In the simulation, the patch arrays are excited at the workingfrequency of f � 146.7 MHz. Figure 6 shows the radiation patternsin the xy-plane with the elevation angle of 10° and also theradiation patterns in the yz-plane, when both arrays are radiatingbroadside. The radiation patterns when only the 5-by-5 array isexcited with the main beam steered 45° away from the broadsideto the ship’s bow is shown in Figure 7. Furthermore, the mutualcoupling between two patch arrays at the presence of the battleshipis studied numerically using the FETI-DPEM algorithm, where the5-by-5 array radiates broadside and the 3-by-3 array operates in thereceive mode. The scattering parameters are calculated first byexciting one antenna in the transmit array at a time, and thenormalized voltages defined in (1) observed at each of the 3-by-3receive patches are then calculated from the scattering parameters,whose magnitudes and phases are shown in Figure 8. The totalnormalized power coupled from the transmit array to the receivearray for each receive array scan angle is calculated using thefollowing:

PUrVr � ��m�1

3 �n�1

3

Vmne�jk0ndxUre�jk0mdy�Vr� 2

(3)

and shown in Figure 9, where dx� � 100 cm and dy� � 77.6 cm arethe center-to-center distances between adjacent patches in the x�-and y�-directions as shown in Figure 5(b), and Ur � sin �r cos�r

and Vr � sin �r sin �r are the parameters related to the receive scanangle defined in the same primed coordinates. In the simulation,the second-order absorbing boundary condition is applied on thetruncation surface that is 6 m away from the metallic surface. Thecomputational domain is automatically partitioned into 204 sub-domains, which yields a total number of 1.1 � 107 finite-elementunknowns and 1.1 � 106 dual unknowns. In total, a wall clocktime of 5 h is required to calculate all the scattering parametersusing 68 processors.

4. CONCLUSIONS

The FETI-DPEM method has been applied to the full-wave anal-ysis of mutual coupling between antenna arrays, where the geo-metrical repetition associated with the antenna array has been fully

utilized to reduce the computation time and memory requirements.For general antenna arrays without geometrical repetitions, thefull-wave simulation has been accelerated through parallel com-putation implemented on a distributed-memory system using MPI.Examples have been presented, and the array mutual coupling atthe presence of a platform has been characterized using the re-ceived voltage and power at one array due to the scanning oper-ation of the other array.

ACKNOWLEDGMENTS

This work was supported by a grant from the Air Force Office ofScientific Research via the MURI Program under contract numberFA9550-04-1-0326.

REFERENCES

1. J.M. Jin, Z. Lou, Y.J. Li, N. Riley, and D. Riley, Finite element analysisof complex antennas and arrays, IEEE Trans Antennas Propag 56(2008), 2222–2240.

2. C. Smith, M. Little, B. Porter, and M.N. Vouvakis, Analysis of co-planar array coupling using finite-element domain decomposition, IEEEAP-S Int Symp Dig, Honolulu, HI (2007), 3524–3527.

3. S. Raffaelli, Z. Sipus, and P.S. Kildal, Analysis and measurements ofconformal patch array antennas on multilayer circular cylinder, IEEETrans Antennas Propag 53 (2005), 1105–1113.

4. Y.J. Li and J.M. Jin, A vector dual-primal finite element tearing andinterconnecting method for solving 3-D large-scale electromagneticproblems, IEEE Trans Antennas Propag 54 (2006), 3000–3009.

5. Y.J. Li and J.M. Jin, A new dual-primal domain decomposition ap-proach for finite element simulation 3-D large-scale electromagneticproblems, IEEE Trans Antennas Propag 55 (2007), 2803–2810.

6. J.P. Webb, Hierarchal vector basis functions of arbitrary order fortriangular and tetrahedral finite elements, IEEE Trans Antennas Propag47 (1999), 1244–1253.

7. Z. Lou and J.M. Jin, Finite element analysis of phased array antennas,Microwave Opt Technol Lett 40 (2004), 490–496.

8. Y.J. Li and J.M. Jin, Simulation of photonic crystal nanocavity using theFETI-DPEM method, Microwave Opt Technol Lett 50 (2008), 2083–2086.

9. Y.J. Li and J.M. Jin, Parallel implementation of the FETI-DPEMalgorithm for general 3D EM simulations, J Comput Phys, in press.

© 2009 Wiley Periodicals, Inc.

