Efficient mutual coupling analysis of circular polarised microstrip antennas J. Heinstadt Indexing terms: Antenna theory, Microstrip antennas, Antenna arraju, Numerical methods The current expansion of a circular polarised electrodynamically coupled patch in small rooftop basis functions gives excellent results but leads to numerical problems in the case of array computation. To increase efficiency the currents of each element in the array are approximated by the current distribution of a single isolated patch which leads to a tremendous decrease in computation time and shows good agreement with an exact calculation. 270 Fig. 3 E-plane and H-plane radiation patterns of U D R for d = 2mm at 20GHz t i ] nic.iwrud I I I I nie.i,urud tiii, E-plms patiern H-plans p.,ttcrii culculutions the nic:isurcmznt sn\’ironnient. I n d d i t i o n . our cxpsrimsnt.; chou th:Lt t h s xididtion from the coupling dpsrture I\ \er! small. because the nimsured input reflection coeificient o i the structure uithout the dielectric revxiator I> almost OdH in the mcxwreiiicnt irsqum-) rdngs. Cini<lu\;m 4 nt\\ txhniquc is described i o r i s d i n g tinidirccdielectric rddiaiors ( I ~ I ) K > I in nonr.idiiiting diclcctric uaieguide ( N K I ) ) structures. Measurement o i a protot!pz this kind o i r,di.itor uurking at ?OGllz >lloujthat the coupling sificisncy I\ vcr) high and goad matching ciln c.dhil! bs o h t i n e d . Such a circuit configuration . i l l o ~ sths combination a i planar millimetre \\;i\c MtHjMIC tuchniqueh and KRD tcchniquc’s i n one .;!.itcm for the he\t .IW of technique, Ibr diiferent itinctions. Introduction: In future communication systems, such as satellitecommunication or traffic-guidance systems, a more frequent use of circularly polarised antennas is expected. For use in microstrip arrays, electrodynamically coupled patches, shown in Fig. 1, are very well suited. The two required spatial orthogonal modes are easily excited by a 45” rotation of the quadratic resonator with respect to the feeding microstrip line. Owing to the small insets at two opposite edges, the resonance frequencies of both modes are shifted apart a little so that the 90” phase shift, which results in the desired circular polarisation, occurs somewhere at the centre frequency. Because of this skilful design n o hybrids are required for realising the orthogonal modes, so that there is ample room for the feed network. This feed network is embedded deep in the substrate material and is characterised by its weak spurious radiation. radome circulor polarised resonator feed line tioiial A~.~n~,ilki14iiii,n 1thi, nark wci> supportcd b! the Natiunal Siience mid Fnginesring Rcseurch Council (NStR(‘1 oi Canadd. The author< u , ” ~ l dlike t o thank 41. (‘uhiici and A. Ittipihoon o i the Conimunic.dtion Rereurch Center i n Ottaira fur their great help in t h s .intennd nica\urcmcnt, 0 IEE 1995 I I November 1994 Electronics Letters Online No: 19950104 H. An, R.G. Bosisio and K. Wu (POLY-GRAMES, Departement de GPnie Electrrque et Gdnie Informatique, CP 6079, Succ. Centre Ville, Ecole Poljtechniqne de Montrdal, Montreal, Quebec H3C 3A7, Canada) Fig. 1 Electrodynamicallj coupled circular polarised mir rostrip antenna In addition to the patch size and the proper location of the feeding line, the size of the insets essentially influences the polarisation quality. For this reason an exact analysis of such complex shaped patches is only ensured when the whole structure and especially the insets are modelled precisely. For this purpose the current distribution o n the feedline and the stacked patch has to be expanded in typically 250 small rooftop basis functions, as can be seen in Fig. 2. Then an integral equation technique (EFIE) using the Green function of the infinite multilayered dielectric slab and moment method (MOM) can be applied and leads to a matrix equation which has to be solved for the unknown amplitudes of the expansion functions. References x -directed basis function YONEYAMA. T., and NISHIDA. s.: ‘Nonradiative dielectric waveguide for millimeter-wave integrated circuits’, IEEE Trans., 1981, MTT29. pp. 1188-1 192 YONEYAMA. T.: ’Millimeter-wave integrated circuits using nonradiative dielectric waveguide’, Electron. Commun. Jpn.. 1991, 74, ( 2 ) , pp. 87-94 (Part 2) KUROKI. F., and YONEYAMA, T.: ‘Nonradiative dielectric waveguide circuit components using beam-lead diodes’, Electron. Commun. Jpn., 1990, 73, (9) pp. 71-76 (Part 2) REDDY. C.J. ITTIPIBOON, A., and CUHACI. M.: ‘Aperture coupled microstrip antenna by nonradiating dielectric waveguide’, Electron. Lett., 1993, 29, (25), pp. 2157-2158 wu. K., JI. L., and BOSISIO. R.G.:‘A