mode and shorter for the TM01 mode than that of the same-sizepatch antenna without the notches. Therefore, the resonant fre-quencies of TM10 and TM01 are moved to lower and higherfrequencies, respectively; that is, the frequency ratio of the pro-posed dual-frequency antenna can be controlled by d and w.

3. RESULTS

At the beginning, the square patch antenna without notches wasconstructed as a reference [3]. In this case, the coplanar microstripfeed line is directly connected to the edge of the patch, and themeasured resonant frequencies of ports 1 and 2 are 2450 and 2550MHz, respectively, where the resonant frequency is defined as thefrequency with minimum return loss. The reason why the tworesonant frequencies have such a small difference is that the twoports use different matching designs to obtain 50� input imped-ance. Then, several prototypes of the proposed dual-frequencyantennas with different notch sizes were constructed and mea-sured. Figure 2 shows the measured return loss at each port andisolations between the two ports for the cases of d � 2, 8, and 10mm when w is fixed to be 3 mm. From the results, it can beobserved that the resonant frequencies of ports 1 and 2 have a455-MHz decrease (�19%) and a 90-MHz increase (�3.5%),respectively, when the inset length is increased from 2 to 10 mm.It means the larger the inset length, the higher the frequency ratioof the two resonant frequencies. Comparing to the results of thesame-size square patch antenna without the notches, the frequencyratio is increased from 1.04 to 1.36 when the inset length of thecoplanar microstrip line is 10 mm. In addition, the higher fre-quency ratio of the dual-frequency antenna would reduce thecoupling strength of the two resonant modes, which results in ahigher isolation between the two ports. With regard to the effectsof the notch width w on the resonant frequencies, Figure 3 presentsthe measured return loss and isolation for the three cases of w �3, 5, and 7 mm when d is fixed to be 2 mm. It can be found thatports 1 and 2 have a 40-MHz decrease (�1.7%) and a 25-MHzincrease (�1%), respectively, which are relatively smaller thanthose of the case the inset length was changed. These measuredresults are also summarized in Table 1.

For the prototype with notch dimensions of d � 8 mm and w �3 mm, Figure 4 plots the measured E-plane and H-plane radiationpatterns at 2090 MHz for port 1 and 2630 MHz for port 2. Goodbroadside radiation patterns are obtained, and the peak gains are2.6 and 3.1 dBi for ports 1 and 2, respectively. Cross-polarizationlevels of less than �25 dB in the broadside direction are alsoobserved.

4. CONCLUSION

The design of a dual-frequency microstrip antenna for operation atdifferent frequency ratios has been presented. By adjusting theinset length of coplanar microstrip feed line, the frequency ratio

can be varied from 1.04 to 1.36, and an isolation level of less than�27 dB is also obtained. The antenna’s structure makes it suitableas an array element.

REFERENCES

1. R. Shavit, Y. Tzur, and D. Spirtus, Design of a new dual-frequency anddual-polarization microstrip element, IEEE Trans Antennas Propagat 51(2003), 1443–1451.

2. J.S. Row and C.Y. Ai, A dual-band rectangular patch antenna stackedwith parasitic gridded patch, Microwave Opt Technology Lett 38(2003), 44–46.

3. H. Kim, J. Kwon, Y. Yoon, J. Yoon, and S. Jeon, Dual-feeding micro-strip antenna with high isolation, Microwave Opt Technology Lett 35(2002), 45–47.

4. J.S. Row, Two-element dual-frequency microstrip antenna with highisolation, Electron Lett 39 (2003), 1786–1787.

5. L.I. Basilio, M.A. Khayat, J.T. Williams, and A.L. Long, The depen-dence of the input impedance on feed position of probe and microstripline-fed patch antennas, IEEE Trans Antennas Propagat 49 (2001),45–47.

6. D.M. Pozar, A Reciprocity method of analysis for printed slot andslot-coupled microstrip antennas, IEEE Trans Antennas Propagat 34(1986), 1439–1446.

© 2005 Wiley Periodicals, Inc.

