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1 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 57, NO. 3, MARCH An Inline Coaxial Quasi-Elliptic Filter With Controllable Mixed Electric and Magnetic Coupling Huan Wang, Student Member, IEEE, and Qing-Xin Chu, Member, IEEE Abstract Based on the concept of using controllable mixed electric and magnetic coupling to design planar filters in our earlier work, we propose a novel inline coaxial filter, in which the electric and magnetic coupling can be separately controlled. Due to this controllable mixed coupling, the filter can operate with a quasielliptic characteristic. By modifying resonator structure and inserting additional coupling components, the filter size is substantially reduced and the coupling becomes more easily controllable, thus being able to produce a highly selective filter with a compact size. In addition, asymmetric response can be easily achieved. For the -order filter, a maximum of 1 finite transmission zeros can be realized. Practical designs, concerning a global system for mobile communication specification, show the advantages of this filter. Index Terms Coaxial, elliptic filtering characteristic, inline filter, mixed coupling. I. INTRODUCTION AS THE frequency spectrum becomes more crowded, specifications for channel filters have tended to become more severe. These specifications can be met with quasi-elliptic bandpass filters, where one or more transmission zeros are introduced into the stopbands at finite frequencies [1], [2]. Crosscoupled, bypass-coupled, and source load-coupled filters have been rapidly developed in the past few decades, and they are now being held as the main approaches to realize quasi-elliptic filters. A quasi-elliptic filter with the inline resonator arrangement had been proposed since the early 1970s [3], but following a long period after that time, due to the lack of more microwave realizations, inline quasi-elliptic filters have rarely been reported. The difference of the filter in [3] from those common combline filters with a Chebyshev response is that the resonant conductors are placed together more closely so that both electric and magnetic coupling between conductors becomes stronger, resulting in some internal antiresonances [4]. The mechanism of the generation of transmission zeros through mixed electric and magnetic coupling has been discussed recently by us in [5] and [6]. The filter in [3] may be suitable for the applications in VHF and UHF bands; however, if it is used in higher frequency bands, there will be manufacturing problems due to the too small gaps Manuscript received August 07, 2008; revised November 21, First published February 06, 2009; current version published March 11, This work was supported by the Science Fund of China under Grant U and by the Nature Science Fund of China for the Youth under Grant The authors are with the School of Electronic and Information Engineering, South China University of Technology, Guangzhou , China ( pactreewh@yahoo.com.cn; qxchu@scut.edu.cn). Color versions of one or more of the figures in this paper are available online at Digital Object Identifier /TMTT between resonators. Besides, once the filter is fabricated, there will be also tuning problems (the electric and magnetic coupling cannot be separately tuned) for this type of filter. Inline filters are attractive for some specific applications in comparison with their cross-coupled counterparts. They can avoid isolation problems between the input and output, which often exist in filters having folded cross-coupled topologies [2]. Moreover, the input and output at opposite sides make it much easy to employ the filter in duplexers and multiplexers, which are widely used in base stations and satellite communications. Multiplexers composed of inline filters will have a more compact size. In [7], a comb filter composed of cascaded triplet and quadruplet filtering sections was presented. Strictly speaking, it is not an inline filter, though the input and output are on different sides. The maximum number of transmission zeros of this filter is, where is the filter order. As the improved product of the filter in [7], a more inline filter has been proposed in [8]; however, only two transmission zeros can be generated by the first and last resonators, which do not contribute transmission poles to the passband, no matter how many resonators the filter has. Today, coaxial cavity filters are widely employed in base-station applications. A large number of studies in the