low-loss unidirectional dielectric resonator (UDR) for antenna and space power combining circuits’, IEEE Trans., 1994, MTT-42, (2) pp. 339-341 AN. H., wu. K., and BOSISIO, R.G.: ‘Radiation pattern prediction of the unidirectional dielectric resonator (UDR)’, IEEE Microw. Guid. Wave Left., 1994, 4, (II), pp. 367-369 146 y-directed LTIIJY discret;sotion grid I Fig. 2 Discrete grid to expand the patch currents in rooftop basis functions I-and y-directed The elements of the so-called reaction matrix are computed very efficiently by a combination of a spectral- and a space-domain approach [I]. The matrix itself is solved by a conjugate residual algorithm  so that the analysis of different-shaped patches and frequencies is carried out in less time (a few seconds). In Fig. 3 the computed input impedance is compared to measured data and shows the excellent performance of the computation procedure. ELECTRONICS LEl7ERS 2nd February 1995 Vol. 31 No. 3 rents and the complex amplitude of the feedline currents. This matrix is solved easily. -m Fig. 3 .Meiisiired ond c n i i i i ) i i r i ~ diiipur iiiiiiedniice I!/ ii circiilur poliirised iiiicrosrrip pnrcli nnfeiziiii A computation 0 measurement 6.2GH7. AF = IOOMHz, L = 13.Omm. 11= 0.541mm. g = 3.061nm. t = 1.53mm. d = 1.082nim, 11' = 3.2445nini. E , = tl = E, = 2.33. l i , = l.52mm. liI = 1.52mm. 17, = 0.76mm. Z,, = 5 5 n F = 5.3 4 r r g coinputorion: 'Iremendous computational problems arise when this precise method is used for array computation. Keeping the introduced discretisation for all patches in the array leads to an increase in the unknowns proportional to the number of elements used in the array times the number of basis functions for each patch (see Fig. 4 (U)).The resulting computation time, needed to derive and solve the moment method matrix equation by an iterative conjugate gradient method using a CRAY-Y-MP. is also given in Fig. 4 (+). It becomes clear that this kind of array computatioii is restricted to small arrays. To enable the computation of moderate or large arrays within a justifiable expense of computation time, a reduction in unknowns is essential. feedline currents 22' 5--2.4 1 Fig. 5 Curreiir di.sfribiitiui7 uf i.soliircrl elerrinit '" h Patch currents c Feeding currents 11, 25n , 1 5 0 -5 -1 0 02 06 0 4 Sih0 08 e' e Fig. 6 ResiiIf am1 w r i i i i i / i . s ~~l r r o rof ~ippro.~~iilili~ioi7 li~diiriqiir - compared to an exact computation as a function of edge spacing For patch geomctrl see Fig. 3 0 Re (Z14 A 1111 ( Z , : ) ~ Kcduction qf u i i k i i o i i ~ i i fiv . ~ ifficieiil a r r q coiizpurotioii: As has heen shown in a previous paper  the number of unknowns for array computation can be reduced to one or two for each patch. when an array of equally shaped rectangular elements is assumed. Then the currents on each element can be approximated by the current distribution of one single isolated element because only the amplitude of the currents varies in the array environment. The shape of the currents on each element is almost equal to that o f t h e isolated element. This aproach is now employed for the mutual coupling analysis of tu'o circularly polarised patches. First, the current distribution of one isolated element. which is presented in Fig. 5, is computed using the previously introduced high accuracy computation method for single elements. The resulting numerical representations of the patch and feedline currents are used for the antennashape-matched new basis functions. In the following step. these numerical basis functiolis are used to approximate the currents of both patches in the coupled configuration. Using EFlE and MOM iiou gives a reduced reaction matrix equation of only three unknowns per element. the complex amplitudes of both patch cur- ELECTRONICS LETTERS 2nd February 1995 Vc The resulting coupling impedances are given in Fig. h as a function of edge-spacing. Thcy are compared to an exact computation where the curent distribution on both patches has been expanded in 250 rooftop basis functions. The error in the coupling impcdance is less than 1.0% as the edge spacing exceeds 0.2h,,. so that the developed approximation technique is valid for the mutual coupling analysis in standard array configurations. Owing to the reduction in unknowns, a significant decrease of computation time is achieved. so that a 16-element arraq of circularly polarised patches can now be computed in less than 20s (see Fig. 4 (xi). C~inclusioii: The presented approximation technique allows the efficient mutual coupling analysis of arbitrarily shaped patches and gives excellent results. as has been shown in the case of two coupled circularly polarised patches. Owing to the use o f a numerical basis function which is matched to the patch shape. a considerable decrease in storage requirement aiid computation time for array computation is achieved. References HEINSTADT. I : 'An efficient calculation procedure for single element and finite linear microstrip array antennas'. 