NUMERICAL STUDY OF A PIFA WITHDISPERSIVE MATERIAL FILLINGS

Mikko Karkkainen, Sergei Tretyakov, and Pekka IkonenRadio LaboratoryDepartment of Electrical and Communications EngineeringHelsinki University of TechnologyPO Box 3000FIN-02015 HUT, Finland

Received 14 September 2004

ABSTRACT: The effects of different dispersive material fillings on theinput return loss of a planar inverted-F antenna (PIFA) are explored. Inparticular, we consider magnetic fillings, which allow the resonant fre-quency of the PIFA to be reduced while approximately maintaining therelative bandwidth. Uniaxially anisotropic magnetic fillings are alsoinvestigated and interesting features are revealed. A PIFA with an infi-nite ground plane is numerically studied using finite-difference time-domain (FDTD) method. © 2005 Wiley Periodicals, Inc. Microwave OptTechnol Lett 45: 5–8, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20706

Key words: mobile terminal antennas; FDTD; dispersive materials

TABLE 1 Measured Results of the Proposed Dual-Frequency Antennas with Different Notch Sizes

d w

Port 1 Port 2

Isolation fc2/fc1

fc1

[MHz]BW1

[MHz]fc2

[MHz]BW2

[MHz]

0 0 2450 60 2550 54 �27 dB 1.0412 3 2405 53 2565 55 �27 dB 1.0672 5 2375 52 2575 56 �29 dB 1.0842 7 2365 53 2590 57 �34 dB 1.0958 3 2090 39 2630 82 �34 dB 1.258

10 3 1950 33 2655 80 �37 dB 1.362

fc1 and fc2 respectively denote the center frequencies of ports 1 and 2, and BW1 and BW2 denote 10-dB input-impedance bandwidths

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 45, No. 1, April 5 2005 5

1. INTRODUCTION

The planar inverted-F antenna (PIFA) is a popular antenna inmobile devices because it is compact in size and inexpensive tomanufacture (see, for example, [1, 2, 3]). A more compact size canbe achieved by using various material fillings between the groundplane and the radiating element. However, the relative bandwidthdecreases if dielectric material fillings are used [4]. Magneticmaterials have been found to be useful for reducing the resonantfrequency of PIFAs while approximately retaining the relativebandwidth [5–7]. In these papers, the magnetic material parame-ters were assumed to be dispersion-free and isotropic (modeled bya constant scalar-permeability parameter). However, microwavemagnetic materials that are practically available exhibit a ratherstrong dependence of the permeability upon the frequency, andthey are usually anisotropic. Various designs and correspondingeffective medium models for magnetic materials can be found inthe literature. Since the practical magnetic materials themselveshave a resonant magnetic permeability, the antenna system withsuch a filling becomes a dual-resonant structure whose behaviorcannot be properly understood using a single-resonance model ofthe antenna filled by a nondispersive material. Patch antennas withresonant magnetized ferrite substrates have been studied in [8],where the magnetic filling was used as a means to provide elec-trical control of the resonant frequency and the antenna pattern, butnot as a means to reduce the antenna size.

In this paper, the effective-medium model is used to study theeffect of dispersive magnetic-material fillings upon the perfor-mance of PIFAs. Our FDTD-based results indicate that the reso-nance of the material and the resonance of the radiator tend to beseparate in the sense that it is difficult to merge the two in order toobtain a wideband antenna. This is due to a strong couplingbetween the antenna and the material filling. However, a consid-erable reduction of the resonant frequency is possible if the reso-nance of the material filling is well above the resonance of anempty PIFA. We have also found that the direction of anisotropyof a uniaxially anisotropic material filling has a significant effectupon the antenna characteristics.

2. PIFA GEOMETRY

Consider a single-resonant PIFA with an infinite ground planeformed by a square patch of size 19 � 19 mm. The distance fromthe patch to the ground plane is 7 mm. The shorting strip withwidth 2.5 mm is located at a corner of the patch. The innerconductor of the coaxial feed is located 5.9 mm from the samecorner so that there is a 3.4-mm slot between the shorting strip andthe feed. The thickness of the shorting strip and the diameter of thefeeding probe are 0.5 mm. The geometry of the PIFA is shown inFigure 1. The effect of the ground-plane size is known to be very

critical to the design of PIFAs [9]. In this work, we consider aninfinitely large ground plane in order to eliminate the effect of theground plane and to better see the effect of the material filling onPIFA characteristics.