area of analysis and design of coaxial cavity filters have been conducted over the past two decades [9] [12]. For coaxial filters, most of the current research interests have been focusing on the sophisticated cross-coupled configurations to reduce manufacturing costs. In this paper, a novel inline coaxial cavity filter is proposed, and it will be shown that costs can be further reduced by exploring mixed coupling techniques, which can reduce the number of resonators and filter size (the resonator lines are only ). In addition, asymmetric filtering characteristics, which can prevent transmitter-to-receiver interference, can be easier to realize as compared with cross-coupled designs. The mixed coupled equivalent circuit for the coaxial filter, as will be shown below in this paper, is, in fact, a complementary circuit to that presented in [6]. Thus, for a two-pole mixed coupled coaxial filter, the transmission zero will occur at the lower side of the passband when electric coupling dominants, and vice versa at the upper side when magnetic coupling dominants. This phenomenon is different from that in [6], but is the same as that in [3]. In order to build mixed coupling, conventional coaxial filters are modified in such a way that both electric and magnetic coupling with strong intensities can be easily obtained, and due to this enhancement of coupling, the proposed filter has an achievable bandwidth of 5%, which is broader than that reported in [3]. The manufacturing and tuning problems to the filter in [3] do not exist in the proposed filter. For the -order filter, since the mechanism of generating transmission zeros of /$ IEEE

2 668 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 57, NO. 3, MARCH 2009 Fig. 2. Frequency responses obtained by replacing the two shorts with two ports in Fig. 1, while f =1:7475 GHz. Fig. 1. (top) Structure of two electrically and magnetically mixed coupled coaxial cavities, consisting of two modified resonator rods, a coupling strip, and a coupling pin. (bottom) Resulting equivalent circuit when the reference planes are taken at the ends of the inner rods. the proposed inline filter is completely different from that in [7] and [8], a maximum of finite transmission zeros can be realized. For example, the proposed three-pole filter has two independently tunable transmission zeros, which can be located either above or below the passband. The factor of the new coaxial filter is evaluated as 855. The losses are largely due to the additional coupling components, which are used to realize strong electric coupling. Asymmetrical mixed coupled cases are also included in this paper, and a complete design process of a three-pole filter with two prescribed transmission zeros, concerning a global system for mobile communication (GSM) application, is discussed at length. It should be mentioned that the new coaxial filter is also applicable for satellite communications. II. IMPLEMENTATION OF MIXED COUPLING In order to construct mixed electric and magnetic coupling, which is usable and controllable for our inline elliptic filter design, the inner rods of a conventional coaxial filter are modified as shown in Fig. 1. The metallic cap on the open end of the inner rod greatly increases the capacitance loading the coaxial resonator, thus not only reducing the required filter size (the resonator line is only ), but also enhancing the electric coupling between two cavities [13]. In order to further strengthen electric coupling, a conducting strip adhered to a dielectric substrate is inserted in the coupling iris, and connects the caps of both inner rods. Besides, the current through a conducting pin, which taps the bellies of two adjacent rods, will behave as a coupling inductance. The modeling method for coaxial filter design developed in [14] and [15] is very useful here to illustrate and prove our interpretation on the coupling structure in Fig. 1. If the bottom shorts are removed, the structure can be seen as a section of two coaxial cables that couple to each others. The only difference between the equivalent circuits given in [14] and Fig. 1 is the additional series inductance, which shunts the current flowing into the reference plane. Following the element extraction method in [14] and [15], we can use ports, in place of shorts, to simulate the mixed coupled structure (all simulations in this paper are carried out via Ansoft Corporation s High Frequency Structure Simulator (HFSS) [16]). The element values and can then be extracted at (the center frequency