Design of Compact and Sharp-Rejection Ultra ... - Semantic Scholar
IEICE TRANS. ELECTRON., VOL.E90–C, NO.8 AUGUST 2007
1652
LETTER
Design of Compact and Sharp-Rejection Ultra Wideband Bandpass Filters Using Interdigital Stepped-Impedance Resonators Cheng-Yuan HUNG† , Student Member, Min-Hang WENG†† , Member, Yan-Kuin SU†a) , Ru-Yuan YANG† , and Hung-Wei WU† , Student Members
SUMMARY In this paper, a compact ultra-wideband bandpass filter (UWB-BPF) using pseudo-interdigital stepped-impedance resonators (PIDT-SIRs) is designed and implemented on a commercial printed circuit board (PCB) of RT/Duroid 5880 substrate. The first two resonant modes of the SIR are coupled together and they are applied to create a wide passband. The proposed filter at center frequency f0 of 7.1 GHz has very good measured characteristics including the bandwidth of 3.68–10.46 GHz (3dB fractional bandwidth of 95%), low insertion loss of −0.5±0.4 dB, sharp rejection due to two transmission zeros in the passband edge created by the inter-stage coupling. Experimental results of the fabricated filter show a good agreement with the predicted results. key words: ultra-wideband, pseudo-interdigital, stepped impedance resonators, transmission zeros, bandwidth
1.
Introduction
A small size and high selectivity microwave bandpass filter (BPF) is widely used to enhance the performance of radio frequency (RF) front end. These requirements are stricter recently because of the rapidly expanding Ultra-Wideband (UWB) systems. Being one of the important component blocks, attempts to develop a UWB-BPF were made in [1]– [3] in order to achieve such a specified UWB passband with a 100% fractional bandwidth (FBW) at the central frequency around 7 GHz. In the past, conventional microstrip interdigital bandpass filters (IDT-BPFs) using quarter-wavelength resonators were compact while they require short-circuit connections with via holes. A new type of miniaturized IDT-BPFs by using pseudo-IDT structure (PIDT) without via holes ground was reported [4], showing more compact size and an attenuation pole due to the effect of interstagecoupling. On the other hand, a PIDT-BPF using tapped input/output (I/O) and stepped-impedance resonator (SIR) was reported to improve the skirt characteristics and stopband rejections [5]. However, these microstrip PIDT-BPFs fabricated on PCB have a relatively small bandwidth [4], [5], since the coupling level of interdigital electrode using conventional design methods were limited. In this paper, we developed a very compact UWB-BPF with FBW larger than 95% based on PIDT-SIRs. By combining the first two resonant modes of the SIR, the UWB Manuscript received October 4, 2006. The authors are with Advanced Optoelectronic Technology Center, Institute of Microelectronics, Department of Electrical Engineering, National Cheng Kung University, Taiwan. †† The author is with the National Nano Device Laboratories, Taiwan. a) E-mail: [email protected] DOI: 10.1093/ietele/e90–c.8.1652
performance is obtained. Additionally, it is able to place two transmission zeros near the passband edge so that higher selectivity with fewer resonators could be obtained. After optimizing the filter design using a complete full-wave electromagnetic (EM) simulation [6], the fabricated filter is executed on commercial PCB of RT/Duroid 5880 substrate to experimentally verify the predicted results of our design. 2.
UWB-BPF: Schematic and Principle
Figure 1 depicts the schematic of the proposed UWB-BPF using PIDT-SIR on commercial PCB RT/Duroid 5880. This filter basically consists of two identical SIR and two tapped I/O at the two sides. It is noted that two arms of each PIDTSIR are coupled each other to form the strong coupling and compact structure. The SIR is symmetrical and has two different characteristic impedance lines, low-impedance (Z1 ) line in center and two identical high-impedance (Z2 ) lines in two sides, where R is the impedance ratio of the SIR defined as R = Z2 /Z1 . For a uniform resonator with near half-wavelength, the first spurious response mode f s1 is centered at twice the fundamental frequency f0 , the second spurious response mode f s2 at triple the fundamental frequency f0 , and so on [7]. It is well known that the typical SIR with R = Z2 /Z1 < 1, has shorter electrical length and shifts the first spurious response mode f s1 to higher frequency. However, in our UWB-BPF, the first two resonant modes ( f0 and f s1 ) are used and taken into account together and they are applied to create a wide passband. Therefore, the SIR with R = Z2 /Z1 > 1, as shown in Fig. 2(a), is used in our design. The resonance conditions can be described by the equation from [7]:
†
Fig. 1 Practical layout of the designed UWB-BPF designed on a 0.787mm-thick substrate with a dielectric constant of 2.2.
