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A single layer ultra-miniaturized FSS operating in VHF
Accepted Manuscript Title: A Single Layer Ultra-miniaturized FSS Operating in VHF Author: Mingbao Yan Shaobo Qu Jiafu Wang Hua Ma Jieqiu Zhang Wenjie Wang Lin Zheng Hangying Yuan PII: DOI: Reference:
S1569-4410(15)00058-9 http://dx.doi.org/doi:10.1016/j.photonics.2015.08.002 PNFA 515
To appear in:
Photonics and Nanostructures – Fundamentals and Applications
Received date: Revised date: Accepted date:
29-10-2014 2-8-2015 13-8-2015
Please cite this article as: M. Yan, S. Qu, J. Wang, H. Ma, J. Zhang, W. Wang, L. Zheng, H. Yuan, A Single Layer Ultra-miniaturized FSS Operating in VHF, Photonics and Nanostructures - Fundamentals and Applications (2015), http://dx.doi.org/10.1016/j.photonics.2015.08.002 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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A Single Layer Ultra-miniaturized FSS Operating in VHF Mingbao Yan, Shaobo Qu*, Jiafu Wang*, Hua Ma, Jieqiu Zhang, Wenjie Wang, Lin Zheng, Hangying Yuan
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College of Science, Air Force Engineering University, Xi’an, 710051, China were presented. Other miniaturized element FSSs were developed by adding active components [18]-[20], or using lumped elements [21]-[24]. Although the element size is reduced, these designs require bulk components and increase the cost. In this paper, we present a new type of interwoven and convoluted element from simple spiral dipole arrays on a surface. The single-layer FSS has the merits of ultra-miniaturization and low-profile performance. The element size and thickness are less than λ0/60 and λ0/1200, respectively, where λ0 is the free space wavelength at the first resonant frequency. Its transmission responses, including angle-stability, polarization independence, and wide-band properties are discussed. The induced current on the metallic pattern are further analyzed based on plasmon resonance.
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Abstract— In this paper, we propose an ultra-miniaturized FSS element, which is composed of interwoven and convoluted dipoles printed on one side of a dielectric substrate. The design procedure is briefly presented. Simulations results show that the element size is reduced to 0.016λ0×0.016λ0, where λ0 is the wavelength in vacuum at the resonant frequency. The thickness of FSS is only 0.0008λ0. Due to the ultra-miniaturized size, the proposed FSS exhibits excellent angle-stability under both TE and TM polarizations. Furthermore, wide-band performance is also achieved, with a fractional bandwidth 73.5% under normal incidence. When the incidence angle reaches up to 75°, the central operating frequency is only shifted by 0.36%. Based on plasmon resonance, the induced currents on metallic pattern are analyzed to explain the miniaturization performance. Keywords—miniaturized FSS, convoluted element, angular stability, polarization insensitivity, wide-band performance.
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1. INTRODUCTION
For several decades, frequency selective surfaces (FSSs) have been studied intensively and used widely at microwave frequencies as spatial filers [1]-[5]. Especially, FSSs have been applied to wireless communication systems with the purpose of electromagnetic shielding [6]-[7]. Generally, FSSs operating in WLAN bands, mobile bands or below should have large physical size elements, since the effective element size must approach half a wavelength. The large element size will lead to difficulties in conforming to curved surfaces and also result in grating lobe in operating bands. If the element size is reduced sufficiently, it becomes possible to employ FSSs as shielding walls for indoor communications in buildings [8]-[10]. To reduce the element size, a class of convoluted FSS structures was extensively investigated [11]-[17]. In [11], several convoluted dipole array elements were introduced to produce low-frequency resonances in a small periodicity surface. In addition, the convoluted FSS elements improve the angle stability, keeping the operating bands far away from the grating region determined by the periodicity of the array. Symmetrical Hilbert space filling curves were used to design dual-polarized FSS in [12] and [13]. An unsymmetrical Hilbert curves with single polarized response was proposed in [14]. Recently, a type of interwoven convoluted FSS elements which extend beyond their individual unit cells into neighboring cells, were further developed in [14]-[16]. The word “interwoven” was first introduced in [17], and used to design high impedance surface (HIP). Except single-polarized FSS, dual-polarized FSS with miniaturized element was also investigated in [14]. In [15] and [16], small size elements with wide-band performances
l1
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l2 l3
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l4
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ln
G4
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Gn Fig.1 Description of successive iterations procedure
y
y
o
x
o
x
(a) (b) Fig.2 Spiral curve derived from the Gnth generation
2. INTERWOVEN CONVOLUTED ELEMENT DESIGN The rotated linear dipoles arrays are one of the simplest configurations for designing frequency selective surfaces [25]. The initial purpose of using rotated linear dipoles was to keep the operating bands away from the grating region determined by the periodicity of the array [11]. For a given periodicity, the length of the dipole is about λ/2, where λ is operating wavelength. To increase λ, the length of dipole should be lengthened. Based on the transmission-line theory, the first
*Corresponding author, E-mail address: [email protected] (Shaobo Qu) and [email protected] (Jiafu Wang).
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resonant frequency of the FSS is given by ω0=1/(LC)1/2, where L represents the inductance of metal strips and C denotes the capacitance between the two neighboring strips[1]. The simplest way of increasing L and C is to increase the length and to reduce their spacing distance. Based upon the above analysis, a self-similar generating technique is used to accomplish the convoluted element array design. The detailed process is described in Fig.1. It has a geometric configuration that begins with a line segment connecting with an acclivitous short line, and with the acclivitous angle θ. The lengths of the two parts are li and d, respectively. The distance between two horizontal lines is h. The parameter li is defined as li+1-li=a, (i=1, 2, ···, n), where a is a constant. The other parameters (d, h, θ) are chosen such that d=h/sinθ, where h and θ are unchanged in each generation and therefore d is a constant. It is obvious that the curve of the Gnth generation becomes longer and longer as the iteration arrays increases. It means that this curve needs large space to accommodate it. However, in actual application, this is not desirable due to the limitation of space. Hence, an improvement is implemented where the Gnth generation curve is convoluted at the midpoint (represented by red point) on each horizontal line along clockwise direction. The spiral pattern derived from the Gnth generation curve is illustrated in Fig.2 (a). To obtain a compact and symmetrical structure, an effective method was employed. Firstly, choose the midpoint on line of l1 as a vertex, and a quadrangle is drawn with a side length of (a+h·ctgθ), as shown in Fig.2 (a), where θ = 45°. Secondly, the center of the quadrangle is selected to construct a xoy coordinate. Lastly, the spiral pattern curve is successively generated by 90 degree along clockwise direction in x-y plane. Then, the Gnth generation pattern with compact and four-fold rotational symmetry structure can be obtained, as shown in Fig.2 (b). It is obvious that the proposed array is a rotated symmetrical structure, whose frequency responses are insensitive to both TE and TM polarizations. Furthermore, one important advantage of this design is that such elements can increase the length of dipole, so that the operating frequency can be reduced significantly. The other advantage is that the elements can be compactly arranged, which leads to an enhanced bandwidth: a closer spacing generally produces a wider bandwidth [1].