of a filter). Fig. 2 plots the frequency responses of such a physical structure and its equivalent circuit in Fig. 1. From Fig. 2, we can see perfect agreement between the responses obtained from the circuit and physical structure. Therefore, the coexistence of mixed electric and magnetic coupling in our novel coaxial structure is proven. III. SECOND-ORDER FILTER To design a second-order mixed coupled filter is very typical since that it includes most problems on how to transform an ideal filtering function into practice, e.g., how to determine coupling dimensions of physical structures to realize the wanted coupling coefficients and transmission zeros. A second-order mixed electric and magnetic coupling coaxial filter inclusive of external coupling structures is shown in Fig. 3. Replace the parallel capacitance and transmission lines of length in Fig. 1with the lumped elements and in Fig. 3, then we can find that the form of the circuit in Fig. 3 is a complement to that given in our previous work [6] where are the frequencies of the even and odd modes, respectively. (1) (2) (3)

3 WANG AND CHU: INLINE COAXIAL QUASI-ELLIPTIC FILTER WITH CONTROLLABLE MIXED ELECTRIC AND MAGNETIC COUPLING 669 Fig. 4. Impact of changing the strip length P, when G = 24mm and S = 7:5 mm. Fig. 3. (top) Two-pole filter structure including tap feeders. (bottom) Equivalent circuit in terms of lumped elements. represents electric coupling and magnetic coupling coefficients, respectively. (4) represents the transmission zero induced by mixed coupling and the self-resonant frequency of each individual resonator, respectively. In Fig. 3, denotes the length of the coupling strip, denotes the length of the substrate, denotes the distance between the coupling pin and rod end, and denotes the position of the feeding line. By intuition, it seems that the larger the strip length, the stronger the electric coupling ; the smaller the spacing, the stronger the magnetic coupling. This assumption is based on the facts that the distributed capacitance between the strip and rod ends depends on the area of the strip, and that the inductive current on the coupling pin depends upon the magnetic flux through the loop, which is shaped by the pin, cavity, and two rods. To verify our assumption, and to investigate the character of the proposed mixed coupled coaxial, the structure in Fig. 3 will be driven under the same port condition (e.g., mm) in the following simulations. The dielectric substrate that sustains the coupling strip is of relative permittivity and mm. A. Impact of the Coupling Strip Keeping unchanged (e.g., mm) and altering, the simulated responses are given in Fig. 4. We can find that both the odd-mode frequency and transmission zero shift to the left as increases, whereas the even-mode frequency does not change. This is so because the series capacitance or coupling capacitance strongly depends on the capacitance existing between the strip and rod-ends, and increasing will enlarge [refer to (2) and (4)]. B. Impact of the Coupling Pin Keeping unchanged (e.g., mm) and altering, the simulated responses are given in Fig. 5. Once again, both the Fig. 5. Impact of changing the pin position S when G = 24mm and P = 19 mm. odd-mode frequency and transmission zero shift to the left as increases, whereas the even-mode frequency is not changed. This is because the series inductance strongly depends on the position of the coupling pin, and increasing will enlarge [refer to (2) and (4)]. It should be noted that, in order to clearly show the two resonant peaks or mode frequencies, all curves plotted in Figs. 4 and 5 are obtained by renormalizing the ports impedances to a small value, in our case, 2. In the design of a two-pole filter, external coupling must be predetermined, viz., before the extraction of those mode frequencies or coupling coefficients, the tap line feeder should be included. This is because, in the real world, the feeding structure would not be an ideal transformer, and it will not only affect the mode frequencies, but also alter the transmission zero that is obtained from the coupled coaxial cables excluding external coupling (see Fig. 1). Next, we will present in detail how to design a two-pole mixed coupled coaxial filter that has a transmission zero of GHz, center frequency of GHz, a bandwidth of 45 MHz, and maximum return loss of 20 db. This specification is considered for a GSM application. Designing a coaxial filter with mixed coupling would not be much different from designing a planar filter that was introduced in [6]. According to the specification, the design parameters of the simple prototype shown in Fig. 3 can be given as follows: GHz,. The tap point of mm is first of all determined to satisfy the right external, and then we normalize the port