c 2007 The Institute of Electronics, Information and Communication Engineers Copyright
LETTER
1653 Table 1 Design parameters of the SIR on a substrate of dielectric constant 2.2 and thickness 0.787 mm.
(a)
(b) Fig. 2 (a) Typical structure of the SIR (R = Z2 /Z1 > 1), (b) resonant electric length of first spurious response mode versus stepped percentage x with impedance ratio R = 1, 1.2, 2, 3 as a parameter.
R = tan θ1 tan θ2 or R = − cot θ1 tan θ2
(1)
The low-impedance wavelength θ1 is not equal to highimpedance wavelength θ2 in this study. To increase the extra design freedom, the stepped percentage x is defined as the portion of θ1 and θ2 to the total wavelength of the SIR (θt = 2(θ1 + θ2 )), i.e., (1 − x) · θt 2 x · θt θ2 = 2
θ1 =
Substituting (2) and (3) into (1) yields [8] x · θ (1 − x) · θt t R · cot = tan 2 2 or x · θ (1 − x) · θt t R · cot = − cot 2 2
(2) (3)
(4)
The resonant electric length of first spurious response mode versus with impedance ratio R = 1, 1.2, 2, 3 as a parameter is analyzed and plotted in Fig. 2(b). From the analyzed results, it is found that the first spurious response mode f s1 goes toward the fundamental response mode f0 as stepped percentage x is around 0.76. The first spurious response mode f s1 in SIR with more lager R value is closer to the fundamental response mode f0 . By properly choosing different combinations of x and R values, the first two resonant
Fig. 3 The simulated frequency responses of case 1, case 2 and case 3. The designed parameters of case 1, case 2 and case 3 are shown in Table 1.
modes can be combined together to create a wide passband. Three cases are designed and simulated, including case 1, case 2 and case 3 of SIR with the parameters listed in Table 1. The SIRs are designed with fixed fundamental frequency, but different first spurious response modes ( f s1 ) by choosing different combinations of x and R from Fig. 2(b) and, thereby, the dimensions of each SIR can be determined. In an actual design, the impedance ratio R and stepped percentage x should be slightly tuned in a complete full-wave electromagnetic (EM) simulation [6] to consider the equivalent capacitances of the step discontinuities, the dependence of the propagation constants of the width of the transmission lines, and so on [8]. The simulated frequency responses of case 1, case 2 and case 3 are shown in Fig. 3. In case 1 with R = 1.2 and x = 0.76, the first spurious response mode f s1 is far away to the fundamental frequency f0 , due to the small R value. Therefore, the first spurious response mode f s1 can not couple to the fundamental frequency f0 to form a broader passband. In case 3 with R = 3 and x = 0.76, a passband with a center frequency f0 = 6.83 GHz and bandwidth of 3.6– 9.16 GHz (3-dB FBW= 87%) is obtained. The FBW is not large enough since the first spurious response mode f s1 is close to the fundamental frequency f0 , due to the larger R value. In case 2 with R = 2 and x = 0.76, a satisfied pass-
IEICE TRANS. ELECTRON., VOL.E90–C, NO.8 AUGUST 2007
1654
band at center frequency f0 = 7.1 GHz and bandwidth of 3.74–10.43 GHz (3-dB FBW= 94%) is obtained. It is obvious that the case 2 has better performance than the other filters. Therefore, the case 2 is optimum design condition of UWB-BPF in this paper. Additionally, the frequency skirts of the passband edge are very sharp, since two transmission zeros are produced from the multi-path effect of the PIDT-SIRs [7]. This is a very useful feature for many RF transmitters and receives in rejecting image frequencies and enhancing the attenuation characteristics in the stopband of the filter. 3.