3. RESULTS

To obtain a good reference for our results with dispersive materialfillings, we start with constant material parameters. Input-return-loss parameters with different constant material parameters areshown in Figure 2(a). The empty PIFA has a resonant frequency of1.98 GHz. An isotropic nondispersive magnetic filling with �r �2 reduces the resonant frequency to 1.64 GHz. The effect of thedispersionless dielectric filling is also shown in the same figure. Inthese examples, matching was not adjusted for various fillings, thatis, all the geometrical parameters are kept the same in all simula-tions. This study will focus on dispersive magnetic fillings. Let usfirst consider an isotropic magnetic material, obeying the Lorentztype dispersion rule with one resonant frequency:

���� � �0�1 ����0m

2

�0m2 � �2 � j�m�� . (1)

Figure 1 Geometry of the PIF antenna under investigation. [Color figurecan be viewed in the online issue, which is available at www.interscience.wiley.com.]

Figure 2 Input-return-loss parameters of the PIFA with (a) constantmaterial parameters and (b) dispersive isotropic material fillings. [Colorfigure can be viewed in the online issue, which is available at www.interscience.wiley.com.]

6 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 45, No. 1, April 5 2005

The numerical scheme used here to implement frequency dis-persion of the material in FDTD is the auxiliary differential equa-tion technique discussed in [10]. Fixing the loss factor �m � 1.0 �109 rad/s, and �� � 0.5, we first explore the effect of the resonantfrequency of the material filling on the S11 characteristics of thePIFA. We choose one resonant frequency which is well above theresonant frequency of the nonfilled PIFA, one which is well below,and two which are close to the resonant frequency of the nonfilledPIFA. The results of these simulations are shown in Figure 2(b),with fr (�0m � 2�fr) denoting the resonant frequency of thematerial filling. It is seen that the resonant magnetic material withfr � 3.0 GHz enables us to reduce the resonant frequency of thePIFA by 20% from 1.98 GHz to 1.58 GHz, while the correspond-ing relative bandwidths (�6 dB) are 11.5% and 11.1%, respec-tively. Hence, smaller antennas can be realized with artificialmagnetic materials, while essentially retaining the relative band-width. This conclusion agrees with the conclusion of [5], obtainedby analytical considerations.

The possibility to merge the resonance of the PIFA and theresonance of the magnetic material has been also investigated.Towards this end, we chose fr � 1.8 GHz and fr � 1.4 GHz. Theresults in Figure 2(b) indicate that the resonant frequency of thePIFA is further decreased to near 1.2–1.4 GHz and the matching atthose frequencies becomes worse. The resonances at higher fre-quencies in the range of 2–3 GHz reflect the resonance of thematerial. The material resonances are shifted to higher frequenciesdue to interactions of the PIFA resonance and the material reso-nances. Thus, merging the two resonances for a wideband PIFA,with acceptable radiation losses at the operation frequencies, doesnot seem to be achievable in this configuration when the filling isso strongly coupled with the antenna field. If the resonant fre-quency of the material filling is well below the resonant frequencyof the nonfilled PIFA (0.5 GHz in our example), there are twodistinctively separated resonances, as expected. The resonance at0.6 GHz is due to the resonance of the filling, while the resonantfrequency at 2.02 GHz is only slightly larger than the resonantfrequency of the nonfilled PIFA. The small difference occursbecause the real part of �r(�) is slightly smaller than 1 (it is about0.95) near 2 GHz.

A practical realization of a magnetic material filling as a densearray of split-ring resonators, also called metasolenoids [11] in theliterature, would exhibit anisotropy. Therefore, we also studyanisotropic material fillings numerically, similarly as above. Theresonant frequency �0m � 2� � 3.0 � 109 rad/s is chosen, basedon simulations with isotropic material filling. The results withdifferent anisotropic fillings are shown in Figure 3. For example,results with dispersive �y have been obtained with constant �x and�z. The loss factor is equal to �m � 1.0 � 109 rad/s and �� � 0.5.Thus, in the range of 1.5–2.0 GHz, the real part of �y is approx-imately 2. It is seen from the results in Figure 3 that the largestreduction in the resonant frequency occurs in the case when �y isdispersive. This result is important, since it suggests how anartificially engineered uniaxially anisotropic material filling shouldbe oriented inside the PIFA in order to attain the largest benefitfrom it. If only �z is dispersive with dispersion similar to that of�y above, the effect on S11 is negligible, as compared with anonfilled PIFA (see Fig. 3). This is expected, since the magneticfields generated by the vertical ( z-polarized) electric currents liepredominantly in the x–y plane.

