LETTER

3-D dual-polarized bandpass frequency selective surface with quasi-elliptic response based on rectangular waveguide cavity

Zhengyong Yu1,2, Jianping Zhu3, Cheng Wang3, Xia Yang1, Wanchun Tang1a), and Yuehua Li3

Abstract A new three-dimensional (3-D) frequency selective surface(FSS) based on rectangular waveguide cavities is presented, which realizesa quasi-elliptic bandpass response by multiple transmission zeros/poles.Each unit cell of the proposed FSS is composed of an empty rectangularwaveguide cavity and a cuboid circuit board with two back-to-back squareloops. With the help of the rectangular waveguide cavities, the electricaland magnetic coupling paths are constructed, resulting in two transmissionpoles. The constructed out-of-phase signal paths cause two transmissionzeros in the upper stopband. To explain the operating principle of theproposed FSS, an equivalent circuit model is given and analyzed usingthe odd- and even-mode method. A prototype of the proposed FSS isfabricated and measured. The measured results agree well with the simu-lated results, and show that the FSS can achieve a stable response tovariations of incident angle from 0° to 60° for both TE and TM polar-izations with wide out-of-band rejection. In addition, the proposed designalso realizes a relatively small unit cell.Keywords: bandpass, dual-polarized, frequency selective surface (FSS),rectangular waveguide cavity, quasi-elliptic response, three-dimensional(3-D)Classification: Microwave and millimeter-wave devices, circuits, andmodules

1. Introduction

Frequency selective surfaces (FSSs), acting as ordinaryspatial filters for incoming electromagnetic waves, arewidely used in various systems over the past few decades,such as bandpass radomes, antenna reflectors, electromag-netic shields, as well as absorbers [1, 2, 3, 4, 5, 6, 7, 8].Owing to the demands of some practical applications,bandpass FSSs have been intensively investigated. Espe-cially, it is highly desirable that bandpass FSSs can exhibita quasi-elliptic response, satisfactory angular stability anddual polarizations.

According to the traditional 2-D structures, severalFSSs were designed to meet those demands. In [9], a singlelayer FSS was proposed by using substrate integratedwaveguide technology, which exhibited a quasi-elliptic

bandpass response. With a similar response to that in [9],an FSS based on the tortuous structure realized miniatur-ization [10]. However, those two first-order FSSs hadsingle transmission pole and zero, leading to unflat pass-bands and narrow out-of-band rejections due to the lack ofmultiple transmission zeros/poles. In order to address thatissue, some multilayered 2-D FSSs were designed in acascading fashion. A quasi-elliptic FSS was designed bycascading a two-layer periodic array and a non-resonantgrid inductive layer, leading to a second-order bandpassresponse [11]. Similarly, another second-order bandpassFSS was designed with inductive wire grids and improvedJerusalem slots [12]. As described in [13], a third-orderbandpass FSS was presented by a multilayered structurefor X-band application. Nevertheless, those cascaded 2-DFSSs usually had complicated and thick structures, suffer-ing from difficult following-up fabrication and largeweight. In addition, some attractive bandpass 2-D FSSswith stable responses were typically designed through thecross coupling resonators [5, 14, 15], but those FSSs werealso difficult for the fabrication and miniaturization. Fur-thermore, as an alternative approach, a reported concept of3-D FSSs could construct multi-mode resonant cavitiesfor the desired response [16, 17, 18, 19, 20, 21, 22, 23].In [17, 18], two 3-D elliptical bandpass FSSs were studiedby utilizing the shielded micro-strip lines. Based on short-circuited and open-circuited resonators, a highly-selectiveFSS was proposed, which could provide two transmissionzeros located at each side of the passband [21]. Unfortu-nately, these three designs only operated under singlepolarization. Recently, a 3-D bandpass FSS was designedbased on square coaxial waveguides, with dual polariza-tions and quasi-elliptic response [23]. Nonetheless, thistype of FSS had lots of building blocks, which mightcause an inevitably inaccurate implementation.

In this paper, a dual-polarized 3-D FSS is proposed.The unit cell of the proposed FSS is created by an emptyrectangular waveguide cavity and a cuboid circuit boardwith two back-to-back square loops. Due to the electricaland magnetic couplings between the square loops throughthe rectangular waveguide cavities, multiple transmissionzeros/poles are obtained, achieving a quasi-elliptic band-pass response. In order to understand the operating princi-ple, an equivalent circuit model is investigated. At last, aprototype has been fabricated and measured. The resultsshow a good consistency between the full-wave simula-tions and the measurements. The proposed 3-D FSS ex-hibits dual polarizations, good angular stability, small in-

DOI: 10.1587/elex.16.20190178Received March 19, 2019Accepted April 19, 2019Publicized May 13, 2019Copyedited June 25, 2019

1School of Physics and Technology, Nanjing NormalUniversity, Nanjing 210023, China2School of Computer and Communication Engineering,Huai’an College of Information Technology, Huai’an223003, China3School of Electronic and Optical Engineering, NanjingUniversity of Science and Technology, Nanjing 210094,Chinaa) eewctang@njnu.edu.cn

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Copyright © 2019 The Institute of Electronics, Information and Communication Engineers

sertion loss (IL), wide out-of-band rejection and relativelysmall unit cell.