Experimental Results and Discussion
A RT/Duroid 5880 substrate with a relative dielectric constant of 2.2, a loss tangent of 0.001, and a thickness of 0.787 mm, is used for the simulation and practical fabrication. The tapped-line I/O are designed for 50 Ω. To further enhance the rejection level of the passband skirt, the position of the tapped-line I/O (t = 7 mm) is designed for the optimum external quality by using a complete fullwave EM simulation [6]. Using the above guidelines with case 2, the fabricated filter consists of two SIRs having the low-impedance (Z1 =69 Ω) line section with a strip width of 1.44 mm and the high-impedance (Z2 =138 Ω) line sections with a strip width of 0.3 mm. At the stepped percentage x = 0.76, the length L is 11.2 mm. Additionally, the coupling level has been improved in this study, since the spacing (s = 0.1 mm) between a pair of PIDT-SIRs is scaled down. The designed filter is then fabricated and measured by an HP8510C Network Analyzer. Figure 4 shows the predicted and measured results of designed UWB-BPF at center frequency f0 = 7.1 GHz. The measured results of the fabricated BPF have low insertion loss of −0.5±0.4 dB and bandwidth of 3.68–10.46 GHz (3-dB FBW= 95%). The finite transmission zeros occur in the lower side of passband edge at 3.26 GHz with −35 dB attenuation, indicating a high sensitivity of the stopband behavior with 76.2 dB/GHz attenuation slope and in the higher side of passband edge at 11.3 GHz with −38 dB attenuation, in-
Fig. 4 Predicted and measured frequency response of the fabricated UWB-BPF. The designed parameters are those in case 2, shown in Table 1.
dicating a high sensitivity of the stopband behavior with 42 dB/GHz attenuation slope. As the predicted results, two transmission zeros at the passband edges are clearly observed. It is an interesting performance, since the proposed UWB-BPF only uses two SIRs to realize better attenuation rate. Moreover, the whole size of the fabricated filter is 5.6 mm × 11.5 mm, i.e., approximately 0.18λg by 0.36λg , where λg is the guided wavelength on the substrate at the center frequency, as shown in the inset of Fig. 4. The size of the proposed is smaller than those of the five-resonators broadband microstrip filter (FRBMF, size of 4.56 mm × 20 mm) fabricated on RT/Duroid 6010 (εr =10.8) at 6 GHz [1] and the parallel coupled-line microstrip broadband filter (PCMBF, size of 2 mm × 35 mm) fabricated on RT/Duroid 6010 (εr =10.8) at 5 GHz [2]. Although the measured results are slightly different from the predicted results in the higher band, which can be considered as the manmade fabricated error or material dispersion, the proposed UWB-BPF using PIDT-SIRs still shows a good potential to be advantageous in the more advantages for broadband communications, and compact realization on the commercial printed circuit board (PCB) substrate without using expensive lithography process. 4.
Conclusion
In this paper, we have developed an ultra-wideband bandpass filter (UWB-BPF) using pseudo-interdigital steppedimpedance resonators (PIDT-SIRs), for the first time, with improved skirt characteristics and very compact size. In our design, the first two resonant modes of the SIR with stepped impedance ratio larger than 1 are taken into account together and they are applied to make up a wide dominant passband. The designed filter was fabricated and measured, showing good characteristics. References [1] W. Menzel, L. Zhu, K. Wu, and F. B¨ogelsack, “On the design of novel compact broad-band planar filters,” IEEE Trans. Microw. Theory Tech., vol.51, no.2, pp.364–370, Feb. 2003. [2] C.C. Chen, J.T. Kuo, M. Jiang, and A. Chin, “Study of parallel coupled-line microstrip filter in broadband,” Microw. Opt. Technol. Lett., vol.48, no.2, pp.373–375, Feb. 2006. [3] S. Sun and L. Zhu, “Capacitive-ended interdigital coupled lines for UWB bandpass filters with improved out-of-band performances,” IEEE Microw. Wireless Compon. Lett., vol.16, no.8, Aug. 2006. [4] J.S. Hong and M.J. Lancaster, “Development of new microstrip pseudo-interdigital bandpass filters,” IEEE Microw. Guid. Wave Lett., vol.5, no.8, pp.261–263, Aug. 1995. [5] M.H. Weng, W.N. Chen, T.H. Huang, C.Y. Hung, and H.W. Wu, “Stepped impedance resonator bandpass filters using tapped-line for controlling spurious response,” Microw. Opt. Technol. Lett., vol.40, no.6, pp.481–484, March 2004. [6] Zeland Software, Inc., IE3D Simulator, 1997. [7] M. Makimoto and S. Yamashita, “Bandpass filters using parallel coupled stripline stepped impedance resonators,” IEEE Trans. Microw. Theory Tech., vol.28, no.12, pp.1413–1417, Dec. 1980. [8] C.F. Chen, T.Y. Huang, and R.B. Wu, “Design of microstrip bandpass filters with multiorder spurious-mode suppression,” IEEE Trans. Microw. Theory Tech., vol.53, no.12, pp.3788–3793, Dec. 2005.