AN ULTRA-WIDEBAND BANDPASSFILTER HAVING SHARP SKIRTPROPERTY AND LARGEATTENUATIONS IN ITS STOPBAND

Koji Watanabe,1 Zhewang Ma,1 Chun-Ping Chen,2 andTetsuo Anada2

1 Graduate School of Science and Engineering, Saitama University,Saitama 338-8570, Japan; Corresponding author: ma@ees.saitama-u.ac.jp2 High-Tech Research Center, Kanagawa University, Kanagawa-ku,Yokohama, Japan

Received 3 December 2008

ABSTRACT: An ultra-wideband (UWB) bandpass filter having amidband frequency of 4.1 GHz and a fractional bandwidth of 34.1%is developed to meet Japan’s UWB low-band spectrum limit. To getsharp skirt property near the passband and large attenuations over awide stopband, a microstrip stub-loaded ring resonator and parallel-coupled stepped-impedance two-mode resonators are used simulta-neously, and their advantages are fully exploited. Both the simulated

Figure 9 Normalized received power (unit in dB) as the function of thescan angle of the 3-by-3 receive array with the 5-by-5 transmit arrayradiating broadside

DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 51, No. 9, September 2009 2093

and measured frequency responses of the filter satisfy well Japan’slow-band spectrum limit. © 2009 Wiley Periodicals, Inc. MicrowaveOpt Technol Lett 51: 2093–2097, 2009; Published online in WileyInterScience (www.interscience.wiley.com). DOI 10.1002/mop.24557

Key words: bandpass filter; UWB; microstrip line; ring resonator; two-mode resonator

1. INTRODUCTION

The Federal Communications Commission (FCC) of the UnitedStates released the frequency band 3.1–10.6 GHz for ultra-wide-band (UWB) communications in 2002. On the other hand, differ-ent regulations on UWB systems are chosen in Europe and Japan,respectively, to avoid interference with existing or other futurewireless systems. In Japan, the frequency bands 3.4–4.8 GHz(low-band) and 7.25–10.25 GHz (high-band) are allocated forUWB applications. Although the bandwidth of both Japan’s low-band and high-band is smaller than that of FCC’s regulation, muchsteeper attenuations near the passband and larger attenuations inthe stopband are required according to Japan’s spectrum mask forUWB systems.

Many articles on UWB filters developed based on FCC’s UWBspectrum mask are available now. Typical examples include filtersdesigned using microstrip stub-loaded ring resonators [1–5] andfilters using microstrip stepped-impedance multimode resonators[6–10], as well as one with a hybrid of microstrip and coplanarstructure [11]. However, up to now, there has been no report onUWB filters that meet Japan’s UWB limit because of the criticalrequirements on the attenuation properties of the filters.

In this article, based on Japan’s UWB low-band spectrummask, a novel UWB bandpass filter (BPF) is developed. The filterhas a midband frequency of 4.1 GHz and a fractional bandwidth of34.1%. A microstrip stub-loaded ring resonator and stepped-im-pedance two-mode resonators are used simultaneously. The stub-loaded ring resonator features in sharp attenuations because of thetransmission zeros produced very close to the passband. Theparallel-coupled stepped-impedance two-mode resonator has avery wide passband and monotonously increasing attenuations inthe stopband. These advantages are fully extracted in the design,

and sharp skirt property near the passband and large attenuationsover a wide stopband of the filter are obtained.

2. MICROSTRIP STUB-LOADED RING RESONATOR

Figure 1 shows the configuration of a microstrip square ringresonator loaded with two open stubs. The ring is one wavelength(�) long at the center frequency of the low-band and has a char-acteristic impedance of Z1. The open-stubs, having a characteristicimpedance of Z2, are chosen here 3/4 wavelength long so that thepassband bandwidth of the ring resonator is close to that of thelow-band [3–5]. Both the input and output lines of the resonatorhave a characteristic impedance of Z0.

The resonator is bisected into two halves by the broken diag-onal line shown in Figure 1 because of the symmetry of the circuit.Then, only half of it needs to be analyzed based on the even- andodd-mode method [3]. Figures 2(a) and 2(b) show the equivalenttransmission line models of the resonator in the case of even- andodd-mode excitations, with open- and short-terminals at the sym-metrically bisected planes, respectively.

Analysis of the transmission line models in Figures 2(a) and2(b) results in the following equation, which relates the electricallength � at which the transmission zeros occur, and the impedanceratio a � Z1/Z2 of the ring and the open stubs of the resonator [3].

tan� � ��(6�3a)��9a2�28a�36

2a(1)

Formula (1) reveals that the electrical length � at which thetransmission zeros occur is only determined by the impedanceFigure 1 Configuration of a microstrip stub-loaded ring resonator

Figure 2 Equivalent transmission line models of the stub-loaded ringresonator in the case of (a) even-mode excitation and (b) odd-modeexcitation

2094 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 51, No. 9, September 2009 DOI 10.1002/mop

ratio, a � Z1/Z2, of the ring and the open stubs. Figure 3 shows thevariation curves of the transmission zeros versus the impedanceratio a, which are calculated using Eq. (1). It is seen that fourtransmission zeros occur in the range 0� � ��, with 0 � �L1, �L2

