a feasible bandwidth compensation technique for fss radome

A feasible bandwidthcompensation technique forFSS radome design

Ning Liu1, Xianjun Sheng2a), Chunbo Zhang3, Jingjing Fan2,and Dongming Guo11 School of Mechanical Engineering, Dalian University of Technology,

Dalian 116024, China2 School of Electrical Engineering, Dalian University of Technology,

Dalian 116024, China3 Research Institute of Aerospace Special Materials and Processing Technology,

Beijing, 100071, China

a) [email protected]

Abstract: In this paper, a feasible compensation technique has been

proposed to improve the bandwidth angular stability of FSS radome. Stacked

structure composed of different mechanical suitable materials has been

adopted to construct the bandwidth compensation layer in the proposed

technique. Hence, the problem that mechanical suitable materials with lower

permittivity are not available in the classic bandwidth compensation tech-

nique has been solved. The validity of the proposed technique is verified by

designing an FSS radome composed of modified second-order miniaturised

FSS (MFSS) and bandwidth compensation layers. Simulation results show

that the proposed technique has equal performance in stabilizing the band-

width of FSS radome under oblique incidence with the classic one.

Keywords: frequency selective surface, radome, bandwidth compensation

technique

Classification: Microwave and millimeter-wave devices, circuits, and

modules

References

[1] B. A. Munk: Frequency Selective Surfaces: Theory and Design (Wiley, NewYork, 2000) 14.

[2] T. K. Wu: Frequency-Selective Surface and Grid Array (New York, 1995).[3] E. Martini, et al.: “Fast analysis of FSS radome for antenna RCS reduction,”

IEEE Int. Symp. on Antennas and Propagation Society (2006) 1801 (DOI: 10.1109/APS.2006.1710917).

[4] H. Chen, et al.: “Design of frequency selective surfaces radome for a planarslotted waveguide antenna,” IEEE Antennas Wireless Propag. Lett. 8 (2009)1231 (DOI: 10.1109/LAWP.2009.2035646).

[5] S. N. Azemi, et al.: “Angularly stable frequency selective surface withminiaturized unit cell,” IEEE Microw. Wireless Compon. Lett. 25 (2015) 454(DOI: 10.1109/LMWC.2015.2429126).

[6] N. Liu, et al.: “A compact miniaturized frequency selective surface with stable

© IEICE 2017DOI: 10.1587/elex.14.20170510Received May 15, 2017Accepted June 5, 2017Publicized June 16, 2017Copyedited July 10, 2017

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LETTER IEICE Electronics Express, Vol.14, No.13, 1–8

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http://dx.doi.org/10.1109/LAWP.2009.2035646




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resonant frequency,” PIERL 62 (2016) 17 (DOI: 10.2528/PIERL16070608).[7] G. Yang, et al.: “A novel stable miniaturized frequency selective surface,”

IEEE Antennas Wireless Propag. Lett. 9 (2010) 1018 (DOI: 10.1109/LAWP.2010.2089776).

[8] H. Liu, et al.: “Miniaturised bandpass frequency selective surface with lumpedcomponents,” Electron. Lett. 44 (2008) 1054 (DOI: 10.1049/el:20081763).

[9] K. Sarabandi and N. Behdad: “A frequency selective surface with miniaturizedelements,” IEEE Trans. Antennas Propag. 55 (2007) 1239 (DOI: 10.1109/TAP.2007.895567).

[10] H. Y. Yang, et al.: “A novel miniaturized frequency selective surface withexcellent center frequency stability,” Microw. Opt. Technol. Lett. 51 (2009)2513 (DOI: 10.1002/mop.24604).

[11] W. T. Wang, et al.: “Compact angularly stable frequency selective surface usinghexagonal fractal configurations,” Microw. Opt. Technol. Lett. 51 (2009) 2541(DOI: 10.1002/mop.24676).

[12] X. Liu, et al.: “On the improvement of angular stability of the 2nd-orderminiaturized FSS structure,” IEEE Antennas Wireless Propag. Lett. 15 (2016)826 (DOI: 10.1109/LAWP.2015.2476384).

