A Dual Wideband Filter Design Using Frequency Mapping and

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 56, NO. 12, DECEMBER 2008

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A Dual Wideband Filter Design Using Frequency Mapping and Stepped-Impedance Resonators An-Shyi Liu, Ting-Yi Huang, and Ruey-Beei Wu, Senior Member, IEEE

Abstract—A dual-wideband filter design implemented by stepped-impedance resonators, which involves the frequency mapping approach, is presented in this paper. The dual-band filter can be divided into two parts: the wideband virtual passband filter and the narrowband virtual stopband filter. Both filters are designed by conventional synthesis methods, under the assumption that the common connecting lines serve as J- and K-inverters simultaneously. The basic building resonators formed by paralleling open- and shorting-stubs are implemented by unbalanced stepped-impedance resonators, exhibiting the desired resonating frequencies and susceptance slope parameters at these two bands. Two filters are tested to validate this design. Index Terms—Dual-band filter, frequency mapping, slope parameters, stepped-impedance resonator.

I. INTRODUCTION ITH THE recent increase in applications for wireless and satellite communications, microwave filter designs have garnered a great deal of attention from both the wireless industry and academy. The microwave filter is the key component in the front-end of communication systems that reject unwanted signals. Planar filters, which are implemented by a microstrip, possess the properties of compact size, low cost, flexible layout, and easy fabrication. Because of these traits, they are preferred for integration in low-power transceiver systems. Conventional microwave filter design procedures suitable for single-band operation have been discussed in previous studies, e.g., [1] and [2]. In recent years, microwave filters with dual-band or multiband characteristics have become popular because of the demand of multichannel wireless communications. Different design procedures have been proposed in [3]–[27]. One general approach is to cascade a wideband passband filter and a narrowband stopband filter using Z-transform synthesis for dual-passband response, as can be seen in [3]. This design occupies a larger circuit size. Another straightforward approach is to optimize both the physical dimensions and the structures of the designed filter to meet the required dual-band specifications noted in [4] and [5]. This kind of optimization approach, which can be regarded as simplified genetic algorithm-programming (GA-P)

W

Manuscript received April 23, 2008; revised July 25, 2008. First published November 18, 2008; current version published December 05, 2008. This work was supported in part by the National Science Council under Grant NSC 96-2219-E-002-017 and by the Excellent Research Projects of National Taiwan University under Grant 97R0062-03. The authors are with the Department of Electrical Engineering and Graduate Institute of Communication Engineering, National Taiwan University, Taipei, Taiwan 10617 (e-mail: [email protected]; [email protected]; [email protected]). Digital Object Identifier 10.1109/TMTT.2008.2007357

[6], lacks design guides during the optimization process. Currently, microwave filter designs using the coupling matrix are very popular for dual-band or multiband applications. These approaches are divided into two categories. One is to find the suitable coupling matrix so that the dual-band or multiband response is created by placing transmission zeros within the bandwidth of a wideband filter [7]–[13]. The other is to implement the dual-band or multiband stepped-impedance resonators (SIR) and find suitable coefficients and external quality factors at the desired bands simultaneously [14]–[16]. The former usually requires an initial estimation of coupling coefficients because of the optimization process. In addition, the implementation requires a sufficiently large coupling coefficient to cover the complete set of dual passbands. The latter may present complications in implementing dual wideband passband responses because the coupling coefficients obtained are only applicable for narrowband. Some systematic procedures for designing dual-band filters, either on the basis of the dual-band inverter [17], [18] or the frequency mapping between a single-band and a dual-band response [19]–[21], was proposed. The dual-band inverter technique alone with the dual-band resonator leads to the bandwidth reduction problem [17] owing to the band-limit of the dual-band inverter. Another approach using the frequency mapping technique is suitable for narrow dual-band filter design. To our knowledge, the dual wideband counterpart has not been proposed at this time. The ultra-wideband (UWB) technology on wireless communication applications calls for the operation frequency band ranging from 3.1 to 10.6 GHz. When considering the interference from the wireless local area network (WLAN), the desired UWB filter is required to provide the capability of rejection band from 5 to 6 GHz [22]. Therefore, the dual-wideband passband filter integrated into the system is more suitable. Several compact designs have been proposed in [23]–[27]. However, these filters appear have a narrow rejection band and poor passband return loss. This paper proposes a systematic design procedure of a dual-wideband passband filter using the frequency mapping approach of the dual-band filter design [19]. Due to the wide passband response, the stub-type filter is chosen as the desired topology. Section II describes the design procedure of the dual wideband passband filter with the Chebyshev response. Section III discusses the characteristics of the step-impedance resonator as a dual- band resonator. Section IV reports the experimental and theoretical results of dual wideband passband filters, which show good agreement. Section V concludes the paper.

