Compact Quad-Mode BPF Based on Half-Mode Short-Circuited Semicircular Patch Resonator

Abstract

Wideband bandpass filter (BPF) design using a half-mode patch resonator with multiple resonant modes is proposed in this paper. The resonator is formed from a short-circuited circular patch loaded with radial slots. The metallized vias are positioned in a circle. Its radius is used to tune the resonant frequencies of the resonator. According to the surface current distributions of the eigenmodes, different numbers of the radial slots can be distributed on the patch to prolong the current paths of the relevant eigenmodes, the resonant frequencies of which can be shifted down to that of the dominant mode, the TM010 mode. As a result, a semicircular patch resonator loaded with three slots is used to design a compact quad-mode wideband BPF, which employs TM010, TM110, TM210, and TM310 modes. Furthermore, the coupling between input and output feeding lines is introduced to realize two transmission zeros at both sides of the passband. Therefore, the selectivity is improved. The experiment has verified the theoretical analysis and the design approach.

1. Introduction

Microstrip filters are widely studied in modern communication systems because of the advantages of low cost, simple profile, easy fabrication, and high integration. The microstrip patch resonators that can be excited by multiple resonant modes in one resonator are specifically researched to design wideband bandpass filters (BPFs) with compact size [1,2,3,4]. In order to lower the resonant frequencies and reduce the size, the arc- or radial-oriented slots are positioned on the patch resonators to extend the surface current paths of the resonant modes. The first resonant frequency of the short-circuited patch resonator is reduced to be lower than that of the patch resonator without a grounded via in [4] and [5], which can also be used to reduce the size.

In addition, in substrate integrated waveguide (SIW) BPF design, the short-circuited pins are introduced in the resonator to excite the TM010 mode as the dominant mode [6,7]. Furthermore, the half-mode, quarter-mode, and eight-mode resonators with short-circuited vias are employed to realize compactness [8,9,10,11,12,13]. Another widely applied approach in SIW BPF design is the folded SIW. It can reduce the size up to 50% or more combined with ridged, half-mode, or other technologies. However, it is difficult to fabricate [14,15,16].

In [17], compared with the theory of the half-mode SIW resonator, the semi-circular patch resonators can realize half-mode with half size, the structures of which are also proper for obtaining the required coupling coefficients. In [18], the short-circuited vias are introduced in a circular patch to reduce the first resonant frequency. The vias arranged as an inner circle can be used to tune the resonant modes in a large range, which can adjust the bandwidth. The grounded via can also be used in a square patch resonator to design single/dual-band BPF [19]. Another method using multi-mode resonators is the stub-loaded resonator or the coupling line resonator [20,21]. The even-odd mode method is proper for analyzing the transmission poles and transmission zeros.

In this paper, for compactness and good selectivity, a half-mode patch resonator with a semicircular structure is proposed with symmetrical field distribution, as that of the circular structure at resonances, the size of which is reduced to a half of the circular resonator. In addition, the radial slots and short-circuited vias are introduced in the patch resonator for ‘mode shifting’ [8]. The circular patch resonator with a grounded pin at the center can be excited by the TM010 mode as its fundamental mode [5]. The proposed short-circuited patch resonator employs grounded vias arranged in a circle. The radius of the circle can be tuned to adjust the frequencies of the resonances, and the length of the slots can be changed to shift the frequencies of the resonant modes as well. Therefore, the center frequency (CF) and passband bandwidth can be tuned easily. The analysis is shown in Section 2. In Section 3, the proposed resonator is used to design quad-mode BPF with TM010, TM110, TM210, and TM310 modes. Moreover, the coupling between input and output feeding lines is introduced to generate two transmission zeros (TZs) on both sides of the passband, which can improve the selectivity. The theoretical analysis is illustrated in detail for wideband BPF design. A quad-mode half-mode semicircular patch resonator loaded with three slots is designed. The fabricated filter is measured for verification. Finally, a conclusion is given in Section 4. The proposed BPF has compact size and good selectivity performance.

2. Analysis

Figure 1 displays the geometry of the short-circuited patch resonators. The resonators have grounded vias arranged in a circle, which play the role of an electrical wall. The cavity model can be used to analyze the resonant frequencies. According to the boundary conditions, the resonant frequencies can be calculated from Equation (1) [5]. The first resonant mode is the TM010 mode, which is proven by Equation (1). The resonant frequency of the TM010 mode is lower than that of the first resonant mode (TM110) of the conventional circular patch resonator without a grounded via.

$$J_m{}^{\prime }(k_{mn})N_m(k_{mn}\frac{r}{R})-J_m(k_{mn}\frac{r}{R})N_m{}^{\prime }(k_{mn})=0,$$

(1)

where J_m′ (x) denotes the first derivative of the first kind of the mth degree Bessel function, and N_m (x) denotes the second kind of the mth order Bessel function. The roots k_mn relate to the resonant frequencies f_mn, f_mn = k_mn∙c/(2πR∙$\sqrt{{\epsilon }_r}$), where c is the light velocity and ${\epsilon }_r$ is the permittivity of the cavity.