1 Introduction

Frequency selective surfaces (FSSs) are periodic structures, which are widely

applied to construct radomes, antenna reflectors, electromagnetic shelters and so

on [1, 2]. Within these typical applications, FSS radome has been intensively

studied for its crucial importance in reducing the antenna Radar Cross Section

(RCS) of aircrafts [3, 4]. For this purpose, an FSS radome should provide stable

frequency filter property under different incident angles and polarisations. Actually,

stable frequency filter of FSS radome can be obtained by improving the stability of

resonant frequency and bandwidth, simultaneously. The resonant frequency stabil-

ity can be obtained by miniaturised FSSs [5, 6, 7, 8, 9, 10, 11] and the bandwidth

stability can be improved by bounding outer compensation layers with a lower

permittivity [1]. However, when fabricating the bandwidth compensation layers,

mechanical suitable materials with such a lower permittivity may be not available

in engineering. Hence, the classic bandwidth compensation technique in [1] cannot

be applied to design practical FSS radomes.

In this paper, we proposed a feasible bandwidth compensation technique, which

solved the problem that mechanical suitable materials with lower permittivity are

not available.

2 FSS radome with bandwidth compensation layer

As shown in Fig. 1, an FSS radome composed of modified second order MFSS and

bandwidth compensation layers has been adopted in our work to investigate the

bandwidth compensation technique. As proposed in [12], the modified second order

MFSS is constructed by two sets of basic resonating units and a center supporting

dielectric layer for coupling.

Transmission coefficients of the modified second order MFSS without band-

width compensation layers are analyzed and shown in Fig. 2. It can be found that


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IEICE Electronics Express, Vol.14, No.13, 1–8

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http://dx.doi.org/10.1002/mop.24604










frequency filter property of the modified second order MFSS is sensitive to incident

angles. With the increase of incident angle, bandwidth decreases and the bandpass

ripple level increases for TE polarization. For TM polarization, the increase of

incident angle will result in the broadening of bandwidth. Changes in bandwidth

with different polarizations under oblique incidence are not acceptable for an FSS

radome design.

3 The proposed compensation technique

Based on the theory of Munk, bandwidth of FSS structure can be compensated by

outer compensation layer with a lower permittivity. And the permittivity and

thickness of the outer compensation layer can be determined by

"out ¼ 1 þ cos �max ð1Þ

hout ¼ 0:25�0ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi"out � cos �max

p ð2Þ

where �max is the largest incident angle to be compensated. However, mechanical

suitable materials with the permittivity determined by (1) may be not available in

Fig. 1. Geometric configuration of the FSS radome designed by classicbandwidth compensation technique.

(a) (b)

Fig. 2. Transmission coefficients of the modified second order MFSS(a) TE polarization (b) TM polarization. Optimized parametersare: " ¼ 3:4, T ¼ 5:8mm, h ¼ 0:4mm, H ¼ 2:4mm, s ¼0:4mm, w ¼ 0:55mm.


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engineering. Hence, the classic bandwidth compensation technique is not suitable

for practical FSS radome design.

To solve this problem, stacked structure composed of different engineering

materials is adopted in the proposed technique to construct the compensation

layers, as shown in Fig. 3. Based on the concept of effective permittivity, a lower

permittivity can be obtained by combining materials with different permittivity.

And the mechanical suitable materials, which are used to construct bandwidth

compensation layers, can be selected by the following constraint

"2 < "out < "1 ð3Þwhere "out is the effective permittivity of the compensation layer obtained by (1).

After determining the constituting materials of compensation layers, the stacked

structure’s geometric parameters can be calculated by

"1 � h1 þ "2 � h2h1 þ h2

¼ "out ð4Þ

h1 þ h2 ¼ k � �0ffiffiffiffiffiffiffi"out

p ð5Þ

where k is the coefficient to be determined, �0 is the wave length at resonant

frequency in free space.

To determine the value of k, we first define two evaluation indexes (T0 and F )

to depict the frequency filter property. T0 is the transmission coefficient at the

resonant frequency under normal incidence. And F is the stability factor, which

describes the stability of the filter property under oblique incidence. The stability

factor F is determined by

F ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

N

XNi¼1

ðTnormalðfiÞ � TobliqueðfiÞÞ2vuut ð6Þ

where N is the total number of calculated frequency in the pass band. TnormalðfiÞand TobliqueðfiÞ are the transmission coefficient at fi under normal and oblique

incidence, respectively. Obviously, the smaller stability factor F is, the better

bandwidth stability is.