2. Structure and operating principle

2.1 FSS structure design and simulationAs shown in Fig. 1, a cuboid circuit board with two back-to-back square loops is inserted into an empty rectangularwaveguide cavity to construct the unit cell of the proposed3-D FSS. As a result, each end-face of one single unit cellprovides a gridded-square loop (GSL) structure. The peri-ods along the x- and y-axes are denoted by dx and dy. Thewall thickness of the rectangular waveguide cavity is t, andits height is represented by h. The side-length and line-width of the square loop are l and w, respectively. The gapdistance between the grid and square loop is s. The dielec-tric constant of the cuboid circuit board is "r. Moreover, theincident angle θ denotes the angle between the wave vectork of the incident wave and the normal to the FSS structure.

In Fig. 2, it provides the transmission and reflectioncoefficients of a design example by using the full-wavesimulator HFSS. The physical dimensions denoted inFig. 1 are as follows: dx ¼ dy ¼ 9:4mm, l ¼ 7:4mm,w ¼ 0:5mm, s ¼ 0:5mm, h ¼ 4:6mm, t ¼ 0:5mm, and"r ¼ 4:4. The simulated results show that a quasi-ellipticbandpass response is realized, with two transmission polesfp1 ¼ 6:08GHz and fp2 ¼ 6:25GHz in the passband, aswell as two transmission zeros fz1 ¼ 6:87GHz and fz2 ¼7:6GHz in the stopband. It is also observed that the 3-dBrelative bandwidth (RBW) of the passband is 10.1%, andthe 20-dB RBW of the stopband is 40.1% at the centerfrequency of the passband (fc ¼ 6:1GHz).

2.2 Equivalent circuit analysisIn order to provide direct physical insight into the operatingprinciple of the proposed 3-D FSS, an equivalent circuitmodel (ECM) for normal incidence is established anddemonstrated in Fig. 3. For simplicity, all losses are notconsidered in this circuit model.

The ECM can be divided into three parts which are twoLC resonators and one transmission line resonator, when y-polarized plane waves strike upon the FSS structure. Thetwo same LC resonators consisting of L1, L2, and C1,represent the GSL structures on the top and bottom end-faces of the proposed FSS. The inductors L1 and L2 are theself-inductance of the square loop and grid, respectively.

The capacitor C1 denotes the gap capacitance between thegrid and square loop. Here, the transmission line resonatorexpresses the rectangular waveguide cavity with the fre-quency-dependent characteristic impedance ZðfÞ and theelectrical lengths θ under the dominant mode TE10. Withregard to the mutual capacitance Cm and the mutual in-ductance Lm, their existences can be justified by the vectorfield distributions in Fig. 4. In Fig. 4(a), the current direc-tions of the square loops on the top and bottom end-facesare in-phase, which reveals the existence of a positivemutual inductance. From Fig. 4(b), it can be seen thatsome of the electric field vectors direct vertically into thedielectric substrate, implying that the capacitive effectbetween two square loops, is not negligible.

For more convenient analysis, the mutual capacitanceCm is represented by an admittance inverter J ¼ !Cm, andthe mutual inductance Lm is denoted by an impedanceinverter K ¼ !Lm. Thus, a modified ECM is obtained, asshown in Fig. 5(a). It is found that the signal path directlythrough the waveguide ðZðfÞ; �Þ and the coupling paths(Cm and Lm) are achieved, and the out-of-phase signalpaths contribute to multiple transmission zeros at finitefrequencies. Considering the waveguide cavity effects,the self-capacitance C1 and self-inductance L1 of the res-onators can be defined by C1 ¼ C0 � Cm and L1 ¼L0 þ Lm, where C0 and L0 represent the resonator capaci-tance and inductance without the coupling waveguidecavities, respectively [24]. The initial values of the elec-trical parameters L0, C0 and L2 for the GSL structures arecalculated directly by using the given formulas in [25, 26,27], and Cm, Lm are extracted by using the methods in [28].With a curve-fitting method [29], the final parameter values

Fig. 1. Periodic unit cell of the proposed 3-D FSS.