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Fig. 2. Schematic of dual-passband filter. (a) Prototype equivalent circuit. (b) Tx-line circuit.

Fig. 1. Frequency response of: (a) a Chebyshev low-pass filter and (b) a Chebyshev dual-passband filter.

II. DESIGN PROCEDURE OF DUAL-PASSBAND FILTER WITH CHEBYSHEV RESPONSE A. Mapping Function for Dual-Passband Filter The dual wideband passband filter can be divided into two parts: the wideband virtual bandpass filter (VBPF) and the narrowband virtual bandstop filter (VBSF). Both the wideband VBPF and the narrowband VBSF can be designed by the synthesis method [1]. In order to be specific, we consider the classical all-pole Chebyshev prototype of order n for the filter synthesis. Fig. 1(a) shows its normalized frequency response, while the desired de-normalized frequency response of the dual passband filter is shown in Fig. 1(b). By modifying the frequency mapping approach [19], a suitable mapping function from the frequency transformation of a low-pass response to the dual passband can be written as

(1)

where is the radian frequency, is the normalized radian freand are fractional bandwidth quency, the parameters and are those and center frequency of the VBPF, while of the VBSF, respectively. They can be related to the radian freand which define the dual quencies and , passbands, e.g., while the exact relations have been derived in [19]. This transformation is practical to use with dual-band resonators, implemented by paralleling shunt and series LC resonators, as shown in Fig. 2(a). The shunt LC resonators, which realize the wideband VBPF, can be implemented by the shorting-stub filter [1], while the series LC resonators for implementing the narrowband VBSF could be obtained with open-stubs [1]. With proper selection of the first and last resonators, the first and last J-inverters in Fig. 2(a) can be neglected. As a result, the prototype equivalent circuit can be realized by the Tx-line circuit shown in Fig. 2(b). The connecting lines between the parallel open- and shorting- stubs perform as the J-inverters of the dual-passband filter shown in Fig. 2(a). , , , After the evaluation of the four parameters , the transformation of the radian frequency to the and normalized radian frequency can be obtained by (1). For the required passband ripple dB and the minimum stopband dB at , the filter order with the Chebyattenuation shev response is illustrated as

(2)

B. Wideband VBPF Design The design approaches of various BPFs are discussed in [1] and [2]. One appropriate topology for wideband VBPF is shown conin Fig. 3. It is composed of shunt shorting-stubs and is the guided wavelength at the center necting lines, where frequency of the passband. For an th-order filter, the

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Fig. 4. Narrowband stopband filter implemented by open-stubs. Fig. 3. Wideband passband filter implemented by shorting-stubs.

the characteristic impedances of the open-stubs can be given by

characteristic admittances of the connecting lines are given by [1] as

for

for

to

to

(3)

and the characteristic admittances of the shorting-stubs are

for

even,

for

odd,

(5)

where are the element values of a low-pass prototype filter could with the Chebyshev response. Note that the values of owing to the choice of different be different from those of levels of ripples. for

for

to

to

D. Design Procedure of Dual-Wideband Filter

(4)

where are the element values of a low-pass prototype with the Chebyshev response. The parameter is an arbitrary constant in order to adjust the admittance level in the interior of the filter.

