MODERN microwave communication systems require

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 2, FEBRUARY 2006 755 Novel Compact Net-Type Resonators and Their Applications to Microstrip Bandpass Filters Chi-Feng Chen, Ting-Yi Huang, and Ruey-Beei Wu, Senior Member, IEEE Abstract Novel compact net-type resonators and their practical applications to microstrip bandpass filters have been presented in this paper. Three kinds of filters are designed and fabricated to demonstrate the practicality of the proposed compact net-type resonators. In addition, by adjusting the structural parameters of the net-type resonators, the spurious frequencies can be properly shifted to higher frequencies. As a result, a three-pole Chebyshev net-type resonator filter with a fractional bandwidth (FBW) of 6.8% has a spurious resonance of up to 4 1 0, and it has more than 80% size reduction in comparison with the conventional U-shaped resonator filter. A four-pole quasi-elliptic net-type resonator filter with a FBW of 3.5% has a spurious resonance of up to 5 0, and it has approximately 67% size reduction in comparison with the cross-coupled open-loop resonator filter. A three-pole trisection net-type resonator filter with a FBW of 4.7% has a spurious resonance of up to 6 5 0, and its size is reduced by 68% in comparison with the trisection open-loop resonator filter. Consequently, each of the designed filters occupies a very small circuit size and has a good stopband response. The measured results are in good agreement with the full-wave simulation results by IE3D. Index Terms Coupling coefficient, external quality factor, microstrip filter, net-type resonator. I. INTRODUCTION MODERN microwave communication systems require miniaturized high-performance bandpass filters with high-selectivity and wide stopband response. These filters can be designed and fabricated on various materials. However, up to the present time, planar filters are particularly attractive because of their smaller size, easier manufacture, and lower fabrication cost [1]. Many applications to planar filters have been widely used in many microwave communication systems. Among them, parallel-coupled microstrip bandpass filters have originally been proposed in [2], and they have the advantages of wide realizable bandwidth and simple synthesis procedures [3] [5]. Another popular one is the cross-coupled bandpass filter, which is often used to improve selectivity because it has one pair of transmission zeros in the stopband to reject possible interference [6] [10]. To reduce the filter size, a more practical way is to miniaturize the resonator circuit. Therefore, many compact resonators like U-shaped hairpin resonators [4], [5], open-loop resonators [6], [7], and other miniaturized resonators [8] [10] have been proposed. However, with the rapid evolution of modern communica- Manuscript received August 10, 2005; revised October 7, 2005. This work was supported in part by the National Science Council under Grant NSC 93-2752-E-002-003-PAE. The authors are with the Department of Electrical Engineering and Graduate Institute Communication Engineering, National Taiwan University, Taipei, Taiwan 10617, R.O.C. Digital Object Identifier 10.1109/TMTT.2005.862626 tion systems, the sizes of these resonators are not small enough to be used. Wide stopband response has currently been an important issue in developing microwave filters in order to enhance the circuit performance because many planar bandpass filters using half-wavelength resonators have the inherent spurious passband at twice the midband frequency. One popular solution is to impose the stepped impedance resonators (SIRs). The SIR was presented not only to control the spurious responses, but also to reduce the resonator size [11], [12]. By adequately selecting the values of the impedance and length ratios of the SIR, its size can be reduced and its first spurious frequency can be properly moved to a higher frequency so as to extend the stopband. In addition, filter based on a defected ground structure (DGS) can also obtain a good stopband performance [13], [14]. However, it has no significant improvement in size reduction. Recently, a net-type resonator has been proposed and employed to design a bandpass filter [15]. In this paper, several novel compact net-type resonators have been presented, analyzed theoretically, and verified by several filters. In comparison