Triple-mode bandpass ﬁlter based on short-circuited patch resonator

The letterpresentsa triple-mode short-circuitedcircularpatchresonator for bandpass ﬁlter (BPF) design. The resonator employs the TM 010 mode as its dominant mode, the resonant frequency of which is lower than that of the TM 110 mode. In addition, four radial slots are etched on the patch to extend the current paths of the TM 110 and TM 210 modes, shifting down the resonant frequencies of the two modes. The adjacent triple modes can be used to design wideband BPF. Meanwhile, the cen- tre frequency (CF) and bandwidth (BW) can be tuned by the length of the slots. Furthermore, the short-circuited vias are arranged in a circle providing a tuneable parameter to control the CF and BW as well. According to the symmetry of the geometry, the resonator can be bisected to realise half-mode resonance. Two cascaded half-mode semi-circular patch resonators are applied to design BPF with high selectivity. BPFs using the circular patch resonator and the semi-circular patch resonator are designed and measured for demonstration.

The letter presents a triple-mode short-circuited circular patch resonator for bandpass filter (BPF) design. The resonator employs the TM 010 mode as its dominant mode, the resonant frequency of which is lower than that of the TM 110 mode. In addition, four radial slots are etched on the patch to extend the current paths of the TM 110 and TM 210 modes, shifting down the resonant frequencies of the two modes. The adjacent triple modes can be used to design wideband BPF. Meanwhile, the centre frequency (CF) and bandwidth (BW) can be tuned by the length of the slots. Furthermore, the short-circuited vias are arranged in a circle providing a tuneable parameter to control the CF and BW as well. According to the symmetry of the geometry, the resonator can be bisected to realise half-mode resonance. Two cascaded half-mode semi-circular patch resonators are applied to design BPF with high selectivity. BPFs using the circular patch resonator and the semi-circular patch resonator are designed and measured for demonstration.
Introduction: Microstrip patch resonators with different structures for filter design are widely researched because of their low cost, light weight, small size, easy fabrication, and high integration [1][2][3][4]. Meanwhile, the patch resonators can excite multiple resonant modes for single-and dual-band bandpass filters (BPFs) design with compact size. The mostly used resonant modes are TM 110 and TM 210 modes, which are usually the first two modes of a patch resonator. Recently, the resonators with perturbations of metallic vias are extensively applied in BPF design for shifting the TM 010 mode near to the TM 110 and TM 210 modes [5]. Such as in [1], the new generated first mode by the grounded via and two degenerated TM 110 modes are excited to design a wideband BPF. The theoretical analysis in [2,3] is similar for designing a BPF with triple mode. In order to reduce the size, the perturbation of slot is etched on a resonator to lengthen the current path of the resonance, which is the most popular method for drawing down the resonant frequencies [1]. In addition, the half-mode, quarter-mode, even eighthmode substrate-integrated waveguide (SIW) technology has developed for size compactness [6][7][8].
Here, a short-circuited circular patch resonator loaded with four radial slots is proposed to design a triple-mode BPF. The metallic vias are arranged in a circle at the centre of the patch, which brings down the resonant frequency of the TM 010 mode lower than that of the TM 110 mode. At the same time, the four radial slots move the resonant frequencies of the TM 110 and TM 210 modes near to that of the TM 110 mode. Therefore, the proposed resonator can be used to design a triple-mode BPF with easily tuneable centre frequency and bandwidth. Meanwhile, the circular patch resonator can be bisected to realise half-mode BPF design, which can improve the selectivity and the stopband suppression. Finally, a triple-mode patch filter and a two semi-circular cascaded patch filter are designed, fabricated, and measured for illustration.
Proposed short-circuited patch resonator: Figure 1a shows the configuration of the proposed short-circuited circular patch resonator. Two 50-Ohm input/output feeding lines are directly connected to the resonator. The metallic vias are arranged in a circle with a radius r at the centre of the circular patch, which are similar to that of the SIW for easy fabrication. The four radial slots are etched on the patch with the same disperse angle of 90 degrees. The width and the length of the slots are denoted by  Figure 1b, the circular patch can be bisected into two semi-circular patches along the symmetric plane A-A´.