C. Narrowband VBSF Design Fig. 4 shows the topology of a narrowband VBSF implemented by open-stubs. Note that the connecting lines have already been determined from the desired admittances and electrical lengths in the previous VBPF design. If the deviation beand the stopband tween the passband center frequency is sufficiently small, the connecting lines center frequency are sufficient to be K-inverters in the VBSF. By modifying the conventional BSF design [1], the values of the K-inverters and

Fig. 5 illustrates the flowchart of the design procedure for the dual-wideband filter as well as the design equations which are listed in each block. As indicated in Fig. 2, the dual-wideband filter can be divided into two virtual filters using the frequency mapping technique, one being the wideband VBPF and , the other, the narrowband VBSF. Then, the four parameters , , and for defining the specifications of VBPF and VBSF can be obtained, and the dimensions of VBPF and VBSF can be synthesized sequentially. The dimensions of the connecting lines are determined in the VBPF design procedure; therefore, the limitation of the present cannot design is that the center frequency of the stopband . The larger the dedeviate far from that of the passband viation, the greater the passband return loss will be. In order to improve the return loss, we can set the passband ripple to a lower and will level. In the meantime, the deviation between result in reduction of the stopband’s bandwidth. Hence, we can intentionally set a wider stopband bandwidth than the desired, as indicated in Fig. 5. III. CHARACTERISTICS OF DUAL-BAND RESONATOR A. Characteristics of Step-Impedance Resonator (s-SIR) The parallel pair of open- and shorting-stubs (POSSs), which make up the dual-passband resonators, can be realized by an unbalanced s-SIR. The s-SIR with characteristic impedance

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Fig. 7. Design graph of s-SIR.

order mode frequencies can be determined by choosing a suitable combination of the impedance and the length ratios of the s-SIR. According to (6)–(8), the susceptance slope parameters at resonant frequencies [1] is given as

Fig. 5. Flowchart of the design procedure.

(9)

Fig. 6. Structure of SIR shorting-stub for: (a)

K > 1 and (b) K < 1.

and and electrical length and for the cases of and , where is the impedance ratio, are shown in Fig. 6(a) and (b), respectively. Its input admittance is given by [28] (6) If the length ratio of the s-SIR is defined as (7) then the resonance condition yields (8) where is the total electrical length. It should be noted that the fundamental frequency and the other higher

where is the resonant radian frequency. The equation shows that different susceptance slope parameters of s-SIR can be obeven when its length ratio tained by adjusting the impedance , stepped-impedance ratio , and total electrical length are given. Note that the susceptance slope parameters of s-SIR are independent of the impedance ratio . As one can see, Fig. 7 shows the design graph for the s-SIR. , versus the resThe susceptance slope parameter ratio, , for the fundamental and the first onant frequency ratio, higher order resonant modes are plotted with different combiand . In the design of s-SIR, the parameters nations of and are first determined graphically from the desired slope parameter ratio and resonant frequency ratio by the help of Fig. 7. Then, the parameters and can be obtained from , , and by (8). Finally, the impedance levels and can be adjusted to achieve the desired susceptance slope parameter at the fundamental frequency by (9). –5 One can observe that, with typical values of –0.7, realizable is 1.73–6.47, and and is 0.0037–2.4. The case of , i.e., point A in Fig. 7, denotes a traditional quarter-wavelength transmission line resonator. The first higher resonant frequency is triple its funda, which mental frequency, and the slope parameter ratio, is the same as the bandwidth ratio of the second passband to the

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Fig. 8. Equivalence between POSS and s-SIR.

designed one in the shorting-stub filter, is one third. Thus, the will determine the bandwidth ratio slope parameter ratio if the J-inverters are all ideal. and For example, if a resonator with is required, one can locate point B with and to satisfy the given specifications. Since the objective of our design is to identify he resonators that meet the required dual-band resonant frequencies and bandwidths, Fig. 7 is very useful in our design procedure. B. Equivalence Between POSS and S-SIR Fig. 8, which shows the POSS and the s-SIR, assumes that the POSS resonates at frequencies and , with and , recorresponding susceptance slope parameters spectively. The equivalence between the POSS and the s-SIR in the dual-band operation can be applied by imposing the following conditions:

Fig. 9. Verification of equivalence between POSS and s-SIR.

