ACKNOWLEDGMENT

This work was made possible with the support of the Post-doctoralFellowship Program of the Korea Science and Engineering Foun-dation (KOSEF).

REFERENCES

1. K. Hirasawa and M. Haneishi, Analysis, design, and measurement ofsmall and low-profile antenna, Artech House, Boston, 1992.

2. S. Dey and R. Mittra, Compact microstrip patch antenna, MicrowaveOpt Technol Lett 13 (1996), 12–14.

3. K.L. Wong, C.L. Tang, and H.T. Chen, A compact meandered circularmicrostrip antenna with a shorting pin, Microwave Opt Technol Lett15 (1997), 147–149.

4. C.J. Wang and C.F. Jou, Compact meander slot antennas, MicrowaveOpt Technol Lett 24 (1999), 413–414.

5. H.Y. Wang, J. Simkin, C. Emson, and M.J. Lancaster, Compactmeander slot antennas, Microwave Opt Technol Lett 24 (2000), 377–380.

6. K.L. Wong and W.S. Chen, Compact microstrip antenna with dual-frequency operation, Electron Lett 33 (1997), 646–647.

7. C.L. Tang, H.T. Chen, and K.L. Wong, Small circular microstripantenna with dual-frequency operation, Electron Lett 33 (1997), 1112–1113.

8. K.L. Wong and S.C. Pan, Compact triangular microstrip antenna,Electron Lett 33 (1997), 433–434.

9. H.K. Kan and R.B. Waterhouse, Size reduction technique for shortedpatches, Electron Lett 35 (1999), 948–949.

10. E. Lee, P.S. Hall, and P. Gardner, Compact wideband planar monopoleantenna, Electron Lett 35 (1999), 2157–2158.

11. A.K. Shackelford, K.F. Lee, K.M. Luk, and R.C. Chair, U-slot patchantenna with shorting pin, Electron Lett 37 (2001), 729–730.

12. J.S. Row, Patch antenna fed by shorting coplanar microstrip line,Electron Lett 39 (2003), 958–959.

13. J. George, K. Vasudevan, P. Mohanan, and K.G. Nair, Dual-frequencyminiature microstrip antenna, Electron Lett 34 (1998), 1168–1170.

14. S.H. Yeh, K.L. Wong, T.W. Chiou, and S.T. Fang, Dual-band planarinverted F antenna for GSM/DCS mobile phones, IEEE Trans Anten-nas Propagat 51 (2003), 1124–1126.

15. R.B. Waterhouse, Small microstrip antenna, Electron Lett 31 (1995),604–605.

16. Ensemble, Design User’s Guide, Ansoft, 1998.

© 2006 Wiley Periodicals, Inc.

DESIGN OF AN INTERNAL ANTENNAWITH WIDE AND MULTIBANDCHARACTERISTIC FOR MOBILEHANDSET

Hoon Park, Myoung il Kang, and Jaehoon ChoiDivision of Electrical and Computer EngineeringHanyang University17 Haengdang-dong, Seongdong-guSeoul, 133-791, Korea

Received 14 November 2005

ABSTRACT: The development of a small electrical antenna plays animportant role in the rapidly growing mobile communication market.This paper presents the design of a novel small and wideband planarinverted F-antenna that simultaneously covers the GSM900/GPS/DCS1800/DCS1900/IMT2000/WLAN/DMB service bands. A very wideimpedance-bandwidth characteristic was achieved by optimizing boththe distance between the feed line and short strip and the width of ashort strip. The commercial electromagnetic software CST MicrowaveStudio is used to design the structure. The maximum gains at the fre-quencies of 915, 1850, 2025, and 2450 MHz were 1.79, 3.56, 3.65, and1.67 dBi, respectively. The overall radiation pattern is suitable for mo-bile application. © 2006 Wiley Periodicals, Inc. Microwave OptTechnol Lett 48: 947–950, 2006; Published online in Wiley Inter-Science (www.interscience.wiley.com). DOI 10.1002/mop.21528

Key words: internal antenna; multiband antenna; planar inverted-Fantenna (PIFA); wideband antenna

