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IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, VOL. 24, NO. 2, FEBRUARY 2014
Quarter-Wavelength Stepped-Impedance Resonator Filter With Mixed Electric and Magnetic Coupling Fang Zhu, Student Member, IEEE, Wei Hong, Fellow, IEEE, Ji-Xin Chen, Member, IEEE, and Ke Wu, Fellow, IEEE
Abstract—This letter proposes a new type of microstrip quarterwavelength stepped-impedance resonator (SIR) filter with controllable mixed electric and magnetic coupling. A conducting pin and an open gap between two coupled SIRs are jointly used to create the mixed coupling, and the electric and magnetic coupling can be separately controlled by adjusting the spacing between the gap and the position of the conducting pin. Based on the proposed structure, a second-order filter and a third-order filter are designed and fabricated. Good agreement between the measured and simulated data is obtained. Index Terms—Bandpass filter (BPF), mixed-coupling, steppedimpedance resonator (SIR), transmission zero (TZ).
I. INTRODUCTION
M
ORDEN communication systems require bandpass filters with high selectivity, low insertion loss (IL), wide stopband and compact size. To meet these specifications, proper transmission zeros (TZs) should be introduced. In general, TZs are implemented by using source-load coupling, cross-coupling or bypass-coupling topologies [1]–[3]. The mixed electric and magnetic coupling between two resonators can also produce TZs [4]–[7]. A microstrip quarter-wavelength filter with separate electric and magnetic coupling paths was presented in [4]. However, the increase of the magnetic or electric coupling will shift the operating frequency down due to the loading effects in two coupling paths. Planar quasi-elliptic filters with inline stepped-impedance resonators (SIRs) were proposed in [5], but the circuit area is larger than twice the size of a quarter-wavelength filter. A microstrip open-loop filter with mixed electric and magnetic coupling was proposed in [6], however, an equal return loss (RL) ripple is not shown. Moreover, for realizing quasi-elliptic filtering function, all the filters in [4]–[6] have to cascade some two-pole section and require at least four resonators, which increase the IL and circuit size. SIW filters with mixed coupling have also been proposed [7], in which a conventional inductive window between two cavities introduces the Manuscript received July 19, 2013; revised September 16, 2013, October 11, 2013; accepted November 03, 2013. Date of publication December 03, 2013; date of current version February 10, 2014. This work was supported in part by Chinese National 973 project 2010CB327400, and in part by the Scientific Research Foundation of Graduate School of Southeast University. F. Zhu, W. Hong, and J. X. Chen are with the State Key Laboratory of Millimeter Waves, School of Information Science and Engineering, Southeast University, Nanjing 210096, China (e-mail:
[email protected]; weihong@seu. edu.cn;
[email protected]). K. Wu is with the Poly-Grames Research Center, Department of Electrical Engineering, Ecole Polytechnique de Montreal, Montreal, QC H3T 1J4, Canada (e-mail:
[email protected]). Digital Object Identifier 10.1109/LMWC.2013.2290225
magnetic coupling and an embedded short-ended strip is employed to create the electric coupling. However, a two-layer substrate is required, which increases the cost. In addition, SIW occupies a much larger size compared with microstrip or coplanar waveguide components, especially at lower frequency band. In this letter, a new type of microstrip quarter-wavelength SIR filter with mixed electric and magnetic coupling is proposed. The electric and magnetic coupling can be separately controlled by tuning the spacing between SIRs and the positions of conducting pins. Compared with the filters in [4]–[6], the proposed filter provides more choices for the resonators’s alignment and requires less number of resonators for realizing quasi-elliptic filtering characteristic, therefore, lower IL and smaller circuit size can be obtained. Compared with the SIW filters proposed in [7], much smaller circuit size and lower cost is obtained. II. FILTER DESIGN A. Second-Order Filter Fig. 1 shows the configuration of the second-order SIR filter, as well as its equivalent circuit. Each resonator has a highand low- section, which behaves as an inductor and a capacitor, respectively. The choice of the dimensions for the SIR has been extensively studied in [2]. The electric coupling is generated between the gap of the coupled low- sections, since the SIR has the maximum electric fringe field density at the open end. The magnetic coupling is achieved by a conducting pin, which taps the two SIRs together and behaves as a coupling inductance. To investigate the character of the proposed structure, the structure is designed on a Rogers RT/Duroid 5880 dielectric substrate with and thickness of 0.508 mm and simulated by HFSS. During the simulation, except for the pin position and the spacing , all of the dimensions are fixed as: (unit: mm). Fig. 2 shows the simulated resonant responses of the coupled structure with different under an constant ( mm). When increases, both the odd-mode frequency and TZ shift to the left, whereas the even-mode frequency does little change. From Fig. 2, the inductive coupling coefficient , the capacitive coupling coefficient , and the total coupling coefficient can be extracted by the procedure proposed in [8], and the position of TZ can be determined by ( represents the self-resonant frequency of the SIR). Fig. 3 shows the simulated and against for various . Both and increase with the increase of , and decrease with the increase of .