, , , and defined at 1.85 GHz. As indicated in Fig. 9, input susceptances of the POSS and the s-SIR are all the same in the dual passbands. However, the second poles of input susceptances around 3.7 GHz are transmission zeros when filters are realized by POSSs and s-SIRs, respectively. Although there is a small discrepancy, it will only influence the performance of the out-band rejection not the pass band. This result shows that the POSS could be replaced with the s-SIR without undermining the performance of the designed filter response. B. Test Filter 1

(10) where and are given by (6) and (9), respectively. In and are the first and second resonant radian addition, frequencies, respectively. IV. SYNTHESIS OF TWO TEST FILTERS Here, two test filters are designed and fabricated by the 20-mil . Rogers RO4003 substrate with dielectric constant The wiring rules require the widths of transmission lines ranging from 0.2 to 4.0 mm and the via diameter should be at least 0.2 mm. In order to minimize the variation effect of via diameter, the via diameter is set to be 0.5 mm. A. Verification of Equivalence Between POSS and s-SIR In order to verify the equivalence between the POSS and the s-SIR, the two structures are shown side by side in Fig. 8. Consider that the open- and shorting-stubs have characteristic impedances of 361.01 and 138.64 , and their electrical lengths at 1.816 and 1.85 GHz, respectively. By enforcing the are constraints listed in (10), the corresponding s-SIR has

The first example considers a dual wideband filter with the following specifications: • seventh-order Chebyshev response; • passband 1: 0.96–1.6 GHz; • passband 2: 2.02–2.68 GHz; • stopband: 1.63–1.99 GHz. The constant in (4) in this design is set to be 1.5, for which the resultant connecting-line admittances are realizable for practical fabrication. Since the quarter- wavelength transmission-lines fail to exhibit the ideal responses of the J-inverters over a wide passband, the passband ripple is set to be lower than desirable. In this case, both the ripples for VBPF and VBSF are 0.01. Fig. 10 shows the simulated frequency response of filter 1 by prototype equivalent circuit and Tx-line circuit as shown in Fig. 2(a) and (b), respectively. Because of the nonideal J-inverter realized by the quarter-wavelength transmission-line in the Tx-line circuit, the return loss in the dual passbands is slightly higher than the desired level. Although a slight discrepancy between the two simulated frequency responses is found, the results validate the feasibility of the design approach. For the desired Chebyshev response of the dual-wideband filter in the specification, the design procedure indicated in Fig. 5 gives the required electrical parameters of the associated

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Fig. 11. Topology and dimensions of filter 1.

TABLE II DIMENSIONS OF DUAL-PASSBAND FILTER IMPLEMENTED BY SIR-SHORTING STUBS WITH (TEST FILTER 1)

N =7

Fig. 10. Frequency response of filter 1 by prototype equivalent circuit and Tx-line circuit.

TABLE I DIMENSIONS OF DUAL-PASSBAND FILTER IMPLEMENTED BY POSSS WITH (TEST FILTER 1)

N =7

POSSs in Table I. Also listed in the table are the susceptance slope parameters and at the first two resonant frequenand , respectively. Note from the specifications cies that the two passbands have fractional bandwidths of 50% and 28%. As shown in Table I, the susceptance slope parameter for , to 4, are close to the bandwidth ratios, ratio of the second passband to the first one [1], [18]. These POSSs can be implemented by s-SIRs with characterand ) and electrical lengths ( and istic impedances ( ) as listed in Table II. Note that in yielding the final values of , the electrical length should be slightly reduced to account for the finite inductance effect of vias, which are simulated in advance by full-wave software An-Soft Ensemble 8.0 [29]. As a result, the final topology is demonstrated in Fig. 11. The simulated and measured frequency responses of the filter , are shown in Fig. 12. They agree well with each other in which can be attributed but illustrate a small discrepancy in to the inaccurate fabrication of via holes of the s-SIRs. As noted in the figure, the filter meets the specifications well. The two passbands have different fractional bandwidths of 50.0% and

Fig. 12. Measurement and simulation results for filter 1.

28.1%, respectively, while the fractional bandwidth of the stopband is 19.9% if the rejection is measured by 15 dB. Fig. 12 also plots the measured group delay, which ranges from 1.65 to 11.78 ns and 6.92 to 1.88 ns in the first and second

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TABLE III DIMENSIONS OF DUAL-PASSBAND FILTER IMPLEMENTED BY POSSS WITH (TEST FILTER 2)

N =9

TABLE IV DIMENSIONS OF DUAL-PASSBAND FILTER IMPLEMENTED BY SIR-SHORTING STUBS WITH (TEST FILTER 2)

N =9

Fig. 13. Frequency response of filter 2 by prototype equivalent circuit and Tx-line circuit.