1652
LETTER
Design of Compact and Sharp-Rejection Ultra Wideband Bandpass Filters Using Interdigital Stepped-Impedance Resonators Cheng-Yuan HUNG† , Student Member, Min-Hang WENG†† , Member, Yan-Kuin SU†a) , Ru-Yuan YANG† , and Hung-Wei WU† , Student Members
SUMMARY In this paper, a compact ultra-wideband bandpass filter (UWB-BPF) using pseudo-interdigital stepped-impedance resonators (PIDT-SIRs) is designed and implemented on a commercial printed circuit board (PCB) of RT/Duroid 5880 substrate. The first two resonant modes of the SIR are coupled together and they are applied to create a wide passband. The proposed filter at center frequency f0 of 7.1 GHz has very good measured characteristics including the bandwidth of 3.68–10.46 GHz (3dB fractional bandwidth of 95%), low insertion loss of −0.5±0.4 dB, sharp rejection due to two transmission zeros in the passband edge created by the inter-stage coupling. Experimental results of the fabricated filter show a good agreement with the predicted results. key words: ultra-wideband, pseudo-interdigital, stepped impedance resonators, transmission zeros, bandwidth
1.
Introduction
A small size and high selectivity microwave bandpass filter (BPF) is widely used to enhance the performance of radio frequency (RF) front end. These requirements are stricter recently because of the rapidly expanding Ultra-Wideband (UWB) systems. Being one of the important component blocks, attempts to develop a UWB-BPF were made in [1]– [3] in order to achieve such a specified UWB passband with a 100% fractional bandwidth (FBW) at the central frequency around 7 GHz. In the past, conventional microstrip interdigital bandpass filters (IDT-BPFs) using quarter-wavelength resonators were compact while they require short-circuit connections with via holes. A new type of miniaturized IDT-BPFs by using pseudo-IDT structure (PIDT) without via holes ground was reported [4], showing more compact size and an attenuation pole due to the effect of interstagecoupling. On the other hand, a PIDT-BPF using tapped input/output (I/O) and stepped-impedance resonator (SIR) was reported to improve the skirt characteristics and stopband rejections [5]. However, these microstrip PIDT-BPFs fabricated on PCB have a relatively small bandwidth [4], [5], since the coupling level of interdigital electrode using conventional design methods were limited. In this paper, we developed a very compact UWB-BPF with FBW larger than 95% based on PIDT-SIRs. By combining the first two resonant modes of the SIR, the UWB Manuscript received October 4, 2006. The authors are with Advanced Optoelectronic Technology Center, Institute of Microelectronics, Department of Electrical Engineering, National Cheng Kung University, Taiwan. †† The author is with the National Nano Device Laboratories, Taiwan. a) E-mail: [email protected] DOI: 10.1093/ietele/e90–c.8.1652
performance is obtained. Additionally, it is able to place two transmission zeros near the passband edge so that higher selectivity with fewer resonators could be obtained. After optimizing the filter design using a complete full-wave electromagnetic (EM) simulation [6], the fabricated filter is executed on commercial PCB of RT/Duroid 5880 substrate to experimentally verify the predicted results of our design. 2.
UWB-BPF: Schematic and Principle
Figure 1 depicts the schematic of the proposed UWB-BPF using PIDT-SIR on commercial PCB RT/Duroid 5880. This filter basically consists of two identical SIR and two tapped I/O at the two sides. It is noted that two arms of each PIDTSIR are coupled each other to form the strong coupling and compact structure. The SIR is symmetrical and has two different characteristic impedance lines, low-impedance (Z1 ) line in center and two identical high-impedance (Z2 ) lines in two sides, where R is the impedance ratio of the SIR defined as R = Z2 /Z1 . For a uniform resonator with near half-wavelength, the first spurious response mode f s1 is centered at twice the fundamental frequency f0 , the second spurious response mode f s2 at triple the fundamental frequency f0 , and so on [7]. It is well known that the typical SIR with R = Z2 /Z1 < 1, has shorter electrical length and shifts the first spurious response mode f s1 to higher frequency. However, in our UWB-BPF, the first two resonant modes ( f0 and f s1 ) are used and taken into account together and they are applied to create a wide passband. Therefore, the SIR with R = Z2 /Z1 > 1, as shown in Fig. 2(a), is used in our design. The resonance conditions can be described by the equation from [7]:
†
Fig. 1 Practical layout of the designed UWB-BPF designed on a 0.787mm-thick substrate with a dielectric constant of 2.2.
c 2007 The Institute of Electronics, Information and Communication Engineers Copyright
LETTER
1653 Table 1 Design parameters of the SIR on a substrate of dielectric constant 2.2 and thickness 0.787 mm.
(a)
(b) Fig. 2 (a) Typical structure of the SIR (R = Z2 /Z1 > 1), (b) resonant electric length of first spurious response mode versus stepped percentage x with impedance ratio R = 1, 1.2, 2, 3 as a parameter.
