FDTD analysis of a slot-loaded meandered rectangular patch antenna for dual-frequency operation

S.-C.Gao, L.-W.Li,T.-S.Yeo and M.-S.Leong

Abstract: The characteristics of a compact, dual-frequency antenna using the slot-loaded meandered rectangular microstrip patch are analysed. The theoretical analysis is based on the finite-difference time-domain (FDTD) method. The FDTD programs are developed and validated by available measurement results. Three different dual-frequency antennas, which include the slot-loaded rectangular patch, the slot-loaded meandered rectangular patch with five slits, and the slot-loaded meandered rectangular patch with,10 slits, are analysed and compared. It is shown that more slits and longer slits could lead to a smaller size of the dual-frequency antenna. The effects of slit lengths on the resonant frequencies and the frequency ratio of the slot-loaded meandered rectangular patch with 10 slits are shown. Several design curves are presented. The electric current distributions on the patch at two resonant frequencies are described, together with the results illustrating the electric field distributions under the patch. The radiation patterns of three dual-frequency antennas are also presented and compared.

1 introduction

Microstrip patch antennas have the well known advantages of low profile, light weight, low cost, conformability, ease of fabrication and integration with R F devices, etc. [14]. Dual-frequency microstrip antennas with a single feed are urgently required in radar and conmunications systems, such as synthetic aperture radar (SAR), dual-band GSMI DCS 1800 mobile communications systems, global posi- tioning system (GPS). Generally speaking, the dual-fre- quency microstrip antennas may be divided into two categories, namely: multiresonator antennas and reactive loading antennas. In the first lund of structure, the dual-fre- quency operation is achieved by means of multiple radiat- ing elements, each supporting strong currents and radiation at resonance. This category includes the multilayer stxked- patch antennas using circular, annular, rectangular, and tri- angular patches [5-71. A multiresonator antenna with coplanar structure can also be fabricated by using aperture- coupled parallel microstrip dipoles [XI. As these antenna structures usually involve multiple substrate layers, they are of high cost. Large size is another drawback of the mul- tiresonator antenna, which makes it difficult for the antenna to be installed in hand-held terminals.

The reactive-loading microstrip patch antenna consists of a single radiating element in which the double resonant behaviour is obtained by connecting co-axial[9] or micros- trip stubs [lo] at the radiating edges of a rectangular patch. This solution cannot allow a frequency ratio higher than 1.2. Higher values of frequency ratio can be obtained by

0 IEE, 2001 IEE Proceedings online no. 20010225 DOL 10.1049/ipmap:20010225 Paper fmt received 24th May and in revised form 6th November 2000 The authors are with the Department of Electrical and Computer Engineering, National University of Singapore, 10 Kent Ridge Crescent, Republic of Singa- pore 119260

IEE Proc. -Microlo. Anteniins P r o p q . , Vol. 148, No. 1. Febiuciry 2001

using two lumped capacitors connected from the patch to the ground plane [ll]. By using multiple shorting pins symmetrically located with respect to the patch axes, dual- band operations can also be realised, as shown in [12]. Another kind of reactive loading can be introduced by etching slots on a patch. The slot loading allows one to strongly modify the resonant mode of a rectangular patch, particularly when the slots cut the current lines of the unperturbed mode. In [13], it is shown that the simultane- ous use of slots and shortcircuit vias, allows to obtain a frequency ratio from 1.3 to 3, depending on the number of vias. Dual-frequency operation of the microstrip antenna with a spur-line filter embedded in the patch has also been reported [14] in which a frequency ratio of -2.0 between the two operating frequencies is shown. In such a dual- frequency scheme, the lower and higher operating frequen- cies are designed, respectively, at the resonant frequencies of a new resonant mode, generated by the perturbation of the embedded spur-line filter in the patch, and the TMol mode. Other dual-frequency antennas with shorting pins, square slot or rectangular slot loading are reported in [ 15-17]. An interesting antenna with dual-frequency opera- tion has been reported in [18], where two parallel narrow slots are etched in the rectangular patch close to its radiat- ing edges. The slot length is chosen to be close to the length of the radiating edge. In the case, the radiating characteris- tics of the antenna operating at the TMol and TMo3 modes are similar and have parallel polarisation planes. Also, these two modes can be excited with good impedance matching using only a single probe feed.