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(a) (b) Fig.3. (a) un-interwoven convoluted dipoles, (b) interwoven convoluted dipoles
Fig.4. Transmission response under normal incidence
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The term “interwoven” was first proposed in [17], and further adopted in reference [16] and [14]. Using this design technique, the improved interwoven structure derived from Fig.3 (a) can be obtained as shown in Fig.3 (b). In the simulation, the geometrical parameters are identical to these in Fig.3 (a). The transmission response under normal incidence is also given in Fig.4, marked with solid line. It is observed that the first resonant occurs at f1=3.9GHz, the corresponding wavelength is λ1=76.9mm and the electrical size of the element is p/λ1=0.078. Apparently, the interwoven element reduces the size by 52%, with respect to the un-interwoven element in Fig.3 (a). This convincingly demonstrates that the interwoven state can significantly reduce the electrical size of FSS elements. This is mainly because that the length of interwoven dipole becomes twice that of un-interwoven ones. Based upon the transmission-line theory, the equivalent inductance of the metallic strip in the interwoven structure is much larger than the metallic strip in the un-interwoven structure. To understand the interwoven effect on miniaturization and principle of the multi-band resonances, the current distributions at the two resonance frequencies for TE polarization are given in Fig. 5. Fig.5 (a) shows the current distributions of the un-interwoven element shown in Fig.3 (a). The left panel represents the current distribution at the first resonance frequency 8.1GHz. There is one current segment on each convoluted dipole strip. This indicates that the first resonance mode is resulted from the first-order plasmon resonance [27]. The right panel shows the induced current distribution at the second resonance frequency 17.3GHz. There are two current segments with opposite direction on each convoluted dipole strip. Therefore, the second resonance is resulted from the second-order plasmon resonance. Fig.5 (b) represents the current distribution of the interwoven element. To clarify the
3. SIMULATION AND RESULTS DISCUSSIONS To clarify the resonant principle, the G4 generation pattern is taken as an example for analysis. The element is presented in Fig.3 (a), where the gray and black regions represent dielectric substrate and metallic pattern, respectively. The simulation was implemented using CST Microwave Studio, in which periodic boundaries and frequency domain solver were adopted. The element periodicity p=6mm, the width of metallic strip w=0.2mm and the gap between two adjacent strips s=0.45mm. The dielectric substrate is F4B-2 with εr=2.65 and loss tangentδ=0.001. The substrate thickness is 1mm. The transmission response under normal incidence for TE polarization is plotted in Fig.4, and marked with the dashed-line. It is shown that the first resonance occurs at f1=8.1GHz. The corresponding wavelength in free space is λ1=37mm, correspondingly, the electrical size of the element is p/λ1=0.162. 2
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3 effect of interwoven mode on miniaturization, the current on two adjacent elements are given together. The left panel represents the current distribution at the first resonance 3.9GHz. It is interesting that the directions of the current flows on the lengthened convoluted dipole are uniform in two adjacent elements. Therefore, there is only one current segment on each lengthened convoluted dipole. Thus, the first resonance is also resulted from the first-order plasmon resonance. The right panel gives the current distribution at the second resonance frequency 12.9GHz. There are three current segments on the lengthened dipole strip. Hence, it can be summarized that the second resonance is resulted from the third-order plasmon resonance.
f=8.2GHz
(a)
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the resonance frequency shifts to lower frequencies. The lower the resonance frequency is, the smaller the element size (p/λ1) is. Therefore, in the design, the smallest element size can be obtained by reducing the widths or gaps of the metallic strip as much as possible. Nevertheless, considering the fabrication precision, the strip width and the gap are kept larger than 0.2mm, typical precision of printed circuit board (PCB) techniques.
f=17.3GHz
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f=12.9GHz (b) Fig.5. Induced current distributions on the metallic strip at the two resonance frequencies. (a) un-interwoven element and (b) interwoven elements.
(b) Fig.6. Transmission response under normal incidence, (a) different widths and (b) different gaps
f=3.9GHz
Fig.7. Transmission response under normal incidence with different p
In reference [16], an interwoven and convoluted element FSS was designed, and the electrical size p/λ1=1/27 with the periodicity p=10.8mm. Its fractional bandwidth is 63% under normal incidence. When the incidence angle reaches up to 45°, the fractional bandwidth increases to 85% for TE polarization while decreases to 46% for TM polarization. Furthermore, its electrical size of p/λ1 would get smaller by increasing the periodicity. To validate the periodicity effect on p/λ1, the transmission responses with different periodicities are simulated, shown in Fig.7, where only the first resonances are given. In the simulation, the width and the gap of metallic strips are 0.28mm. From Fig.7, it can be observed that three resonances occur at about 0.9GHz, 1.4GHz and 2.7GHz, and
As is known, based upon the transmission-line theory, for a given the length of a strip, the narrower the metallic strip is, the larger the equivalent inductance is. The coupling is enhanced by decreasing the gap between two strips. The transmission responses with different width of metallic strip and different gaps under normal incidence were simulated, as shown in Fig. 6. By increasing the metallic strip width (w) alone, the resonance frequency shifts to higher frequencies. This effect is shown in Fig. 6 (a). In addition, the coupling between the two strips may change with the variation of the gap (s). The corresponding results are shown in Fig. 6 (b). It can be observed that the smaller the value of s is, the lower the resonance frequency is. That is to say, by decreasing both the widths (w) and the gaps (s), 3
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the corresponding values of p/λ1 are 1/30, 1/24 and 1/17, respectively. Hence, smaller electrical size can be realized by increasing the periodicity of the unit cell. In reference [14], a dual-polarized convoluted loop element was proposed to realize a very small electrical size p/λ1=1/37, with the periodicity p=20 mm. In our design, the same periodicity p=20 mm is adopted. The value of the generation parameter (n) is 17. The width of the metallic strips is w=0.28 mm, the gap s=0.28 mm. The minimal widths and gaps are larger than 0.2mm, which enables precise fabrication using PCB technology. The metallic element is patterned on one side of F4B-2 substrate (the thickness t=1mm).The proposed FSS element is shown in Fig.8.