Losses in the dispersive substrate raise questions about theefficiency of the PIFA. The Wheeler cap technique has beensuccessfully used to measure the efficiency of PIFAs [12, 13]. Theefficiency can also be calculated numerically using the Wheelercap technique. The Wheeler cap is a metal shield that encloses the

antenna. As the shape of the cap does not considerably affect theresults, we choose the simplest cubic cap. The efficiency is givenby

� � 1 �RWC

RFS, (2)

where the RWC and RFS stand for the input resistances at theresonant frequency in the presence of the Wheeler cap and withoutit, respectively. For the isotropic dispersive filling with the param-eters �0m � 2� � 3.0 � 109 rad/s, �m � 1.0 � 109 rad/s, and �� �0.5, the efficiency with the Wheeler cap method using the FDTDis 82%. When the resonant frequency of the material filling wasdecreased to �0m � 2� � 0.5 � 109 rad/s, we obtained tworesonances, as shown in Figure 2(b). However, the resulting an-tenna cannot be interpreted as a dual-resonant radiating system,since the absorption losses at 0.6 GHz are very high. Indeed, theWheeler cap method yields only 3% efficiency at 0.6 GHz, while89% efficiency is reached at 2 GHz. This means that although atthe lower resonant frequency the magnetic material is stronglyexcited, the total magnetic moment of the piece of magneticmaterial does not effectively radiate power in free space. Rather,the power is absorbed in the filling material.

In the case of dispersive and anisotropic filling (with �y dis-persive, �x � �0, and �z � �0), we obtain 86% efficiency. When�x is dispersive, 93% efficiency is reached. Finally, when �z isdispersive, the losses in the substrate are low, hence the higherefficiency of 98%.

4. CONCLUSION

A planar inverted-F antenna (PIFA) with a dispersive magneticmaterial filling has been numerically studied using the FDTDmethod. The results indicate that if the resonant frequency of thefilling material is considerably larger than the resonant frequencyof the empty PIFA, the filling can be used to reduce the antennasize while approximately preserving the bandwidth. The aniso-tropy direction of the filling has been found to have a significanteffect upon the resonant frequency of the PIFA. This result sug-

Figure 3 Input-return-loss parameters for a PIFA with dispersive aniso-tropic material fillings (permeability is assumed to be dispersive along onecoordinate direction at a time, and constant along other directions; thelargest reduction in the resonant frequency is observed when �y is disper-sive and �x and �z are constant). [Color figure can be viewed in the onlineissue, which is available at www.interscience.wiley.com.]

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 45, No. 1, April 5 2005 7

gests that an artificially realized magnetic material should be, onaverage, oriented inside the PIFA.

REFERENCES

1. T. Taga, Analysis of planar inverted-F antennas and antenna design forportable radio equipment, Analysis, design, and measurement of smalland low-profile antennas, K. Hirasawa and M. Haneishi (Eds.), ArtechHouse, Boston, 1992, ch. 5.

2. T. Taga and K. Tsunekawa, Performance analysis of a built-in planarinverted-F antenna for 800 MHz band portable radio units, IEEE J SelAreas Commun SAC-5 (1987), 921–929.

3. Z.D. Liu, P.S. Hall, and P. Wake, Dual-frequency planar inverted-Fantenna, IEEE Trans Antennas Propagat 45 (1997), 1451–1458.

4. Y. Hwang, Y.P. Zhang, G.X. Zheng, and T.K.C. Lo, Planar inverted Fantenna loaded with high permittivity material, Electron Lett 31(1995), 1710–1712.

5. R.C. Hansen and M. Burke, Antennas with magneto-dielectrics, Mi-crowave Opt Technol Lett 26 (2000), 75–78.

6. S. Yoon and R.W. Ziolkowski, Bandwidth of a microstrip patchantenna on a magnetodielectric substrate, Proc IEEE Antennas Propa-gat Symp, Columbus, OH, 2003.

7. H. Mosallaei and K. Sarabandi, Magneto-dielectrics in electromagnet-ics: Concept and applications, IEEE Trans Antennas Propagat 52(2004), 1558–1567.

