Highly compact quad-band bandpass ﬁlter with ﬂexibly controllable passbands

This letter reports a highly compact microstrip quad-band bandpass ﬁlter based on two folded λ /4 stepped impedance resonators and three folded dual-mode short stub-loaded resonators. The two stepped impedance resonators not only form the ﬁrst passband but also serve as the feed structure and provide the source-load coupling path for the three higher passbands created by the short stub-loaded resonators. Thus, a compact size can be obtained, and three pairs of transmission zeros can be realised near the three higher passbands to improve the frequency selectivity. It has been shown that the centre frequencies and bandwidths of the four passbands can be controlled independently. A microstrip quad-band bandpass ﬁlter centred at 1.1/2.05/3/3.55 GHz is implemented and tested achieving an extremely small size of 0.07 λ g × 0.14 λ g , where λ g is the guided wavelength at 1.1 GHz. This presents one of the smallest quad-band bandpass ﬁlter ever demonstrated in the literature.

✉ Email: zhangfan_uestc@163.com This letter reports a highly compact microstrip quad-band bandpass filter based on two folded λ/4 stepped impedance resonators and three folded dual-mode short stub-loaded resonators. The two stepped impedance resonators not only form the first passband but also serve as the feed structure and provide the source-load coupling path for the three higher passbands created by the short stub-loaded resonators. Thus, a compact size can be obtained, and three pairs of transmission zeros can be realised near the three higher passbands to improve the frequency selectivity. It has been shown that the centre frequencies and bandwidths of the four passbands can be controlled independently. A microstrip quad-band bandpass filter centred at 1.1/2.05/3/3.55 GHz is implemented and tested achieving an extremely small size of 0.07λ g × 0.14λ g , where λ g is the guided wavelength at 1.1 GHz. This presents one of the smallest quad-band bandpass filter ever demonstrated in the literature.
Introduction: Multi-band bandpass filters are indispensable part of the radio frequency (RF) front-ends in multi-band wireless communication systems. Over the past years, a variety of design techniques, developing planar quad-band bandpass filters (QBBPFs), have been reported based on asymmetric stepped impedance resonators (SIRs) [1], stub-loaded resonators (SLRs) [2], quad-mode resonators [3], single stepped impedance ring resonator [4], multi-stub-loaded resonators [5], and SLRs in combination with triangular loop resonators [6]. However, except for [5,6], the passbands of these QBBPFs cannot be controlled flexibly. The filters in [1,2] occupy a relatively large circuit size. With the speedy development of wireless technologies, the demand for QBBPF with smaller size, high selectivity, and flexibly controllable passbands is increasing. To this end, a new microstrip QBBPF composed of λ/4 SIRs and dual-mode short stub-loaded resonators (SSLRs) is proposed in this letter. The filter features a compact size, a high frequency selectivity, and independently controllable frequencies and bandwidths.