(a)
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Fig.9. Transmission responses under oblique incidence: (a) TE case and (b) TM case. Table I COMPARISON OF ELEMENT SIZE
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Fig.8. (a) two neighboring cells of interwoven convoluted dipole strip, (b) zoomed view of the details of the unit cell, (c) side view of the array.
The simulated results are shown in Fig.9, which illustrates the frequency response curves under different incidence angle α (defined as the angle between the k vector and z-axis, 0°≤α≤75°). As shown in Fig.9, the first resonance occurs at 248.9MHz when the FSS is illuminated by plane waves with TE and TM polarizations. The corresponding free-space wavelength λ0 is 1205.3 mm. The element size of the proposed unit cell is drastically reduced to 0.016λ0×0.016λ0. The substrate thickness is only 0.0008λ0. Obviously, the proposed FSS has promising ultra-miniaturized and low-profile properties. A size comparison between the proposed FSS element and other elements in previous papers is provided in Table I. The typical values, including thickness and dielectric constant of the substrate, are considered because these parameters affect the resonant frequency [26]. From Table I, we can find that our design is desirable for realizing miniaturization.
Thickness (mm)
Dielectric constant
Resonant frequency
Size
Ref.[14] This FSS
0.3 0.3
3.0 3.0
400MHz 186 MHz
0.027λ0 0.012λ0
Ref.[16] This FSS
-------
1.0 1.0
1000MHZ 363MHZ
0.036λ0 0.024λ0
Ref.[21] This FSS This FSS
1.6 1.6 0.1
4.4 4.4 4.4
2200MHz 214 MHz 140 MHz
0.080λ0 0.014λ0 0.009λ0
Ref.[21] This FSS
1.0 1.0
2.65 2.65
2400MHz 249 MHz
0.086λ0 0.016λ0
Based upon Munk’s theory, the resonance frequency can be decreased as smaller as f1 r 1 / 2 , and the corresponding resonance wavelength increases as larger as 1 Hence, the electric dimension is reduced to p 1
r 1 / 2 . r 1 / 2 .
The frequency responses are presented in Fig. 10, when the dielectric constant changes. Although, increasing the dielectric constant results in a smaller electric size (p/λ1) of the element, this way is not our intention to accomplish an ultra-miniaturized FSS. In our design, low dielectric constant F4B-2 was chosen as the substrate. In practical indoor applications, we can select FR4 with a relative dielectric constant εr=4.4 and loss tangentδ=0.025 as the supporting substrate. The thickness of the substrate is 0.1mm. The resonant frequency is 140MHz and the operating wavelength is 2143mm. Thus, the electrical size is reduced to 0.009λ0×0.009λ0 and the thickness is only
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5 is shown that the performances of our design are excellent, particularly in reducing the electrical size.
0.000047λ0. The most important advantage of this FSS is that it can be fixed conveniently on the wall, like a wall-paper.
4. CONCLUSIONS
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This paper proposes an ultra-miniaturized element FSS based on interwoven and convoluted dipoles. The element size is 0.016λ0×0.016λ0, and its size may be further reduced by changing parameters such as relative dielectric constant and thickness of the substrate, width of strips and gaps. Considering practical applications, the FSS using FR4 substrate (εr=4.4and thickness 0.1mm) was discussed, and its element size is reduced to 0.009λ0×0.009λ0. The improved FSS can be used as a wall-paper. The electric size of the structure is smaller compared with some other structures presented in relevant literatures. In addition, the FSS exhibits excellent stability for both TE and TM polarizations and incident angles. The deviation of the resonant frequency is less than 0.4% when the incident angle is as large as 75°. Furthermore, the proposed FSS has the advantage of wide-band performance, and the fractional bandwidth is 73.5% under normal incidence. Such FSSs can be used in EM shielding to stop wireless singal om VHF band.
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Fig.10. Transmission response with different dielectric constant of the substrate of the FSS
0°
30°
45°
60°
75°
Resonance frequency (MHz)
TE
248.9
248.90
248.90
248.93
249.80
TM
248.9
248.46
248.39
248.42
248.91
TE
0
0
0
0.01
0.36
TM
0
-0.18
-0.20
-0.19
0.04
TE
73.5
82.1
94.9
118.2
154.8
TM
73.5
65.0
54.6
40.3
20.8
Frequency shift (%) Fractional bandwidth (%)
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p/λ
Normal 0.25
Ref.[16]
1.0
Ref.[14]
0.4
1/6 2 1/2 7 1/3 7
0
-0.2
Fractional bandwidth (%) Normal
TE4 5
TM4 5
73.5
94.9
54.6
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Proposed FSS
Frequency shift (%) TE4 TM4 5 5
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Table III COMPARISON OF PERFORMANCES Incidence
ACKNOWLEDGMENT
The authors are grateful to the supports from the National Natural Science Foundation of China under Grant Nos. 61331005, 61471388, 11204378, 11274389, 61302023, the Natural Science Foundation of Shaanxi Province under Grant Nos. 2015JM6277, 2013JM6005, and the Innovative Team Foundation of Shaanxi Province under Grant No.2014KCT-05.