R = tan θ1 tan θ2 or R = − cot θ1 tan θ2
(1)
The low-impedance wavelength θ1 is not equal to highimpedance wavelength θ2 in this study. To increase the extra design freedom, the stepped percentage x is defined as the portion of θ1 and θ2 to the total wavelength of the SIR (θt = 2(θ1 + θ2 )), i.e., (1 − x) · θt 2 x · θt θ2 = 2
θ1 =
Substituting (2) and (3) into (1) yields [8] x · θ (1 − x) · θt t R · cot = tan 2 2 or x · θ (1 − x) · θt t R · cot = − cot 2 2
(2) (3)
(4)
The resonant electric length of first spurious response mode versus with impedance ratio R = 1, 1.2, 2, 3 as a parameter is analyzed and plotted in Fig. 2(b). From the analyzed results, it is found that the first spurious response mode f s1 goes toward the fundamental response mode f0 as stepped percentage x is around 0.76. The first spurious response mode f s1 in SIR with more lager R value is closer to the fundamental response mode f0 . By properly choosing different combinations of x and R values, the first two resonant
Fig. 3 The simulated frequency responses of case 1, case 2 and case 3. The designed parameters of case 1, case 2 and case 3 are shown in Table 1.
modes can be combined together to create a wide passband. Three cases are designed and simulated, including case 1, case 2 and case 3 of SIR with the parameters listed in Table 1. The SIRs are designed with fixed fundamental frequency, but different first spurious response modes ( f s1 ) by choosing different combinations of x and R from Fig. 2(b) and, thereby, the dimensions of each SIR can be determined. In an actual design, the impedance ratio R and stepped percentage x should be slightly tuned in a complete full-wave electromagnetic (EM) simulation [6] to consider the equivalent capacitances of the step discontinuities, the dependence of the propagation constants of the width of the transmission lines, and so on [8]. The simulated frequency responses of case 1, case 2 and case 3 are shown in Fig. 3. In case 1 with R = 1.2 and x = 0.76, the first spurious response mode f s1 is far away to the fundamental frequency f0 , due to the small R value. Therefore, the first spurious response mode f s1 can not couple to the fundamental frequency f0 to form a broader passband. In case 3 with R = 3 and x = 0.76, a passband with a center frequency f0 = 6.83 GHz and bandwidth of 3.6– 9.16 GHz (3-dB FBW= 87%) is obtained. The FBW is not large enough since the first spurious response mode f s1 is close to the fundamental frequency f0 , due to the larger R value. In case 2 with R = 2 and x = 0.76, a satisfied pass-
IEICE TRANS. ELECTRON., VOL.E90–C, NO.8 AUGUST 2007
1654
band at center frequency f0 = 7.1 GHz and bandwidth of 3.74–10.43 GHz (3-dB FBW= 94%) is obtained. It is obvious that the case 2 has better performance than the other filters. Therefore, the case 2 is optimum design condition of UWB-BPF in this paper. Additionally, the frequency skirts of the passband edge are very sharp, since two transmission zeros are produced from the multi-path effect of the PIDT-SIRs [7]. This is a very useful feature for many RF transmitters and receives in rejecting image frequencies and enhancing the attenuation characteristics in the stopband of the filter. 3.