passbands, respectively. It is important to mention that the occurrence of large group delays are near the edges of the stopband. It is interesting to note that there is a transmission zero on the upper bandstop region before the first spurious response around 3.7 GHz in Fig. 12. This can be explained by the second pole of the input susceptances of s-SIRs, e.g., the pole at 3.71 GHz for the first s-SIR in Fig. 9. C. Test Filter 2 The second example considers the design of a dual wideband filter to meet the specifications for the direct-sequence UWB (DS-UWB) applications. To begin, the filter’s order is determined by the decay of the stopband. In order to achieve the dB at 2.0 GHz, the filter’s minimum order attenuation of with 0.1-dB passband ripple obtained by (2) is 9. Therefore, the specifications of the designed filter are as follows: • ninth-order Chebyshev response; • passband 1: 3.1–4.85 GHz; • passband 2: 6.2–9.7 GHz; • stopband: 5.15–5.85 GHz. The constant in (4) is also set to be 1.5. In addition, the passband ripple is set to be 0.003 to get a better passband response. Fig. 13 shows the simulated frequency responses of filter 2 by prototype equivalent circuit and Tx-line circuit, respectively. departs from that Note that the center frequency of VBSF more significantly in this design. It will be imposof VBPF sible to realize the VBPF J-inverters and the VBSF K-inverters simultanously, thereby incurring worse return loss in both passbands. Nonetheless, the simulated frequency responses by the

Fig. 14. Topology and dimensions of filter 2.

Tx-line circuit indicates that the design methodology is sufficient for practical applications. Once again, the results validate the feasibility of the proposed design approach. Following the design procedure indicated in Fig. 5, the electrical parameters of the dual-band filter implemented by POSSs and s-SIRs are listed in Tables III and IV. The lengths in Table IV have been slightly altered by taking into account the effects of both vias and junction discontinuities of s-SIRs. For the present design, the two passbands have almost the same fractional bandwidths, i.e., 46.5% and 44.8%, respectively. The for to 4, slope parameter ratios in Table III, range from 0.82 to 0.98, which are again close to but slightly lower than the bandwidth ratio. The topology of the dual-band filter along with its dimensions implemented by s-SIRs with the Chebyshev response is demonstrated in Fig. 14. Note that better manufacture capability will be required for the vias fabrication since the present design is at higher frequencies than the test filter 1. Fig. 15 shows the measured and simulated frequency responses of the filter along with the UWB mask [22]. As can be seen, the simulated results . A small discrepancy agree well with the measured data in , which is mainly due to the effect of SMA connectors, in

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with center frequencies at 1.28 and 2.35 GHz, respectively. The bandwidths of the second filter are 47.6% and 48.4% with center frequencies at 3.975 and 7.94 GHz, respectively. The measured results are in good agreement with the simulation results, and both show satisfactory performance. Since the present design calls for the cascade of several quarter-wavelength filter sections, the final filter structure is comparatively large in size, which may limit their application in industry. In addition, the center frequencies of the associated VBPF and VBSF should be close to each other, which somewhat limits the design flexibility. These designs might merit further improvements in future studies. REFERENCES

Fig. 15. Measurement and simulation results for filter 2.

can still be noticed, Nonetheless, the design reasonably meets the specifications, with fractional bandwidth being 47.6% and 48.4% for the two passbands, and 17.7% for the stopband. The measured group delay, shown in Fig. 15, ranges from 0.92 to 6.44 ns and 2.00 to 0.67 ns in the first and second passbands. Again, large group delays occur near the edges of the stopband. The transmission zero on the upper band-stop region before the first spurious response occurs around 12.4 GHz in the present design. It is slightly smaller than the second pole of the input susceptances of s-SIRs which range from 12.5 to 12.8 GHz. The discrepancies are mainly caused by the effect of junction discontinuities between the s-SIRs and connecting lines. V. CONCLUSION A systematic design procedure for the dual-wideband filter, which is implemented by the s-SIRs, is presented in this paper. According to the frequency mapping approach, the dual wideband filter could be divided into two parts: the wideband VBPF and the narrowband VBSF. Both filters could be designed by conventional synthesis methods. First, the specifications of the wideband VBPF and the narrowband VBSF are obtained by the frequency mapping approach. The wideband VBPF is implemented by a shorting-stub filter and synthesized by the conventional approach, while the open-stubs are employed to implement the stopband in the whole frequency range. Eventually, the dual-band resonator comprises the POSSs which are replaced by the s-SIRs to adjust the impedance level to a realizable range. Two filters are tested to validate the design proposed in this paper. The bandwidths of the first filter are 50% and 28%