Subsequently, simulation experiments have been carried out to evaluate the

influence of k on frequency filter property of the FSS radome shown in Fig. 3. In

the simulation experiments, parameters are set as follows: the coefficient k is

Fig. 3. Geometric configuration of the FSS radome designed by theproposed bandwidth compensation technique.


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ranging from 0.1 to 0.4 with a step of 0.01, permittivity of the materials construct-

ing the staked structure is set to be "1 ¼ 2:3 and "2 ¼ 1:2, respectively. As a result,

there will be 30 possible FSS radome structures with different compensation layers.

Commercial software HFSS has been applied to analyze the frequency filter

property of each possible FSS radome structure. Then, the evaluation indexes for

each FSS radome can be obtained to investigate the relationship between coefficient

k and evaluation indexes.

As shown in Fig. 4, the coefficient k has great effect on the two evaluation

indexes. For index T0, it keeps above −0.1 dB when k is below 0.25. However,

if k increases above 0.25, T0 will decrease with the increase of k. As for index F,

with the increase of k, F will decrease first and then increase. The minimum value

of F is obtained when k equals to 0.25 for both TE and TM polarizations, which

means the best bandwidth stability characteristic can be achieved when k equals to

0.25. Hence, the value of k should be chosen around 0.25.

4 Verification of the proposed compensation technique

To verify the validity of the proposed bandwidth compensation technique, band-

width compensation layers of FSS radome are designed by the classic bandwidth

compensation technique and the proposed one, respectively. Resonant frequency of

the designed FSS radome is set to be 10GHz and the largest incident angle to be

compensated is 60°.

Firstly, the bandwidth compensation layers are designed by the classic band-

width compensation technique. The dielectric permittivity and the thickness of

the compensation layers can be determined using (1) and (2), as follows: "out ¼ 1:5

and hout ¼ 8:7mm. Structure parameters of the modified second order MFSS are

as follows: " ¼ 3:4, T ¼ 5:9mm, h ¼ 0:2mm, H ¼ 2:5mm, s ¼ 0:9mm, w ¼1:2mm.

Secondly, the proposed bandwidth compensation technique has been adopted

to design the compensation layers. Considering the mechanical requirements of

practical FSS radome, skin material with a dielectric permittivity of "1 ¼ 3:4 and

foam material with a dielectric permittivity of "2 ¼ 1:1 have been adopted to

construct the bandwidth compensation layers. By using (4) and (5), thicknesses

(a) (b)

Fig. 4. Effect of coefficient k on frequency filter property (a) ontransmission coefficient at resonant frequency T0 (b) on stabilityfactor F


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of the skin material layer and foam material layer can be calculated as follows:

h1 ¼ 1mm and h2 ¼ 5:1mm. As for the modified second order MFSS, optimized

structure parameters are as follows: " ¼ 3:4, T ¼ 5:9mm, h ¼ 0:2mm, H ¼2:5mm, s ¼ 0:8mm, w ¼ 1:3mm.

Finally, commercial software HFSS has been adopted to analyze the trans-

mission coefficients of the two FSS radome structures under different incident

angles and polarizations. Transmission coefficients of the FSS radome designed by

the proposed technique together with those of the FSS radome designed by the

classic one are shown in Fig. 5. It is observed that the frequency filter property can

be maintained well with the aid of bandwidth compensation layer designed by the

proposed technique. Especially for the pass band, its flat-top filtering property

keeps well under oblique incidence with incident angle of 60°. Also, compared with

the classic compensation technique by Munk, the proposed technique has equal

performance in stabilizing the bandwidth under oblique incidence, which demon-

strates the validity of the proposed bandwidth compensation technique.

5 Effect of parameter variation on design robustness

As discussed above, bandwidth angular stability of FSS structure can be improved

with the proposed compensation method and structural parameters of the proposed

bandwidth compensation layers can be determined by using (4) and (5). However,

limited by the manufacturing process, FSS radome with exact structural parameters

calculated by (4) and (5) may be not manufacturable. To investigate the robustness

of the proposed compensation technique in stabilizing bandwidth at oblique

incidence, influences of the structural parameter variations on frequency response

have been discussed in this section.

