction with the expected array excitation, which postlates a symmetric excitation relatie to row 4, with row 4 being the one excited the most. This indicates that an error is present in the array feeding network. The reslt gien by the traditional microwae holography on a plane of 32 cm by 28 cm located on the array apertre is shown in Figre 4. While the pictre shows areas of high and low excitation similar to what is shown in Figre 2 and Figre 3, it is eident that the indiidal slots cannot be resoled, and that the resoltion of the 3D reconstrction is far higher than the one proided by microwae holography. Figre 3 - Amplitde of the y-component of the and enhanced accracy. Figre 2 Amplitde of the y-component of the with patch size of 2 λ and enhanced accracy. Figre 4 - Amplitde of the y-component of the tangential electric field from traditional microwae holography.

4 3.1) Effect of Trncated Measrement Sphere and Sampling Density It was then decided to stdy if trncating the measrement sphere and decreasing the nmber of measred samples had an effect on the reconstrcted field. To stdy the measrement trncation effect, the measred sphere was trncated to, ile keeping t e original sampling o in t eta and. in p i. This gae rise to 3280 measred samples. By zero padding the remaining part of the sphere the aailable samples became 5315 and allo ed to reconstrct t e ield it en anced accracy and 0.8 λ for the patch size. The reslt is shown in Figre 5: the reconstrcted field is less accrate than that presented in Figre 3, i.e. the slots start oerlapping, bt still better than Figre 4 since the slots can still roghly be identified. The trncated sp ere as t en redced to and respectiely, always zero padding the remaining part of the sphere. The reconstrction was performed again with 0.8 λ and it en anced accracy and it as obsered that with 60, see Figre 6, slots cold no longer be resoled and the reslt looked similar to the microwae holography pictre of Figre 4. By inspecting the measred field pattern, it was fond that or t eta elonging to - and to - t e lowest ale of the co-polar component was -35 db from the peak, while for theta belonging to - it became eqal to -30 db. Figre 6 - Amplitde of the y-component of the To stdy the measrement sampling effect, the SWE of the original measred field was sed to compte the field on a fll sp ere it sampling in t eta and p i o.. This ale corresponds to an oersampling factor of 1.6 relatie to t e minimm sampling o.. This prodced 5100 field samples on a fll sphere, which allowed one to se again t e en anced accracy and 0.8 λ of patch size. The reslt of the reconstrction is shown in Figre 7. Figre 5 - Amplitde of the y-component of the Figre 7 - Amplitde of the y-component of the, enhanced accracy, fll sphere data, and oersampling of 1.6. It is seen that all slots are identified and that the reslt almost coincides with that of Figre 3. As long as fll sphere data is aailable, with a sampling according to Eqs. (5)-(6), the sampling does not play a key role in the reconstrction. T e sp ere it. sampling as t en trncated to., giing rise to measred points and ths approximately 4800 possible nknowns. To decrease the nmber of nknowns of the reconstrction, the patch size was kept eqal to 0.8 λ while the accracy as set to normal, generating nkno ns. T e reslt is shown in Figre 8.