[1] G. L. Mattaei, L. Young, and E. M. T. Jones, Microwave Filters, Impedance-Matching Network, and Coupling Structures. Norwood, MA: Artech, 1964, ch. 8–12. [2] J.-S. Hong and M. J. Lancaster, Microstrip Filters for RF/Microwave Applications, 1st ed. New York: Wiley, 2001, ch. Ch.5–6. [3] L.-C. Tsai and C.-W. Hsue, “Dual-band bandpass filters using equallength coupled serial-shunted lines and Z-transform technique,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 4, pp. 1111–1117, Apr. 2004. [4] C.-H. Chien, A.-S. Liu, and R.-B. Wu, “A functional genome optimization method for CPW filters design,” IEEE AP-S. Dig., vol. 3, pp. 2743–2746, Jun. 2004. [5] M.-I. Lai and S.-K. Jeng, “Compact microstrip dual-band bandpass filters design using genetic-algorithm techniques,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 1, pp. 160–168, Jan. 2006. [6] L. M. Howard and D. J. D’Angelo, “The GA-P: A genetic algorithm and genetic programming hybrid,” IEEE Expert, vol. 10, pp. 11–15, Jun. 1995. [7] J. Lee, M. S. Uhm, and I. B. Yom, “A dual-passband filter of canonical structure for satellite applications,” IEEE Microw. Wireless Compon. Lett., vol. 14, no. 6, pp. 271–273, Jun. 2004. [8] S. Tamiazzo and G. Macchiarella, “An analytical technique for the synthesis of cascaded N-tuplets cross-coupled resonators microwave filters using matrix rotations,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 5, pp. 1693–1698, May 2005. [9] J. Lee, M. S. Uhm, and J. S. Park, “Synthesis of self- equalized dualpassband filter,” IEEE Microw. Wireless Compon. Lett., vol. 15, no. 4, pp. 256–258, Apr. 2005. [10] R. J. Cameron, M. Yu, and Y. Wang, “Direct-coupled microwave filters with single and dual stopbands,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 11, pp. 3288–3297, Nov. 2005. [11] P. Lenoir, S. Bila, F. Seyfert, D. Baillargeat, and S. Verdeyme, “Synthesis and design of asymmetrical dual-band bandpass filters based on equivalent network simplification,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 7, pp. 3090–3097, Jul. 2006. [12] M. Mokhtaari, J. Bornemann, K. Rambabu, and S. Amari, “Couplingmatrix design of dual and triple passband filters,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 11, pp. 3940–3946, Nov. 2006. [13] V. Lunot, S. Bila, and F. Seyfert, “Optimal synthesis for multi-band microwave filters,” in IEEE MTT-S Int. Dig., Jun. 2007, pp. 115–118. [14] J. T. Kuo and H. S. Cheng, “Design of quasi-elliptic function filters with a dual-passband response,” IEEE Microw. Wireless Compon. Lett., vol. 14, no. 10, pp. 472–474, Oct. 2004. [15] J. T. Kuo, T. H. Yeh, and C. C. Yah, “Design of microstrip bandpass filters with a dual-passband response,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 4, pp. 1331–1337, Apr. 2005. [16] C.-F. Chen, T.-Y. Huang, and R.-B. Wu, “Design of dual- and triple-passband filters using alternately cascaded multiband resonators,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 9, pp. 3550–3558, Sep. 2006. [17] H.-Y. A. Yim and K.-K. M. Cheng, “Novel dual-band planar resonator and admittance inverter for filter design and applications,” in IEEE MTT-S Int. Dig., Jun. 2005, pp. 12–17. [18] C. M. Tsai, H. M. Lee, and C. C. Tsai, “Planar filter design with fully controllable second passband,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 11, pp. 3429–3439, Nov. 2005. [19] G. Macchiarella and S. Tamiazzo, “Design techniques for dual-passband filters,” IEEE Trans. Microw. Theory Tech., vol. 53, no. 11, pp. 3265–3271, Nov. 2005.

