As one of the effective means to restrain EM interference and realize EM protection, EM shielding means to limit the transmission of EM energy from one side of the material to the other side [37,38]. The mechanisms of EM shielding can be analyzed by transmission line method. Materials with high conductivity are usually used to restrain EM radiation, with the reflection effect of conductor on EM waves. Shielding effectiveness (SE) is usually used to represent the shielding ability and effect of materials on EM [39,40].
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Although traditional metals and alloy materials have a good EM shielding effect, their development is limited by the disadvantages of heavy weight, high cost and poor corrosion resistance. Novel EM shielding materials with lightweight characteristics are becoming more and more popular. EM shielding fabrics have the advantages of low density, good flexibility and light weight, which are widely used in the manufacture of EM protection products such as protective clothing, shielding tents and shielding gun-suit [41]. EM shielding fabrics also have strong one-time molding ability, excellent designability, breathable fabrics properties, both soft and EM shielding properties, which can be made into different geometry to shield radiation source, but also can be processed into shielding suit and shielding cap to make the staff from EM radiation [42]. In addition, metal fibers fabrics also have other functions, such as antistatic, antibacterial and deodorant. EM shielding fabrics are the ideal shielding materials with outstanding properties. The research of EM shielding fabrics can be divided into theoretical calculation and experimental measurement.
2.1. Theoretical Calculation of EM Shielding Fabrics
The expression to measure shielding effect of materials are transmission coefficient T and Shielding Effectiveness (SE). The transmission coefficient T is the ratio of electric field intensity Et (or magnetic field intensity Ht) at a place with a shield to electric field intensity E0 (or magnetic field intensity H0) at the same place without a shield and the formula is as follows,
T=EtE0=HtH0
(1)
SE refers to the shielding capability and effect of a shielding body against EM interference, which is often expressed logarithmically, as defined below [37],
SE=20lg(E0Et)=20lg(H0Ht)=10lg(P0Pt)=20lg1|T|
(2)
where lg=log10; P0 is the power density without shielding; Pt is the power density with shielding body at the same place. For the convenience of calculation, the most used formula is SE=20lg(E0Et).
According to , SE can be composed of reflection loss SER, absorption loss SEA and multiple reflection loss SEM.
SE=SER+SEA+SEM
(3)
The current theoretical calculation methods of EM shielding fabrics are to directly equivalent the conductive yarns with shielding performance to metal plates, and then the equivalent calculation is carried out according to the fabric structures corresponding to metal plate structures, such as no pore, pore structure, metal grid, layered parallel array and other structures, so as to calculate SE of fabrics. Based on transmission line theory, there are three different mechanisms for EM waves attenuation by the shielding body: reflection attenuation, absorption attenuation and multiple reflection attenuation. Firstly, metal plates are classified into no pore, pore structure, metal grid, layered parallel array (as shown in ), then the theoretical formulas or semi-empirical formulas of EM shielding are derived based on transmission line theory and equivalent circuit methods [43,44,45,46].
According to the literature [47,48], under the condition of far-field plane waves, transmission coefficient of no pore metal plates is as follows,
(T=4ηeηme−γd(ηe+ηm)2/[1−(ηm−ηeηm+ηe)2⋅e−2γd]ηm=3.69×10−7fμrσrηe=377Ωγ=(1+j)πμfσ
(4)
where ηe is the impedance of EM wave; ηm is the impedance of the metal plate; γ is the propagation constant of EM wave in metal; d is metal plate thickness; μr and σr are relative permeability and relative conductivity of metal plate; μ and σ are permeability and conductivity of metal plate. Combined with Equation (2), the SE of metal plate without poles can be obtained.
As for pore structure metal plates, the transmission coefficient of pores Th can be obtained according to the literature [49],
Th=4n(qF)3/2. (Circular pore)
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Th=4n(kq’F)3/2. (Rectangular pore)
(6)
where q is the area of a single circular pore; q’ is the area of a single rectangular pore; n is the number of holes; F is the metal plate area; k=baξ23, a and b are short and long sides of rectangle pore, respectively; when the rectangle is square, ξ=1; when ba≫5, ξ=b2aln0.63ba. The transmission coefficient of pore structure metal plate is Th=T+Th. Combined with Equation (2), SE of metal plate with pole structure can be obtained.
Henn et al. [50] first proposed that metallized fabrics were regarded as pores structure metal plates, and deduced the SE formulas of metallized fabrics by calculating the value of pores structure metal plates SE. Safarova et al. [51] used the above method to calculate metal fibers blended fabrics, analyzed the fabrics pore shape with image processing technology, approximated the irregular shape into a rectangle, and established the SE model about fabrics porosity, thickness and fibers volume.
