A miniaturized tri-band bandpass filter (BPF) design uses a quad-mode stub-loaded resonator (SLR). Its characteristics are investigated by using even- and odd-mode analysis. Without occupying additional area, tapped side-coupled open-loop resonators are used to induce the third passband. The three passbands are designed at 1.57, 3.5 and 5.2 GHz for GPS, WiMAX and WLAN applications. The center frequencies of the three passbands are independently controlled and their bandwidths tuned by the filter dimensions. In addition, four transmission zeros improve selectivity.
The multi-band planar bandpass filter is a key component in a modern wireless communication system because of its compact size, high selectivity and low integration cost. As a result, the multi-band bandpass filter is extensively investigated and various design approaches have been reported.1-10
Tri-band filters are commonly achieved with cascaded stepped-impedance resonators (SIR),^{1,2} but are relatively large. Composite configurations consisting of three split-ring resonators have also been used.^{3} To reduce size, a combination of one set of half-wavelength resonators and one set of SLRs has been proposed.^{4} One set of tri-section SIRs has also been utilized;^{5,6} however, the dependence of the resonant frequencies of the SIRs complicates the filter design. Recently, tri-band BPFs have been constructed using a SLR with a defected ground structure (DGS) resonator^{7} and a square ring loaded resonator.^{8,9}
In this article, a compact tri-band BPF using a quad-mode SLR and a pair of side-coupled resonators is described. The former generates the first and second passbands and the latter generates the third passband without increasing circuit size. The three passbands are conveniently tuned by properly controlling the dimensions of the filter. Four transmission zeros improve selectivity and stopband suppression.
ANALYSIS
As shown in Figure 1, the quad-mode SLR consists of one pair of spiral open-circuited stubs, with length (L_{2}) and width (W) connected by a uniform impedance resonator (UIR) with length (2L_{1} + 2L_{3}) and width (W). One short-circuited stub (L_{S}, W_{S}) located along the symmetrical plane is added to provide dual-mode characteristics. Since it is symmetrical to the A-A' plane, even- and odd-mode theory is adopted to analyze the resonator structure. The corresponding odd-mode and even-mode equivalent circuits are shown in Figures 2a and b, respectively. In Figure 2a, the odd-mode equivalent circuit contains two resonant circuits and the resonant frequencies are determined by:
where c is speed of the light in free space and ε_{e} denotes the effective dielectric constant of the substrate. For the even-mode excitation, the required resonant frequencies are determined by:
Equations 3 and 4 are based on the special case where 2Z_{S} = Z. From equations 1-4, it is apparent that adjusting the spiral open-circuited stub length, L_{2}, has no influence on the resonant frequencies f_{even1} and f_{odd1}, whereas it leads to a variation of the resonant frequencies f_{even2} and f_{odd2}. As shown in Figure 3, the high resonant frequencies f_{even2} and f_{odd2} move towards the lower frequency, whereas the resonant frequencies f_{even1} and f_{odd1} remain relatively stationary, as the open-circuited stub length (L_{2}) increases. Figure 4 shows that the quad-mode resonant frequencies decrease with larger L_{3}. Also, from the equations, the short-circuited stub length, L_{S}, changes only the even-mode frequencies.
RESULTS
A compact tri-band BPF is shown in Figure 5. It consists of the quad-mode SLR and a pair of side-coupled resonators with length (L_{4}+L_{5}) and width (W). As previously mentioned, the former is used to generate the first and second passbands and the latter generates the third passband for the tri-band BPF design. Based on the above analysis, it can be seen that the first passband (formed by f_{even1} and f_{odd1}) is determined by L_{1}+L_{3}, and its bandwidth is tuned by L_{S}. Similarly, the second passband (formed by f_{even2} and f_{odd2}) is controlled by tuning L_{2}+L_{3}, and its bandwidth is also changed by L_{S}. The distance between the center frequencies of two passbands is controlled by the difference between L_{1} and L_{2}. As shown in Figure 6, as L_{S} increases, the even mode frequencies (f_{even1} and f_{even2}) shift lower in frequency, while the odd mode frequencies (f_{odd1} and f_{odd2}) are fixed. Thus, the bandwidths of the first and second passbands can be tuned by the length of L_{S}. The bandwidth of the third passband can be tuned by the gap (g_{2}), as shown in Figure 6. Also, the pair of side-coupled resonators encircles the SLR and serves as a part of the feed-line structure for compactness.
The demonstration tri-band BPF is fabricated on a substrate with a relative dielectric constant of 3.5 and a thickness of 0.76 mm. The parameters are L_{1}=24.6 mm, L_{2}=10 mm, L_{3}=4.2 mm, L_{4}=26.3 mm, L_{5}=9 mm, L_{S}=1.15 mm, W=0.2 mm, W_{S}=0.6 mm, g_{1}=0.2 mm, g_{2}=0.58 mm, g_{3}=1.7 mm.
Figure 7 shows good agreement between simulated and measured results. Fractional bandwidths are about 6.3 percent at 1.57 GHz, 3.7 percent at 3.5 GHz, and 4.3 percent at 5.2 GHz, respectively. Measured minimum insertion losses within the three passbands are 1.4, 1.25 and 1.28 dB, respectively. Four transmission zeros located at 1.04, 1.69, 1.84 and 5.65 GHz improve filter selectivity. Also shown in Figure 7 is a photograph of the fabricated BPF. Its overall size is about 0.092λ_{g} by 0.091λ_{g}, where λ_{g} is the guided wavelength at the center frequency of the first passband.
CONCLUSION
A miniaturized tri-band BPF for GPS, WiMAX and WLAN applications using a quad-mode SLR is introduced and analyzed. Center frequencies and bandwidths of the three passbands are adjusted by controlling the filter dimensions. This compact tri-band filter with simple topology is particularly suitable for multi-band and multi-service applications in wireless communication systems.
ACKNOWLEDGMENTS
This work was supported by the National Science Foundation of China, (No. 61061001) and International Cooperation Funds and Science and Technology Innovation Team of Jiangxi Province of China (No. 20121BDH80015, 20122BCB24025).
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