8. A.D. Brown, J.L. Volakis, L.C. Kempel, and Y.Y. Botros, Patchantennas on ferromagnetic substrates, IEEE Trans Antennas Propagat47 (1999), 26–32.

9. P. Vainikainen, J. Ollikainen, O. Kivekas, and I. Kelander, Resonator-based analysis of the combination of the mobile handset antenna andthe chassis, IEEE Trans Antennas Propagat 50 (2002), 1433–1444.

10. J.L. Young and R.O. Nelson, A summary and systematic analysis ofFDTD algorithms for linearly dispersive media, IEEE Antennas Propa-gat Mag 43 (2001), 72–80.

11. P.M.T. Ikonen, S.I. Maslovski, S.A. Tretyakov, and I.A. Kolmakov,New artificial high permeability material for microwave applications,PIERS 2004, Pisa, Italy, 2004.

12. H.A. Wheeler, The Radian sphere around a small antenna, Proc IRE 47(1959), 1325–1331.

13. S.D. Rogers, J.T. Aberle, and D.T. Auckland, Two-port model of anantenna for use in characterizing wireless communications systemsobtained using efficiency measurements, Proc IEEE AP-S Intl Symp,San Antonio, TX, 2002.

© 2005 Wiley Periodicals, Inc.

CHARACTERISTICS OF TUNABLEHALF-WAVELENGTH RESONATORSWITH ATTENUATION POLES

Shinya Watanabe,1 Kouji Wada,2 Ryousuke Suga,2 andOsamu Hashimoto1

1 College of Science and EngineeringAoyama Gakuin University5-10-1 Fuchinobe, Sagamihara-shiKanagawa, 229-8558, Japan2 Department of Electronic EngineeringThe University of Electro-Communications1-5-1 Chofugaoka, ChofuTokyo 182-8585, Japan

Received 9 September 2004

ABSTRACT: This paper focuses on the characteristics of tunable half-wavelength resonators. We examine four types of tunable half-wave-length resonators: an end-coupling type and three types of tap-couplingresonators. Their calculated and measured results are compared. Theresults show that the expected tunable characteristics of the attenuation

poles and the center frequency are obtained. © 2005 Wiley Periodicals,Inc. Microwave Opt Technol Lett 45: 8–12, 2005; Published online inWiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20707

Key words: tunable half-wavelength resonator; tap-coupling; bandpassfilter; attenuation pole

1. INTRODUCTION

A microwave filter using half-wavelength resonators is one ofmost useful structures for high frequency passive filters. Manyresearchers and engineers are very familiar with this filter structureand its characteristics. Various investigations of bandpass filters(BPFs) have been examined in order to improve the indispensablecharacteristics such as insertion loss, spurious responses, and skirtcharacteristics.

One of the authors has proposed a method for improving skirtcharacteristics by manipulating multiple attenuation poles pro-duced by the filters using tap-coupling half-wavelength resonators[1–3]. Its design methodology is essential for out-of-band im-provement without an increase of the number of elements and acomplicated filter design. In addition, suppression or eliminationof the spurious responses of the filters is also achieved, based onthe same approach.

In this paper, we focus on the behavior of the dominant reso-nant frequency and location of the attenuation poles produced byfour types of tunable half-wavelength resonators as the basis forapplying to tunable filters. The calculation and experiment of theresonance characteristics of the tunable half-wavelength resonatorsare carried out. And then, fabrication and experiment of the reso-nators that have the tunable characteristics are evaluated.

2. TUNABLE HALF-WAVELENGTH RESONATORS

Firstly, we examine the characteristics of tunable half-wavelengthresonators theoretically and experimentally. In this study, an end-coupling resonator and three types of tap-coupling resonators arechosen.

Figure 1(a) schematically shows a circuit model of the tunableend-coupling resonator (Type A). The resonator consists of theresonator section and a series-connected circuit Cdv consisting ofa direct current (DC) decoupling capacitor Cd and a varactor diodeCv. In this case, Cdv is loaded to each open-ended portion of theresonator. Figure 1(b) shows a circuit of the tunable tap-coupling

Figure 1 Schematic circuits of tunable half-wavelength resonators

8 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 45, No. 1, April 5 2005