with the conventional open-loop resonator, the areas of the compact net-type resonators have at least more than approximately 67% reduction. In addition, the net-type resonator has the capability to control its spurious frequencies, which is the same as an SIR. Their applications to various microstrip bandpass filters such as parallel-coupled, cross-coupled, and cross-coupled trisection filters have also been proposed. As a result, these filters not only have small sizes, but also have wide upper stopband responses. This paper is organized as follows. Section II describes the theory of a net-type resonator. Section III characterizes two different types of coupling structures encountered in the filter design. Sections IV VI provide the design procedures for the three kinds of microstrip bandpass filters. The experimental data are presented and compared with the simulated results. Finally, Section VII draws some brief conclusions. II. COMPACT NET-TYPE RESONATOR A net-type resonator is formed by a joint connection of several transmission-line sections among which one is short-ended while all the others are open-ended [15]. Let be the number of open-ended transmission-line sections. Fig. 1(a) shows a typical structure of the net-type resonator realized in the microstrip geometry. The resonator can be modeled as a short-ended transmission-line section cascaded with open-ended sections in parallel. With all the microstrip line sections of the same width, its circuit performance is the same as an SIR with an impedance ratio of. The equivalent circuit for an SIR is shown in Fig. 1(b). 0018-9480/$20.00 2006 IEEE

756 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 2, FEBRUARY 2006 TABLE I RESONANT FREQUENCIES AND TOTAL ELECTRICAL LENGTHS OF THE STRUCTURE IN TERMS OF THE GUIDED WAVELENGTH VERSUS N Fig. 1. (a) Typical structure of the net-type resonator. (b) Equivalent circuit. The resonance condition can be expressed by the equation (1) Fig. 2. N =2. (a) Net-type resonator. (b) Compact net-type resonator for the case of where and are the electrical lengths of the short- and open-ended transmission-line sections of the net-type resonator, respectively. For compact and simplified consideration, it is preferable to choose. Based on this condition, the total electrical length of the resonator can be found as (2) where represents the total electrical length corresponding to the fundamental resonant frequency. Moreover, the total electrical length corresponding to the next higher resonant frequency can also be calculated from (1) as Therefore, the ratio of the first spurious and fundamental frequencies of the net-type resonator can then be derived as where and represent the first spurious and fundamental frequencies, respectively. Table I lists the resonant frequencies and the total electrical lengths of the structure in terms of the guided wavelength versus. It can be found that the case for stands for a traditional quarter-wavelength grounded unit impedance resonator (UIR), whose first spurious frequency is centered at three times the midband frequency. It can also be noticed that the larger the value, the smaller the total electrical length and the larger the frequency ratio of the first spurious and fundamental frequencies. (3) (4) Fig. 3. N =3. (a) Net-type resonator. (b) Compact net-type resonator for the case of Several layouts of the novel net-type resonator have been proposed. Figs. 2(a), 3(a), and 4(a) show the typical net-type resonators for and, respectively. In order to further reduce the resonator size, each resonator is folded to be compact. Therefore, the compact net-type resonators are illustrated in Figs. 2(b), 3(b), and 4(b). As can be seen, each resonator not only makes the circuit compact, but also allows various filter configurations to be realized. It is worth mentioning that additional resonant frequencies of the net-type resonator will be introduced when the total lengths of any two open stubs are half-wavelength and if all open stubs have the same lengths. Thus, in order to avoid these spurious responses, all of the open-ended transmission-line section lengths are slightly adjusted to different values in the cases where for the actual design. The major purpose is to irregularly distribute these additional resonant frequencies. Hence, they will cause no significant concern in the spurious response over the stopband, as described in [15].

