Double-Layer Microstrip Band Stop Filters Etching Periodic Ring Electromagnetic Band Gap Structures

: The electromagnetic band gap structure (EBGs) is widely used in microwave engineering, such as ampliﬁers, waveguides, microstrip ﬁlters, due to the fact of its excellent band stop characteristics. In this paper, three kinds of microstrip band stop ﬁlters were proposed which were etched with a hexagonal ring EBGs, octagonal ring EBGs and elliptical ring EBGs. Firstly, the etching coe ﬃ cient of a band stop ﬁlter is proposed, and the performance of ﬁlters with di ﬀ erent etching coe ﬃ cient was analyzed. Secondly, the equivalent circuit of an EBGs band stop ﬁlter is proposed. By comparing the simulation results using advanced design system (ADS) and high frequency structure simulator (HFSS), it was found that the simulation results had the same − 10 dB stopband width which veriﬁes the correctness of the equivalent circuit model. Finally, three kinds of microstrip stopband ﬁlters were fabricated and measured. The experimental results of the − 10 dB stopband width and resonant frequency were in good agreement with the simulation results. The − 10 dB stopband fractional bandwidth of the three kinds of microstrip stopband ﬁlters was more than 63%. The proposed microstrip band stop ﬁlters can be widely used in microwave devices with a wide stopband.


Introduction
The photonic band gap (PBG) structure has a certain periodic structure which can prevent the propagation of microwave in a certain frequency range [1]. The electromagnetic band gap structure (EBGs) originates from the PBG structure which has the characteristics of band resistance and slow wave [2]. In recent years, EBGs has been widely used in microwave device design. In the application of microwave power amplifiers, it has usually been used to improve the efficiency and output power of power amplifiers. In the design of microstrip antennas, it is mainly used to improve the performance of the antenna [3]. In the application of microstrip filters, its superior broad stopband characteristic is suitable for microwave band stop filters [4][5][6][7][8][9].
Microstrip filters based on a variety of EBG structures are realized by a few techniques, and they mainly include the following categories. The first is to realize the filter with notch by coupling an EBGs, adjusting the coupling distance and the size of the unit EBGs. In Reference [4], a microstrip filter based on the Archimedes spiral EBGs is proposed. In Reference [5], a microstrip filter is realized via a coupling T-shaped resonator, and an asymmetric coupling line band-pass filter is proposed in Reference [6], and the performance of the filter is adjusted by adding coupling variables. In Reference [7], an ultra-wideband bandpass filter based on a coupled EBGs is proposed. The second is based on the periodic EBGs which reduces the passband ripple, increases the stopband width, and achieves better band stop characteristics. For example, Reference [8] proposed a DP-EBG structure to achieve band stop characteristics; Reference [9] proposed a filter embedded in a multi-mode resonator; Reference [10] proposed a filter based on a tapered Cauchy microstrip Koch fractal EBGs; and Reference [11] proposed a filter based on a multi-cycle conical etching EBGs. The third is based on the integration of EBGs and a multi-layer PCB. For example, multi-layer PCB adopts the locally embedded planar EBGs [12] and biplane EBG microstrip filter [13]. The fourth is to optimize the EBGs based on high performance optimization algorithm, and analyze its band resistance characteristics to obtain better band resistance. In Reference [14], Particle swarm optimization (PSO) is used to optimize EBGs, and in Reference [15] PSO is used to optimize the EBG common mode filter by using an artificial neural network.
In this paper, three kinds of double-layer microstrip stopband filters with an etched EBG ring structure are proposed. First, a band stop filter based on a gradient line is proposed. In the upper layer of the dielectric plate, the basic band stop filter was realized by using the butterfly gradient microstrip line. The periodic elliptical ring, hexagonal ring, and octagonal ring were etched on the floor, further increasing the stopband width of −10 dB and the maximum attenuation. Second, the influence of the etching factor of the three band stop filters on the band stop width and attenuation was analyzed, and the equivalent circuit of the band top filter was further analyzed. The correctness of the proposed equivalent circuit model was verified by comparing the simulation and measured results. Finally, the three band stop filters were compared with those proposed in other studies. The proposed filters etched with three kinds of EBGs rings can be applied to the broadband band stop RF devices.