� �/2/2 and �/2 � �H1, �H2 � �. This means that two transmis-sion zeros appear on the lower and upper sides of the passband,respectively. The passband is formed between the two transmis-sion zeros, � L2 and ��1. When a is varied from 0.5 to 3.3, thebandwidth of the passband increases from about 32 to 55%. Basedon the results described earlier, a stub-loaded ring resonator isdesigned following Japan’s low-band spectrum mask. The mid-band frequency is 4.1 GHz, and the bandwidth between the twotransmission zeros is 34.1%. A substrate with a dielectric constantof 9.7 and a thickness of 0.635 mm is used, and the geometricalparameters are shown in Figure 4. A small square perturbationpatch is added to one corner of the ring so that the ring becomesa dual-mode resonator, and each of the transmission zeros near thepassband splits into two transmission zeros, respectively, as shownby the frequency response in Figure 5, which is obtained by usinga full-wave electromagnetic simulator, Sonnet em [12]. The curvesin Figure 5 reveal that the passband covers the desired 3.4–4.8GHz, but both the lower and upper stopbands are very narrow.

3. PARALLEL-COUPLED SIR FILTER

A microstrip parallel-coupled stepped-impedance resonator (SIR)is a cascade of high-, low-, and high-impedance lines that couplesto the input/output feeds through parallel lines. With appropriatechoose of the high and low impedance ratio Z1/Z2, we can getdesired wide passband. Detailed description on the design methodof UWB filters using parallel-coupled multiple-mode SIRs can befound in [6–10].

In this article, a folded two-degree BPF consisting of two-modeSIRs is designed to meet Japan’s low-band spectrum mask. Figure6 shows the configuration of the BPF, where the parallel-coupledhigh-impedance lines are folded to make the circuit size small. Thefrequency response of this filter, simulated by Sonnet em, is drawn

in Figure 7. It is seen that large attenuations in the stopband areobtained, which satisfy Japan’s low-band spectrum mask except atfrequencies nearing the passband.

4. UWB BPF CONSISTING OF A RING RESONATOR ANDTWO SIRS

The aforementioned investigations show that the ring resonatorloaded with 3�/4 open stubs has sharp attenuations near its pass-band, but its lower and upper stopbands are very narrow. On theother hand, the parallel-coupled SIR filter exhibits large attenua-tions in its stopband, but the rate of attenuations near the passbandis slow. Then, a novel UWB bandpass filter is proposed, which, asshown in Figure 8, is configured by cascading the stub-loaded ring

Figure 3 Variation of the transmission zeros of a stub-loaded ringresonator versus the impedance ratio a. [Color figure can be viewed in theonline issue, which is available at www.interscience.wiley.com]

Figure 4 A stub-loaded dual-mode ring resonator having the desiredpassband bandwidth

Figure 5 Simulated frequency response of the ring resonator. [Colorfigure 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. 51, No. 9, September 2009 2095

resonator with two SIRs. The geometrical dimensions are basicallythe same as those designed in sections 2 and 3, but some adjust-ments are made to reduce return loss in the passband. Figure 9shows a photograph of the fabricated filter. In the EM simulationof the filter, we can take into accounts of the conductor anddielectric losses, respectively, by using a conductivity of 58 � 106

S/m for the metallic films of the microstrip lines and a loss tangentof 0.003 for the substrate. Radiation loss is also included in thesimulation by removing shielding box from the filter. The simu-lated and measured frequency responses of filter are shown inFigure 10(a). It is seen that the desired wide passband is obtained,

and the simulated and measured return loss within the passband arelarger than 15 dB. The simulated insertion loss within the passbandis about 1.6 dB, and the measured about 2.8 dB. Sharp attenuationsnear the passband and wide stopbands with attenuations larger than30 dB are achieved. Japan’s low-band spectrum mask is alsodrawn in Figure 10(a) for a comparison, and it is met quite wellover a very wide frequency range.

The simulated group delay of filter is drawn in Figure 10(b) andis less than 2 ns within the passband.

5. CONCLUSIONS

A novel UWB bandpass filter is developed by taking advantages ofboth the microstrip stub-loaded ring resonator and two-mode SIRs,to satisfy Japan’s low-band spectrum limit for UWB applications.The measured frequency response of the designed filter agrees well

Figure 6 Configuration of a folded two-degree UWB BPF using micro-strip parallel-coupled two-mode SIRs

Figure 7 Simulated frequency response of the two-degree BPF shown inFigure 6. [Color figure can be viewed in the online issue, which is availableat www.interscience.wiley.com]

Figure 8 Configuration of a new UWB BPF using a stub-loaded ringresonator and two SIRs

Figure 9 Photograph of the fabricated UWB BPF. [Color figure can beviewed in the online issue, which is available at www.interscience.wiley.com]

2096 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 51, No. 9, September 2009 DOI 10.1002/mop

with the simulated one and shows sharp skirt property near thepassband and large attenuations over a wide stopband.