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Table II TRANSMISSION PERFORMANCES
0.2
-0.2
63
85
46
1
1
126
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REFERENCES [1] B. Munk, Frequency selective surfaces: theory and design, New York: John Wiley & Sons, 2000. [2] B. Munk, R. Kouyoumjian, and L. Peters, Jr., Reflection properties of periodic surfaces of loaded dipoles, IEEE Trans Antennas Propagat vol.19,612-617, 1971. [3] N. Behdad, A second-order band-pass frequency selective surface using nonresonant subwavelength periodic substrates, Microwave Opt. Technol Lett . vol.50, 1639-1643, 2008. [4] A. K. Rashid and Z. Shen, A novel bang-reject frequency selective surface with pesude-elliptic response, IEEE Trans Antennas Propag . vol.58, 1220-1226, 2010. [5] Kamal Sarabandi, Nader Behdad, A frequency selective surface with miniaturized elements, IEEE Trans Antennas Propag , vol.55, 1239-1245, 2007. [6] M. Raspopoulos and S. Stavrou, “Frequency selective buildings through frequency selective surfaces, ” IEEE Trans. Antennas Propag., vol. 59, pp. 2998-3005, 2011. [7] M. B. Yan, S. B. Qu, J. F. Wang, J. Q. Zhang, H. Zhou, H. Y. Chen and L. Zheng, “A Miniaturized Dual-Band FSS with Stable Resonance Frequencies of 2.4GHz/5GHz for WLAN Applications.” IEEE Antennas Wireless Propag. Lett., vol.13, pp.895-898, 2014. [8] M. Philippakis, C. Martel, D. Kemp, R. Allan, M. Clift, S. Massey, S.Appleton, W. Damerell, C. Burton, and E. A. Parker, “Application of FSS Structures to selective control the propagation of signals into and out of buildings,” Ofcom ref AY4464A, 2003. [9] M. Hook, K. D.Ward, and C. Mias, “Project to demonstrate the ability of frequency selective surface structures to enhanced the spectral efficiency of radio systems when used within buildings,” Ofcom ref AY4462A, 2003. [10] E. A. Parker, J.-B. Robertson, B. Sanz-Izquierdo, and J. C. Batchelor, “Minimal size FSS for long wavelength operation,” IET Electron. Lett., vol. 44, no. 6, pp. 394–395, Mar. 2008.
In addition, the proposed FSS’s transmission properties including wide-band response, angle-stability, and polarization independence are summarized in Table II. The angle-stability of the transmission response is very good. The deviation is only 0.36% for TE polarization when the incident angle is as great as 75°. The maximal shift between TE and TM polarizations is only 0.32% under the same incident angle 75°. As to bandwidth, the proposed FSS is wide-band. Taking -10dB transmission as a benchmark, the fractional bandwidth achieves to 73.5% under normal incidence. Generally, the TE bandwidth increases as the incident angle increases while the TM bandwidth decreases, as is typical for element with band-stop response. As the incident angle varies from 0° to 75°, the minimal bandwidth is more than 20% for TM polarization. This bandwidth satisfies practical applications for requiring wide incidence angles. Furthermore, the performances of the proposed FSS, such as electrical size, frequency shift, and fractional bandwidth, are compared with these in other works. The comparisons are listed in Table III. It
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[11] E. A. Parker and A. N. A. El Sheikh, “Convoluted dipole array elements,”Inst. Elect. Eng. Electron. Lett., vol. 27, no. 4, pp. 322–323,1991. [12] E. A. Parker and A. N. A. El Sheikh, “Convoluted array elements and reduced size unit cells for frequency-selective surfaces,” Proc. Inst.Elect. Eng. Microw., Antennas Propag., vol. 138, pt. H, pp. 19–22, Feb.1991. [13] E. A. Parker, A. N. A. El Sheikh, and A. C. Lima, “Convoluted frequency-selective array elements derived from linear and crosseddipoles,” Proc. Inst. Elect. Eng. H, vol. 40, no. 5, pp. 378–380, 1993. [14] Benito Sanz-Izquierdo, Edward A. “Ted” Parker, Jean-Baptiste Robertson, and John C. Batchelor, “Singly and Dual Polarized Convoluted Frequency Selective Structures,” IEEE Trans. Antennas Propag., vol.58, pp. 690-696, 2010. [15] Barbagallo, S., Monorchio, A., and Manara, G.: ‘Small periodicity FSS screens with enhanced bandwidth performance’, Electron. Lett., 2006, 42, (7), pp. 382–384 [16] F. Huang, J. C. Batchelor, and E. A. Parker, “Interwoven convoluted element frequency selective surfaces with wide bandwidths,” IEE Electron.Lett., vol. 42, pp. 788–790, Jul. 14, 2006. [17] Tse, S., et al.: ‘Reduced sized cells for high impedance ground planes’,Electron. Lett., 39, (24), pp. 1699–1701, 2003. [18] F. Bayatpur and K. Sarabandi, “ Single-Layer high-order miniaturized-element frequency-selective surfaces, ” IEEE Trans. Microw.Theory Tech., vol. 56, no. 4, pp. 774-781, Apr. 2008. [19] C. Mias, “ Frequency selective surfaces loaded with surface-mount reactive components,” Electron. Lett.,vol. 39, no. 9, pp. 724-726, May. 2003. [20] B. Philips, E. A. Parker, and R. J. Langley, “ Active FSS in an experimental horn antenna switchable two beamwidths,” Electron.Lett., vol. 31, no. 1, pp. 1-2, Jan. 1995. [21] C.-N. Chiu, W.-Y. Wang, “A Dual-Frequency Miniaturized Element FSS With Closely Located Resonance,” IEEE Antennas Wireless Propag. Lett., vol. 12, pp.163-165, 2013. [22] H. L. Liu, K. L. Ford, and R. J. Langley, “Design methodology for a miniaturized frequency selective surface using lumped reactive components,” IEEE Trans. Antennas Propag., vol. 57, no. 9, pp. 2732-2738, Sep. 2009. [23] R.-R.Xu, Z.-Y. Zong, and W. Wu, “Low Frequency miniaturized dual band frequency with close band spacing,” Microw. Opt. Technol. Lett., vol. 51, no.5, pp. 1238-1240, May 2009. [24] X.-D. Hu, X.-L. Zhou, L.-S. Wu, L. Zhou, and W.-Y. Yin, “A miniaturized dual-bandfrequency selective surface (FSS) with closed loop and its complementary pattern,” IEEE Antennas Wireless Propag. Lett., vol. 8, pp.1374-1377, 2009. [25] T. W. Kornbau, “Analysis of periodic arrays of rotated linear dipoles, rotated crossed dipoles, and of biplanar diploe arrays in dielectric,” Ph. D. Dissertation, Ohio State Univ., Dept. of Electrical Eng., Columbus, 1984. [26] Callaghan, P., Parker, E.A., and Langley, R.J.: ‘Influence of supporting dielectric layers on the transmission properties of frequency selective surfaces’, IEE Proc., H, vol.138, pp. 448–454, 1991. [27] Mingde Feng, Jiafu Wang, Hua Ma, Weidong Mo, Hongjun Ye, and Shaobo Qu, “Broadband polarization rotator based on multi-order plasmon resonances and high impedance surfaces,”J. Appl. Phys. Vol.114, pp. 074508-074508-5, 2013.