Design Principle of Microstrip Band Stop Filter
The three band stop filters designed in this paper were composed of a two-layer EBGs. The top layer was the patch microstrip line of butterfly element, and the bottom layer was etched with three different periodic ring EBGs on the floor. According to Reference [14], when the period of the butterfly element is six, the band stop filter can obtain good stopband characteristics and small passband ripple. The dielectric material was Rogers ro4003, the thickness of the dielectric plate was 1.5 mm, and the relative dielectric constant was 3.55. According to Bragg reflection conditions, Formulas (1)-(4) can be derived. The distance between two adjacent circles on the ground plate was d 1 , β was the phase constant of the dielectric plate, λ g was the wavelength of the waveguide, f 0 was the center frequency of the band resistance, ε eff was the effective dielectric constant plate of the medium, and C was the speed of light. The central frequency of the three filters was 5.2 GHz, the period d 1 and d 2 of the upper butterfly structure were 17.1 mm, and the corresponding w 1 was 3.5 mm and w 2 was 0.2 mm.
The top layer of the three double-layer band stop filters proposed in this paper adopted the butterfly gradient structure with a thickness of 0.035 mm. The top view and the 3D view are shown in Figure 1a,b, respectively. In order to analyze the effect of w 1 and w 2 on the band stop, HFSS was adopted to sweep the frequency from 2 GHz to 8 GHz for w 1 and w 2 . As shown in Figure 2a, with the increase of w 1 , the −10 dB bandwidth increased from 1.59 GHz to 1.91 GHz, the maximum stopband attenuation increased from 19.41 dB to 23.95 dB, the low-frequency ripple decreased from 2.73 dB to 2.29 dB, and the high-frequency ripple increased from 1.99 dB to 3.93 dB. As shown in Figure 2b, with the increase of w 2 , the −10 dB bandwidth decreased from 2.01 GHz to 1.49 GHz, the maximum stopband attenuation decreased from 25.39 dB to 18.3 dB, and the low-frequency ripple and high-frequency ripple decreased accordingly. As shown in Figure 3a, with the increase of d 1 , the resonance frequency decreased continuously, but the −10 dB bandwidth and the maximum stopband attenuation increased. The simulation of the band stop filter based on the asymptote structure are shown in Figure 3b. The frequency of stopband resonance center was set at 5.2 GHz, and the size of gradient line optimized by HFSS sweeping was as follows: d 1 = d 2 = 17.1 mm; w = 10 mm; w 1 = 3.5 mm; w 2 = 0.2 mm; dielectric constant = 3.55; and thickness = 1.5 mm.

Band Stop Filter with Etched Periodic Hexagon Ring EBG Structure
The upper layer of the microstrip band stop filter is a butterfly-shaped gradient line which is made of copper with a thickness of 0.034 mm. The floor of the filter is covered with copper and etched with a hexagon ring EBGs. The etched depth is equal to the thickness of copper, which is 0.034 mm. The side length of the outer hexagon is c 1 , and the side length of the inner hexagon is c 2 . The etching factor of hexagon is k h = c 2 /c 1 . A perspective view of a microstrip band stop filter etched with a periodic hexagon ring on the floor is shown in Figure 4a, and Figure 4b is a 3D view of a microstrip band stop filter etched with a periodic hexagon ring modeled using HFSS.

Band Stop Filter of Etched Periodic Octagonal Ring EBG Structure
The upper layer of the microstrip band stop filter is a butterfly-shaped gradient line which is made of copper with a thickness of 0.034 mm. The floor of the filter is covered with copper and etched with an octagonal ring EBGs. The etched depth is equal to the thickness of copper which is 0.034 mm. Figure 5a shows a perspective view of a microstrip band stop filter etched with a periodic octagon ring on the floor. The center distance of the outer octagon is e 1 , the center distance of the inner octagon is e 2 , and the relationship between k o = e 2 /e 1 . Figure 5b is a 3D diagram of a microstrip band stop filter with periodic octagonal ring etched by HFSS.

Band Stop Filter of Etched Periodic Elliptic Ring EBG Structure
The upper layer of the microstrip band stop filter is a butterfly-shaped gradient line which is made of copper with thickness of 0.034 mm. The floor of the filter is covered with copper and etched with an elliptical ring EBGs. The major axis of the outer ellipse ring is a 1 , the minor axis is b 1 , the major axis of the inner ellipse ring is a 2 , and the minor axis is b 2 . The ratio of the long axis to the short axis of the outer elliptic ring is r a1 , r a1 = b 1 /a 1 . The ratio of the major axis to the minor axis is r a2 , r a2 = b 2 /a 2 . The proportion of the long axis and the short axis of the inner and outer elliptic rings is equal, that is r a = r a1 = r a2 . Let the etching factor of elliptical ring be k e , k e = a 2 /a 1 . Figure 6a is a perspective view of a microstrip band stop filter etched with a periodic elliptical ring, and Figure 6b is a 3D view of a microstrip band stop filter etched with a periodic elliptical ring modeled with HFSS.