1. INTRODUCTION

Modern portable communication systems have experienced highmarket demand in recent years and the trend is likely to continuein the future. The usage of mobile communications has grownfrom its original applications such as mobile phones, paging andGlobal Positioning System (GPS) to new multimedia applicationssuch as imaging, messaging, wireless computer links, wirelessInternet, and digital mobile broadcasting. To fulfill the demand forthis broad range of applications, modern mobile handsets requireantennas having multiband or wideband impedance bandwidthcharacteristics [1–3]. Furthermore, portable devices such as mobilephones cannot accommodate multiple antennas due to space, size,weight, and cost constraints. A small internal antenna that can beintegrated into the handset offers many advantages over the con-ventional external monopole or helical antenna. Among variousinternal antennas for mobile phones, the planar inverted-F antenna(PIFA) [4–7] is very attractive for mobile handset due to its smalland low-profile structure, simple design, and ease of fabrication.However, one of the principal disadvantages of PIFA is its narrowbandwidth of about 19% for 6-dB return loss requirement [3]. Inthis paper, a novel compact internal PIFA with a very wideimpedance-bandwidth characteristic was designed to operate at thecenter frequencies of 920, 2000, and 2500 MHz at the same time.

The designed antenna simultaneously satisfied the 6-dB return-loss requirement to cover the GSM900 (global system for mobilecommunication, 880–960 MHz), GPS (global positioning system,1574–1577), DCS1800 and DCS1900 (digital communication sys-tem, 1710–1880 MHz and 1850–1990 MHz), IMT2000 (InternalMobile Telecommunication, 1885–2220 MHz), WLAN (wirelesslocal area network, 2400–2483 MHz) and DMB (digital mobilebroadcasting, 2605–2655 MHz) services. In the following sections,a PIFA with wide impedance bandwidth is designed and its return-loss and radiation-pattern characteristics are analyzed.

Figure 5 Simulated and measured antenna gain for operating frequen-cies across the 5-GHz band. [Color figure can be viewed in the online issue,which is available at www.interscience.wiley.com]

DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 48, No. 5, May 2006 947

2. ANTENNA DESIGN

Figure 1 shows the proposed antenna mounted on a ground planewith dimensions of 80 � 36 mm2.

The antenna consists of main patch with slits at the top layer,short strip, feed line, and an additional strip between the mainpatch and ground plane. The main patch and additional strip areconnected by a short strip.

The main patch is coaxially fed through a metallic strip. Theantenna has overall dimensions of 16 mm (length) � 36 mm(width) � 6 mm (height). The main patch structure is located at theleft edge of the ground plane. To obtain the triple resonant fre-quencies, the lengths of the slits and strip are adjusted. The totallength of the main patch and strip is determined for the GSM bandwhile the length of a main patch’s slit is affected for the secondand third resonant frequencies. To achieve the best matching andenhance the bandwidth performance, both the distance between thefeed line and short strip and the width of short strip are optimized.

The optimized design parameters for the proposed antenna areLp1 � 12.8 mm, Lp2 � 3.2 mm, Wp1 � Wp3 � 3 mm, Wp2 �29 mm, Wp4 � 5 mm, Wp5 � 16 mm, Wp6 � 15 mm, Wp7 �31.8 mm, Wp8 � 10 mm, Lg1 � Lg2 � Lg3 � 1 mm, Lp3 � 2.8mm, Lp4 � 8 mm, Lp5 � 13.8 mm, H1 � 6 mm, H2 � 5 mm,Ws � Wf � 2 mm, and Dsf � 10 mm.

3. EXPERIMENT RESULTS

Figure 2 shows the measured return-loss characteristics of theproposed antennas for different values of Wp4 and Wp6 while Wp5

is fixed at 16 mm. As shown in Figure 2, the variation in Wp4 and

Figure 1 Geometry of proposed antenna: (a) top view; (b) side view; (c)3D view. [Color figure can be viewed in the online issue, which is availableat www.interscience.wiley.com]

Figure 2 Measured return-loss characteristics for different values of Wp4

and Wp6

Figure 3 Measured return loss for various values of Wp8

Figure 4 Measured return loss for various distances between the shortstrip and feed

948 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 48, No. 5, May 2006 DOI 10.1002/mop

Wp6 has the largest impact on impedance bandwidth at the secondresonant frequency.

As it is illustrated in Figure 3, it is observed that increasing thelength of Wp8 lowers the resonant frequency at the first and thirdresonant frequencies. It can be seen from Figure 4 that the distancebetween the feed line and short strip has a large impact on resonantfrequency and impedance bandwidth, especially at the second andthird resonant-frequency bands.

