диафрагмированные волноводные фильтры / c0ece39a-5d22-4539-95e3-f5e2e2c46a74

Abstract—A new design method based on folded substrate is proposed in this paper to reduce the thickness of 3-D bandpass frequency-selective structure (FSS). A 67% and 79% thickness reduction compared to the basic 3-D bandpass FSS is achieved by employing three-layer and five-layer folded substrates, respectively. Singleand dual–polarized designs are presented. By integrating one more substrate with a different dielectric constant, dual-band thin structure is achieved. One structure with five-layer folded substrate is designed, fabricated and measured using the parallel-plate waveguide measurement setup. It has a center frequency of 3.57 GHz with 26.9% transmission bandwidth. The structure thickness is only 0.06 λ0, where λ0 is the free-space wavelength at the center frequency of the passband. Stable frequency response is achieved under oblique incidence. A good agreement is accomplished between simulated and measured results. Moreover, a semi-cylindrical radome is constructed based on the thin 3-D FSS and integrated with a broadband horn antenna. The radiation characteristics of the entire antenna-radome system are finally investigated and its good filtering feature is demonstrated. A fabricated prototype of this radome is measured in the presence of a broadband horn antenna.

Index Terms—3-D frequency-selective structure, conformal frequency-selective structure, folded substrate, radome.

I.INTRODUCTION

3-D FREQUENCY-selective structure (FSS) was presented recently [1], [2] to overcome some of the disadvantages associated with traditional 2-D FSSs [3], [4]. The 3-D FSS can accomplish a sharp filtering response with a stable performance under oblique incidence because its unit cell size is small compared to the operating wavelength. It was used to design bandpass/bandstop responses [1], [5]–[7], wideband microwave absorber [8], [9], absorptive frequency-selective transmission structures [10]–[13] and absorptive frequencyselective reflectors [13], [14]. Although it exhibits a good performance, the new structure is thick, which may limit its practical applications. Several design methods were presented

Manuscript received June 13, 2018; revised September 04, 2018, September 29, 2018; accepted October 11, 2018.

The authors are with the School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798 (e-mail: ahmedabd001@e.ntu.edu.sg, ezxshen@ntu.edu.sg).

Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TAP.xxxx.xxxxxxx.

in the literature to solve this problem for bandstop and bandpass responses. Utilizing stepped-impedance resonator in the unit cell of the bandstop FSS [15], the thickness can be reduced by 36%. Employing a loop resonator with steppedimpedance resonator instead of microstrip line resonator in the unit cell of bandstop FSS, an 80% thickness reduction was achieved [16]. For 3-D bandpass FSS, stepped-impedance parallel-plate waveguide was utilized as the unit cell [17], [18] and the structure’s thickness was 0.083 λ0, where λ0 is the free-space wavelength at the operating frequency.

On the other hand, FSSs can be integrated with antennas in several forms. Bandstop FSS was used instead of a ground plane to reduce the out-of-band radar cross-section of a patch antenna [19]. When FSS was employed as a superstrate, wide bandwidth and high directivity was achieved [20]–[22]. Dualband high directivity antenna was reported in [23] by employing high-impedance surface in the ground and superstrate layer, which was based on FSS design. Controlling the beamwidth of antennas was presented in [24] by utilizing active FSS as a superstrate. Active FSSs were also used to electronically steer antenna beam either by controlling the transmission phase of the surface to achieve gradient phase distribution [25] using varactor diodes or employing reconfigurable bandstop FSS using PIN diodes [26], [27]. FSS was utilized as a filter in front of a horn antenna [28], monopole [29], and wide-scanning array of dipoles [30].

The purpose of this paper is to propose a new design method aiming to minimize the thickness of the 3-D bandpass FSS, then utilize this thin FSS as a conformal radome with good filtering properties. The main idea is to fold the substrate several times, which leads to a substantial reduction in thickness. The principle of operation is introduced in Section II along with the equivalent circuit model, a five-layer folded design, and its fabricated prototype. In Section III, the design of dual-polarized and dual-band responses are presented. To demonstrate the application of the proposed design, a semicylindrical radome is built as an example and integrated with a horn antenna. The simulated reflection coefficient, realized gain and far-field radiation pattern results are illustrated in Section IV. In Section V, a fabricated prototype of the whole antenna-radome system is measured and a comparison between the performance of the antenna with and without radome is presented. Finally, a conclusion is given in Section VI.