Analysis of Band Stop Filter with an Etched Periodic Hexagon Ring EBG Structure
In order to analyze the influence of the etching coefficient of a band stop filter with a hexagon ring, we used HFSS to analyze the frequency sweep of k h , c 1 = 3.6 mm, where the k h value was 0.5~0.9, and the step size was 0.1. The center frequency was 5.2 GHz, and the optimized parameters were c 1 = 4.2 mm and k h = 0.22. As shown in Figure 7a,b, when c 1 = 3.6 mm, as k h increased from 0.5 to 0.9, the maximum attenuation of the stopband decreased from 41.9 dB to 36 dB, the bandwidth of −10 dB decreased from 3.05 GHz to 2.66 GHz, and the resonance frequency of band stop filter decreased from 5.24 GHz to 5.2 GHz. As shown in Figure 8a, when k h = 0.3 and c 1 increased from 3.0 mm to 3.8 mm, the maximum attenuation of band resistance increased from 35.56 dB to 42.87 dB, and the −10 dB bandwidth increased from 2.66 GHz to 3.07 GHz, but the ripple of high and low frequency increased slightly. As shown in Figure 8b, the simulation results of the single-layer graded linear EBGs band stop filter, the filter in Reference [14] and the proposed double-layer band stop filter etching hexagon ring EBGs were compared. The results showed that the performance of the double-layer band-stop filter was obviously better than the former two. When the resonant frequency was 5.2 GHz, c 1 = 4.2 mm, k h = 0.22, the −10 dB band stop width was 3.34 GHz and the maximum band resistance attenuation was 48.84 dB.  Figure 10a,b. The performance of the band stop filter was tested with the S5180 vector network analyzer by Copper Mountain Technologies. The vector network analyzer was directly connected to the amplitude and phase stabilization test module of N small a type (N-SMA) using the Gore test cable. The calibration was carried out at the SMA port of the test cable of the vector net, and the reference end face was automatically moved to the calibration end face after calibration. Taking the microstrip band stop filter with etched periodic hexagon ring as an example, the equivalent circuit of band stop filter was analyzed. The equivalent lumped circuit of the microstrip band stop filter based on gradient line EBGs is shown in Figure 11a. The equivalent lumped circuit of the microstrip band stop filter etched with periodic hexagon ring is shown in Figure 11b. The ring EBGs is etched on the floor of the microstrip band stop filter of the asymptote, which is equivalent to adding inductance capacitance (LC) series resonance in the asymptote equivalent circuit and improving the stopband width of the circuit. The three resonant frequencies of the stopband are determined by inductance capacitance series resonance as shown in Formula (5).  Advanced design system (ADS) is used to simulate the equivalent lumped circuit of the microstrip band stop filter etched with periodic hexagon ring. The LC parameters are optimized as shown in Table 1. As shown in Figure 12, the simulation results of ads and HFSS show that they have the same −10 dB stopband width, which verifies the correctness of the proposed equivalent circuit.

Analysis of Band Stop Filter of Etched Periodic Octagonal Ring EBG Structure
In order to analyze the influence of etching coefficient k o on the performance of the octagonal band stop filter, the scanning frequency of k o was analyzed using HFSS, and the sweep range of k o was from 0.5 to 0.9 in steps 0.1 with the condition e 1 = 3.6 mm. The optimized parameters of HFSS were e 1 = 4.1 mm and k o = 0.25. As shown in Figure 13a  As shown in Figure 14a, when k o = 0.3 and e 1 increased from 3.0 mm to 3.8 mm, the maximum attenuation of the band stop increased from 38.1 dB to 44.41 dB, and the −10 dB bandwidth increased from 2.74 GHz to 3.13 GHz, but the high and low frequency ripple slightly increased. As shown in Figure 14b, the HFSS simulation results of single-layer gradual linear EBGs band stop filter, the filter proposed in Reference [14], and the double-layer band stop filter etching octagonal ring EBGs were compared. The results showed that the performance of the double-layer band stop filter was better than the former two filters. When the resonance frequency was 5.2 GHz and e 1 = 4.1 mm, k o = 0.25, the band stop width of −10 dB was 3.46 GHz, and the maximum band stop attenuation was 50.25 dB. The simulation results showed that by increasing e 1 or decreasing the etching factor k o , the band stop width of the filter can be increased and the band stop attenuation can be increased.  The results showed that the resonance frequency of the band stop filter was 5.2 GHz, the stopband width of −10 dB was 3.41 GHz, and the maximum attenuation of the stopband was 49.24 dB. The experimental results of the −10 dB stopband width and resonant frequency were in good agreement with the simulation results. The physical test photos and the physical measurement results of the band stop filter etched periodic hexagon ring EBGs are shown in Figure 16a,b.