5 resoled and the reslt almost coincides with that proided by microwae holography. Figre 8 - Amplitde of the y-component of the If we compare it with Figre 4 and Figre 6 we can see that the pictres are ery similar. This means that a lower oersampling, combined with a trncated sphere, affects the resoltion achieable with the 3D reconstrction, prodcing reslts almost eqialent with the traditional microwae holography. This conclsion is also confirmed by the reslts presented in [11], where the 3D reconstrction achieed the same reslts as microwae holography, when applied to a slotted waegide array with measred data trncated to a 80 sphere and an oersampling factor of Conclsions The 3D reconstrction algorithm was applied to a slotted waegide array measred at the DTU-ESA Spherical Near-Field Antenna Test Facility. One slot of the array was coered by condctie tape and an error was present in the array excitation. Both defects cold sccessflly be detected, and all slots cold be identified. It was shown that the spatial resoltion proided by the 3D reconstrction is mch higher than that proided by traditional microwae holography, where the indiidal slots cannot be resoled. This happens when measred fll sphere data are aailable and when the measred field sampling is almost a factor 3 or 1.5 higher the minimm sampling defined by spherical wae theory. It was also illstrated that when the length of the patches describing the reconstrction srface is chosen eqal to the spacing of the array elements the accracy of the reconstrcted field increases. Finally it was shown that trncated measrements data affects the accracy of the reconstrcted field. When the measred field is trncated bt oersampled by a factor 3 relatie to the minimm sampling defined by spherical wae theory, this redction in accracy is howeer limited and the obtained reslts still allow to roghly identifying the indiidal slots. Howeer, when the oersampling of the trncated measred field is decreased to arond 1.5, slots cannot be 5. REFERENCES 1 H. G. Booker, P. C. Clemmo, T e concept o anglar spectrm of plane waes and its relation to that of polar diagram and apertre distri tion, Proc. Inst. Elec. Eng., ol. 9 (1), pp , Janary [2 C. Cappellin, O. Brein jerg, A. Frandsen, Properties o t e transformation from the spherical wae expansion to the plane ae expansion, Radio Science, ol. 43, no. RS1012, doi: /2007rs003696, Febrary [3 T. K. Sarkar, A. Taag ol, Near-field to near/far-field transformation for arbitrary near-field geometry tilizing and eqialent electric crrent and MoM, IEEE Trans. Antennas Propagat., ol. 47, no. 3, pp , Mar [4] Y. Alarez, F. Las-Heras, M. R. Pino, Reconstrction o eqialent crrents distribtion oer arbitrary three-dimensional sr aces ased on integral eqation algorit ms, IEEE Trans. Antennas Propagat., ol. 55, no. 12, pp , Dec [5 J. L. A. Qijano, G. Vecc i, Improed-accracy sorce reconstrction on arbitrary 3-D sr aces, IEEE Antennas and Wireless Propagation Letters, ol. 8, pp , K. Persson and M. Gsta sson, Reconstrction of eqialent crrents sing a near-field data transformation - with radome applications, Progress in Electromagnetics Researc, ol. 54, pp , [7 T. F. Ei ert, C. H. Sc midt, Mltileel ast mltipole accelerated inerse eqialent crrent method employing Rao- Wilton-Glisson discretization of electric and magnetic srface crrents, IEEE Trans. on Antennas Propag., ol., no., pp , [8] E. Jørgensen, P. Meincke, C. Cappellin, and M. Sabbadini, Improed sorce reconstrction techniqe for antenna diagnostics, Proc. of the 32 nd ESA Antenna Workshop, ESTEC, Noordwijk, The Netherlands, [9] E. Jørgensen, P. Meincke, O. Borries, and M. Sabbadini, Processing o measred ields sing adanced inerse met od of moments algorit m, Proc. of the 33rd ESA Antenna Workshop, ESTEC, Noordwijk, The Netherlands, [10] E. Jørgensen, J. L. Volakis, P. Meincke, and O. Breinbjerg, Hig er order ierarc ical Legendre asis nctions for electromagnetic modelling, IEEE Trans. Antennas Propagat., ol. 52, no. 11, pp , No [11] E. Jørgensen, D. W. Hess, P. Meincke, O. Borries, C. Cappellin, J. Ford am, Antenna diagnostics on planar arrays sing a 3D sorce reconstrction techniqe and spherical nearfield measrements, Proc. of ECAP 2012, Prage, F. Jensen, A. Frandsen, On t e nm er o modes in sp erical ae expansions, Proc. Antenna Meas. Tec. Ass. Symposim, AMTA 2004, pp , [13] J. J. Lee, E. M. Ferren, D. P. Woollen, K. M. Lee, Nearfield probe sed as a diagnostic tool to locate defectie elements in an array antenna, IEEE Trans. Ant. Prop., ol., no., Jne D. W. Hess, S. T. McBride, Imaging o element excitations it sp erical scanning, Proc. Antenna Meas. Tech. Ass. Symposim, AMTA 2011, pp , 2011.