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Fig. 1. (a) 3-D view of a unit cell of a conventional 3-D bandpass FSS [6]. (b) 3-D view of a unit cell of 3-D bandpass FSS with three-layer folded substrate.

0

Fig. 2 (a) and (b) Simulated reflection and transmission coefficients for unit cells shown in Figs. 1(a) and (b), respectively. (b = 5 mm, ha = 2 mm, L = 10.5 mm, d = 1.524 mm, w = 3 mm, Lb = 4 mm, tb = 1.2 mm, Dv1 = 0.5 mm, Dv2 = 0.06 mm, εr = 3.55).

II.3-D FSS BASED ON FOLDED SUBSTRATE

A. Principle of Operation

Fig. 1(a) shows the 3-D view of a unit cell of the 3-D bandpass FSS presented in [6] and Fig. 1(b) shows a unit cell based on three-layer folded substrate. The simulated reflection and transmission coefficients under TE-polarized wave (E in the y-direction) for the two unit cells are shown in Figs. 2 (a) and (b). It is seen that the transmission frequency is reduced by employing the folded substrate with the same structure

2

(b)

Fig. 3. Simulated vector electric field distribution. (a) Unit cell shown in Fig. 1 (a) at 6.7 GHz. (b) Unit cell shown in Fig. 1 (b) at 2.25 GHz.

thickness. The simulated results are obtained by using a fullwave simulator CST Microwave Studio (CST-MWS). These two designs, presented in Fig. 1, have the same substrate material and thickness. By utilizing the folded substrate, the transmission path is prolonged and the transmission frequency band is reduced. The center frequency of the structure shown in Fig. 1(a) is 7.23 GHz and its -3 dB bandwidth is 38%. While the center frequency of the structure with three-layer folded substrate shown in Fig. 1(b) is 2.4 GHz with -3 dB bandwidth of 31.7%. This means that 67% thickness reduction is achieved utilizing the three-layer folded substrate. Both structures exhibit a passband when the path length equals to λg/2, where λg is the guided wavelength, which occurs at 7.6 and 2.5 GHz for unit cells shown in Figs. 1(a) and (b), respectively.

The two transmission zeros at 12 and 16 GHz shown in Fig. 2(a) are produced due to the reflection from the two air paths resulting from blocking the air region with a metallic block [6]. There are no transmission zeros presented in the folded substrate case because the frequencies of the transmission zeros are beyond the second harmonic of the transmission frequency. Fig. 3 shows the simulated vector electric field distribution for unit cells shown in Fig. 1(a) and (b) at 6.7 and 2.25 GHz, respectively. It is seen that the electric field propagation path follows the folding profile.

B. Equivalent Circuit Model and Parametric Study

The equivalent circuit model of the unit cell shown in Fig. 1(b) is shown in Fig. 4 (a). It consists of two main transmission lines (TLs) denoted as air and substrate TLs, as detailed in [6]. The substrate TL contains an inductor representing the via hole in the folded substrate. The substrate TL is responsible for producing the second-order passband, which contains two reflection zeros (transmission poles) and may be analyzed using the even-odd mode method detailed in [17]. It is considered as two coupled resonators. One resonator

(a) 0

Fig. 4. (a) Equivalent circuit model of the unit cell shown in Fig. 1(b). (b) Simulated reflection and transmission coefficients using CST and ADS (Zp = 495.5 Ω, Ca = 0.01 pF, Cs = 0.04 pF, Lv = 0.96 nH, Za = 155 Ω, βa1l = 180 @ 13.8 GHz, βa2l = 180 @ 18.4 GHz, Zs = 70 Ω, βsl = 180 @ 2.85 GHz).

is half-TL with an inductor connected to its end, which produces the low-frequency reflection zero (Rz1) and represents the even resonant mode. The other resonator is the open-circuited full-length TL, which exhibits the highfrequency reflection zero (Rz2) and represents the odd resonant mode. The inductance of the via controls the coupling coefficient, which affects the separation between the two reflection zeros. The air TL contains a short circuit representing the metallic block in the air region, which divides the air TL into two short-circuited sections. Two transmission zeros are produced when the two short-circuited TLs resonate. The port characteristic impedance is termed as Zp, which

equals to 120π×(3 + ). A comparison between the simulated

reflection and transmission coefficients using CST and Agilent Advanced Design System (ADS) is shown in Fig. 4(b). The parameters of the circuit are calculated in the same way as the one detailed in [6].