The excited resonant modes of the circular patch resonator in Figure 1a can be illustrated by the weak coupling between the two feeding lines and the resonator, which are shown in Figure 2. Figure 3 plots the electric distributions of the three resonant modes. The field distributions in Figure 3b,c near the slots are strengthened. Therefore, the four radial slots have no effect on the first resonant mode, but have great effect on the next two resonant modes. The corresponding current distributions of the three resonant modes are plotted in Figure 4. It can be seen from the electric field and current distributions that the first resonant mode is TM 010 mode, the second resonant mode is TM 110 mode, and the third resonant mode is TM 210 mode.
As shown in Figure 3a and Figure 4a, the radial slots have no effect on the current distribution of TM 010 mode, but they have a great effect on that of TM 110 and TM 210 modes. It can be deduced that the longer the length of the slot is, the longer the current paths of TM 110 and TM 210 modes are. As a result, the resonant frequencies of the two modes gets  Figure 5a. The upper sideband frequency decreases with the increase of the length of the slots and the lower sideband frequency is unchanged.
In addition, the inner metallic vias behave like an electric wall, which has a great effect on the TM 010 mode. The resonant frequency of TM 010 mode can be calculated by the characteristic equation in [9]. As shown in Figure 4a, the radius r becomes larger, the current patch of TM 010 mode gets shorter, which results in the increase of the resonant frequency of TM 010 mode. It can also be observed from Figure 5b that the lower sideband frequency gets larger when the parameter r increases. Meanwhile, the inner circle has less effect on the TM 210 mode. Therefore, the upper sideband frequency remains unchanged.
The width of the four identical slots also has effect on the resonant frequencies of the resonator. It can be observed in Figure 6 that the wider the width is, the lower the upper edge of the passband gets, because of the longer way the current goes, which results in an increase of the resonant frequency.
Through the modes analysis, the proposed resonator has two main parameters r and L to tune the centre frequency and the bandwidth independently. According to the symmetry of the resonator structure, the half-mode method for compactness can be applied in the proposed resonator. The symmetric plane A-A´ can be considered as a magnetic wall, the half-mode resonances keep the same resonant frequencies as that of the circular patch resonator with the symmetrical electric field distributions. The current distributions of the first three resonant modes are described in Figure 7, which are similar to that of the circular patch resonator shown in Figure 4.
Furthermore, the two semi-circular resonators can be cascaded to improve the performances and remain compact size as that of one circular resonator, which is shown in Figure 1b. Since the resonant frequency of each excited mode has a great difference to the centre frequency, the coupling topology of the cascaded resonators shown in Figure 1b can be described by the transversal coupling topology. The coupling topology of the two resonators is given in Figure 8. Due to the symmetry of the electromagnetic fields of the resonant modes, each resonator has three resonant modes and each mode couples to the same mode of the other resonator. Since more resonances are introduced in the BPF design, the selectivity and the upper stopband suppression performances can be improved.
Simulated and measured results: Based on the above theoretical analysis, a triple-mode BPF (BPF-I) using short-circuited circular patch res- The photographs of the fabricated filters are given in Figure 9. Figure 10 plots the responses of the fabricated filters. The measured centre frequency (CF) f 0 , insertion loss (IL) at the CF, minimum return loss (RL) in passband, and 3 dB FBW of BPF-I are 4.66 GHz, 1.6 dB, 10 dB, and 54.8%, respectively. While the measured CF, IL, RL, and FBW of BPF-II are 4.25 GHz, 0.6 dB, 25 dB, and 29.6%, respectively. The two filters have the same size of 0.41λ g × 0.41λ g , where λ g is the guided wavelength at f 0 . The slight discrepancies between simulations and measurements are due to the fabrication errors, substrate losses, and the radiation losses from the slots. Due to the feeding structure, it is not easy to adjust the coupling between the resonances and the feeding lines. Therefore, the number of the transmission poles are not relevant to that of the resonances. Table 1 gives the comparisons of the proposed filter with the reported multi-mode microstrip planar filters. It can be seen that the proposed filters have wide upper stopband with good compactness.
Conclusion: A triple-mode wideband BPF design based on shortcircuited circular patch resonator is presented in this paper. The resonant frequencies of the proposed resonator can be tuned independently, which results in tuneable CF and BW as well. Meanwhile, a half-mode resonator is produced from the circular resonator to design cascaded BPF with high selectivity and compactness.