The method of equivalent metal yarns to pores structure metal plates provides an idea for solving the SE of EM shielding fabrics. However, these models have certain limitations, requiring that the whole fabric has good electrical connectivity, resistance must equal to that of metal plates, fabrics must have a certain thickness, and the pores in fabrics need to be regular. In addition, simply approximating the shape of a single pore to a rectangle or a circle will cause a large error. When metal fibers content is too low, these models are not applicable, which is not conducive to the development of EM shielding fabrics.
SE formulas of metal mesh can be obtained from Literature [52].
SE=Aa+Ra+Ba+K1+K2+K3
(7)
where Aa is absorption loss of pores; Ra is reflection loss of pores; Ba is multiple reflection loss; K1 is the modification item related to the unit area and the number of pores K2 is the modification item related to skin depth; K3 is the modification item for coupling of adjacent pores. The calculation formula of each item was shown in , and the data was derived from [52].
Table 1
SymbolsThe Calculation FormulaInstructions
Aa
27.3dw,(rectangular);32dD,(circular)
d is the depth of pores, cm; D is the diameter of a circular hole.
Ra
20lg|1+4K24K|
Rectangular pores: K=j6.69×10−5fw
Circular pores: K=j5.7×10−5fw
Ba
20lg|1−(K−1K+1)210−0.1Aa|
f, MHz
K1
−10lg(a⋅n),r≫w
r is the distance between shield and field source;
a is the area of a single pore, cm2;
n is the number of pores per square centimeter
K2
−20lg(1+35p−2.3)
P=Width of conductor between holesSkin depth
K3
20lg[coth(Aa8.686)]
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It is difficult to accurately calculate the SE of metal grids. For the convenience of calculation, under approximate conditions, the SE of metal materials with good electrical conductivity mainly comes from reflection loss, and the absorption loss can be ignored. Engineering calculation of SE can be obtained that [53],
SE=20lg1s[0.265×10−2Rf]2+[0.265×10−2Xf+0.333×10−8f(lnsa−1.5)]2
(8)
where s is the pitch of the metal grid; Rf is AC resistance per unit length of metal grid; a is metal fibers radius; Xf is the reactance per unit length of the metal grid.
Chen et al. [54] made polypropylene fibers woven with copper wire and stainless-steel wire conduct fabrics, respectively, proposed the metal grid structure, and calculated conduct fabrics SE by using the formulas of metal grid structure from the literature. In the frequencies range of 30 MHz–1.5 GHz, the measured values were quite different from theoretical values, which may be caused by poor contact or low conductivity of fabrics at yarn intersections. Cai et al. [55] used a metal grid structure model to calculate the SE of stainless-steel fibers blended fabrics. When the content of stainless-steel fibers was 5%, 10% and 15%, respectively, the calculated results were close to experimental results under low frequencies conditions. Rybicki et al. [56] established an equivalent circuit model of conductive grid yarns based on a periodic metal grid structure, believing that SE depends on grid size, thickness and resistivity of grid material. Compared with simulation experiments, this method had certain feasibility.
Although the structure of metal mesh is close to real 2D fabrics in shape, the method requires that the intersecting points of fabrics grid should be conductive, the pores should be regular, and the content of conductive fibers should not be too low. Moreover, the yarns containing metal fibers are a mixture of metal fibers and other fibers, which will affect its EM parameters and cause large errors. This method is not suitable for the large degree of buckling or 3D fabrics, which will limit the development of EM shielding fabrics structure to a certain extent.
Other optimization methods to calculate SE include Sabrio’s metal parallel array method, as shown in [57]. The metal grid was divided into two periodic arrays of parallel metal plates with different angles, and SE of each periodic array metal plate can be calculated. Liang et al. [58] derived a SE model of 2D metal fibers blended woven fabrics base on this method. According to the comparison between theoretical values and measured values, yarn diameter, electrical conductivity and weaving Angle all have a certain influence on SE. Whether the fabric is conductive at the yarn crossing point has no effect on this model, which has high applicability.
Yin et al. [59] established the SE model of plain weave fabrics by the way of the weighted average based on fabrics buckling surface equation and fabrics structure. This model explained the mathematical relationship between SE and the parameters of plain weave fabrics such as pitch, thickness and fiber volume content. The trend of this model was basically consistent with the experiment, which provided a theoretical reference for the effective design of EM shielding fabrics with a large degree of buckling.
The metal yarn was equivalent to the structure of no pores, pores, metal grid and so on, requiring yarn crossing point conductive, and fabrics need to have a certain thickness, which will limit fabrics design and development to a certain extent and there will be considerable limitations. The method equivalent to parallel metal array structure was more accurate and had no effect on whether the yarn crossing point was conductive or not, but this model was not suitable for 2D fabrics with a large degree of buckling and 3D fabrics. At present, the research on SE are limited to 2D fabrics, and there are few reports on 3D fabrics. 3D fabrics have greater development potential and stronger functions than 2D fabrics. The study of the influence of fabrics structure on SE will be the theoretical guiding significance to the development of 3D EM shielding fabrics.
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