Wideband Band-Pass Filter Design Using Coupled Line Cross-Shaped Resonator

Abstract

In this paper, a wideband bandpass filter with a coupled line cross-shaped resonator (CLCSR) is proposed. The proposed bandpass filter is composed of two open-end parallel coupled lines, one short-end parallel coupled line, one branch microstrip line, and the parallel coupled line feed structure. With the use of the even and odd mode approach, the transmission zeros and transmission poles of the proposed bandpass filter are analyzed. The coupling coefficient of the parallel coupled line feed structure is big, so the distance between the parallel coupled line is too small to be processed. A three microstirp lines coupled structure is used to realize strong coupling and cross coupling. This structure also can reduce the return loss in passband and increase the out-of-band rejection. The transmission zeros can be adjusted easily by varying the lengths of the open-end parallel coupled line or the short-end parallel coupled line. The proposed bandpass filter is fabricated and measured. The simulated results agree well with the measured ones, which shows that the design method is valid.

1. Introduction

The multi-mode resonator can design a wideband bandpass filter with high performance, and is thus attracting researchers’ attention. Numerous multi-mode resonators have been proposed to construct wideband bandpass filters. H. Wang introduced a cross-shaped resonator with a wide passband [1]. By cascading a two cross-shaped resonator, a compact ultra-wideband band-pass filter is designed. K. D. Xu proposed a bandpass filter that consists of two parallel coupled lines, two open stubs, and four shorted stubs [2]. The frequency selectivity of the bandpass filter is improved by introducing transmission zeros. In [3], W. J. Feng proposed a compact broadband balanced filter based on the three-line coupled structure. The three-line coupled feed structure raises coupling strength. By introducing cross coupling, the bandpass filter’s stopband and passband performance is improved. L. Li proposed a novel filter composed of a shorted quarter wavelength microstrip line side-coupled to two open-ended stubs [4]. It achieves strong coupling characteristics and has good filtering performance.

A novel wideband bandpass filter using dumbbell-shaped DGSs is presented in [5], where the odd and even mode approach is used to design and analyze the bandpass filter. By using dumbbell-shaped DGSs, the frequency selectivity and return loss are improved. A compact lowpass filter for satellite communication systems is proposed in Ref. [6]. The LC equivalent circuit is used for the lowpass filter design. Based on the neural network model, Ref. [7] proposes an efficient parallel decomposition technique for parametric modeling, where the values of geometrical parameters change in a large range. The method can be used for microwave filter design and optimized. Ref. [8] presents a novel compact microstrip bandpass filter. By increasing stages of SIRs, multiple transmission zeros are generated and an ultra-wide stopband is achieved. In Ref. [9], two filter with ultra-wide stopband are proposed. Based on U-shape DGSs, an ultra-wide stopband is achieved. In [10,11,12,13,14,15,16,17], the cross-shaped resonator and the coupled line have been proposed and studied. Open-circuit lines, short-circuit lines, and others are used to construct a good performance bandpass filter, which provides ideas for the design of this filter.

In this paper, a wideband bandpass filter composed of a cross-coupled line structure is proposed. To clarify the proposed filter design, it is analyzed by even and odd mode equivalent circuits. The transmission zeros and transmission poles of the proposed bandpass filter are analyzed. In order to raise the coupling strength and improve the filter’s performance, the parallel coupled line feed structure is replaced with a three microstirp lines coupled structure. Based on the HFSS simulation, the bandwidth can be changed by varying the lengths of the short-end parallel coupled line or the open-end parallel coupled line. Finally, the proposed bandpass filter is fabricated and measured. Good agreement between the simulated and measured results is obtained. 2. Filter Analysis and Design 2.1. Bandpass Filter’s Equivalent Circuit Analysis