Fig. 2. Simulated transmission and reflection coefficients of the designexample

Fig. 3. Equivalent circuit model of the proposed 3-D FSS.

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of the ECM are obtained by the repeated optimization.The free space at top and bottom sides of the FSS ismodeled as transmission lines with characteristic impe-dance of Z0 ¼ 377Ω, and corresponding admittanceY0 ¼ 1=Z0. Owing to the symmetry of the model, theodd- and even-mode analysis method is adopted to analyzethis circuit. The symmetry plane T-T 0 is subsequentlyreplaced by a magnetic wall (an open circuit, or OC

for short) and an electrical wall (a short circuit, or SC

for short). The even- and odd-mode equivalent circuitsare achieved, as displayed in Fig. 5(b) and Fig. 5(c),respectively.

From Fig. 5(b), the even-mode input admittance Yevenis derived as

Yeven ¼ 1

j!L2þ 1

1

j!ðC1 � CmÞþ j!ðL1 þ LmÞ

þ 1

Zocð1Þ

Zoc ¼ �jZðfÞ=tanð�=2Þ ð2Þ

� ¼ h

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið2�fÞ2�0"0"r � �

dx

� �2s

ð3Þ

Where Zoc is the input impedance of the rectangular wave-guide transmission line in open circuit state, and θ is theelectrical length.

The characteristic impedance of the rectangular wave-guide transmission line is defined as [30]

ZðfÞ ¼ �2

8

dydx

ffiffiffiffiffiffiffiffiffi�0"0"r

r1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1 ���ðfÞ2dx

�2s ð4Þ

�ðfÞ ¼ 1

fffiffiffiffiffiffiffiffiffiffiffiffi�0"0"r

p ð5Þ

Where �0 is the permeability in free space, and "0 is thedielectric constant in free space. The parameter "r is therelative dielectric constant.

Similarly, the odd-mode input admittance Yodd is ob-tained from Fig. 5(c), as follows:

Yodd ¼ 1

j!L2þ 1

1

j!ðC1 � CmÞþ 1

j!ð2CmÞ þ 1

j!ðL1 � LmÞ

þ 1

Zscð6Þ

Zsc ¼ jZðfÞ tanð�=2Þ ð7ÞWhere Zsc is the input impedance of the rectangular wave-guide transmission line in short circuit state.

Consequently, the scattering matrix parameters can beobtained based on the odd- and even-mode input admit-tances [31].

S11 ¼ S22 ¼ Y02 � YevenYodd

ðY0 þ YevenÞðY0 þ YoddÞ ð8Þ

S21 ¼ S12 ¼ Y0ðYodd � YevenÞðY0 þ YevenÞðY0 þ YoddÞ ð9Þ

In Fig. 6, it compares the simulated scattering parame-ters from HFSS with those obtained from the ECM, wherea very good agreement can be observed. However, a slightdeviation appears in the high frequencies. The main reasonis that the rectangular waveguide cavity is characterizedunder the dominant mode TE10 without considering theeffect of the higher modes.

3. Implementation and measurement

3.1 ImplementationA practical example is implemented to validate the perform-ance of the proposed 3-D FSS. These building parts anddetailed physical dimensions are shown in Fig. 7. It isunderstood that the implemented prototype is made up oftwo kinds of building parts. Part 1 is one piece of alumi-nium plate with a thickness of 1.0mm. The opening slotscut half way along the width direction of each aluminiumplate, are created in Part 1. Part 1 is obtained by using wirecutting. Part 2, being made of microwave ceramic material("r ¼ 4:4, tan � ¼ 0:003), is one piece of cuboid circuit

(a)

(b) (c)

Fig. 5. Modified equivalent circuit model: (a) Impedance andadmittance conversion; (b) Even-mode circuit; (c) Odd-mode circuit.

(a)

(b)

Fig. 4. Vector field distributions at the center frequency of the passband:(a) Surface current density; (b) Electric field vector.

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board with a thickness of 4.6mm. Part 2 pieces are realizedby using ordinary printed circuit board technology. Thelayouts of the assembly process mainly contain two steps:1) Part 1 pieces are cross-joined together through the open-ing slots to construct an aluminium frame, which supportsperiodic rectangular waveguide cavities. 2) Part 2 pieces areinserted into the constructed frame one by one, so as toachieve the proposed design. Fig. 8 shows the prototype ofthe fabricated 3-D FSS, which is 265:4mm � 265:4mm insize and consists of 26 � 26 (676) unit cells. The dimen-sions of each unit cell dx � dy � h is 0:19�0 � 0:19�0 �0:093�0, where �0 is the free-space wavelength at the centerfrequency of the passband.