4 670 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 57, NO. 3, MARCH 2009 impedance to a small value to clearly show two eigenmode frequencies. It is obvious that the changes of the odd mode and transmission zero frequencies lead to the changes of and, as shown in Figs. 4 and 5. However, at the same time, the self-resonant frequency also changes. Therefore, using and to design a mixed coupled coaxial filter seems a little inconvenient. It will be easier if we take note of the invariable even-mode frequency. By considering (1) (4), the exact relationship between the mode frequencies and coupling coefficients can be derived as follows: (5) Thus, the goals of the designing parameters GHz,, and can be expressed in terms of even/odd mode and transmission zero frequencies GHz, GHz, and GHz. By now, the design method may clearly show itself to us: choose initial values and, as well as the length of the coaxial resonators, to insure GHz; then adjust and to satisfy the other goals GHz and GHz. The curves of odd-mode frequency as functions of and are partly given in Fig. 6, as are the curves of the transmission zero. For all lines in Fig. 6, the even-mode frequency is at GHz. We can read from Fig. 6 that, when mm and mm (the strip width has been fixed as 4.5 mm), the two-pole mixed coupled coaxial filter will tally with the given specification. All the circuit simulation, electromagnetic (EM) simulation, and measurement results are given in Fig. 7, where good matches can be observed. A fabricated photograph is illustrated in Fig. 8. From (1), we can find that it is hard to simultaneously realize a larger coupling coefficient and closer-to-band transmission zero, except that both and are very large. In our coaxial filter, both and are able to possess larger values, and therefore, the transmission zero of the proposed filter is much closer to the passband while the passband has not been narrowed. Fig. 6. Changes of odd-mode frequency f and transmission zero f, while f =1:775 GHz (G =20mm). Fig. 7. Frequency responses of the two-pole filter. IV. THIRD-ORDER FILTER Section III has presented the basic concept and design method for the electrically and magnetically mixed coupled coaxial filter. However, two resonator filters are not sufficient for wireless base-station filters. There is a problem to realize filters with a higher number of resonators: if we directly cascade some two-pole sections, as we have done in [6], the effects of mixed coupled transmission zeros may deteriorate the passband behavior. That is why the fourth-order filter in [6] has not shown an equal return-loss ripple. This problem should not be neglected for base-station filters. Now we try to show the design of a third-order quasi-elliptical filter having two asymmetrical transmission zeros GHz and GHz, a center frequency of 1.73 GHz, and a bandwidth of 4.5%. These frequencies are near one of the GSM bands. Since the specification requires asymmetric response, it is necessary to consider the self-coupling for each resonant element. The coupled topology is shown in Fig. 9, wherein the self-resonance of each resonator is different from two others. Therefore, the asymmetric coupling coefficients should be redefined as follows [17], [18]: (6)

5 WANG AND CHU: INLINE COAXIAL QUASI-ELLIPTIC FILTER WITH CONTROLLABLE MIXED ELECTRIC AND MAGNETIC COUPLING 671 Fig. 10. Comparison of the mixed coupled filter and conventional CT filter. Fig. 8. Fabricated two-pole coaxial filter. Fig. 9. Three-pole mixed coupled filter network. Fig. 11. Three-pole mixed coupled coaxial filter with asymmetric configuration. where denotes the mutual capacitance between resonators and and denotes the mutual inductance between resonators and. By taking into account Fig. 9, the given specification can be translated into loaded factor, electric and magnetic coupling coefficients, as follows: GHz GHz GHz Fig. 12. Equivalent network for the structure between ports 1 and 2 in Fig. 11, exclusive of Resonator 3. The first transmission zero is produced by the mixed coupling and while the second is produced by and. Fig. 10 plots the ideal filtering responses of this three-pole filter. The response of a conventional cascade trisection (CT) filter, which has a same upper transmission zero as the mixed