ACKNOWLEDGMENTS

This work is supported in part by the Grant-in-Aid for ScientificResearch (KAKENHI 17560303) from the Japan Society for thePromotion of Science, in part by the High-Tech Research CenterProject from the Ministry of Education, Culture, Sports, Science,and Technology, Japan.

REFERENCES

1. L.H. Hsieh and K. Chang, Compact, low insertion loss, sharp rejectionwideband bandpass filters using dual-mode ring resonators with tuningstubs, Electron Lett 37 (2001), 1345–1347.

2. L.H. Hsieh and K. Chang, Compact, low insertion-loss sharp-rejection,and wide-band microstrip bandpass filters, IEEE Trans MicrowaveTheory Tech 51 (2003), 1241–1246.

3. P. Cai, Z. Ma, X. Guan, Y. Kobayashi, and T. Anada, Novel compactmicrostrip dual-mode ring resonator wideband bandpass filter withsignificantly Improved stopband property, IEICE Trans ElectronE89-C (2006), 1858–1864.

4. P. Cai, Z. Ma, X. Guan, Y. Kobayashi, T. Anada, and G. Hagiwara,Compact millimeter-wave ultra-wideband bandpass filter using dual-mode ring resonator and multiple-mode parallel-coupled line structure,Asia-Pacific Microwave Conf Proc 1 (2006), 163–166.

5. Z. Ma, P. Cai, X. Guan, Y. Kobayashi, and T. Anada, A novelmillimeter-wave ultra-wideband bandpass filter using microstrip dual-mode ring resonators loaded with open tuning stubs of differentlengths, IEEE MTT-S Int Microwave Sym Dig WE3E-03 (2007),743–746.

6. L. Zhu, S. Sun, and W. Menzel, Ultra-wideband (UWB) bandpassfilters using multiple mode resonator, IEEE Microwave Wireless Com-pon Lett 15 (2005), 796–798.

7. C. Quendo, E. Rius, and C. Person, An original topology of dual-bandfilter with transmission zeros, IEEE MTT-S Int Microwave Symp Dig,Philadelphia, PA (2003), 1093–1096.

8. L. Zhu and H. Wang, Ultra-wideband bandpass filter on aperture-backed microstrip line, Electron Lett 41 (2005), 1015–1016.

9. P. Cai, Z. Ma, X. Guan, Y. Kobayashi, T. Anada, and G. Hagiwara,Synthesis and realization of novel ultra-wideband bandpass filtersusing 3/4 wavelength parallel-coupled line resonators, Asia-PacificMicrowave Conf Proc WE3B-3 (2006), 159–162.

10. C.-P. Chen, Z. Ma, N. Nagaoka, and T. Anada, Synthesis of ultra-wideband bandpass filter employing parallel coupled SIRs of one-wavelength, Proc 37th Eur Microwave Conf EuMC42–4 (2007), 787–790.

11. K. Li, UWB bandpass filter structure, performance and application toUWB pulse generation, Asia-Pacific Microwave Conf Dig, Suzhou,China (2005), 79–82.

12. Sonnet suite, ver. 9.52, Sonnet Software, Liverpool, NY, 2004.

© 2009 Wiley Periodicals, Inc.

FABRICATION OF A POLYMER CPWELECTRO-OPTIC MODULATOR USINGA STRIP-LOADED WAVEGUIDESTRUCTURE

Weinan Gao, Jie Sun, Xiaoqiang Sun, Yunfei Yan, Lei Gao,and Daming ZhangState Key Laboratory on Integrated Optoelectronics, College ofElectronic Science and Engineering, Jilin University, Changchun130012, People’s Republic of China; Corresponding author:gaoweinan0602@yahoo.com.cn

Received 9 December 2008

ABSTRACT: In this letter, the successful demonstration of a coplanarwaveguide (CPW) Mach-Zehnder (MZ) electro-optic (EO) modulatorusing a strip waveguide structure is described and fabricated. The EOactive hybrid material is synthesized by sol–gel process. A large EOcoefficient of r33 � 50 pm/V with a long-term stability at 80°C for 200 hwas gained. It also has a controllable refractive index and permits ahigh-loading concentration. A simple and easily fabricated strip-loadedwaveguide structure is designed and demonstrated to utilize the EO ma-terial, which is suitable to reduce the coupling loss with optical fiber.The measured half wave voltage (V� ) of the CPW MZ modulator is

Figure 10 Simulated and measured frequency response of the novelUWB filter taking into accounts of losses. (a) Wideband amplitude re-sponse. (b) Group delay around the passband. [Color figure can be viewedin the online issue, which is available at www.interscience.wiley.com]

DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 51, No. 9, September 2009 2097