A compact microstrip, triband, bandpass filter (BPF) using shortcircuited stubloaded stepped impedance resonators (SIR) is proposed in this article. First, the hairpin SIR generates a dualmode, dualband response by loading a shortcircuited stub. The nature of the proposed resonator is investigated through the evenodd mode analysis. Second, a pair of extended feedlines adds a new transmission path to produce the third passband. The proposed SIR and extended feedlines are folded and thus result in a compact size for the filter. Three passbands are designed to operate at 1.57, 3.5 and 5.2 GHz, respectively. All the theoretical analysis has been successfully verified by experiment results.
In recent years, the rapid development of multiple band operations for wireless communication applications has attracted the attention of many researchers. Compact tripleband bandpass filters have been studied extensively as a key circuit block in triband wireless communication systems.^{13} In multiband communication systems, the bandpass filter (BPF) plays an important role in the RF frontend of the communication system. To design a multiband BPF, twosection stepped impedance resonators (SIR) have been used as a building block.^{4} However, this results in a larger circuit size and a more complex BPF configuration. A tripleband BPF was constructed using conventional λ/4 SIRs.^{5} Chu and Lin presented a triplesection SIR for tripleband BPF design.^{6} Design techniques for tripleband filters based on several parallel and crosscoupled resonators have been used, but they are still challenging to the designer because it is difficult to fit the specifications at three bands due to the limited degrees of freedom in the design parameters.
In this article, a tripleband filter is proposed using a shortcircuited stubloaded SIR, which is explained by an evenodd mode method. The tripleband filter has a small size, only extending a set of feedlines without increasing the circuit size. Simulations and measurements are given to prove this improved structure of the filter.
DualMode DualBand ShortStub Loaded SIR
As shown in Figure 1, a compact microstrip BPF is composed of the proposed dualmode, dualband shortcircuited stubloaded SIR and two transmission lines with characteristic impedance of 50 Ω, which act as input and output ports.^{7} Since the proposed SIR is a symmetrical structure, evenodd mode theory can be adopted to implement it and its equivalent circuits are described in Figure 2. For the odd and even mode excitation, the symmetry plane TT" is considered as a short end and an open end, respectively. The input admittance Y_{ineven}, Y_{inodd} of the even and oddmode resonator can be extracted:
According to the resonance condition of Y_{inodd} = 0 and Y_{ineven} = 0, the resonant frequencies can be expressed as:
where Y_{i} (i = 1, 2, 3) are the characteristic admittances of the widths W_{i} (i = 2, 3, 4), and θ_{i} (i = 1, 2, 3) are electrical lengths of the three sections of the length L_{i} (i = 2, 3, 4), respectively.
From Equation 3, it can be seen that the oddmode resonant frequencies (f_{o1}, f_{o2}) are determined by θ_{1}, θ_{2}, Y_{1} and Y_{2}. Thus, by reasonably designing these parameters, the resonant frequencies f_{o1} and f_{o2} are approximately allocated in the first and second passbands, respectively. Also, the total electrical length θ of the odd mode resonator is defined:
where R is the impedance radio Y_{2}/Y_{1}. The relation between the normalized total electrical length θ versus θ_{1} with R as a parameter is shown in Figure 3. There are various solutions for θ, which are dependent on the choice of R and θ_{1}.^{8} From the figure, it can be seen that a compact size may be obtained by having an appropriated θ_{1} and small impedance ratio R.
From Equation 4, the evenmode resonant frequencies depend exclusively on θ_{3}, Y_{3}. Furthermore, as the electrical length θ_{3} decreases, the evenmode resonant frequencies (f_{e1}, f_{e2}) will correspondinglygetclose to the oddmode resonant frequencies (f_{o1}, f_{o2}), whereas the oddmode resonator frequencies (f_{o1}, f_{o2}) remain stationary. Hence, the four resonant frequencies can be allocated within the desired passbands to realize a dualband, dualmode filter by reasonably choosing the parameters of SIR and short stub, respectively.