CHEN et al.: NOVEL COMPACT NET-TYPE RESONATORS AND THEIR APPLICATIONS TO MICROSTRIP BANDPASS FILTERS 757 Fig. 4. N =5. (a) Net-type resonator. (b) Compact net-type resonator for the case of Fig. 5. Layout of the three-pole Chebyshev bandpass filter using compact net-type resonators with N =2. III. COUPLING BETWEEN COMPACT NET-TYPE RESONATORS Before designing bandpass filters, some instructive discussion on how to construct different types of couplings between adjacent resonators is given here. It can be shown that at resonance of the fundamental mode, each of the net-type resonators has the maximum electric-field density near the open-ended transmission-line sections and the maximum magnetic field density near the short-ended transmission-line section. Thus, the electric coupling can be obtained if the open-ended line sections of the two compact net-type resonators are closely placed, and the magnetic coupling can be obtained if the short-ended line sections of the two compact net-type resonators are closely placed. Since it is well known that the electric and magnetic couplings are out-of-phase, we can employ these structures of different coupling types to implement filters with various responses, such as Chebyshev and quasi-elliptic response bandpass filters. In this paper, we will present the design of various filters through the method based on coupling coefficients. Both experimental and simulated data are presented to demonstrate the practicality of the proposed net-type resonators. IV. DESIGN OF A THIRD-ORDER PARALLEL-COUPLED BANDPASS FILTER To demonstrate the usefulness of the proposed net-type resonator, a third-order parallel-coupled bandpass filter using compact net-type resonators was designed. In this example, the resonator structure shown in Fig. 2(b) is employed to construct this bandpass filter. The resonator is constructed by a short-ended and two open-ended transmission line sections. The lateral size of the compact net-type resonator is only approximately 1/12 guided wavelength at the center frequency and its first spurious frequency is at around, which can be calculated by using (3). Fig. 5 shows the structure of the third-order parallel-coupled microstrip bandpass filter, which are composed of three compact net-type resonators. The third-order Chebyshev filter with a 0.1-dB ripple level was designed with the given specifications. The center frequency of the filter is 0.91 GHz, and the fractional bandwidth (FBW) is 6.8%. The circuit was designed to be fabricated using copper metallization on a Rogers RO4003 substrate with a relative dielectric constant of 3.38, a thickness of 0.508 mm, and a loss tangent of 0.0027. The Fig. 6. Coupling coefficients versus the distances between the resonators. design followed the traditional design procedure described in [16]. The design parameters of bandpass filters, i.e., the coupling coefficients and external quality factor, can be obtained from circuit elements of a low-pass prototype filter. The element values of the low-pass prototype filter are found to be and. To determine the physical dimensions of the filter, the coupling coefficients and the input/output external quality factors are to be calculated. It turns out that The full-wave simulator IE3D has been used to extract the above parameters. The coupling coefficient can be evaluated from two dominant resonant frequencies and as [7] where represents the coupling coefficient between resonators and. Fig. 6 plots the simulated coupling coefficients versus the distances between the resonators in which and curves are almost the same. The external quality factor can be characterized by [7] where and represent the resonant frequency and the 3-dB bandwidth of the input or output resonator. Fig. 7 illus- (5) (6) (7)

758 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 2, FEBRUARY 2006 Fig. 7. External quality factor versus the tapped line position of the resonator. trates the simulated external quality factor against the tapped line position. Once these figures are reconstructed for the specific substrates, the other procedures in this paper can be directly repeated. The filter has realizable design geometric parameters such as mm, mm, mm, mm, and mm. The prototype circuit size of the filter is around 35.45 mm 15.85 mm, i.e., only approximately, where is the guided wavelength on the substrate at the center frequency. It shows that the proposed filter has a very small size, which is much smaller than the conventional parallel-coupled hairpin resonator filters using the half-wavelength resonator [2] [5]. Fig. 8(a) shows the simulated and measured passband responses of the designed filter. The measured passband return loss is less than 17 db. The measured passband insertion loss is approximately 2.2 db. This is mainly attributed to the conductor and dielectric losses of the substrate. Fig. 8(b) presents the simulated and measured wide-band responses of the filter. It