3rd Int. Symp. on antennas and EM theory, Nanjing, September 1993 w.: 'Elektrodynamische Analyse geometrisch komplexer 2 WERTGEN. (M)-MIC-Strnkturen mit efficienten numerischen Strategien'. Dissertation Universitat Gesamthochschule Duishurg, Dez. 1989 3 HEINSTADT, I.: 'New approximation technique for current distribution in microstrip array antennas', Electron. Lett., 1993, 29, pp. 1809-1810 1 ever, in the feeding scheme shown in Fig. l , only the mode which radiates like a y-directed magnetic dipole is excited. The return loss of the unbiased F R A is shown in Fig. 2. The resonance frequency was measured to be 7.2GHz. For the FRA disk parameters given in Fig. 1, the resonance frequency was calculated to be 6.7GHz using (eqn. 5 in ). O i ' " ' , ' ' " ~ ' ~ ~ ~ , ~ ' Switchable LP/CP ferrite disk resonator antenna A. Petosa, R.K. Mongia, A. Ittipiboon and J.S. Wight Indexing terms: Dielectric resonators, Dielectric-loaded antennas, Ferrites A switchable linearlcircular polarised ferrite resonator antenna is investigated. It is shown that the polarisation can be switched from linear to circular by applying a static magnetic bias to the ferrite resonator antenna. The return loss and radiation patterns - 25 60 coupling aperture \ t 1 (dirnensionsinrnm) microstrip feed line ___----__________-____________________ 8 0 75 m Fig. 2 Measured return loss of FRA ~ Introduction: The recently developed ferrite resonator antenna (FRA) [1,2] has demonstrated many of the advantages associated with dielectric resonator antennas . These advantages include small size, large impedance bandwidth, high radiation efficiency, ease of manufacturing and simple feedcoupling mechanisms. In addition, it was shown that the resonance frequency of the FRA can be tuned using a static magnetic field [1,2]. This Letter presents a magnetically switchable LP/CP ferrite disk resonator antenna. The ability of the FRA to switch from linear to circular polarisation by the application of a static magnetic field is demonstrated. 7 0 frequency G H z - - - - for the two polarisations are presented. 6 5 unbiased biased A 1.2kgauss permanent magnet placed parallel to the x-axis was used to bias the FRA, as shown in Fig. I . When the FRA is biased, the resonance frequencies of the degenerate H E , , &modes split. The resonance frequency of the mode with magnetic field parallel to the y-direction decreases while the resonance frequency of the mode with magnetic field parallel to the x-direction increases [1,2]. Fig. 2 shows the return loss response of the biased FRA in which the two split resonance frequencies are clearly observed. Both orthogonal modes are excited because of the tensor nature of the permeability of a biased ferrite, which results in crosscoupling between the two modes . It is known that if an antenna is operated at a frequency in between the resonance frequencies of two nearly degenerate, mutually orthogonal modes, circular polarised radiation can be obtained. This principle has been used in the past to design circular polarised microstrip antennas with a single feed . The circular polarised operation of the antenna reported in this Letter is based on the same principle. angle from boresite s i d e view appiied magnetic blas fields / ground plane Duroid substrate permanent magnet connector Fig. 1 Ferrite resonator antenna geometry FRA dimensions: diameter = 16.0mm, height = 3.0mm Substrate: thickness = 0.64mm, permittivity = 10.2 Slot aperture: length = 6.lmm, width = 1.2mm Ferrite disk resonator antenna: The FRA was made of a ferrite material (TT72-1300 from Trans-Tech, with 4aM, = 1356Gauss and E, = 17.6) which was machined into a disk of circular crosssection with a diameter of 16.0mm and a height of 3.0mm (Fig. I). The FRA was excited using microstrip slot coupling and was operated in the H E , , , mode. When unbiased, the permeability of the ferrite is scalar, thus the FRA behaves as a dielectric resonator antenna. The H E , , s modes of the dielectric disk resonator are degenerate and mutually orthogonal. The two degenerate H E , , , modes radiate like x- and y-directed magnetic dipoles . How- 148 Fig. 3 Measured radiation patterns of unbiased FRA at 7.2GHz ~ copolarised _ _ _ _ crosspolarised ELECTRONICS LE7TERS 2nd February 1995 Vol. 31 No. 3 ~~ ~ ~- ~ '