To verify the theoretical analysis, a dualmode dualband filter has been designed, which works in the GPS band (1.57 GHz) and the WLAN band (5.2 GHz). The proposed filter is simulated by Ansoft HFSS 10. The substrate has a thickness of h = 0.8 mm and a relative dielectric constant of ε_{r}= 4.5. Its dimensions are as follows: L_{1} = 14.45 mm, L_{2} = 5 mm, L_{3} = 19.05 mm, L_{4} = 1.056 mm, W_{1} = 0.65 mm, W_{2} = 1.2 mm, W_{3} = 0.6 mm W_{4} = 1 mm and g_{0} = 0.2 mm. The simulated frequency responses are shown in Figure 4. It is clearly observed that the center frequencies are generated at 1.57 and 5.2 GHz. The return losses within the two passbands are below 20 dB.
TriBands BPF Design and Results
Based on the dualmode, dualband discussion, a triple bandpass response can be achieved by adding an additional transmission path at a different resonant frequency. In this article, the extended feedlines are folded outside to produce the third bandpass, without significantly increasing the circuit size. The schematic of the proposed triband BPF is shown in Figure 5. Besides, the resonator frequency of the extended feedlines can be independently tuned to the desired passband (WiMAX, 3.5 GHz). It is approximately given by:
where L_{5} is the length of the extended feedlines. The electric field distributions at the resonant frequencies of the triband BPF are illustrated in Figure 6. It is evident that the odd modes have an electric field distribution similar to that of the single SIR. Hence, the tapping point of the short stub is actually a virtual ground for the odd modes. As a consequence, the short stub does not affect the oddmode characteristic, including its resonant frequencies. On the contrary, the short stub can affect the even characteristic, which can be demonstrated in the electric field distribution at evenmode frequencies. That is the reason why the change of θ_{3} controls the resonant frequencies of the even mode. Figures 6 (e) and (f) show that the electric field is mainly concentrated in the extended feedlines.
The proposed filter is fabricated on the same substrate as mentioned previously. The physical dimensions of the filter are chosen as follows: L_{5} = 21.5 mm, L_{6} = 5 mm, L_{7} = 19.05 mm, L_{8} = 0.6 mm, W_{5} = 0.65 mm, W_{6} = 1.2 mm, W_{7} = 0.6 mm, W_{8} = 0.4 mm, g_{1} = 0.2 mm and g_{2} = 0.2 mm. The fabricated proposed filter occupies only about 13.7 × 14.55 mm (approximately 0.13 λg × 0.14 λg, where λg is the guided wavelength at the center frequency of the first passband).
Simulated and measured results for the proposed triband filter with its photograph are compared in Figure 7. The results show that the three passbands are centered at 1.57, 3.5 and 5.2 GHz, with fractional bandwidth of 8.92, 8 and 8.46 percent, respectively. The maximum insertion loss within the passband is less than 1.18 dB, which would be mainly attributed to the conductor and dielectric loss. The configuration also displays extra transmission zeros at 1.18, 1.80, 4.03 and 5.74 GHz. The designed filter shows excellent performance for GSP, WiMAX and WLAN applications. Good agreement between the simulated and measured results demonstrates the proposed structure performance.
Conclusion
In this article, a miniature triband BPF using a shortstub loaded SIR has been proposed. Based on the proposed SIR, a compact triband BPF with extended feed lines is implemented to achieve the miniaturization. Furthermore, four transmission zeros are produced and greatly improve the selectivity and stopband suppression. The measured result agrees with the electromagnetic (EM) simulation. For a system integrating GPS, WiMAX and WLAN, this concept could be applied to filter signals among these commercial bands.
Acknowledgments
This work was supported by the National Science Foundation of China (No. 61061001) and 555 Talent Program of Jiangxi Province of China.
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