Analysis of Band Stop Filter with Etched Periodic Elliptic Ring EBG Structure
In order to analyze the influence of etching coefficient k e on the performance of band stop filter etched elliptical ring EBGs. In the case of r a = r a1 = r a2 , the frequency sweep of k e was analyzed using HFSS. The relationship between etching coefficient and −10 dB band stop bandwidth, maximum insertion loss, and passband ripple were analyzed. When the resonance frequency was 5.2 GHz, the optimized parameters were a 1 = 4.1 mm, r a = 0.95, and k e = 0.24. As shown in Figure 17a,b, a 1 = 3.6 mm, r a = r a1 = r a2 = 0.85, when k e increased from 0.5 to 0.9, the maximum attenuation of band stop decreased from 42.6 dB to 36.9 dB, the bandwidth of −10 dB decreased from 3.04 GHz to 2.72 GHz, and the resonance frequency of the band stop filter decreased from 5.22 GHz to 5.2 GHz. As shown in Figure 18a, as r a increased from 0.5 to 0.9, the maximum attenuation of the band stop increased from 37.29 dB to 43.25 dB, −10 dB bandwidth increased from 3.77 GHz to 3.69 GHz, low-frequency ripple increased from 3.8 dB to 6.17 dB, and high-frequency ripple increased from 4.46 dB to 9.75 dB. As shown in Figure 18b, the microstrip band stop filter based on single-layer gradient EBGs, the band stop filter proposed in Reference [14], and the double-layer band stop filter etched with tthe elliptical ring EBGs were compared. The results showed that the band stop filter etched with elliptical ring EBGs increased the −10 dB stopband width and the maximum attenuation of stopband, but the ripple in the band also increased.
The top layer and bottom layer of the microstrip band stop filter based on the gradient line structure and etched elliptical ring EBGs with SMA joint are shown in Figure 19a. The comparison between the measured and the simulation is shown in Figure 19b   In order to compare the effect of three etching factors on the stopband characteristics of the three band stop filters, under the condition of a 1 = c 1 = e 1 = 3.6 mm, Figure 21a compares the −10 dB bandwidth with the three etching factors, and Figure 21b analyzes the maximum stopband attenuation with the three etching factors. Simulation results show that the curves of the −10 dB bandwidth of stopband and the maximum attenuation of k e are in good agreement with the curves of k h which shows that the etching factor k e and k h can achieve the same stopband characteristics. Therefore, when a 1 = c 1 is determined, the required −10 dB bandwidth and the maximum attenuation of the stopband can be adjusted by changing k e or k h . In this paper, three kinds of double-layer microstrip band stop filters were proposed which were designed with a butterfly-shaped gradual microstrip line on the upper layer of the dielectric plate and the EBGs of a periodic elliptic ring, hexagonal ring, and octagonal ring etched on the floor.

Conclusions
By etching the EBGs, a wider band stop and a larger band stop attenuation microstrip band stop filter were realized comparing Reference [14]. Given that a 1 , c 1 , and e 1 were constant, the −10 dB bandwidth and the maximum attenuation of the three microstrip stop band filters decreased with the increase of the etching parameters k e , k h , and k o . The simulation of the designed filter and other band stop filters are compared in Table 2. Compared with References [14] and [15], the stopband center frequency of 5.2 GHz, the −10 dB fractional bandwidths of the three stopband filters proposed in this paper were all greater than 63% which is significantly larger than the former two. In this paper, three kinds of double-layer microstrip band stop filters were proposed. The same butterfly gradient microstrip line was used in the upper layer of the dielectric plate, and the periodic elliptical ring, hexagonal ring, and octagonal ring were etched on the floor. Compared with References [14] and [15], the three band stop filters designed in this paper had wider stopband widths and larger maximum attenuations.
In the case of c 1 = e 1 and k h = k o , the trend of maximum attenuation and relative bandwidth of the band stop filter etched with elliptical ring EBGs and the band stop filter etched with hexagon ring EBGs were consistent.
The simulation and measurement results show that the maximum attenuation and the stopband width of −10 dB can be improved by reducing the corrosion factor of the three microstrip band stop filters. The fractional stopband bandwidths of the three microstrip band stop filters were all over 63%, which can be used in radio frequency (RF) devices with wide stopband bandwidth requirements. In practical application, on the basis of ensuring performance, the filter size should be further reduced and the cost should be reduced.