Experimental Results and Discussion
A RT/Duroid 5880 substrate with a relative dielectric constant of 2.2, a loss tangent of 0.001, and a thickness of 0.787 mm, is used for the simulation and practical fabrication. The tapped-line I/O are designed for 50 Ω. To further enhance the rejection level of the passband skirt, the position of the tapped-line I/O (t = 7 mm) is designed for the optimum external quality by using a complete fullwave EM simulation [6]. Using the above guidelines with case 2, the fabricated filter consists of two SIRs having the low-impedance (Z1 =69 Ω) line section with a strip width of 1.44 mm and the high-impedance (Z2 =138 Ω) line sections with a strip width of 0.3 mm. At the stepped percentage x = 0.76, the length L is 11.2 mm. Additionally, the coupling level has been improved in this study, since the spacing (s = 0.1 mm) between a pair of PIDT-SIRs is scaled down. The designed filter is then fabricated and measured by an HP8510C Network Analyzer. Figure 4 shows the predicted and measured results of designed UWB-BPF at center frequency f0 = 7.1 GHz. The measured results of the fabricated BPF have low insertion loss of −0.5±0.4 dB and bandwidth of 3.68–10.46 GHz (3-dB FBW= 95%). The finite transmission zeros occur in the lower side of passband edge at 3.26 GHz with −35 dB attenuation, indicating a high sensitivity of the stopband behavior with 76.2 dB/GHz attenuation slope and in the higher side of passband edge at 11.3 GHz with −38 dB attenuation, in-
Fig. 4 Predicted and measured frequency response of the fabricated UWB-BPF. The designed parameters are those in case 2, shown in Table 1.
dicating a high sensitivity of the stopband behavior with 42 dB/GHz attenuation slope. As the predicted results, two transmission zeros at the passband edges are clearly observed. It is an interesting performance, since the proposed UWB-BPF only uses two SIRs to realize better attenuation rate. Moreover, the whole size of the fabricated filter is 5.6 mm × 11.5 mm, i.e., approximately 0.18λg by 0.36λg , where λg is the guided wavelength on the substrate at the center frequency, as shown in the inset of Fig. 4. The size of the proposed is smaller than those of the five-resonators broadband microstrip filter (FRBMF, size of 4.56 mm × 20 mm) fabricated on RT/Duroid 6010 (εr =10.8) at 6 GHz [1] and the parallel coupled-line microstrip broadband filter (PCMBF, size of 2 mm × 35 mm) fabricated on RT/Duroid 6010 (εr =10.8) at 5 GHz [2]. Although the measured results are slightly different from the predicted results in the higher band, which can be considered as the manmade fabricated error or material dispersion, the proposed UWB-BPF using PIDT-SIRs still shows a good potential to be advantageous in the more advantages for broadband communications, and compact realization on the commercial printed circuit board (PCB) substrate without using expensive lithography process. 4.
Conclusion
In this paper, we have developed an ultra-wideband bandpass filter (UWB-BPF) using pseudo-interdigital steppedimpedance resonators (PIDT-SIRs), for the first time, with improved skirt characteristics and very compact size. In our design, the first two resonant modes of the SIR with stepped impedance ratio larger than 1 are taken into account together and they are applied to make up a wide dominant passband. The designed filter was fabricated and measured, showing good characteristics. References [1] W. Menzel, L. Zhu, K. Wu, and F. B¨ogelsack, “On the design of novel compact broad-band planar filters,” IEEE Trans. Microw. Theory Tech., vol.51, no.2, pp.364–370, Feb. 2003. [2] C.C. Chen, J.T. Kuo, M. Jiang, and A. Chin, “Study of parallel coupled-line microstrip filter in broadband,” Microw. Opt. Technol. Lett., vol.48, no.2, pp.373–375, Feb. 2006. [3] S. Sun and L. Zhu, “Capacitive-ended interdigital coupled lines for UWB bandpass filters with improved out-of-band performances,” IEEE Microw. Wireless Compon. Lett., vol.16, no.8, Aug. 2006. [4] J.S. Hong and M.J. Lancaster, “Development of new microstrip pseudo-interdigital bandpass filters,” IEEE Microw. Guid. Wave Lett., vol.5, no.8, pp.261–263, Aug. 1995. [5] M.H. Weng, W.N. Chen, T.H. Huang, C.Y. Hung, and H.W. Wu, “Stepped impedance resonator bandpass filters using tapped-line for controlling spurious response,” Microw. Opt. Technol. Lett., vol.40, no.6, pp.481–484, March 2004. [6] Zeland Software, Inc., IE3D Simulator, 1997. [7] M. Makimoto and S. Yamashita, “Bandpass filters using parallel coupled stripline stepped impedance resonators,” IEEE Trans. Microw. Theory Tech., vol.28, no.12, pp.1413–1417, Dec. 1980. [8] C.F. Chen, T.Y. Huang, and R.B. Wu, “Design of microstrip bandpass filters with multiorder spurious-mode suppression,” IEEE Trans. Microw. Theory Tech., vol.53, no.12, pp.3788–3793, Dec. 2005.