The equivalent circuit of the CLCSR filter is shown in Figure 1a, which consists of two open-end parallel coupled lines, a short-end parallel coupled line, and a single microstrip line. The feed structure of the CLCSR is the parallel coupled line. The even-mode and odd-mode equivalent circuits are shown in Figure 1b,c, respectively. The odd mode characteristic impedance and even mode characteristic impedance of the parallel coupled line feed structure are denoted as_zce1=_z1(1+_k1)/(1−_k1)and_zco1=_z1(1−_k1)/(1+_k1). The electrical length of the parallel coupled line feed structure is_θ1. The odd mode characteristic impedance and even mode characteristic impedance of the open-end parallel coupled line are denoted as_zce2and_zco2._θ2is the electrical length of the open-end parallel coupled line._zce3and_zco3denoted the odd mode characteristic impedance and even mode characteristic impedance of the short-end parallel coupled line. The electrical length of the short-end parallel coupled line is_θ3. For the convenience of calculation, the impedance values use the normalized impedances.

The coupled line feed structure in Figure 1 is the same as that in Ref. [16], so the input impedance of the odd and even mode is shown in Equation (1):

_zine(o)=1−_k1 ²_{z1 zLe(o)}+j_z12[_k1 ²tan_θ1−(1−_k1 ²)cot_θ1]1−_k1 ²_z1+j(1−_k1 ²)_zLe(o)tan_θ1

According to the odd and even mode analysis method, the even mode load impedance is in Equation (2) and the odd mode load impedance is in Equation (3):

_zLe=8j(_zce3(−tan_θ2tan_{θ1 z4}+14_zce2)tan_θ3+12tan_{θ1 z4 zce2})_z4−4_zce3(_z4tan_θ2+14tan_{θ1 zce2})tan_θ3+2_{z4 zce2}

_zLo=0

2.2. Transmission Zero Analysis

The transmission zeros of the CLCSR filter fulfill the conditions|_S21|=0, which corresponds to_zine=_zino(_zLe=_zLo). When the value range of the parameter of_θ1,_θ2,_θ3is in[0,π], there are three transmission zeros:_fz1,_fz2,_fz3. By assuming_θ1=_θ3=θ,_fz1=0(θ=0) and_fz3=_f0(θ=π) do not change with the changing of the normalized impedances and the electrical length_θ2. Meanwhile, by setting_θ1=θand_θ2=θ/2,_fz3=_f0(θ=π) does not change with the changing of the normalized impedances and the electrical length_θ3.

In order to simplify the calculation, the electrical length parameters_θ1=_θ3=θand_θ2=θ/2are set. According to the following resonant condition_zLe=_zLo, the transmission zero_fz2can be obtained. When the transmission zero_fz2of the CLCSR filter is close to the passband, the CLCSR filter selectivity is better, and the stopband bandwidth of the CLCSR filter is wider.

_fz2=[2_f0arctan(2_{z4 zce2}+_{zce2 zce3}2_{z4 zce2}+8_{z4 zce3}+_{zce2 zce3})]π

By setting_zino=∞or_zine=∞, the transmission poles can be obtained. The odd-mode transmission pole_fp3=_f0/2is obtained when_θ1is equal toπ/2in Equation (1). The transmission pole_fp3is only related to the electrical length_θ1.

The even mode resonant condition is_zine=∞and the even mode transmission poles can be obtained through Equation (5):

1−_k1 ²_z1+j(1−_k1 ²)_zLe(o)tanθ=0

By solving Equation (5), there are three transmission poles in the frequency range[0,π], which are_fp1,_fp2, and_fp4.

Figure 2 shows the distribution of the transmission poles and transmission zeros in the frequency range [0,_f0]. The numbers and relative positions of the transmission zeros and transmission poles are shown in Equation (6).

_fz1<_fp1<_fz2<_fp2<_fp3<_fp4<_fz3

The transmission zero_fz2is affected by the parameters_zce2and_zce3.The impedance parameters and coupling coefficient of the CLCSR filter are assumed as_k1=0.8,_z1=0.5,_z4=2,_zce2=2.8,_zce3=2.4 . From Figure 3, when the value of_zce2increases,_fz2moves to high frequency and the CLCSR filter’s bandwidth decreases. Meanwhile, with the increase of_zce3,_fz2moves to low frequency and the proposed CLCSR’s bandwidth increases.