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S1569-4410(15)00058-9 http://dx.doi.org/doi:10.1016/j.photonics.2015.08.002 PNFA 515
To appear in:
Photonics and Nanostructures – Fundamentals and Applications
Received date: Revised date: Accepted date:
29-10-2014 2-8-2015 13-8-2015
Please cite this article as: M. Yan, S. Qu, J. Wang, H. Ma, J. Zhang, W. Wang, L. Zheng, H. Yuan, A Single Layer Ultra-miniaturized FSS Operating in VHF, Photonics and Nanostructures - Fundamentals and Applications (2015), http://dx.doi.org/10.1016/j.photonics.2015.08.002 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
1
A Single Layer Ultra-miniaturized FSS Operating in VHF Mingbao Yan, Shaobo Qu*, Jiafu Wang*, Hua Ma, Jieqiu Zhang, Wenjie Wang, Lin Zheng, Hangying Yuan
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College of Science, Air Force Engineering University, Xi’an, 710051, China were presented. Other miniaturized element FSSs were developed by adding active components [18]-[20], or using lumped elements [21]-[24]. Although the element size is reduced, these designs require bulk components and increase the cost. In this paper, we present a new type of interwoven and convoluted element from simple spiral dipole arrays on a surface. The single-layer FSS has the merits of ultra-miniaturization and low-profile performance. The element size and thickness are less than λ0/60 and λ0/1200, respectively, where λ0 is the free space wavelength at the first resonant frequency. Its transmission responses, including angle-stability, polarization independence, and wide-band properties are discussed. The induced current on the metallic pattern are further analyzed based on plasmon resonance.
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Abstract— In this paper, we propose an ultra-miniaturized FSS element, which is composed of interwoven and convoluted dipoles printed on one side of a dielectric substrate. The design procedure is briefly presented. Simulations results show that the element size is reduced to 0.016λ0×0.016λ0, where λ0 is the wavelength in vacuum at the resonant frequency. The thickness of FSS is only 0.0008λ0. Due to the ultra-miniaturized size, the proposed FSS exhibits excellent angle-stability under both TE and TM polarizations. Furthermore, wide-band performance is also achieved, with a fractional bandwidth 73.5% under normal incidence. When the incidence angle reaches up to 75°, the central operating frequency is only shifted by 0.36%. Based on plasmon resonance, the induced currents on metallic pattern are analyzed to explain the miniaturization performance. Keywords—miniaturized FSS, convoluted element, angular stability, polarization insensitivity, wide-band performance.
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1. INTRODUCTION
For several decades, frequency selective surfaces (FSSs) have been studied intensively and used widely at microwave frequencies as spatial filers [1]-[5]. Especially, FSSs have been applied to wireless communication systems with the purpose of electromagnetic shielding [6]-[7]. Generally, FSSs operating in WLAN bands, mobile bands or below should have large physical size elements, since the effective element size must approach half a wavelength. The large element size will lead to difficulties in conforming to curved surfaces and also result in grating lobe in operating bands. If the element size is reduced sufficiently, it becomes possible to employ FSSs as shielding walls for indoor communications in buildings [8]-[10]. To reduce the element size, a class of convoluted FSS structures was extensively investigated [11]-[17]. In [11], several convoluted dipole array elements were introduced to produce low-frequency resonances in a small periodicity surface. In addition, the convoluted FSS elements improve the angle stability, keeping the operating bands far away from the grating region determined by the periodicity of the array. Symmetrical Hilbert space filling curves were used to design dual-polarized FSS in [12] and [13]. An unsymmetrical Hilbert curves with single polarized response was proposed in [14]. Recently, a type of interwoven convoluted FSS elements which extend beyond their individual unit cells into neighboring cells, were further developed in [14]-[16]. The word “interwoven” was first introduced in [17], and used to design high impedance surface (HIP). Except single-polarized FSS, dual-polarized FSS with miniaturized element was also investigated in [14]. In [15] and [16], small size elements with wide-band performances
l1
te
d
G2
l2 l3
h
l4
G3
ln
G4
Ac ce p
Gn Fig.1 Description of successive iterations procedure
y
y
o
x
o
x
(a) (b) Fig.2 Spiral curve derived from the Gnth generation
2. INTERWOVEN CONVOLUTED ELEMENT DESIGN The rotated linear dipoles arrays are one of the simplest configurations for designing frequency selective surfaces [25]. The initial purpose of using rotated linear dipoles was to keep the operating bands away from the grating region determined by the periodicity of the array [11]. For a given periodicity, the length of the dipole is about λ/2, where λ is operating wavelength. To increase λ, the length of dipole should be lengthened. Based on the transmission-line theory, the first
*Corresponding author, E-mail address: [email protected] (Shaobo Qu) and [email protected] (Jiafu Wang).
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p
resonant frequency of the FSS is given by ω0=1/(LC)1/2, where L represents the inductance of metal strips and C denotes the capacitance between the two neighboring strips[1]. The simplest way of increasing L and C is to increase the length and to reduce their spacing distance. Based upon the above analysis, a self-similar generating technique is used to accomplish the convoluted element array design. The detailed process is described in Fig.1. It has a geometric configuration that begins with a line segment connecting with an acclivitous short line, and with the acclivitous angle θ. The lengths of the two parts are li and d, respectively. The distance between two horizontal lines is h. The parameter li is defined as li+1-li=a, (i=1, 2, ···, n), where a is a constant. The other parameters (d, h, θ) are chosen such that d=h/sinθ, where h and θ are unchanged in each generation and therefore d is a constant. It is obvious that the curve of the Gnth generation becomes longer and longer as the iteration arrays increases. It means that this curve needs large space to accommodate it. However, in actual application, this is not desirable due to the limitation of space. Hence, an improvement is implemented where the Gnth generation curve is convoluted at the midpoint (represented by red point) on each horizontal line along clockwise direction. The spiral pattern derived from the Gnth generation curve is illustrated in Fig.2 (a). To obtain a compact and symmetrical structure, an effective method was employed. Firstly, choose the midpoint on line of l1 as a vertex, and a quadrangle is drawn with a side length of (a+h·ctgθ), as shown in Fig.2 (a), where θ = 45°. Secondly, the center of the quadrangle is selected to construct a xoy coordinate. Lastly, the spiral pattern curve is successively generated by 90 degree along clockwise direction in x-y plane. Then, the Gnth generation pattern with compact and four-fold rotational symmetry structure can be obtained, as shown in Fig.2 (b). It is obvious that the proposed array is a rotated symmetrical structure, whose frequency responses are insensitive to both TE and TM polarizations. Furthermore, one important advantage of this design is that such elements can increase the length of dipole, so that the operating frequency can be reduced significantly. The other advantage is that the elements can be compactly arranged, which leads to an enhanced bandwidth: a closer spacing generally produces a wider bandwidth [1].