Figure 5 shows the measured return-loss characteristics of theproposed antennas with changing the width of a short strip. It canbe seen from this figure 5 that an impedance bandwidth is im-proved at the second resonant-frequency band.

Figure 6 shows the measured return-loss characteristic of theoptimized proposed internal antenna. The measured impedancebandwidths for �6-dB return loss are 90 MHz (880–970 MHz) atthe first resonant frequency band, as large as 700 MHz (1510–2210 MHz) at the second frequency band, and 255 MHz (2400–2655 MHz) at the third frequency band. The measured character-istics meet all the bandwidth requirements for mobile handsetsoperating at the GSM900, GPS, DCS1800, DCS1900, IMT200,WLAN, and DMB bands.

The measured far-field radiation patterns in the y–z and x–zplanes at 915, 1850, 2025, and 2450 MHz are shown in Figure 7.Reasonable radiation patterns are obtained in the y–z and x–zplanes for all frequency bands of interest.

The measured maximum gain has the highest value of 3.65 dBiat 2025 MHz and the lowest value of 1.67 dBi at 2450 MHz, asgiven in Table 1.

4. CONCLUSION

In this paper, a novel broadband PIFA for satisfying the GSM900,GPS, DCS1800, DCS1900, IMT200, WLAN, and DMB servicesat the same time is proposed. The designed antenna is implementedon a ground plane of dimension of 80 � 36 mm2. The measuredresults show that the return-loss characteristics are satisfied in allseven frequency bands and reasonable radiation characteristics areachieved. The proposed antenna is among the best candidates forhandheld application.

ACKNOWLEDGMENT

This work was supported by the Korea Research Foundation undergrant no. KRF-2004-042-D00155.

REFERENCES

1. F.R. Hsiao, H.T. Chen, T.W. Chiou, G.T. Lee, and K.L. Wong, Adual-band planar inverted-F patch antenna with a branch-line slit, Mi-crowave Opt Technol Lett 32 (2002), 310–312.

2. R. Hossa, A. Byndas, and M.E. Bialkowski, Improvement of compactterminal antenna performance by incorporating open-end slots inground plane, IEEE Microwave Wireless Compon Let 14 (2004), 283–285.

3. I. Ang, Y.X. Guo, and M.Y.W. Chia, Compact internal quad-bandantenna for mobile phones, Microwave Opt Technol Lett 38 (2003),217–223.

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

5. K.L. Wong and K.P. Yang, Modified planar inverted F antenna, Elec-tron Lett 34 (1998), 6–7.

Figure 5 Measured return-loss characteristics for various short stripwidths

Figure 6 Measured return loss of the proposed internal antenna

Figure 7 Measured radiation patterns at (a) 915 MHz, (b) 1850 MHz, (c)2025 MHz, and (d) 2450 MHz. — ■ — E�, — � — E� (at y–z plane); —F — E�, — E — E� (at x–z plane). [Color figure can be viewed in theonline issue, which is available at www.interscience.wiley.com]

TABLE 1 Measured Gains

Frequency [MHz] 915 1850 2025 2450

Gain [dBi] 1.79 3.56 3.65 1.67

DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 48, No. 5, May 2006 949

6. W.P. Dou and Y.W.M. Chia, Novel meandered planar inverted-F an-tenna for triple-frequency operation, Microwave Opt Technol Lett 27(2000), 58–60.

7. C.R. Rowell and R.D. Murch, A compact PIFA suitable for dual-frequency 900/1800-MHz operation, IEEE Trans Antennas Propagat 46(1998), 596–598.

© 2006 Wiley Periodicals, Inc.

EQUIVALENT CIRCUIT MODELING OFBROADBAND ANTENNAS USING ARATIONAL FUNCTION APPROXIMATION

Youngwook Kim and Hao LingDepartment of Electrical and Computer EngineeringThe University of Texas at AustinAustin, TX 78712-1084

Received 11 November 2005

ABSTRACT: This paper describes a technique for synthesizing anequivalent circuit for a broadband antenna. A method is proposed forgenerating a rational function approximation with real coefficients inorder to model the input impedance of the antenna in the frequency do-main. An algorithm is then developed to find the best-fit positive-realrational function that is realizable by passive circuits. The technique isapplied to a planar UWB antenna from 3 to 10 GHz. The results showthat a modeling error of 0.59% can be achieved. The Brune’s theoremis used to synthesize an equivalent circuit of the antenna. © 2006 WileyPeriodicals, Inc. Microwave Opt Technol Lett 48: 950–953, 2006;Published online in Wiley InterScience (www.interscience.wiley.com).DOI 10.1002/mop.21529