To reduce the size of a dual-frequency antenna, it is shown in [19] that, by meandering the slot-loaded rectangu- lar patch with five slits inset at the nonradiating edges of the patch, the resonant frequencies of the two operating modes can be significantly lowered, with the radiation char- acteristics slightly affected. This indicates that a large reduc- tion of antenna size can be obtained by using the proposed design, as compared with the slot-loaded patch without slits

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previously in [18]. Experimental results of the slot-loaded, rectangular patch with five slits have been presented in [19]. However, to provide more useful information on this antenna, more detailed numerical results based on a full- wave analysis are required, which is the motivation of this paper.

2 Theoretical method of analysis: FDTD method

Three different dual-frequency antennas, which include the conventional slot-loaded rectangular patch proposed in [ 181, the slot-loaded meandered rectangular patch with five slits proposed in [19], and the slot-loaded, meandered rec- tangular patch with ten slits, are studied. Configurations of the three antennas are shown in Figs. 1-3. The slot-loaded microstrip antenna in Fig. 1 consists of a rectangular patch, measuring a x b supported on a grounded dielectric sheet of thickness h and dielectric constant E,.. Two parallel nar- row slots are etched in the rectangular patch close to its radiating edges. The two slots are chosen to have the length 1, and the width w,. For two meandered antennas shown in

Fig. 1 Conventional slot-loaded rectangular patch with no slits

Configurations of dual-jkquency antenna:

Fig. 2 Configuvations of clual-frequency untenna: Slot-loaded meandered rectangular patch with five slits

Fig. 3 Conjguratiom of dual-frequency antenm: Slot-loaded meandered rectangular patch with ten slits

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Figs. 2 and 3, the slot-loaded patch is meandered by inset- ting many slits (five and ten slits in Figs. 2 and 3, respec- tively) of length 1 and width w at the nonradiating edges of the patch. With these slits, the excited surface current paths of the TMol and TMo3 modes are lengthened, which effec- tively lowers the resonant frequencies offal andh3. That is, a reduction in antenna size can be achieved for fixed dual- frequency operation. The feed point is along the central line of the patch length, and the distance between the slot and the radiating edge is s.

2. I To obtain numerical results, we use the FDTD algorithm [2&24]. The first step in designing an antenna with an FDTD code is to grid up the object. A number of parame- ters must be considered in order for the code to work suc- cessfully. The grid size must be small enough so that the fields are sampled sufficiently to ensure accuracy. Once the grid size is chosen, the time step is determined such that numerical instabilities are avoided, according to the cour- ant stability condition.

A Gaussian pulse voltage with unit amplitude, given by:

Outline of the FDTD method

where T denotes the period and to identifies the centre time, is excited in the probe feed. For the feed probe, we use a series resistor R,v with the voltage generator to model the current in the feed probe [17, 241. The series resistor Rs is assumed to be 50Q. To truncate the infinite space, a combi- nation of the Liao's third-order absorbing boundary condi- tions (ABC) and the super-absorbing technique is applied, as in [17, 21-23]. After the final time-domain results are obtained, the current and voltage are transformed to those in the Fourier domain. The input impedance of the antenna is then obtained from:

To get the electric current distributions on the patch and the ground plane, a sinusoidal excitation at probe feed is used, which is given by:

V ( t ) = sin2.rrfot (3 1 where fo denotes the resonant frequency of interest. The field distributions are recorded at one instant of time after the steady state has been reached. In our analysis, the total time for stability is more than six cycles. The electric current distributions on the metal are obtained by the difference between the tangential magnetic fields above and below the metal interface [17, 241. After the field distribu- tion has been obtained, the radiation pattern can be readily calculated by using the near-field to far-field transforma- tion [17, 241.

2.2 Comparisons between calculated and measured results Based on the FDTD algorithm described before, a software package has been developed by us. To verity the FDTD code, we did a lot of simulations and comparisons are made between many sets of theoretical results and meas- ured results available. Here, due to limited space, only one example is shown as follows.

The reflection coefficient of an edge-fed rectangular patch antenna is calculated. The patch has a length of 16.0" and a width of 12.448mm. The substrate has a height of 0.794" and a relative permittivity of 2.2. The results calculated using the present FDTD code and the

IEE PtoL -Microw Antennns Ptopng Val 148, No 1, Febiuary 2001

results measured in [25] are compared in Fig. 4 In general, the measurement confirms the theory over the entire frequency band. Only slight discrepancies between the results are observed, which may be due to numerical errors and the measurement inaccuracies, etc. Two resonance phenomena are shown at 7.6GHz and 18.3GHz, respec- tively, just as expected. Other comparisons are also availa- ble in [17, 231. Generally, we observe a fairly good agreement between these results. From these comparisons, we gain confidence in the present FDTD code. In the following, a numerical study of three dual-frequency micro- strip patch antennas will be performed using the FDTD code.