coupled filter, is also given in Fig. 10. At the lower transmission zero of the mixed coupled filter, the rejection level of the CT filter is lower than 20 db. Extracting and from an asymmetric structure is a little different from that of symmetric case. A coarse physical filter model is shown in Fig. 11, where structural asymmetry is evident. Iris12 and Iris23 separate the total structure into three resonators, i.e., 1 3. Fig. 13. Comparison of the frequency responses obtained from the physical two-pole segment in Fig. 11 and ideal two-pole network in Fig. 12. We only focus on extracting and. Extractions of coupling coefficients between resonators 2 and 3 would follow the same route. If a small rectangular plane, serving as a port, is added at bottom of the right-side wall of Resonator 2, the structure between ports 1 and 2 can be treated as an asymmetric mixed coupled two-pole network (Iris23 shorted), as shown in Fig. 12. Ac-

6 672 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 57, NO. 3, MARCH 2009 of Iris12 are separately determined, we should combine them and again look over the -parameters between ports 1 and 2 to check whether the integrated structure matches the ideal circuit shown in Fig. 12. The -parameters of the physical structure between ports 1 and 2 are shown in Fig. 13, where a comparison of the ideal circuit response is also given. The results of measurement and EM simulation of the threepole mixed coupled coaxial filter are shown in Fig. 14, wherein good agreements are observed. The measured insertion losses are approximately 0.77 db. A closer view of the passband insertion losses and group delays are also given in Fig. 14. A practical filter model is shown in Fig. 15. It should be mentioned that, the dielectric substrate (with a loss tangent of 0.003) used in the filter leads to the decrease of the factor of the structure. An estimate of the value of the new filter is made by using the information indicated in Fig. 14. For the same application, the value of the new filter is evaluated as 855, while a higher value of 3000 can be obtained from an iris-coupled filter having no additional coupling components. V. CONCLUSION An inline coaxial filter with a quasi-elliptic filtering characteristic, which is realized by mixed electric and magnetic coupling, has been shown. We have also discussed the step-by-step design of the mixed coupled coaxial filter, from low order to high order, from a symmetrical case to an asymmetrical case. We trust that the proposed filter is very attractive for wireless base-station filters, as well as satellite communications, due to its size reduction and the reduction in the number of resonators. Fig. 14. Frequency responses of the third-order mixed coupled coaxial filter. (a) Wideband responses. (b) Passband insertion losses. (c) Passband group delays. Fig. 15. Three-pole filter. cording to (6), the left and right parts of Iris12 may be treated independently. Thus, extractions of and is substituted by extractions of and, which can be easily carried out by means of symmetrical technique that was presented in Section III. Once the two parts on both sides REFERENCES [1] R. Levy, R. V. Snyder, and G. Matthaei, Design of microwave filters, IEEE Trans. Microw. Theory Tech., vol. 50, no. 3, pp , Mar [2] R. J. Cameron, General coupling matrix synthesis methods for Chebyshev filtering functions, IEEE Trans. Microw. Theory Tech., vol. 47, no. 4, pp , Apr [3] R. Levy and J. D. Rhodes, A comb-line elliptic filter, IEEE Trans. Microw. Theory Tech., vol. MTT-19, no. 1, pp , Jan [4] S. Amari, G. Tadeson, J. Cihlar, and U. Rosenberg, New parallel =2-microstrip line filters with transmission zeros at finite frequencies, in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2003, vol. 1, pp [5] H. Wang and Q.-X. Chu, Generation of transmission zero through electric and magnetic mixed coupling, in Int. Microwave and. Millimeter Wave Technol. Conf., Apr. 2007, pp [6] Q.-X. Chu and H. Wang, A compact open-loop filter with mixed electric and magnetic coupling, IEEE Trans. Microw. Theory Tech., vol. 56, no. 2, pp , Feb [7] G. Macchiarella and S. C. D Oro, Design of generalized comb filters with asymmetric transmission zeros using arbitrary cascaded triplet and quadruplet sections, in 28th Eur. Microw. Conf., Oct. 1998, vol. 2, pp [8] G. Macchiarella and M. Fumagalli, Inline comb filters with one or two transmission zeros, in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2004, vol. 2, pp [9] H.-W. Yao, K. A. Zaki, A. E. Atia, and R. Hershtig, Full wave modeling of conducting posts in rectangular waveguides and its applications to slot coupled combline filters, IEEE Trans. Microw. Theory Tech., vol. 43, no. 12, pp , Dec [10] Y. Rong and K. A. Zaki, Full-wave analysis of coupling between cylindrical combline resonators, IEEE Trans. Microw. Theory Tech., vol. 47, no. 9, pp , Sep [11] M. El Sabbagh, K. A. Zaki, H.-W. Yao, and M. Yu, Full-wave analysis of coupling between combline resonators and its application to combline filters with canonical configurations, IEEE Trans. Microw. Theory Tech., vol. 49, no. 12, pp , Dec