The transmission zero_fz2is also affected by parameters_θ2and_θ3. The frequency responses of_fz2with different_θ2and_θ3 are shown in Figure 4 under the basic design parameters of_k1=0.8,_z1=0.5,_z4=2,_zce2=2.8,_zce3=2.4. As the values of_θ2or_θ3increase,_fz2moves to low frequency and the CLCSR filter’s bandwidth increases._θ2and_θ3does not significantly affect_fz1and_fz3.

2.3. Transmission Poles Analysis

The transmission poles are affected by parameters_zce2and_zce3 . In Figure 5a, the transmission pole_fp2moves to high frequency and the CLCSR filter’s bandwidth decreases as_zce2 increases. In Figure 5b, as_zce3increase, the transmission pole_fp2moves to low frequency and the proposed CLCSR filter’s bandwidth increases. At the same time, the frequency responses of the transmission poles_fp3and_fp4are basically unchanged.

The transmission poles are also affected by parameters_θ2and_θ3. The transmission poles_fp2and_fp4 affect the bandwidth of the proposed CLCSR filter, so two transmission poles are discussed. In Figure 6a, with the increase of_θ2, the transmission poles_fp2and_fp4move to low frequency. The proposed CLCSR filter’s bandwidth increases with the increase of_θ2. However, the change of the transmission pole_fp4 is small. In Figure 6b, as the value of_θ3increases, the transmission pole_fp2moves to low frequency and the frequency of the transmission pole_fp4is basically unchanged. With the increase of_θ3, the proposed CLCSR filter’s bandwidth increases.

3. Filter’s Results and Discussion 3.1. Filter’s Results

The coupling coefficient of the parallel coupled line feed structure is about equal to 0.8, so the distance between parallel coupled lines is too small to be fabricated. Therefore, the parallel-coupled line feed structure and the single-branch microstrip line are replaced with the three microstirp lines coupled structure based on Ref. [12]. As the equivalent circuit of the proposed bandpass filter shown in Figure 7a, the parallel coupled line feed structure is replaced with the three microstirp lines coupled structure.

The proposed bandpass filter is designed on Rogers RT5880 microwave dielectric board (h=0.508 mm ,_εre=2.2,tanδ=0.0009), whose_f0is4.4 GHz. Based on the impedance parameters, electric lengths and coupling coefficient of the proposed bandpass filter’s equivalent circuit, the initial physical parameters of the proposed bandpass filter are as follows:a=1.08 mm,b=0.16 mm,c=14.60 mm,d=0.78 mm,e=0.18 mm,k=11.5 mm,n=21.6 mm,m=23.4 mm,r=1.54 mm.

As shown in Figure 8, the influence between the structural parameters of the three microstirp lines coupled structure and the quality factor_QL is analyzed. From Figure 8, when_Sris less than 0.3 mm, the values of_W1and_Srhave little effect on_QL.

The resonant characteristics of the proposed bandpass filter are simulated by using ANSYS HFSS. The final physical parameters of the proposed bandpass filter are shown in Figure 7b:a=0.9 mm,b=0.16 mm,c=14.6 mm,d=0.7 mm,e=0.16 mm,_w1=0.15 mm,_w2=0.15 mm,_sr=0.15 mmk=11.5 mm,r=1.54 mm,m=23.4 mm,n=21.6 mm.

The simulated and measured results of the fabricated bandpass filter are illustrated in Figure 9. In the measured results, the center frequency is 2.95 GHz, and the 3-dB bandwidth is about 1.5 GHz. In the passband, the measured insertion loss (IL) is less than 0.4 dB, while the return loss (RL) is greater than 20 dB. Furthermore, the rejection levels of over 35 dB at the upper stop band from 4.4 to 6 GHz have been achieved. From 1 to 2 GHz, the out-of-band rejection levels are greater than 15 dB.

