Introduction
Addressing the need for multi-band microwave devices to support various frequency services, stepped impedance resonators (SIRs) or uniform impedance resonators are widely employed in the design of multi-band filters [1–3]. Notably, since these structures implement separate paths for each resonance band, at least two or more SIRs are used in the case of a triple-band filter. Therefore, drawing on the composite right/left-hand structure, [4] proposed a triple-band filter with an independent current path for each resonance band. However, its applications are limited by the disadvantages of large insertion loss and size.
Recently, stub-loaded resonators (SLRs) have been proposed for the design of triple-band bandpass filters. For instance, a triple-band filter was implemented using a T-shaped SLR in [5]. In [6], the structure of the filter was further improved by employing a stub-loaded SIR to enable triple-passband responses. Meanwhile, [7] presented a compact triple-band bandpass filter (BPF) design using mixed-coupled resonators. In addition, balanced triband BPFs that use SLR [8] or embed multi-band coupled complementary split ring resonators [9] have also been proposed.
Table 1 presents a comparison of the proposed filter with previously reported triple-band BPFs with regard to operating frequency, insertion loss, bandwidth (BW), and number of transmission zeroes (TZs), revealing that the former offers the advantages of good in-band performance, wide stopband, and compact size.
This work presents the design procedure for a tri-band filter operating at 1.93 GHz for digital enhanced cordless telecommunications (DECT) and at 3 GHz and 3.3 GHz for WiMAX.
Triple-Band BPF Configuration
As shown in Fig. 1(a), the length L1 of the slot in the proposed triple-band BPF can be divided into L1,long and L1,short, signifying its short part. Therefore, L1 = L1,long + L1,short + W1. Furthermore, the cross-shaped slot is moved along the right diagonal by d1 in the –x axis and d1 in the –y axis. A pair of slits (length L2 and width W2) is placed at distance d2 from the corner, while a stub of length L3 and width W3 is applied to the feed line. Notably, a substrate of ɛr = 2.2 and h = 0.508 mm was used. The simulation was carried out using the High-Frequency Structure Simulator (HFSS).
Operating Principle
The design process of the proposed filter, as depicted in Fig. 2(a), involved the following steps:
• First design: Since the filter features a symmetrical structure with respect to the right diagonal, f1, f2, and f3 were formed at 2, 3, and 3.5 GHz, respectively.
• Second design: The feed line was moved by 1 mm. Accordingly, f3, which was weakly formed in the first step design, was now observed to be strongly formed. However, the BW at f3 could not be implemented properly.
• Third design: On setting L1,long and L1,short in a different way in the slot, f2 and f3 were formed more clearly than when using the second step design. However, S21 was very weakly formed at −5 dB in the 3.1 GHz band, due to which the TZ for distinguishing the two bands (f2 and f3) was very weak.
• Fourth design: The cross-shaped slot was moved. Accordingly, S21 improved from −5 dB to −10 dB.
• Fifth design: The slits were moved. Accordingly, S21 reached - 20 dB, and good TZ characteristics were realized. Furthermore, L1 = 24.5 mm, △(= L1,long – L1,short) = 4 mm, W1 = 0.5 mm, d1 = 1.2 mm, L2 = 15.5 mm, d2 = 2.3 mm, W2 = 1 mm, L3 = 14 mm, d3 = 2.5 mm, and W3 = 0.7 mm.
Parameter Study
Fig. 3 illustrates the simulation results obtained on changing the length L2. Notably, to exclude the influence of other asymmetries, the first design was employed, and only d3 was changed, with △ = 0 mm and d1 = 1.2 mm. The simulation results revealed that f3 was formed by the stub of the feed line. This finding was verified based on two reasons. First, f3 disappeared when the stub was removed. Second, f1 and f2 hardly changed with a decrease in d3, whereas f3 was both strongly influenced and strongly formed.
Fig. 4 presents the simulated performance based on the presence and absence of the slits and slot. Notably, this analysis was conducted to accurately grasp their influence. The fifth design in Fig. 2 was employed for this purpose.
The filter with a slit at the edge exhibited triple-band performance, but the TZ at 2.6 GHz disappeared when the slit was removed, leaving only f1 and f3. Moreover, although the characteristics of the two filters (5th filter and 5th filter without slit) in the f1 band were almost similar, when the slit placed at the edge was removed, the current path decreased, and f1 increased slightly. Also, the characteristics in the f3 band are almost similar. Based on these observations, it became apparent that f2 was formed by the slit at the edge.
When the slot placed at the center was removed, f1, f2, and f3 were all affected, although f1 changed the most. Owing to the slot’s location at the center, the current path increased, while the resonant frequency of the patch decreased. Furthermore, as shown in the simulation results, in the case of the structure without a cross slot, the first band of the proposed structure formed at 2.5 GHz, which is considerably higher than 2 GHz.
Fig. 5 shows the simulation results obtained for the fifth design on changing L2. Here, the slit at the edge played an important role not only in the formation of f2 but also in ensuring that the proposed structure exhibits triple-band characteristics by forming a TZ between f2 and f3. The simulation results clearly show that as L2 increased from 15.5 mm to 17.5 mm, the TZ between f2 and f3 declined from 3.1 GHz to 2.8 GHz.
Simulated and Measured Results
In this study, a triple-band BPF was successfully designed at center frequencies of 1.96, 2.94, and 3.34 GHz, exhibiting insertion losses of 1.24 dB, 1.35 dB, and 1.62 dB at f1, f2 and f3, respectively. Furthermore, the measured BWs for f1, f2 and f3 were 14.2%, 7.5%, and 10.9% respectively. Notably, the measured resonance frequency decreased slightly due to the fringing effect at the edge.
Conclusion
In this letter, a novel microstrip tri-band BPF is proposed and designed using a square patch. f1, centered at 1.96 GHz, was achieved using a cross slot, while f2 and f3, located at 2.94 GHz and 3.34 GHz, respectively, were achieved using a pair of slits and stubs. Moreover, each passband can be controlled individually.
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