is obvious that the next repeated passband of the filter is at approximately, as expected. It shows a very wide upper stopband between the fundamental and first spurious frequencies. V. DESIGN OF AFOURTH-ORDER CROSS-COUPLED BANDPASS FILTER In this design example, the resonator structure shown in Fig. 3(b) is used to construct a fourth-order cross-coupled bandpass filter. The resonator is constructed by a short-ended and three open-ended transmission-line sections. It shows that the lateral size of this compact net-type resonator is only approximately 1/14 of the guided wavelength. In comparison with the conventional open-loop resonator, the area of the compact net-type resonator is reduced by approximately 67%. The configuration of the miniaturized fourth-order microstrip quasi-elliptic bandpass filter is shown in Fig. 9. This filter is composed of four compact net-type resonators with a cross-coupling between nonadjacent resonators. This special arrangement of resonators helps to create the multipath effect, which is introduced to exhibit a single pair of transmission zeros near the passband at finite frequency in order to improve the selectivity of the filter. Fig. 8. Measured and simulated performances of the filter. (a) Insertion and return losses. (b) Wide-band response. Fig. 9. Layout of the four-pole quasi-elliptic bandpass filter using compact net-type resonators with N =3. The proposed filter was designed with the given specifications. The center frequency of the filter is 1.28 GHz, and the FBW is 3.5%. The circuit was also designed to be fabricated on a Rogers RO4003 substrate. The lumped circuit element values of the low-pass prototype filter are

CHEN et al.: NOVEL COMPACT NET-TYPE RESONATORS AND THEIR APPLICATIONS TO MICROSTRIP BANDPASS FILTERS 759 Fig. 11. External quality factor versus the tapped line position of the resonator. Fig. 10. Coupling coefficients versus the distances between the resonators. and. The coupling coefficients and I/O single-loaded external quality factor are found to be [16] (8) In order to determine the physical dimensions of the filter, the full-wave simulator IE3D has also been used to extract the above parameters. The coupling coefficients and external quality factor can be evaluated from (5) and (6). It should be noted that the coupling coefficients and represent the electric coupling and represents the magnetic coupling. Both electric and magnetic couplings are out-of-phase. Fig. 10 plots the simulated coupling coefficients versus the distances between the resonators in which and curves are almost the same. Fig. 11 illustrates the simulated external quality factor against the tapped line position. As mentioned in Section II, each stub lengths of the net-type resonator must be adjusted to different lengths to improve stopband spurious response. In our experience of tuning the stub lengths in Fig. 9, the range of variation of stub length is approximately 2% of the total physical length of the resonator. Fig. 12 shows the simulated frequency responses of the filter for the cases of all open stub lengths of the net-type resonator are equal and unequal (2% variation of the total physical length of the resonator). Obviously, when all open stub lengths of the net-type resonator are unequal, the spurious response can be suppressed to 30 db at approximately 3.5 GHz. It verifies that the additional spurious response can be effectively suppressed by adjusting the stub lengths to different values. As a result, geometric parameters for the filter are mm, mm, mm, mm, mm, mm, mm, Fig. 12. Simulated performances of the filter for all open stub lengths of the net-type resonators are equal (- - -) and unequal ( ). and mm. The prototype circuit size of the filter is approximately 22.7 mm 21.8 mm, i.e., only approximately, where is the guided wavelength on the substrate at the center frequency. Compared to the conventional fourth-order cross-coupled open-loop resonator filter in [6], the filter has approximately 67% size reduction. The measured and simulated results of the filter are illustrated in Fig. 13(a) and (b). As anticipated, there is a pair of transmission zeros near the passband edge, thus much better selectivity. The measured passband return loss is less than 18 db. The measured passband insertion loss is approximately 2.9 db, which is mainly attributed to the conductor and dielectric losses. Fig. 13(b) shows the wide-band response of this filter. As can be seen, the additional higher order spurious response at approximately 3.5 GHz has been suppressed to a level lower than 30 db. It can be expected that the next higher order resonant frequency of the net-type resonator will correspond to a total electrical length of. As can be seen, the stopband rejection of the filter is better than 30 db up to 6.54 GHz. It shows that the filter has a fairly good upper stopband rejection of up to approximately, which agrees with the anticipation.