p
s
ip t
w
an
us
cr
(a) (b) Fig.3. (a) un-interwoven convoluted dipoles, (b) interwoven convoluted dipoles
Fig.4. Transmission response under normal incidence
Ac ce p
te
d
M
The term “interwoven” was first proposed in [17], and further adopted in reference [16] and [14]. Using this design technique, the improved interwoven structure derived from Fig.3 (a) can be obtained as shown in Fig.3 (b). In the simulation, the geometrical parameters are identical to these in Fig.3 (a). The transmission response under normal incidence is also given in Fig.4, marked with solid line. It is observed that the first resonant occurs at f1=3.9GHz, the corresponding wavelength is λ1=76.9mm and the electrical size of the element is p/λ1=0.078. Apparently, the interwoven element reduces the size by 52%, with respect to the un-interwoven element in Fig.3 (a). This convincingly demonstrates that the interwoven state can significantly reduce the electrical size of FSS elements. This is mainly because that the length of interwoven dipole becomes twice that of un-interwoven ones. Based upon the transmission-line theory, the equivalent inductance of the metallic strip in the interwoven structure is much larger than the metallic strip in the un-interwoven structure. To understand the interwoven effect on miniaturization and principle of the multi-band resonances, the current distributions at the two resonance frequencies for TE polarization are given in Fig. 5. Fig.5 (a) shows the current distributions of the un-interwoven element shown in Fig.3 (a). The left panel represents the current distribution at the first resonance frequency 8.1GHz. There is one current segment on each convoluted dipole strip. This indicates that the first resonance mode is resulted from the first-order plasmon resonance [27]. The right panel shows the induced current distribution at the second resonance frequency 17.3GHz. There are two current segments with opposite direction on each convoluted dipole strip. Therefore, the second resonance is resulted from the second-order plasmon resonance. Fig.5 (b) represents the current distribution of the interwoven element. To clarify the
3. SIMULATION AND RESULTS DISCUSSIONS To clarify the resonant principle, the G4 generation pattern is taken as an example for analysis. The element is presented in Fig.3 (a), where the gray and black regions represent dielectric substrate and metallic pattern, respectively. The simulation was implemented using CST Microwave Studio, in which periodic boundaries and frequency domain solver were adopted. The element periodicity p=6mm, the width of metallic strip w=0.2mm and the gap between two adjacent strips s=0.45mm. The dielectric substrate is F4B-2 with εr=2.65 and loss tangentδ=0.001. The substrate thickness is 1mm. The transmission response under normal incidence for TE polarization is plotted in Fig.4, and marked with the dashed-line. It is shown that the first resonance occurs at f1=8.1GHz. The corresponding wavelength in free space is λ1=37mm, correspondingly, the electrical size of the element is p/λ1=0.162. 2
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3 effect of interwoven mode on miniaturization, the current on two adjacent elements are given together. The left panel represents the current distribution at the first resonance 3.9GHz. It is interesting that the directions of the current flows on the lengthened convoluted dipole are uniform in two adjacent elements. Therefore, there is only one current segment on each lengthened convoluted dipole. Thus, the first resonance is also resulted from the first-order plasmon resonance. The right panel gives the current distribution at the second resonance frequency 12.9GHz. There are three current segments on the lengthened dipole strip. Hence, it can be summarized that the second resonance is resulted from the third-order plasmon resonance.
f=8.2GHz
(a)
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ip t
the resonance frequency shifts to lower frequencies. The lower the resonance frequency is, the smaller the element size (p/λ1) is. Therefore, in the design, the smallest element size can be obtained by reducing the widths or gaps of the metallic strip as much as possible. Nevertheless, considering the fabrication precision, the strip width and the gap are kept larger than 0.2mm, typical precision of printed circuit board (PCB) techniques.
f=17.3GHz
Ac ce p
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(a)
f=12.9GHz (b) Fig.5. Induced current distributions on the metallic strip at the two resonance frequencies. (a) un-interwoven element and (b) interwoven elements.
(b) Fig.6. Transmission response under normal incidence, (a) different widths and (b) different gaps
f=3.9GHz
Fig.7. Transmission response under normal incidence with different p
In reference [16], an interwoven and convoluted element FSS was designed, and the electrical size p/λ1=1/27 with the periodicity p=10.8mm. Its fractional bandwidth is 63% under normal incidence. When the incidence angle reaches up to 45°, the fractional bandwidth increases to 85% for TE polarization while decreases to 46% for TM polarization. Furthermore, its electrical size of p/λ1 would get smaller by increasing the periodicity. To validate the periodicity effect on p/λ1, the transmission responses with different periodicities are simulated, shown in Fig.7, where only the first resonances are given. In the simulation, the width and the gap of metallic strips are 0.28mm. From Fig.7, it can be observed that three resonances occur at about 0.9GHz, 1.4GHz and 2.7GHz, and
As is known, based upon the transmission-line theory, for a given the length of a strip, the narrower the metallic strip is, the larger the equivalent inductance is. The coupling is enhanced by decreasing the gap between two strips. The transmission responses with different width of metallic strip and different gaps under normal incidence were simulated, as shown in Fig. 6. By increasing the metallic strip width (w) alone, the resonance frequency shifts to higher frequencies. This effect is shown in Fig. 6 (a). In addition, the coupling between the two strips may change with the variation of the gap (s). The corresponding results are shown in Fig. 6 (b). It can be observed that the smaller the value of s is, the lower the resonance frequency is. That is to say, by decreasing both the widths (w) and the gaps (s), 3
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the corresponding values of p/λ1 are 1/30, 1/24 and 1/17, respectively. Hence, smaller electrical size can be realized by increasing the periodicity of the unit cell. In reference [14], a dual-polarized convoluted loop element was proposed to realize a very small electrical size p/λ1=1/37, with the periodicity p=20 mm. In our design, the same periodicity p=20 mm is adopted. The value of the generation parameter (n) is 17. The width of the metallic strips is w=0.28 mm, the gap s=0.28 mm. The minimal widths and gaps are larger than 0.2mm, which enables precise fabrication using PCB technology. The metallic element is patterned on one side of F4B-2 substrate (the thickness t=1mm).The proposed FSS element is shown in Fig.8.