3.2. Filter Performance Discussion

The bandwidth of the proposed bandpass filter can be adjusted by changing the_θ2and_θ3 , independently. Figure 10 shows the resonant characteristics of the proposed bandpass filter with different lengthsmandk . In Figure 10a, it is noted that whenmdecreases from 26.4 mm to 20.4 mm, the frequency of the transmission zero_fz2 increases from 1.47 GHz to 1.70 GHz. From Figure 10b, the frequency of the transmission zero_fz2increases from 1.43 GHz to 1.63 GHz whenkdecreases from 13.5 mm to 9.5 mm. With the increase ofmork, the bandwidth of the bandpass filter gets wider.

The surface current distributions at the critical frequencies are shown in Figure 11. Current distributions are used to further research the effects of different sections on its frequency response.

Table 1 gives the performance comparisons of the proposed bandpass filter with some previous works. The proposed bandpass filter is compact. The return loss and insertion loss in passband are better than others. The proposed bandpass filter has better out of band rejection. There are two transmission zeros and the frequency selectivity is better.

4. Conclusions In this paper, a cross-coupled line wide bandpass filter is proposed. With the use of the even and odd-mode approach, the transmission zeros and transmission poles of the proposed bandpass filter are analyzed and discussed. A three microstirp line coupled structure is used to increase coupling coefficient and make the filter compact. This structure also can improve stopband characteristics. The bandwidth can be adjusted by changing the length of the short-end parallel coupled line or the open-end parallel coupled line. Finally, the resonant characteristics of the proposed bandpass filter are measured. Good agreement between the simulations and measurements is obtained, which validates the design method.

Figure 1. Ideal circuit of the CLCSR and its equivalent circuit model, (a) Ideal circuit model, (b) Even-mode circuit, (c) Odd-mode circuit.

Figure 2. Calculated frequency responses of the ideal circuits shown in Figure 1.

Figure 3. Simulated frequency responses of the CLCSR filter with varied designing parameterszce2andzce3.

Figure 4. Simulated frequency responses of the proposed CLCSR filter with varied parameters, (a)θ2and (b)θ3.

Figure 5. Simulated frequency responses of the proposed CLCSR filter with varied parameters (a)zce2and (b)zce3.

Figure 6. Simulated frequency responses of the proposed CLCSR filter with varied parameters (a)θ2and (b)θ3.

Figure 7.(a) The equivalent circuit of the proposed bandpass filter; (b) The design size of the proposed bandpass filter.

Figure 8. Effect of three-line width on quality factor.

Figure 9. Simulated and measured results of the fabricated bandpass filter.

Figure 10. Bandwidth control of the proposed bandpass filter at lower band frequency by (a)mand (b)k.

Figure 11. Current density distributions of the proposed bandpass filter at different frequencies: (a) 2.5 GHz, (b) 2.8 GHz, (c) 3.2 GHz.

Ref.	Center Frequency (GHz)	Lower Stopband (dB)	Upper Stopband (dB)	RL (dB)	IL (dB)	Size(λg × λg)
[1]	6.65	<−20	<−20	20	0.35	0.5 × 0.79
[2]	1.93	<−40	<−35	20	0.4	0.56 × 0.23
[3]	2.05	<−32	<−20	20	0.6	0.48 × 0.24
[5]	8.28	<−20	<−25	15	1.9	1.12 × 0.45
[10]	3	<−10	<−18	16	1.28	0.18 × 0.175
[13]	6.71	<−30	<−25	15	1.45	0.5 × 0.04
[14]	7.6	<−20	<−10	16	0.6	0.64 × 0.31
This work	2.95	<−15	<−35	20	0.4	0.12 × 0.23

Author Contributions

D.-S.L., X.G., and Y.-Y.L. designed the method and wrote the paper; S.-M.C. and J.-W.G. performed the experiments and analyzed the data. All authors have read and agreed to the published version of the manuscript.

Funding

This work was supported by the National Natural Science Foundation of China (61501100), the Fundamental Research Funds for the Central Universities (N2023017), and Natural Science Foundation of Hebei Province (F2019203012).

Conflicts of Interest

The authors declare that there is no conflict of interest regarding the publication of this paper.

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