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LIU et al.: DUAL WIDEBAND FILTER DESIGN USING FREQUENCY MAPPING AND STEPPED-IMPEDANCE RESONATORS

[20] X. Guan, Z. Ma, P. Cai, Y. Kobayashi, T. Anada, and G. Hagiwara, “Synthesis of dual-band bandpass filters using successive frequency transformations and circuit conversions,” IEEE Microw. Wireless Compon. Lett., vol. 16, no. 3, pp. 110–112, Mar. 2006. [21] Lamperez and A. Garcia, “Analytical synthesis algorithm of dual-band filters with asymmetric pass bands and generalized topology,” in IEEE MTT-S Int. Dig., Jun. 2007, pp. 909–912. [22] “Revision of Part 15 of the Commission’s rules regarding ultra-wideband transmission system,” FCC, 2002, Tech. Rep., ET-Docket 98-153. [23] M. Mokhtaari, J. Bornemann, and S. Amari, “Dual-band steppedimpedance filters for ultra-wideband applications,” in Proc. Eur. Microw. Conf., Oct. 2007, pp. 779–782. [24] K. Li, D. Kurita, and T. Matsui, “Dual-band ultra-wideband bandpass filter,” in IEEE MTT-S Int. Dig., Jun. 2006, pp. 1193–1196. [25] H. Shaman and J.-S. Hong, “Ultra-wideband (UWB) bandpass filter with embedded band notch structures,” IEEE Microw. Wireless Compon. Lett., vol. 17, no. 3, pp. 193–195, Mar. 2007. [26] H. Shaman and J.-S. Hong, “Asymmetric parallel-coupled lines for notch implementation in UWB filters,” IEEE Microw. Wireless Compon. Lett., vol. 17, no. 7, pp. 516–518, Jul. 2007. [27] C.-Y. Hsu, L.-K. Yeh, C.-Y. Chen, and H.-R. Chuang, “A 3–10 GHz ultra-wideband bandpass filter with 5–6 GHz rejection band,” in Proc. Asia–Pacific Microw. Conf., Dec. 2007, pp. 1187–1190. [28] M. Makimoto and S. Yamashita, “Bandpass filters using parallel coupled stripline stepped impedance resonators,” IEEE Trans. Microw. Theory Tech., vol. MTT-28, no. 12, pp. 1413–1417, Dec. 1980. [29] Ansoft Ensemble V.8.0, MOM Based Software Package. Ansoft Corporation, Pittsburgh, PA, 2001.

An-Shyi Liu was born in Changhua, Taiwan, in 1973. He received the B.S. degree in physics from National Cheng-Kung University, Tainan, Taiwan, and the M.S. degree in biomedical engineering from National Yang-Ming University, Taipei, Taiwan, in 1996 and 1999, respectively. He is currently working toward the Ph.D. degree at the Graduate Institute of Communication Engineering, National Taiwan University, Taipei. His areas of interest include optimization in computational electromagnetics, base station antennas design, and biomedical signal process.

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Ting-Yi Huang was born in Hualien, Taiwan, on November 12, 1977. He received the B.S. degree in electrical engineering and the M.S. degree in communication engineering from National Taiwan University, Taipei, Taiwan, in 2000 and 2002, respectively. He is currently working toward the Ph.D. degree in communication engineering at National Taiwan University. His research interests include computational electromagnetics, the design of microwave filters, transitions, and associated RF modules for microwave and millimeter-wave applications.

Ruey-Beei Wu (M’91–SM’97) received the B.S.E.E. and Ph.D. degrees from National Taiwan University, Taipei, Taiwan, in 1979 and 1985, respectively. In 1982, he joined the faculty of the Department of Electrical Engineering, National Taiwan University, where he served as the Chairperson from 2004 to 2007 and is currently a Professor. From March 1986 to February 1987, he was a Visiting Scholar with IBM, East Fishkill, NY. From August 1994 to July 1995, he was with the Electrical Engineering Department, University of California, Los Angeles. From 1998 to 2000, he was also appointed Director of the National Center for High-Performance Computing and has served as Director of Planning and Evaluation Division since November 2002, both under the National Science Council. His areas of interest include computational electromagnetics, transmission line and waveguide discontinuities, microwave and millimeter-wave planar circuits, and interconnection modeling for computer packaging.

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