3.2 Measurement resultsThe FSS prototype is measured by using the free-spacemethod, as shown in Fig. 9. The measurement setupmainly includes a pair of horn antennas, a FSS prototype,screens covered by absorbers and a vector network analyz-er. The FSS prototype is placed into the rectangularthrough-hole window in the center of the rotatable screen.Two horn antennas operating from 1 to 18GHz are locatedabout 120 cm apart from each side of the rotatable screen,so as to ensure that the FSS structure is excited withuniform plane waves. Moreover, the whole measurementsystem is surrounded by the absorbing screens. In order toobtain the accurate results, three measurement cases arecarried out: 1) the transmission coefficients without theFSS. 2) the transmission coefficients with the FSS betweenthe two horn antennas. 3) the transmission coefficients withan identically-sized metallic plate instead of the FSS. Then,the measured results of case 2 are calibrated with respect tothe results of case 1 and case 3 by using the time-domaingating function.

The simulated and measured transmission coefficientsof the proposed FSS under oblique incidence for bothTE and TM polarizations, are shown in Fig. 10. It isobserved that the bandpass filtering responses are polar-ization independent and very stable against different inci-dence waves. It is also seen that the quasi-elliptic bandpassFSS is realized, with two measured transmission poles at6.05 and 6.32GHz (Simulated: 6.08 and 6.25GHz) in thepassband, and two measured transmission zeros at 7.02 and7.84GHz (Simulated: 6.87 and 7.6GHz) in the stopband.The measured insertion loss at fc is about 0.8 dB under thenormal incidence. Such acceptable discrepancies betweenthe measured and simulated results may be attributed tofabrication tolerance, actual dielectric constant, assemblytolerance, and measurement error. In Table I, the perform-ances of the proposed FSS are compared with somepreviously designs with similar frequency responses. Ob-viously, it can be observed that the proposed FSS withmultiple transmission zeros/poles exhibits the advantagesin angular stability, dual polarizations, insertion loss andunit cell size.

Fig. 7. Building parts of the fabricated 3-D FSS.

Fig. 8. Photographs of the fabricated 3-D FSS. Fig. 9. Measurement setup.

Fig. 6. Comparison of the simulated reflection and transmission coeffi-cients using HFSS and ECM (dx ¼ dy ¼ 9:4mm, l ¼ 7:4mm, w ¼ 0:5

mm, s ¼ 0:5mm, h ¼ 4:6mm, t ¼ 0:5mm, "r ¼ 4:4; L0 ¼ 6:86 nH,C0 ¼ 0:072 pF, L2 ¼ 5:04 nH, Cm ¼ 0:001 pF, and Lm ¼ 0:05 nH).

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4. Conclusion

In this paper, a dual-polarized 3-D FSS with quasi-ellipticbandpass response based on rectangular waveguide cavitiesis presented. The unit cell is realized by employing anempty rectangular waveguide cavity and a cuboid circuitboard. The electrical and magnetic coupling paths areconstructed through the rectangular waveguide cavities,which provide two transmission poles in the passband.The counteraction of signal paths generates two transmis-sion zeros to improve the out-of-band rejection. An equiv-alent circuit model is proposed to explain the operatingprinciple. Finally, comparing with the previous publica-tions, the measurement results of an implemented exampleverify the properties of the proposed design.

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (No. 61571232), the NationalKey Research and Development Program of China(No. 2017YFB0503500) and the 333 Project of JiangsuProvince (No. BRA2018315).

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Table I. Characteristics comparison of different FSS designs

Ref/DesignUnit Cell Size and

ThicknessIL(dB)

Num.(TPs/TZs)

PolarizationStability(TE/TM)

[9]/3D0:11�0 � 0:11�0�

0:011�01.1 1/1 dual 40°/40°

[11]/2D0:076�0 � 0:076�0

�0:038�0 1.05 2/2 dual 30°/30°

[12]/2D0:2�0 � 0:2�0�

0:3�0- 2/0 dual 45°/45°

[13]/2D0:15�0 � 0:15�0�

0:083�01.5 3/0 dual 60°/60°

[14]/3D0:42�0 � 0:42�0�

0:14�00.5 2/0 dual 40°/40°

[17]/3D0:16�0 � 0:15�0�

0:287�01.2 2/3 single 40°

[18]/3D0:315�0 � 0:21�0�

0:167�0- - 2/2 single 20°

[21]/3D0:16�0 � 0:32�0�

0:268�01.1 2/2 single 50°

[23]/3D0:23�0 � 0:23�0�

0:293�02.1 2/2 dual 40°/40°

Thiswork/3D

0:19�0 � 0:19�0�0:093�0

0.8 2/2 dual 60°/60°

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