E 2 -15 2

-20

I -

-

-25 I I I I

5 10 15 20 f, GHz

Fig. 4 Comparisons between calculuted and mea.wed resuh ~ measured

calculated ~~~~

3 antennas

Numerical results of three dual-frequency

3.0

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3. I Resonant frequencies and frequency ratio According to numerical results of the slot-loaded, mean- dered patch antenna with 10 slits, Fig. 5 shows the two resonant frequencies of fb, and fb3 for the TMol and TMo3 modes against different values of slit length 1. The results show that both the resonant frequencies decrease with the increase in the slit length 1, which indicates a larger size reduction with increased slit length. In this calculation, other parameters are fixed as: a = 3 6 m , b = 2 4 m , 1, = 2 2 m , w , ~ = w = lmm, s = 2 m , E,. = 4.4, h = 1.6". When 1 is O m (a conventional slot-loaded, rectangular patch as proposed in [IS]), the two resonant frequencies of

f o l andA3 reach 1.9GHz and 3.62GHz, respectively. The two resonant frequencies are 1.36GHz and 3.01 GHz, when 1 is 8". For the case of 1 = 15" shown here, the frequencyfo, occurs at 0.65GHz, which is only -33"/0 times that of (1.9GHz) the slot-loaded patch without slits (I = 0), and the resonant frequencyfo3 occurs at 1.88GHz, which is -51% times that of (3.62GHz) the slot-loaded patch with- out slits (I = 0). This implies that this dual-frequency design has the advantage of compact size for fixed operating frequencies. To study the effects of more slits, we compare the results of the meandered patch with 10 slits (I = 10") and that with five slits (1 = 10"). For the case of ten slits (1 = lo"), the frequencyfi, occurs at 1.23GHz, which is -88% times that of (1.389GHz) the slot-loaded patch with five slits (1 = lo"), and the resonant frequencyfo3 occurs at 2.68GHz, which is -87% times that of (3.062GHz) the slot-loaded patch with five slits (I = 10"). Other compar- isons of simulation results show similar characteristics. From these, we conclude that more slits could lead to larger reduction of antenna size. It seems that more reduc-

IEE Proc.-Microiv. Antenncrs Propng.. Vol. 148. No. I , Febrirury 2001

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tion of antenna size could be achieved if we increase the slit length further. However, in the 10 slits case studied here, the numerical results show that, when 1 > 15" (0.625 b), it is difficult to find a feed point for exciting two resonant frequencies with good impedance matching. This means there exists a limit for the increase of slit length. We also did a lot of simulations for the antenna with eight slits. Based on our simulation results, we conclude that it is generally easy to obtain good impedance matching at two resonant frequencies at one feed point, when the slit length is less than 0.5 b. Better impedance matching may be obtained by further tuning the width of slits, the positions of slits, the width of parallel slots, or the width of patch. Adding tuning stub is another method for obtaining impedance matching, as previously proposed in [ 181.