The impact of compensation layer’s structural parameter variations on perform-

ance of the FSS radome discussed above is demonstrated by conducting a number

of full-wave simulations. In these simulations, dielectric permittivity of skin

material "1 is considered to change in the range of 3:4 � 0:6, thickness of skin

material h1 is allowed to vary in the range of 1 � 0:6mm, permittivity of foam

material "2 is changing in the range of 1:1 � 0:6 and thickness of foam material h2

(a) (b)

Fig. 5. Comparisons between the transmission coefficients of the twoFSS radome designed by different bandwidth compensationtechniques (a) TE polarization (b) TM polarization


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varies in the range of 5:1 � 0:6mm. These ranges can be satisfied with the current

manufacturing process and all the structural parameters change with a step of 0.2.

Fig. 6(a) and Fig. 6(b) show the impact of changes in skin material on the

frequency response of the FSS radome. It can be observe that frequency response is

insensitive to the variations in skin material parameters. As indicated in Fig. 6(b),

center resonant frequency of the FSS radome shifts with the change in skin material

thickness h1 slightly and the resonant frequency deviation is below 0.2%. Impact of

variations in foam material parameters on the FSS radome’s performance is shown

in Fig. 6(c) and Fig. 6(d). Observe that as the foam material permittivity "2

decreases, the resonant frequency increases and flat characteristic in the passband

deteriorates. The resonant frequency varies within 0.6% of the expected center

frequency. Also, the frequency response is insensitive to the variations in foam

material thickness h2.

Furthermore, sensitivity of the bandwidth angular stability of the FSS radome

to the structural parameter variations has been investigated. It can be found in

Fig. 7 that bandwidth angular stability is sensitive to the variations in foam material

permittivity "2. Especially, as "2 decreases, stability factor F increases greatly for

TM polarization and the maximum stability factor shift is 703.7%, which means the

bandwidth angular stability deteriorates. As for the parameters of skin material,

thickness h1 has greater impact on the bandwidth angular stability than the

permittivity "1. As skin material thickness h1 increases, stability factor F increases,

which means the bandwidth angular stability becomes worse. As observed in

Fig. 7(a) and Fig. 7(b), with the variations in skin material parameters, maximum

stability factor shift keeps below 67% and 166% with respect to permittivity "1 and

thickness h1, respectively. As for the foam material thickness h2, stability factor F

(a)

(c)

(b)

(d)

Fig. 6. Sensitivity of the frequency response of the FSS radome to thevariations in structural parameters of compensation layers(a) Permittivity of skin material (b) Thickness of skin material(c) Permittivity of foam material (d) Thickness of foam material


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keeps below 0.06, which means bandwidth angular stability maintains well with the

variations in foam material thickness h2.

Based on the parameter sensitivity analysis above, it can be found that

performance of the FSS radome shown in Fig. 3 is sensitive to foam material

permittivity "2 and skin material thickness h1. Compared with the two parameters "2and h1, variations in skin material permittivity "1 have less impact on the perform-

ance. As for the variations in foam thickness h2, performance of FSS radome

maintains well. Considering the current manufacturing process, the main sources of

uncertainty in fabricating the proposed FSS radome are the uncertainties in foam

material permittivity and skin material thickness. As a result, these issues should be

taken into consideration at the design stage.

6 Conclusions

A feasible bandwidth compensation technique for FSS radome design has been

investigated. By introducing the stacked structure to construct the bandwidth

compensation layers, the proposed technique has solved the problem that mechani-

cal suitable materials with a lower permittivity are not available. Simulation results

show that the proposed technique has great performance in stabilizing the band-

width under oblique incidence, which can be applied to design FSS radome with

high bandwidth stability.

Acknowledgments

This work was supported by the National Natural Science Foundation of China

under grant 51575081.

(a)

(c)

(b)

(d)

Fig. 7. Sensitivity of the bandwidth angular stability of the FSSradome to the variations in structural parameters of compensa-tion layers (a) Permittivity of skin material (b) Thickness ofskin material (c) Permittivity of foam material (d) Thickness offoam material


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a feasible bandwidth compensation technique for fss radome

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