(a)
cr
p
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2p
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(b)
z
Element
x
(a)
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d
k
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TE
(b)
Fig.9. Transmission responses under oblique incidence: (a) TE case and (b) TM case. Table I COMPARISON OF ELEMENT SIZE
t
(c)
Ac ce p
Fig.8. (a) two neighboring cells of interwoven convoluted dipole strip, (b) zoomed view of the details of the unit cell, (c) side view of the array.
The simulated results are shown in Fig.9, which illustrates the frequency response curves under different incidence angle α (defined as the angle between the k vector and z-axis, 0°≤α≤75°). As shown in Fig.9, the first resonance occurs at 248.9MHz when the FSS is illuminated by plane waves with TE and TM polarizations. The corresponding free-space wavelength λ0 is 1205.3 mm. The element size of the proposed unit cell is drastically reduced to 0.016λ0×0.016λ0. The substrate thickness is only 0.0008λ0. Obviously, the proposed FSS has promising ultra-miniaturized and low-profile properties. A size comparison between the proposed FSS element and other elements in previous papers is provided in Table I. The typical values, including thickness and dielectric constant of the substrate, are considered because these parameters affect the resonant frequency [26]. From Table I, we can find that our design is desirable for realizing miniaturization.
Thickness (mm)
Dielectric constant
Resonant frequency
Size
Ref.[14] This FSS
0.3 0.3
3.0 3.0
400MHz 186 MHz
0.027λ0 0.012λ0
Ref.[16] This FSS
-------
1.0 1.0
1000MHZ 363MHZ
0.036λ0 0.024λ0
Ref.[21] This FSS This FSS
1.6 1.6 0.1
4.4 4.4 4.4
2200MHz 214 MHz 140 MHz
0.080λ0 0.014λ0 0.009λ0
Ref.[21] This FSS
1.0 1.0
2.65 2.65
2400MHz 249 MHz
0.086λ0 0.016λ0
Based upon Munk’s theory, the resonance frequency can be decreased as smaller as f1 r 1 / 2 , and the corresponding resonance wavelength increases as larger as 1 Hence, the electric dimension is reduced to p 1
r 1 / 2 . r 1 / 2 .
The frequency responses are presented in Fig. 10, when the dielectric constant changes. Although, increasing the dielectric constant results in a smaller electric size (p/λ1) of the element, this way is not our intention to accomplish an ultra-miniaturized FSS. In our design, low dielectric constant F4B-2 was chosen as the substrate. In practical indoor applications, we can select FR4 with a relative dielectric constant εr=4.4 and loss tangentδ=0.025 as the supporting substrate. The thickness of the substrate is 0.1mm. The resonant frequency is 140MHz and the operating wavelength is 2143mm. Thus, the electrical size is reduced to 0.009λ0×0.009λ0 and the thickness is only
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5 is shown that the performances of our design are excellent, particularly in reducing the electrical size.
0.000047λ0. The most important advantage of this FSS is that it can be fixed conveniently on the wall, like a wall-paper.
4. CONCLUSIONS
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This paper proposes an ultra-miniaturized element FSS based on interwoven and convoluted dipoles. The element size is 0.016λ0×0.016λ0, and its size may be further reduced by changing parameters such as relative dielectric constant and thickness of the substrate, width of strips and gaps. Considering practical applications, the FSS using FR4 substrate (εr=4.4and thickness 0.1mm) was discussed, and its element size is reduced to 0.009λ0×0.009λ0. The improved FSS can be used as a wall-paper. The electric size of the structure is smaller compared with some other structures presented in relevant literatures. In addition, the FSS exhibits excellent stability for both TE and TM polarizations and incident angles. The deviation of the resonant frequency is less than 0.4% when the incident angle is as large as 75°. Furthermore, the proposed FSS has the advantage of wide-band performance, and the fractional bandwidth is 73.5% under normal incidence. Such FSSs can be used in EM shielding to stop wireless singal om VHF band.
cr
Fig.10. Transmission response with different dielectric constant of the substrate of the FSS
0°
30°
45°
60°
75°
Resonance frequency (MHz)
TE
248.9
248.90
248.90
248.93
249.80
TM
248.9
248.46
248.39
248.42
248.91
TE
0
0
0
0.01
0.36
TM
0
-0.18
-0.20
-0.19
0.04
TE
73.5
82.1
94.9
118.2
154.8
TM
73.5
65.0
54.6
40.3
20.8
Frequency shift (%) Fractional bandwidth (%)
an
p/λ
Normal 0.25
Ref.[16]
1.0
Ref.[14]
0.4
1/6 2 1/2 7 1/3 7
0
-0.2
Fractional bandwidth (%) Normal
TE4 5
TM4 5
73.5
94.9
54.6
Ac ce p
Proposed FSS
Frequency shift (%) TE4 TM4 5 5
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fr(GHz)
d
Table III COMPARISON OF PERFORMANCES Incidence
ACKNOWLEDGMENT
The authors are grateful to the supports from the National Natural Science Foundation of China under Grant Nos. 61331005, 61471388, 11204378, 11274389, 61302023, the Natural Science Foundation of Shaanxi Province under Grant Nos. 2015JM6277, 2013JM6005, and the Innovative Team Foundation of Shaanxi Province under Grant No.2014KCT-05.
