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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
Fig. 3 E-plane and H-plane radiation patterns of U D R for d = 2mm at
t i ] nic.iwrud
I I I I nie.i,urud
E-plms patiern
H-plans p.,ttcrii
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
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.
circulor polarised
feed line
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.
basis function
T., and NISHIDA. s.: ‘Nonradiative dielectric waveguide
for millimeter-wave integrated circuits’, IEEE Trans., 1981, MTT29. pp. 1188-1 192
’Millimeter-wave integrated circuits using
nonradiative dielectric waveguide’, Electron. Commun. Jpn.. 1991,
74, ( 2 ) , pp. 87-94 (Part 2)
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
discret;sotion grid
Fig. 2 Discrete grid to expand the patch currents in
rooftop basis functions
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 [2] 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.
2nd February 1995 Vol. 31 No. 3
rents and the complex amplitude of the feedline currents. This
matrix is solved easily.
Fig. 3 .Meiisiired ond
c n i i i i ) i i r i ~ diiipur iiiiiiedniice
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
-1 0
0 4
e' e
Fig. 6 ResiiIf am1 w r i i i i i / i . s ~~l r r o rof ~ippro.~~iilili~ioi7
- 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 [3] 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-
2nd February 1995
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.
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
(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
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 [3]).
Switchable LP/CP ferrite disk resonator
A. Petosa, R.K. Mongia, A. Ittipiboon and J.S. Wight
Indexing terms: Dielectric resonators, Dielectric-loaded antennas,
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
coupling aperture
1 (dirnensionsinrnm)
microstrip feed line
8 0
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 [3]. 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
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 [4]. 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 [5]. 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
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 [3]. How-
Fig. 3 Measured radiation patterns of unbiased FRA at 7.2GHz
_ _ _ _ crosspolarised
ELECTRONICS LE7TERS 2nd February 1995 Vol. 31 No. 3
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