Key words: rational function approximation; equivalent circuit model-ing; positive real characteristic; Brune’s theorem

INTRODUCTION

Modeling the input impedances of an antenna over a broadbandregion by an equivalent circuit has long been a topic of interest. Asis well known, a simple RLC circuit can be used to model anarrowband antenna over its resonance region. It is not as easy,however, to devise an equivalent circuit over a broadband region.Yet, such an equivalent circuit would have important applications.For example, it would provide insights into the operation anddesign of a broadband antenna, provided that the circuit is closelyrelated to the geometry of the antenna [1]. Second, such anequivalent circuit would be useful in circuit simulations involvingmixed frequency and time domains [2]. Furthermore, an equivalentcircuit would enable simulations of antenna systems that includenonlinear devices, such as amplifier-and-antenna combinations inthe time domain, as with SPICE-like circuit simulators.

To our knowledge, the first practical method to extract anequivalent circuit model of a broadband radiating structure waspresented by Schaubert in 1979 [3]. In the paper, Prony’s methodwas applied to time-domain reflectometer data in order to find arational function with real coefficients. Prony’s method, however,may be susceptible to noise, especially for low-Q systems. More-over, the method requires a considerable amount of data that arefinely sampled in time. Recently, equivalent-circuit models ofbroadband dipoles have been reported [4, 5].

In this paper, we propose an alternative approach to the circuit-modeling problem of the broadband antenna using frequency-domain data from simulations or measurements. While the inputimpedance of an antenna in frequency can be well represented by

a rational function, not every rational function is realizable by apassive circuit. The issue of realizability of a rational function hasbeen fully discussed and well documented in [6]. The positive-real(p.r.) characteristic is a necessary and sufficient condition forrealizability. The conditions of a p.r. function are summarized asfollows.

A rational function with real coefficients is p.r. if and only if:

(a) all poles and zeroes are on the left half-plane;(b) its real part is nonnegative;(c) any j-axis poles are simple and have positive-real residues.

Our approach entails first devising a procedure to obtain arational-function approximation with real coefficients. The stan-dard Cauchy method is a well established technique for finding thecoefficients of the rational-function model [7]. However, the re-sulting coefficients of the rational function are in general complex.In order to find a rational-function representation with real coef-ficients, we divide the equation into its real and imaginary parts.The Cauchy procedure is then applied to arrive at a set of realcoefficients for the model.

To achieve the positive-real characteristic, we generate a num-ber of different rational-function representations by changing themodel parameters, including model order, number of samplepoints, and frequency bands. We then pick the best representationthat is both positive real and the closest approximation to theoriginal impedance data.

Our algorithm is tested using the ultra-wideband (UWB) an-tenna reported in [8], and an equivalent circuit is constructed. Wesynthesize the circuit by using the Brune’s theorem, which resultsin an equivalent circuit with a minimum number of lumped ele-ments. The following sections report the theoretical formulation,the developed algorithm, and the test example.

RATIONAL FUNCTION MODEL WITH REAL COEFFICIENTS

In this section, we describe the proposed method to generate arational function model with real coefficients. As is generallyknown, the input impedance Zin of a radiating structure can beproperly modeled as a summation of poles, which in turn is arational function. Zin can be expressed as follows:

Zin�s� �¥k�0

k�p aksk

¥k�0k�q bks

k �a0 � a1 � s � a2 � s2 � · · · � ap � sp

b0 � b1 � s � b2 � s2 � · · · � bp � sq ,

(1)

where ak and bk are coefficients of the terms in the numerator andthe denominator, respectively. At multiple frequency points sn �j�n, Eq. (1) can be written as

Zin�sn� � �k�0

k�q

bksnk � �

k�0

k�p

aksnk � 0, (2)

where Zin(sn) and snk are complex numbers, while ak and bk are

assumed real. Writing out the complex Zin(sn) and snk explicitly in

term of their real and parts, we obtain

�ZR��n� � j � ZI��n�� � � �k�0

k��q/ 2�

��1�k � b2k�n2k

950 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 48, No. 5, May 2006 DOI 10.1002/mop