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Incidence
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Table II TRANSMISSION PERFORMANCES
0.2
-0.2
63
85
46
1
1
126
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REFERENCES [1] B. Munk, Frequency selective surfaces: theory and design, New York: John Wiley & Sons, 2000. [2] B. Munk, R. Kouyoumjian, and L. Peters, Jr., Reflection properties of periodic surfaces of loaded dipoles, IEEE Trans Antennas Propagat vol.19,612-617, 1971. [3] N. Behdad, A second-order band-pass frequency selective surface using nonresonant subwavelength periodic substrates, Microwave Opt. Technol Lett . vol.50, 1639-1643, 2008. [4] A. K. Rashid and Z. Shen, A novel bang-reject frequency selective surface with pesude-elliptic response, IEEE Trans Antennas Propag . vol.58, 1220-1226, 2010. [5] Kamal Sarabandi, Nader Behdad, A frequency selective surface with miniaturized elements, IEEE Trans Antennas Propag , vol.55, 1239-1245, 2007. [6] M. Raspopoulos and S. Stavrou, “Frequency selective buildings through frequency selective surfaces, ” IEEE Trans. Antennas Propag., vol. 59, pp. 2998-3005, 2011. [7] M. B. Yan, S. B. Qu, J. F. Wang, J. Q. Zhang, H. Zhou, H. Y. Chen and L. Zheng, “A Miniaturized Dual-Band FSS with Stable Resonance Frequencies of 2.4GHz/5GHz for WLAN Applications.” IEEE Antennas Wireless Propag. Lett., vol.13, pp.895-898, 2014. [8] M. Philippakis, C. Martel, D. Kemp, R. Allan, M. Clift, S. Massey, S.Appleton, W. Damerell, C. Burton, and E. A. Parker, “Application of FSS Structures to selective control the propagation of signals into and out of buildings,” Ofcom ref AY4464A, 2003. [9] M. Hook, K. D.Ward, and C. Mias, “Project to demonstrate the ability of frequency selective surface structures to enhanced the spectral efficiency of radio systems when used within buildings,” Ofcom ref AY4462A, 2003. [10] E. A. Parker, J.-B. Robertson, B. Sanz-Izquierdo, and J. C. Batchelor, “Minimal size FSS for long wavelength operation,” IET Electron. Lett., vol. 44, no. 6, pp. 394–395, Mar. 2008.
In addition, the proposed FSS’s transmission properties including wide-band response, angle-stability, and polarization independence are summarized in Table II. The angle-stability of the transmission response is very good. The deviation is only 0.36% for TE polarization when the incident angle is as great as 75°. The maximal shift between TE and TM polarizations is only 0.32% under the same incident angle 75°. As to bandwidth, the proposed FSS is wide-band. Taking -10dB transmission as a benchmark, the fractional bandwidth achieves to 73.5% under normal incidence. Generally, the TE bandwidth increases as the incident angle increases while the TM bandwidth decreases, as is typical for element with band-stop response. As the incident angle varies from 0° to 75°, the minimal bandwidth is more than 20% for TM polarization. This bandwidth satisfies practical applications for requiring wide incidence angles. Furthermore, the performances of the proposed FSS, such as electrical size, frequency shift, and fractional bandwidth, are compared with these in other works. The comparisons are listed in Table III. It
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[11] E. A. Parker and A. N. A. El Sheikh, “Convoluted dipole array elements,”Inst. Elect. Eng. Electron. Lett., vol. 27, no. 4, pp. 322–323,1991. [12] E. A. Parker and A. N. A. El Sheikh, “Convoluted array elements and reduced size unit cells for frequency-selective surfaces,” Proc. Inst.Elect. Eng. Microw., Antennas Propag., vol. 138, pt. H, pp. 19–22, Feb.1991. [13] E. A. Parker, A. N. A. El Sheikh, and A. C. Lima, “Convoluted frequency-selective array elements derived from linear and crosseddipoles,” Proc. Inst. Elect. Eng. H, vol. 40, no. 5, pp. 378–380, 1993. [14] Benito Sanz-Izquierdo, Edward A. “Ted” Parker, Jean-Baptiste Robertson, and John C. Batchelor, “Singly and Dual Polarized Convoluted Frequency Selective Structures,” IEEE Trans. Antennas Propag., vol.58, pp. 690-696, 2010. [15] Barbagallo, S., Monorchio, A., and Manara, G.: ‘Small periodicity FSS screens with enhanced bandwidth performance’, Electron. Lett., 2006, 42, (7), pp. 382–384 [16] F. Huang, J. C. Batchelor, and E. A. Parker, “Interwoven convoluted element frequency selective surfaces with wide bandwidths,” IEE Electron.Lett., vol. 42, pp. 788–790, Jul. 14, 2006. [17] Tse, S., et al.: ‘Reduced sized cells for high impedance ground planes’,Electron. Lett., 39, (24), pp. 1699–1701, 2003. [18] F. Bayatpur and K. Sarabandi, “ Single-Layer high-order miniaturized-element frequency-selective surfaces, ” IEEE Trans. Microw.Theory Tech., vol. 56, no. 4, pp. 774-781, Apr. 2008. [19] C. Mias, “ Frequency selective surfaces loaded with surface-mount reactive components,” Electron. Lett.,vol. 39, no. 9, pp. 724-726, May. 2003. [20] B. Philips, E. A. Parker, and R. J. Langley, “ Active FSS in an experimental horn antenna switchable two beamwidths,” Electron.Lett., vol. 31, no. 1, pp. 1-2, Jan. 1995. [21] C.-N. Chiu, W.-Y. Wang, “A Dual-Frequency Miniaturized Element FSS With Closely Located Resonance,” IEEE Antennas Wireless Propag. Lett., vol. 12, pp.163-165, 2013. [22] H. L. Liu, K. L. Ford, and R. J. Langley, “Design methodology for a miniaturized frequency selective surface using lumped reactive components,” IEEE Trans. Antennas Propag., vol. 57, no. 9, pp. 2732-2738, Sep. 2009. [23] R.-R.Xu, Z.-Y. Zong, and W. Wu, “Low Frequency miniaturized dual band frequency with close band spacing,” Microw. Opt. Technol. Lett., vol. 51, no.5, pp. 1238-1240, May 2009. [24] X.-D. Hu, X.-L. Zhou, L.-S. Wu, L. Zhou, and W.-Y. Yin, “A miniaturized dual-bandfrequency selective surface (FSS) with closed loop and its complementary pattern,” IEEE Antennas Wireless Propag. Lett., vol. 8, pp.1374-1377, 2009. [25] T. W. Kornbau, “Analysis of periodic arrays of rotated linear dipoles, rotated crossed dipoles, and of biplanar diploe arrays in dielectric,” Ph. D. Dissertation, Ohio State Univ., Dept. of Electrical Eng., Columbus, 1984. [26] Callaghan, P., Parker, E.A., and Langley, R.J.: ‘Influence of supporting dielectric layers on the transmission properties of frequency selective surfaces’, IEE Proc., H, vol.138, pp. 448–454, 1991. [27] Mingde Feng, Jiafu Wang, Hua Ma, Weidong Mo, Hongjun Ye, and Shaobo Qu, “Broadband polarization rotator based on multi-order plasmon resonances and high impedance surfaces,”J. Appl. Phys. Vol.114, pp. 074508-074508-5, 2013.
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