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ZHU et al.: QUARTER-WAVELENGTH SIR FILTER WITH MIXED ELECTRIC AND MAGNETIC COUPLING
Fig. 3. Coupling coefficient and the ratio of
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against
for various .
Fig. 1. (a) Configuration of the second-order filter. (b) Equivalent circuit.
Fig. 4. Configuration of the third-order SIR filter.
filter are: , and (unit: mm). B. Third-Order Filter
Fig. 2. Simulated resonant mode splitting phenomena by changing the position with mm.
A second-order mixed coupled SIR filter example was designed with the given specifications: the in-band RL is 20 dB with a center frequency of 3.46 GHz and a bandwidth of 5.9%, a TZ is prescribed at 3.7 GHz. Suppose we are designing a second-order Chebyshev filter, the corresponding and can be calculated from [9] and given as: and . Considering the location of the TZ, and can be calculated from and [8]. Firstly, the initial dimensions of the SIR are chosen, and the can be extracted from the phase response of of a singly fed SIR [9]. Then, the , and values against different and can be extracted by the procedure proposed in [8] and plotted as Fig. 3. From Fig. 3, and can be determined to satisfy the required , and . Finally, the filter is optimized by HFSS. The optimized and the coupling parameters are: . The dimensions of the
Fig. 4 shows the configuration of the third order filter, which can be constructed by cascading two second-order mixed coupling units (FL and FR). In this design, the electric coupling is dominant in FL unit and magnetic coupling is dominant in FR unit, thus, two TZs can be produced in the lower and upper stopband by FL and FR, respectively. The filter is designed at 3.5 GHz with a bandwidth of 8.6%, and two TZs are prescribed at 3.1 GHz and 3.75 GHz, respectively. From [9] and [8], the and the coupling parameters are given as: and . In the realization of the filter, the initial dimensions of the first resonator and the third resonator can be firstly determined. According to [8], we have (1) where is the self-resonant frequency of resonator . From (1), the resonant frequency of can be determined as (2)
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IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, VOL. 24, NO. 2, FEBRUARY 2014
III. SIMULATION AND MEASUREMENT The simulated and measured responses of the two filters are shown in Figs. 5 and 6, respectively, good agreement between them is observed. The second-order filter is centered at 3.46 GHz with a bandwidth of 200 MHz. The measured RL is better than 20 dB, and the minimum IL is 0.65 dB. Two TZs are observed, the first one (3.77 GHz) is introduced by the mixed coupling, while the second one (4.75 GHz) is introduced by the harmonic effects [4]. The third-order filter is centered at 3.5 GHz, and the bandwidth is 300 MHz. The measured RL is better than 19 dB, and the minimum IL is 1.2 dB. The first two TZs (3.04 and 3.84 GHz) are introduced by FL and FR units, respectively, and the extra TZ (5.75 GHz) is introduced by the harmonic effects [4]. Additionally, the filter exhibits a wide upper stopband and occupies a small area of 12.7 mm 5.8 mm (excluding the I/O feed lines), i.e., only ( is the guided wavelength on the substrate at center frequency).
Fig. 5. Simulated and measured responses of the second-order filter.
IV. CONCLUSION In this letter, two novel SIR filters with mixed electric and magnetic coupling are designed and measured. Controllable TZs for each filter are introduced. The proposed filters show the advantages of high selectivity, low insertion loss, wide upper stopband and compact size. REFERENCES
Fig. 6. Simulated and measured responses of the third-order filter.
Thus, the dimensions of could be determined to extract the two pairs of coupling (FL and FR). It should be noted that, Fig. 3 does not apply to the third-order filter design. During the extraction of the coupling values, and should be re-simulated for FL and FR units, respectively. This is because the geometries of the SIRs are different from that in Section II.A. Finally, the filter is optimized by HFSS. The optimized coupling parameters and the external quality factors are: . The dimensions in Fig. 4 are given as:
, and (unit: mm).
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