Filter design: Figure 1 shows the layout of the proposed QBBPF with two-pole bandpass response. It consists of two folded λ/4 SIRs (labelled as R 1 and R 2 ) and three folded dual-mode SSLRs (labelled as R 3 , R 4 , and R 5 ). Compared with conventional SIR, the λ/4 SIR is more compact [7]. In our design, the resonators R 1 and R 2 not only form the first passband, but also serve as the feed structure and provide source-load coupling for the second, third, and fourth passbands, created by the resonators R 3 , R 4 , and R 5 , respectively. Therefore, a highly compact multiband filter structure can be realised. Three pairs of transmission zeros (TZs) are generated near the three higher passbands, which improve the filter selectivity. In addition, the resonators R 3 and R 5 are connected to a common metallic hole to further save the filter footprint. The operation principle of the dual-mode SSLR is depicted in Figure 2. Figure 2b,c gives its odd-and even-mode equivalent circuits, respectively. Here, Y 1 is the characteristic admittance of the halfwavelength resonator with a length of L 1 , and Y 2 is the characteristic admittance of the short stub with a length of L 2 . Assuming Y 2 = 2Y 1 , the fundamental odd-and even-mode resonant frequencies of the SSLR can be expressed by where c is the speed of light in free space and ε r represents the effective permittivity of substrate. Inspecting (1) and (2), the odd-mode frequency f odd is determined by L 1 , and the even-mode frequency f even can be controlled by L 2 , independently. Moreover, f even is lower than f odd . Thus, the short stub length L 2 can be utilized to adjust the lower passband edge of the BPF created by the SSLR, as will be demonstrated in Figure 4 later. The QBBPF was implemented on a Rogers 5880 substrate with a relative dielectric permittivity of 2.2 and a thickness of 0.508 mm. The centre frequencies and 3-dB fractional bandwidths (FBWs) of the four passbands were set as follows: f 01 = 1.1 GHz, FBW 1 = 14.6%, f 02 = 2.05 GHz, FBW 2 = 5.1%, f 03 = 3 GHz, FBW 3 = 3.1%, f 04 = 3.55 GHz, and FBW 4 = 4.2%. For the first passband, its design procedure follows the conventional coupled resonator filter theory [8]. Its external coupling is determined by the tap position L 1 , while its interresonator coupling is determined by the coupling gap g 1 as well as the coupling length L 5 . Regarding to the other three bands, their external couplings can be adjusted by the coupling gaps g 2 , g 3 , and g 4 . Their bandwidths can be conveniently controlled by the short stub lengths L 11 , L 14 , and L 15 , respectively.
It is worth mentioning that due to the special layout arrangement, the QBBPF can enable all passbands to be controlled independently. The simulations of the filter were performed by Ansys EM simulator HFSS. Figures 3 and 4 show that the centre frequency and bandwidth of each passband can be controlled independently. The tuning of each of the three higher bands has negligible impact on the other bands. However, the tuning of the first passband affects the bandwidth and TZs of the higher bands slightly as seen in Figures 3a and 4a. This is expected because the external couplings and source-load couplings for the three higher passbands are provided via the resonators R 1 and R 2 (forming the lowest band). The geometric dimensions of the filter shown in Figure 1 are L 1 = 4.88, L 2 = 3.96, L 3 = 12.83, L 4 = 4.12, L 5 = 12.37, L 6 = 2.92, L 7 = 11.5, L 8 = 3.06, L 9 = 11.42, L 10 = 2.11, L 11 = 0.71, L 12 = 13.44, L 13 = 5.76, L 14 = 0.94, L 15 = 0.68, L 16 = 10.9, L 17 = 7.14, L 18 = 2.85, Measured results: The measurements were performed using Agilent E8363B network analyser. The photograph of the fabricated filter is shown in the inset of Figure 5. The measured S-parameters are given in Figure 5 in comparison with the simulated ones. Good agreements are obtained between them, while the slight discrepancy may be due to the fabrication tolerance. The measured centre frequencies of the four passbands are 1.1/2.05/2.99/3.52 GHz with 3-dB FBWs of 14.6/4.9/2.8/4%, respectively. The measured insertion losses (ILs) of the four passbands are 0.68/1.85/2.72/1.97 dB, respectively. The measured return losses (RLs) over the four passbands are better than 15 dB. In addition, due to the source-load coupling through the path provided by resonators R 1 and R 2 , three pair of TZs are generated at the stopband of the three higher passbands. This enhances the filter selectivity and stopband suppression. The overall filter size is only 0.07λ g × 0.14λ g , where λ g is the guided wavelength at 1.1 GHz. Table 1 tabulates the performance comparison between our work with several previously reported QBBPFs. It can be  seen that the proposed filter features high selectivity and the smallest normalized circuit size.
Conclusion: A microstrip QBBPF with highly compact size, high selectivity, and flexibly controllable passbands has been presented in this letter. The normalized circuit size of the filter is only 0.07λ g × 0.14λ g , which is among the smallest ever demonstrated in QBBPFs. The experimental results have verified the design. The presented filter demonstrated a competitive compact multi-band filter technique.