Because of the symmetry of the circular patch resonator, the symmetrical plane of the structure is considered as a magnetic wall. Therefore, the semicircular patch resonator has the same electric field distribution to that of the half part of the circular patch resonator. The commercial electromagnetic simulation software HFSS is used to display the electric and current distributions of the resonant modes by eigenmode analysis, and it can also calculate the S-parameters of the components. As shown in Figure 2, the fundamental mode of the two resonators is the TM010 mode. The electric field distributions are uniform along the circumferential direction in Figure 2a,b. Moreover, the electric field distributions of the TM110, TM210, and TM310 modes are similar to those of the short-circuited circular patch resonator, as shown in Figure 3, Figure 4 and Figure 5. Therefore, the resonant frequencies and field distributions are unchanged when the structure of the proposed resonator is half of that of the circular patch, which can be used to obtain a compact size for the resonator.

From Equation (1), the resonant frequencies of a circular patch with shorted pins are determined by the ratio of the inner and outer radii. By EM simulation of the semicircular patch resonator on a substrate with permittivity 2.65, the resonant frequency variation of the first four resonant modes with radius r is plotted in Figure 6, where R = 10 mm. As shown in the figure, when the inner radius r gets smaller, the resonant frequencies of the semicircular patch resonator drop, which can be used to obtain a compact size when the component works at a lower frequency.

Furthermore, when introducing perturbation on the current path of some resonant mode, the related resonant frequencies of the mode will also be lowered. As shown in Figure 7, three slots can be added to the maximum positions of the current distribution of the TM310 mode. The changed frequencies of the related resonant modes are shown in Figure 8, which demonstrate the analysis, where R = 10 mm and r = 1 mm.

3. Design BPF

Based on the theoretical analysis, wideband BPF designs with multi-mode are presented on F4B substrate with permittivity of 2.65 and thickness of 1 mm. The loss tangent is approximately 0.003. The structure of the BPF is shown in Figure 9. It employs capacitive coupling between the feeding lines and the resonator. Therefore, there are two parameters that can be applied to adjust the coupling between the source/load and the resonant modes: the length of the open stub L₁ and the angle of the arc-shaped open stub θ_f. Moreover, the open stubs of length L₁ can introduce coupling between the input and output feeding lines, which can improve the selectivity of the filter.

The transversal coupling topology is proper for multi-mode BPF design [8], the diagram of which is shown in Figure 10, where the number n represents the nth resonant mode in the resonator. Because the structure of the semicircular resonator is still symmetrical, the electric fields in the resonator have the same directions near the source and load at the resonances, such as the TM010 mode and the TM210 mode, which results in M_Li = M_Si. In contrast, the directions of the electric fields at resonant modes TM110 and TM310 are opposite, resulting in M_Li = −M_Si.

A quad-mode BPF employing the TM010, TM110, TM210, and TM310 modes with CF of 4 GHz and 3 dB fractional bandwidth (FBW) of 50% is designed. The unloaded Q-factors of the TM010, TM110, TM210, and TM310 modes are 200, 198, 217, and 217, respectively. The synthesis matrix is depicted in Equation (2) [8].

$$M=\left[\begin{array}{cccccc}0& -0.5438& 0.5791& 0.4991& 0.3576& 0\\ -0.5438& 1.6310& 0& 0& 0& 0.5438\\ 0.5791& 0& 0.3785& 0& 0& 0.5791\\ 0.4991& 0& 0& -0.5846& 0& -0.4991\\ 0.3576& 0& 0& 0& -1.0702& 0.3576\\ 0& 0.5438& 0.5791& -0.4991& 0.3576& 0\end{array}\right],$$

(2)

The diagonal element can be calculated from the frequency of the ith resonant mode f_i and the center frequency f₀, M_ii = (f₀² − f_i²)/ (BW·f_i) [8]. The coupling coefficient can be derived by M_si = 1/√(FBW∙Q_ei) [8], where Q_ei = 2πf_i*GD_S11(f_i)/4. The coupling between the input and output feeding lines can also be extracted, as in [22,23]. The extracted external quality factor Q_ei and M_si of triple-mode BPF are shown in Figure 10. The parameters of the structure are determined by the resonant frequency of the excited resonant mode and the coupling coefficients between the source/load and the resonator.

The final parameters of the triple-mode filter are R = 10 mm, w = 0.2 mm, g = 0.1 mm, L₁ = 10 mm, L₂ = 8.3 mm, r = 1 mm, and θ_f = 15.4°. The synthesized and simulated S-parameters of the proposed quad-mode BPF are shown in Figure 11. As can be seen in Figure 11, the simulated results illustrate two TZs that are produced by the coupling between the feeding lines. The measured S-parameters agree well with the simulated S-parameters, as shown in Figure 12. Figure 13 shows the structure of the fabricated filter with connected SMA.

Table 1. Comparison with the related references.

Ref.	f0	IL (dB)	FBW (%)	Stopband	Modes	Size (λg)
[3]	3.5	1.1	8.7	1.4 f0	3	0.48 × 0.48
[8]	5.8	1.4	4.1	1.5 f0	2	1.0 × 0.71
[9]	7.71	1.24	14.8	2.52 f0	3	0.46 × 0.46
[22]	3.95	2.4	14	>1.15 f0	2	0.6 × 1.19
[23]	2.95	0.4	50	>2 f0	3	0.41 × 0.63
This work	4	1.4	50	3.7 f0	4	0.21 × 0.41

λ_g is the guided wavelength on the substrate at center frequency of the passband.

compares the performances of the reported filters with those of the designed filters, which shows compactness and good performance.

4. Conclusions

A novel half-mode short-circuited patch resonator has been introduced to realize compact size and good selectivity performance for BPF design. A four-pole wideband BPF employing the proposed resonator has been designed. The simulated and fabricated BPF is measured for demonstration. The measured S-parameters prove the validation of the theoretical analysis.