The effect of the unit cell’s parameters on the passband characteristics of the structure is shown in Fig. 5. The resonant frequency and bandwidth of the passband are solely controlled by the substrate transmission path, as mentioned above. The via radius “rvia” affects the resonant frequency of Rz1 (even resonant mode) and as rvia decreases, the frequency of Rz1 decreases. When rvia decreases, the inductance increases and so does the coupling coefficient, which leads to an increase in the separation between the two resonant frequencies. It is seen from Fig. 5(b) that the strip width “w” influences both resonant frequencies. As w increases, the two edge capacitors “Cs” increase and this leads to a decrease in the resonant frequencies. Moreover, Cs controls the coupling between the

E y

Hφ K

xΘ Φ

-z

w

d

Frequency (GHz)

(b)

Fig. 6. (a) 3-D view of the unit cell of 3-D bandpass FSS with five-layer folded substrate. (b) Simulated reflection and transmission coefficients under the normal and oblique incidences (b = 6 mm, L = 10.5 mm, d = 1.524 mm, w = 4 mm, Dv = 0.16 mm, εr = 3.55).

reflection and transmission coefficients of the folded structure. A conical metallic disk is utilized to achieve the transition from a coaxial cable to parallel-plate waveguide [9]. In order to excite the dominant TEM mode inside the parallel-plate waveguide, the height of the cone is selected to be 10 mm. The purpose of a tapering section is to gradually transform the separation from 10 mm at the source to 24 mm at the FSS under test.

Because the measurement setup is suitable for measurement from 1.8 GHz to 15 GHz, the thickness (L) of the FSS unit cell, presented in Fig. 6, is modified from 10.5 mm to 5 mm. Therefore, the transmission band of the FSS under test lies within the bandwidth of the measurement setup. The two sidewalls of substrates can be fabricated with either via holes or deposit copper on the side of substrates; and the latter method is used in our fabrication. The size of the measurement setup at the side of structure under test is 24 mm × 144 mm (height × width) and the size of the unit cell presented in Fig. 6 is 7.8 mm × 6 mm. Therefore, 3 rows and 25 columns are required to construct the 3-D FSS to be measured. Fig. 7(a) shows the top and bottom views of the fabricated fifteen substrates required to build the FSS prototype. These substrates are combined together with Nylon screws and nuts at the two ends, as shown in Fig. 7(b). A comparison between

Substrate 15 (a)

3-D view of the structure

Fig. 7. Experimental verification. (a) Photograph of the top and bottom view of the fabricated substrates. (b) Photograph of 3-D FSS constructed by combined substrates. (c) A comparison between measured and simulated reflection and transmission coefficients under the normal incidence (b = 6 mm, L = 5 mm, d = 1.524 mm, w = 4 mm, Dv = 0.5 mm, εr = 3).

the measured and simulated reflection and transmission coefficients is shown in Fig. 7(c). A good agreement is achieved between the simulated and measured results. The slight difference between them is due to the tolerance in the fabrication and assembly.

III.DUAL-POLARIZED AND DUAL-BAND FSSS

A. Dual-Polarized Structure

The 3-D FSS proposed in the previous section can be easily extended to dual-polarized FSS, as shown in Fig. 8. The unit cell is divided into four sub-cells and arranged in a rotational fashion. Here, three-layer folded substrate is utilized to show

(b)

Fig. 9. (a) Equivalent circuit model of the unit cell shown in Fig. 8(a). (b) Simulated reflection and transmission coefficients using CST and ADS (Zp = 377 Ω, Cp = 0.08 pF, Cs = 0.04 pF, Zpp = 50 Ω, βp1l = 180 @ 7.6 GHz, Zs = 70 Ω, βsl = 180 @ 2.85 GHz).

plate waveguide is formed between the y- and x-polarized subcells, as illustrated in Fig. 8(a) for the 2-D front view. This parallel-plate waveguide produces two transmission poles when its input impedance equals the load impedance. This condition is fulfilled when “tan βL” equals to zero, which occurs at zero, the first transmission pole (Tp0) and when the length of the parallel-plate waveguide equals to λg/2, where λg is the guided wavelength in the parallel plate waveguide, which happens at 7.6 GHz, the second transmission pole (Tp7.6). It is known that a transmission zero is generated between two different transmission poles. Therefore, two transmission zeros (TzL and TzR) are formed around the transmission band of the folded substrate. The first transmission pole (Tp0) is a spurious passband, which may be considered as a shortcoming of the proposed structure.