t -.-

0 5 10 15 slit length, mm

Fig. 5 Resonunt frequency uguimt slit length for untennu shown in Fig. 3 ./a1

~ ./a3

~~~~

U

c / I'

1.8 I I I I

0 5 10 15 slit length, mm

Fig. 6 Frequency ratio uguinst slit length for antennu shown in Fig. 3

The variation of frequency ratio between two resonant frequencies with respect to different values of slit length is presented in Fig. 6. In this calculation, other parameters of the slot-loaded, meandered patch antenna with ten slits are fixed as those in Fig. 5. The frequency ratio shows a general trend of slow increase with the increase in the slit length, before a small dip occurs near the point of 1 = 10mm. After this small dip, the increase in frequency ratio is more significant. This behaviour provides the present dual-frequency design with a tunable frequency ratio range of 1.9-2.9.

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3.2 Electric fields and current distributions To get a clear picture of the physical mechanism of the slot-loaded meandered patch antenna, it would be helpful if we could know the electric field and current distributions. Figs. 7-12 show the distributions of the electric fields E, at two resonant frequencies for the three different antennas, namely, the conventional slot-loaded rectangular patch ( I = 0) proposed in [ 181, the slot-loaded meandered rectangular patch with five slits ( I = 10") proposed in [19], and the slot-loaded, meandered rectangular patch with 10 slits ( I = 10"). Other parameters of the three antennas are fixed as a = 36mm, b = 2 4 m , 1, = 2 2 m , w , ~ = w = lmm, s = 2mm, E, = 4.4, h = 1.6". In Figs. 7-12, the grid size is

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Fig. 7 Distribution of electric ?Id, Ez ut, resonmzt fiequency I.YGHz fbr untennci in Fig. 1 where observedp m e IS ut height of 1.06mm,fi.oni groundplane

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~ -0.5 N"

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Fig. 8 Distribution,y of electric field E= ut sesonunt ,frequency 3.62GHz Fir utzterim in Fig, 1 whese observedptune is at height of 1.06nitnjbn groundplune

1 .o

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0.5

-1 .o 80

Fig, 9 Distribution of electsic field E, ut reJonmit fiequency 1.38GHz ,for untennci in Fig 2 whese olxervedplune is ut height of 1.06mmji.oin ground plane

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0.5" in both x and y directions. These Ez field distribu- tions are for the region with 14" extension in x on both sides of the patch area, and 16" extension in y on both sides of the patch area. In Figs. 7 and 8, the field distribu- tions for the slot-loaded antenna with no slits are calculated at 1.9GHz and 3.62GHz, respectively. The observed plane is at the height of 1.06" from the ground plane. For the slot-loaded, meandered rectangular patch with five slits (I = 10") in Figs. 11 and 12, these field distributions at reso- nance are calculated at 1.38GHz and 3.06GHz, respec- tively, while for the slot-loaded, meandered rectangular patch with ten slits (1 = 10") in Figs. 11 and 12, these field distributions at resonance are calculated at 1.23GHz

Fig. 10 Distriliution f electric fiekl E, at sesonmt jizpency 3.06GHz for mitennu in Fig. 2 where o servedplcine I S ut height of I.06ninifi.om groimdplune

1 0

$ 0.5 3 c Q - s o W" N"-0 5

-1 0 80

50

Fig. 1 1 Distsilmtion of electric Jeld Ez at resonunt frequency 1.23GHz fbr unteimn in Fig, 3 where observedplune is ut height Ofl.06mmjorn ground plune

0

Fig. 12 Di.striliirti& of electric field E.. L I ~ resonunt fiequency 2.68GHz for cmtennu in fig. 3 d i w ohser~~edplc~ne is (ifheight of I.&innz j ioni groundplune

IEE P r o c - M i c m v . Antennas Propug.> Vol. 148, No. I , Februorji 2001

and 2.68GHz, respectively. Distributions of the electric field E, at two resonant frequencies are quite different from each other. At the TMol mode for three different antennas, the distributions of the electric field Ez are antisymmetric along the centre of patch length, which is in accordance with that of the conventional rectangular patch. The elec- tric field E, has the maximum value near the radiating edges of the patch. The distributions E: at TMo3 mode are more complex than those at the TMo, mode and different from each other in the three antennas. The maximum value seems to occur at points located between two parallel slots etched near the radiating edges. Those distributions at TMo3 mode are also quite different from that of TMo3

1 0

0

r Q

05 - $ 0 c c 2 -05

-1 0 60

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80

Fig. 13 1.9GHz for rmtenna in Fig, I

Distribution of'electric current on patch ut re.sonrrnt,fi.e~/iret7cy J , ut

80

'20 x, width

Fi . I 4 3.8GHzfor crntennri in Hg. I

Distrbution of electric current on putch crt resonm1t,fiegiret7cy J , ut

Fi . I 5 1.33GHzfOr (intennu h Fig. 2

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Distribution of electric current on pcitcli at re.~onrrnt,Ji.ec/ueti1enry J , rrt

mode of the conventional rectangular patch antenna. This means a strong modification of the field distribution by both the etching slots and the narrow slits.