760 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 2, FEBRUARY 2006 Fig. 15. Coupling coefficients versus the distances between the resonators. Fig. 13. Measured and simulated performances of the filter. (a) Insertion and return losses. (b) Wide-band response. all of the open-ended transmission-line sections are tuned to different lengths. The reason is to avoid the additional resonant responses. In our experience of tuning the stub lengths in Fig. 14, the range of variation of stub length is approximately 20% of the total physical length. This modified range is larger than that of the above case because the stubs are larger in number. As described in [16], if the cross-coupling and the direct coupling are all positive, the transmission zero will occur at the lower side of the passband; whereas if the cross-coupling is negative and the direct coupling is positive, the transmission zero will occur at the upper side of the passband. In our design, all of the coupling structures of the coupled resonators are electric coupling. Thus, it can be expected that one transmission zero will occur at the lower side of the passband. The trisection filter was designed with the given specifications. The center frequency of the filter is 1 GHz, and the FBW is 4.7%. The circuit was also designed to be fabricated on a Rogers RO4003 substrate. The coupling matrix and I/O single-loaded external quality factor are found to be (9) Fig. 14. Layout of the three-pole trisection bandpass filter using compact net-type resonators with N =5. VI. DESIGN OF ATHIRD-ORDER TRISECTION BANDPASS FILTER In the last example, a third-order cross-coupled trisection bandpass filter is realized by using the compact net-type resonator with shown in Fig. 4(b). The lateral size of the resonator is only 1/14 of the guided wavelength. Fig. 14 shows the structure of the filter. Similar to the above, it is obvious that The design curves of the simulated coupling coefficients and external quality factor are shown in Figs. 15 and 16, respectively. Geometric parameters for the filter are mm, mm, mm, mm, mm, mm, mm, mm, and mm. The prototype circuit size of the filter is around 28.41 mm 28.18 mm, i.e., only approximately, where is the guided wavelength on the substrate at the center frequency. As a result, the circuit size of the filter is approximately 68% less than that of the conventional cross-coupled trisection open-loop resonator filter in [16]. The simulated and measured results are plotted in Fig. 17(a) and (b). As expected, a transmission zero at the lower side of the passband is observed. Thus, the selectivity on the lower side is

CHEN et al.: NOVEL COMPACT NET-TYPE RESONATORS AND THEIR APPLICATIONS TO MICROSTRIP BANDPASS FILTERS 761 also mainly due to the conductor and dielectric losses. Fig. 17(b) shows the wide-band response of this filter. It is clear that the additional spurious response at approximately has been suppressed. The frequency response exhibits that the filter has a quite good upper stopband rejection of up to approximately. Fig. 16. External quality factor versus the tapped line position of the resonator. VII. CONCLUSION In this paper, novel compact net-type resonators have been presented to build up several types of microstrip bandpass filters. Both theory and experiments are provided. The results demonstrate that the filter size can be extremely reduced by using the proposed resonator. The measured results are in good agreement with simulated predictions. In fact, besides the three types of filters mentioned above, the compact net-type resonators can also allow various filter topologies to be realized. Filters based on the compact net-type resonator have some advantages of small size and wide upper stopband, which can be quite useful for applications in mobile communication systems. Fig. 17. Measured and simulated performances of the filter. (a) Insertion and return losses. (b) Wide-band response. higher than that on the higher side of the passband. This property is suitable for some applications such as the diplexers. The measured passband return loss is less than 18 db. The measured passband insertion loss is approximately 2.8 db, which is REFERENCES [1] D. M. Pozar, Microwave Engineering, 2nd ed. New