The equivalent circuit model of the dual-polarized unit cell under TE-polarized wave is shown in Fig. 9(a). The equivalent circuit model consists of two block diagrams. The upper block represents the left-side of the dual-polarized unit cell shown in Fig. 8(a), while the bottom block represents the right-side. A comparison between the simulated reflection and transmission coefficients using CST and ADS is shown in Fig. 9(b). The parallel-plate waveguide is modeled as a TL, which is responsible for producing the two transmission poles located at zero and 7.6 GHz.

Fig. 10. Dual-band 3-D FSS. (a) 3-D view of the unit cell. (b) Simulated reflection and transmission coefficients under the normal and oblique incidences (b = 6 mm, L = 8 mm, d1 = 1.524 mm, d2 = 1.27 mm, w = 5 mm, Dv1 = 0.25 mm, Dv2 = 2.2 mm, εr1 = 3, εr2 = 11.2).

B. Dual-Band Structure

Dual-band response can also be accomplished by adding one more substrate of different dielectric constant to act as another passband path. Fig. 10 shows the unit cell and simulated reflection and transmission coefficients under the normal and oblique incidences. As shown, a dual-band bandpass response is achieved. This structure can be fabricated and measured utilizing the same method presented in the previous section. It exhibits center frequencies at 3.3 and 6.2 GHz with -3 dB bandwidths of 35% and 13.5%, respectively. The bandwidths of the two bands can be controlled by adjusting the diameter of the via in each path, which controls the coupling between resonators.

IV. CONFORMAL RADOME BASED ON 3-D FSS

b1

z

L3 x

(b)

Fig. 11. Half-cylindrical radome integrated with a broadband horn antenna. (a) 3-D view. (b) Top view (b1 = 42 mm, b2 = 66 mm, b3 = 100 mm, L = 5 mm, L1 = 50 mm, L2 = 79 mm, L3 = 21 mm, a1 = 62 mm, a2 = 86 mm, a3 = 100 mm, rradome = 100 mm, d = 1.524 mm, Dv = 0.3 mm, εr = 3).

A. Description of the Structure

As shown in the previous sections, thin 3-D bandpass FSS is achievable employing the folded substrate, which makes it suitable for practical applications. As an example, the 3-D bandpass FSS, shown in Fig. 7, can be employed as a conformal radome with excellent filtering performance. For simplicity, a semi-cylindrical radome is designed. The 3-D and top views of the semi-cylindrical radome based on folded substrate and integrated with a horn antenna is shown in Fig. 11. The dimensions of the radome unit cell is the same as the one shown in Fig. 7. The radome radius is chosen to be 100 mm so that it is appropriate for the horn antenna available in our lab. The broadband horn antenna is A-INFO LB-20245 with an aperture size of 84 mm × 64 mm. The horn antenna

illustrated in Fig. 11 consists of two parts. The first part (Part I) is a pyramidal horn antenna with an aperture size equal to the broadband horn antenna in the lab. The second part (Part II) is an extension, added to make the beam width of the horn antenna narrower, which lowers the side lobe level of the whole antenna-radome system.

B. Simulated Results

The simulated reflection coefficients for the horn antenna alone and the whole antenna-radome system are shown in Fig. 12(a). The whole system shows a good matching in the transmission band of the radome, which is similar to the one

Fig. 12. Simulated results of the design shown in Fig. 11. (a) Reflection coefficient for the horn antenna with and without radome. (b) Realized gain at +z-axis direction for the horn antenna with and without radome. (c) A comparison between difference in realized gain shown in (b) and transmission coefficient of infinite planar structure excited by plane wave.

shown in Fig. 7. The two reflection dips shown in Fig. 12(a) are corresponding to the two transmission poles of the radome. The out-of-band mismatching is due to the reflections from the radome, which lead to a high reflection coefficient. Fig. 12(b) shows the realized gain at the Θ = 0° direction with and without the radome. As shown, the whole system demonstrates a sharp filtering property. The simulated normalized gain as well as the difference between realized gain of the horn antenna with and without radome, are compared with the simulated transmission coefficient of the infinitely large planar 3-D FSS, as illustrated in Fig. 7. The comparison is shown in Fig. 12.c, which indicates an excellent agreement between the two curves. To ensure accuracy and reduce the time of simulation, a frequency range from 2.5 to 5.5 GHz is considered.

The simulated far-field radiation patterns for the horn antenna with and without radome at three different frequencies are shown in Fig. 13. The results are shown in two different