7 WANG AND CHU: INLINE COAXIAL QUASI-ELLIPTIC FILTER WITH CONTROLLABLE MIXED ELECTRIC AND MAGNETIC COUPLING 673 [12] C. Wang and K. A. Zaki, Full wave modeling of electric coupling probes in combline resonators and filters, in IEEE MTT-S Int. Microw. Symp. Dig., Jun. 2000, vol. 3, pp [13] G. Matthaei, L. Young, and E. M. T. Jones, Microwave Filters, Impedance-Matching Networks, and Coupling Structures. Norwood, MA: Artech House, 1980, p [14] A. Morini, G. Venanzoni, and T. Rozzi, A new adaptive prototype for the design of side-coupled coaxial filters with close correspondence to the physical structure, IEEE Trans. Microw. Theory Tech., vol. 54, no. 3, pp , Mar [15] A. Morini, G. Venanzoni, M. Farina, and T. Rozzi, Modified adaptive prototype inclusive of the external couplings for the design of coaxial filters, IEEE Trans. Microw. Theory Tech., vol. 55, no. 9, pp , Sep [16] Ansoft HFSS. ver. 10, Ansoft Corporation, Pittsburgh, PA, [17] J.-S. Hong and M. J. Lancaster, Microstrip Filters for RF/Microwave Applications. New York: Wiley, [18] J.-F. Liang, K. A. Zaki, and A. E. Atia, Mixed modes dielectric resonator filters, IEEE Trans. Microw. Theory Tech., vol. 42, no. 12, pp , Dec Huan Wang (S 06) was born in Lanzhou, China, on October 27, He received the B.S. degree in electronic engineering from Xidian University, Xi an, China, in 2004, and is currently working toward the Ph.D. degree in electronic and information engineering at the South China University of Technology, Ghuangzhou, China. His research interests include the design of microwave filters and associated RF modules for microwave and millimeter-wave applications. Qing-Xin Chu (M 99) received the B.S., M.E., and Ph.D. degrees in electronic engineering from Xidian University, Xi an, Shaanxi, China, in 1982, 1987, and 1994, respectively. He is currently a Professor with the School of Electronic and Information Engineering, South China University of Technology, Guangzhou, China. He is also the Head of the Research Institute of RF and Wireless Techniques, School of Electronic and Information Engineering, South China University of Technology. From January 1982 to January 2004, he was with the School of Electronic Engineering, Xidian University. From 1997 to 2004, he was a Professor and later the Vice-Dean of the School of Electronic Engineering, Xidian University. From July 1995 to September 1998 and from July to October 2002, he was a Research Associate and Visiting Professor with the Department of Electronic Engineering, Chinese University of Hong Kong, respectively. From February to May 2001 and from December 2002 to March 2003, he was a Research Fellow and Visiting Professor with the Department of Electronic Engineering, City University of Hong Kong, respectively. From July to October 2004, he visited the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore. From January to March 2005, he visited the Department of Electrical and Electronic Engineering, Okayama University. He has authored or coauthored over 200 papers in j and conferences. He is dedicated to the teaching and research of EM theory, microwave circuits, and antennas. His current research interests include analytical and numerical techniques in electromagnetics, RF/microwave integrated circuits, RF/microwave filters, active integrated antennas, spatial power combining arrays, and antennas in mobile communication. Prof. Chu is a Senior Member of the China Electronic Institute (CEI). He was the recipient of the Tan Chin Tuan Exchange Fellowship Award. He was the recipient of a Fellowship presented by the Japan Society for Promotion of Science (JSPS). He was the recipient of 2003 First-Class Educational Award of Shaanxi Province, the 2002 Top-Class Science Award presented by the Education Ministry of China, and the 1995 Second-Class Award of Science and Technology Advance presented by the Electronic Industry Ministry of China.

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