York: Wiley, 1998, ch. 8. [2] S. B. Cohn, Parallel-coupled transmission-line-resonator filters, IEEE Trans. Microw. Theory Tech., vol. MTT-6, no. 4, pp. 223 231, Apr. 1958. [3] G. L. Matthaei, Design of wide-band (and narrow-band) bandpass microwave filters on the insertion loss basis, IEEE Trans. Microw. Theory Tech., vol. MTT-8, no. 11, pp. 580 593, Nov. 1960. [4] E. G. Cristal and S. Frankel, Hairpin-line and hybrid hairpin-line/halfwave parallel-coupled-line filters, IEEE Trans. Microw. Theory Tech., vol. MTT-20, no. 11, pp. 719 728, Nov. 1972. [5] G. L. Matthaei, N. O. Fenzi, R. J. Forse, and S. M. Rohlfing, Hairpincomb filters for HTS and other narrow-band applications, IEEE Trans. Microw. Theory Tech., vol. 45, no. 8, pp. 1226 1231, Aug. 1997. [6] J. S. Hong and M. J. Lancaster, Coupling of microstrip square openloop resonators for cross-coupled planar microwave filters, IEEE Trans. Microw. Theory Tech., vol. 44, no. 12, pp. 2099 2109, Dec. 1996. [7], Design of highly selective microstrip bandpass filters with a single pair of attenuation poles at finite frequencies, IEEE Trans. Microw. Theory Tech., vol. 48, no. 7, pp. 1098 1107, Jul. 2000. [8] J. T. Kuo, M. J. Maa, and P. H. Lu, A microstrip elliptic function filter with compact miniaturized hairpin responses, IEEE Microw. Wireless Compon. Lett., vol. 10, no. 3, pp. 94 95, Mar. 2000. [9] S. Y. Lee and C. M. Tsai, New cross-coupled filter design using improved hairpin resonators, IEEE Trans. Microw. Theory Tech., vol. 48, no. 12, pp. 2482 2490, Dec. 2000. [10] C. C. Chen, Y. R. Chen, and C. Y. Chang, Miniaturized microstrip crosscoupled filters using quarter-wave or quasi-quarter-wave resonators, IEEE Trans. Microw. Theory Tech., vol. 51, no. 1, pp. 120 131, Jan. 2003. [11] 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. [12] M. Sagawa, M. Makimoto, and S. Yamashita, Geometrical structures and fundamental characteristics of microwave stepped-impedance resonators, IEEE Trans. Microw. Theory Tech., vol. 45, no. 7, pp. 1078 1085, Jul. 1997. [13] C. S. Kim, J. S. Park, D. Ahn, and J. B. Lim, A novel 1-D periodic defected ground structure for planar circuits, IEEE Microw. Guided Wave Lett., vol. 10, no. 4, pp. 131 133, Apr. 2000. [14] J. S. Park, J. S. Yun, and D. Ahn, A design of the novel coupledline bandpass filter using defected ground structure with wide stopband performance, IEEE Trans. Microw. Theory Tech., vol. 50, no. 9, pp. 2037 2043, Sep. 2002. [15] C. F. Chen, T. Y. Huang, and R. B. Wu, A miniaturized net-type microstrip bandpass filter using =8 resonators, IEEE Microw. Wireless Compon. Lett., vol. 15, no. 7, pp. 481 483, Jul. 2005. [16] J. S. Hong and M. J. Lancaster, Microstrip Filter for RF/Microwave Application. New York: Wiley, 2001, ch. 10 and 11.

762 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 2, FEBRUARY 2006 Chi-Feng Chen was born in PingTung, Taiwan, R.O.C., on September 3, 1979. He received the B.S. degree in physics from the Chung Yuan Christian University, Taoyuan, Taiwan, R.O.C., in 2001, the M.S. degree in electrophysics from the National Chiao Tung University, Hsinchu, Taiwan, R.O.C., in 2003, and is currently working toward the Ph.D. degree in communication engineering at National Taiwan University, Taipei, Taiwan, R.O.C. His research interests include the design of microwave filters and associated RF modules for microwave and millimeter-wave applications. Ting-Yi Huang was born in Hualien, Taiwan, R.O.C., on November 12, 1977. He received the B.S. degree in electrical engineering and M.S. degree in communication engineering from National Taiwan University, Taipei, Taiwan, R.O.C., in 2000 and 2002, respectively, and 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, R.O.C., in 1979 and 1985, respectively. In 1982, he joined the faculty of the Department of Electrical Engineering, National Taiwan University, where he is currently a Professor. He is also with the Graduate Institute of Communications Engineering, National Taiwan University, which was established in 1997. 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 at Los Angeles. He was also appointed Director of the National Center for High-Performance Computing (1998 2000) 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.