The distributions of the surface currents on the patch at two resonant frequencies are presented in Figs. 13-18, for three different antennas. These distributions in Figs. 13-1 8 are for the region with 4mm extension in x on both sides of the patch area, and 6mm extension in y on both sides of the patch area. The antenna parameters and calculated fre- quencies are same as those in Figs. 7-12. The distributions of J , (i.e. the co-polar current component) are presented. As expected, the current distributions are quite different from each other due to the modification by the etching

1 0 -

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Fig. 1 7 1.23GI-lz,for uuteunu in Fig 3

Distrilxition of electric current on pcrtcli ot ~ ~ S O I Z L I I Z ~ ,fieguency J,, at

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2 0 5 - a, U

80

slots and the slits. The current distributions become more complex when more slits are added. The magnitude of .Iy (i.e. the cross-polar current component) is also symmetric with respect to the patch centre, but out of phase on two sides. The current distributions on the ground are also cal- culated, but omitted here for brevity. The current distribu- tions on the ground plane seem to be the image of the current distributions on the patch.

3.3 Radiation patterns The radiation patterns of three antennas at two resonant frequencies f o , and f o 3 are shown in Figs. 19-22, respec- tively. Fig. 19 shows the comparisons of E-plane radiation patterns among three antennas resonant at the TMol mode, where the parameters of three antennas are same as those in Figs. 7-12. These patterns are calculated at 1.9GHz, 1.38GHz and 1.23GHz, respectively. It is seen that the radiation patterns are broadened in the E plane when the more slits are added in the nonradiating edges. Fig. 21 shows the comparisons of E-plane radiation patterns among three antennas resonant at the TMo3 mode, where the parameters of three antennas are also same as those in Figs. 7-12. These patterns are calculated at 3.62GHz, 3.06GHz and 2.68GHz, respectively. Again, it is seen that the radiation patterns are broadened in the E plane when the more slits are added in the nonradiating edges. Accord-

0-

-2

-4 -

-6- g g -8- P c g-io - F

-12

-14 -

-

-100 -80 -60 -40 -20 0 20 40 60 80 100 deg.

Fig. 19 ~ Antenna in Fig. 1 ~~~- antenna in Fig. 2 . . . . . . . . . . antenna in Fig. 3

Rudiationpatterns for three untentiiis at&,: E p h e

0 -

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-4

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g -8-

-

m

g P g - I O - E

-12

-14

-

-100 -80 -60 -40 -20 0 20 40 60 80 100 deg.

Fig. 20. Radiation patterns for three antennas at.6,: H plane ~ Antenna in Fig. I _ _ - _ antenna in Fig. 2 , , . . . . . . , . . antenna in Fig. 3

ing to the numerical results, slightly broadening of radia- tion pattern in the H plane is also found. However, in the cases studied, the extent of broadening at Jil is so small in the H plane that they seem to coincide, as shown in the Fig. 20.

deg. Fig. 21 Radiation puttenis for tl7ree otztennas i i t j & : Eplane

Antenna in Fig. I ~ ~ _ . , . . . . . .

a

-2

-4

-6 m

g B -a

.5 -1 0

U

U !!

-1 2

-14

antenna in Fig 2 antenna in Fig. 3

-1 6 -100 -80 -60 -40 -20 0 20 40 60 80 100

deg.

Fig. 22 ~ Antenna in Fig. 1

anleniia in Fig. 2 antenna in Fig. 3

Rndiution patterns jbr tliree antennas at, f&: Hplane ~~~- , . . . . . . , . . .

4 Conclusions

Based on the FDTD method, the characteristics of the slot- loaded, meandered rectangular patch with many slits inset at nonradiating edges are analysed. First, the FDTD code is developed and verified by available measurement results. As the slot-loaded meandered rectangular patch with many slits can achieve both a small size and dual-frequency oper- ation, it is very promising for many practical applications. The variations of two resonant frequencies and the frequency-ratio with respect to different slit lengths are illustrated and discussed. It is shown that the increase of slit length and adding more slits are two very effective ways of reducing the size of dual-frequency antenna. The present dual-frequency design using the slot-loaded, meandered rectangular patch with 10 slits can obtain a tunable frequency ratio range of 1.9-2.9. The electric field distribu- tions, and current distributions on the patch at two reso- nant frequencies for three different antennas, which include the conventional slot-loaded rectangular patch, the slot- loaded meandered rectangular patch with five slits, and the

I E E Proc.-Microiv. Anrenizrrs Propug,, Vol. 148, No. 1, Fcbruciry 2001 70

slot-loaded meandered rectangular patch with 10 slits, are presented and compared. Finally, radiation patterns in the E- and H-planes for three antennas at two resonant frequencies are given. It is shown that the E-plane patterns are broadened with the adding of more slits. Detailed numerical results are presented, which are useful for practi- cal antenna designs. Compared with other techniques of realising compact antenna (i.e. using high dielectric constant material or adding shorting pins) the slot-loaded meandered rectangular patch antenna has advantages of low cost and ease of fabrication.

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