# Modelling the Woven Structures with Inserted Conductive Yarns Coated with Magnetron Plasma and Testing Their Shielding Effectiveness

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials—Weaving

#### 2.2. Materials—Magnetron Plasma Coating

^{−5}mbar. A constant argon flow (purity 6.0) of 50 sccm was continuously introduced into the chamber by means of a Bronkhorst mass flow controller, which allowed to establish the processing pressure around 5 × 10

^{−3}mbar. The chamber is provisioned with a rectangular magnetron sputtering gun from K.J. Lesker, accommodating the high purity copper target. The discharge was ignited by means of a radio frequency generator (13.56 MHz) provisioned with an automatic matching box for adapting the impedance, and the deposition time was set to ensure coating thicknesses in the range 1200–10,000 nm on each side of the textile fabrics. Enhanced deposition uniformity was achieved by rotating the samples during the deposition process (200 rotations/min).

#### 2.3. Textile Samples

#### 2.4. Morphology and Structure of the Textile Sample

#### 2.5. Electric Conductivity Measurements

_{m}) in the case of the washer geometrical shape of the textile shields, tailored according to the requirements imposed by the ASTM ES-07 standard for the determination of the EMSE.

_{w}—the measured resistance value by ohmmeter [Ω] (Figure 8).

#### 2.6. EM Shielding Effectiveness Measurements

## 3. Results

^{5}to 10

^{7}Hz a shielding up to 22 dB for the plain textile, with a small increase of around 4 dB of shielding upon coating with 1200 nm copper layer onto both faces of the material.

^{5}to 10

^{8}Hz, even for the uncoated material. At the same time, one can notice that the additional coating of the structure is conducting to enhanced shielding effectiveness, which is more important as the copper coating thickness increases and present values exceeding 60 dB for 10 µm layer coating, for frequencies up to 10

^{7}Hz. At frequencies above 10

^{8}Hz, one can notice that the copper layer thickness has a limited influence on the shielding efficiency, which remain in the range 30–40 dB.

## 4. The Model for Estimating EMSE

_{grid}, the relation for electric conductive grid structures according to [19] and for EMSE

_{layer}, the relation of impedance method according to [13] are used. Geometric and electric parameters for both relations were applied related to the structure of the grid of inserted conductive yarns and the layer of coating. The following notations for electric and geometric parameters for these types of fabrics apply:

- σ
_{y}—electrical conductivity of the metallic yarns [S/m] - μ
_{y}—magnetic permeability of the metallic yarns [H/m] - σ
_{m}—electrical conductivity of the fabric material [S/m]; - μ
_{m}—magnetic permeability of the material (for copper coating μ_{m}∼μ_{0}= 4π ∗ 10^{−7}H/m); - h—fabric thickness [m]
- d—diameter of the metallic yarn [m]
- D—equivalent diameter of the electric conductor [m]
- r—distance between conductive yarns [m]
- t—thickness of the copper coating [m]
- f—frequency of electromagnetic (EM) field [Hz]

_{grid}, the model related to the woven fabrics with inserted metallic yarns, the following equation applies (4):

- A
_{a}= attenuation introduced by a particular discontinuity, dB - R
_{a}= aperture single reflection loss, dB - B
_{a}= multiple reflection correction term, dB - K
_{1}= correction term to account for the number of like discontinuities, dB - K
_{2}= low-frequency correction term to account for skin depth, dB - K
_{3}= correction term to account for the coupling between adjacent holes, dB

- h—fabric thickness (depth of opening) [m]
- r = distance between conductive yarns (width of the rectangular opening perpendicular to E-field) [m]

- S—the area of each hole (sq cm)
- n—number of holes/sq cm

_{y}is a property of the yarn. The skin depth of the yarn δ

_{y}has the following electric parameters:

_{we}= fabric density in yarns/100 mm.

_{layer}, the model related to the shielding of the copper coating was given by the general expression of the impedance method according to [13]:

- δ
_{m}—skin depth of copper coated fabric with inserted metallic yarns [m]; - γ—propagation constant, α—attenuation constant, β—phase constant.
- $\underset{\_}{\gamma}=\alpha =j\beta =\sqrt{j\omega {\mu}_{m}\left({\sigma}_{m}+{j\omega \epsilon}_{m}\right)}$; for metals, due to σ >> ωε, $\underset{\_}{\gamma}=\sqrt{j\omega {\mu}_{m}{\sigma}_{m}}$ or
- $\underset{\_}{\gamma}=\left(1+j\right)\sqrt{\pi f{\mu}_{m}{\sigma}_{m}}$, then $\alpha =\beta =\sqrt{\pi f{\mu}_{m}{\sigma}_{m}}$;

_{0}):

- ω = 2πf—angular frequency

_{m}>> ωε. This condition is verified for the sample with lowest electric conductivity (F1) σ

_{m}= 45.60 S/m (Table 3) and ωε

_{0}= 0.0556 S/m for f = 1 GHz. Hence, the condition σ >> ωε is valid for all samples. The shield impedance can be written as:

_{m}, the modulus of shield impedance is:

## 5. Discussion

- -
- -
- -
- -
- The impedance method for multiple shields [19].

_{y}) and the skin depth of the fabric material (δ

_{m}). Both electrical parameters for the skin depth (electric conductivity and magnetic permeability) were measured and calculated in the first phase for the metallic yarns and the coated fabrics. The geometric parameters with high sensitivity were the thickness of the fabric and the diameter of the metallic yarn. The equivalent diameter of the two metallic yarns was computed as the diameter of the circle having the same area as the resulting ellipse formed by the two adjacent metallic yarns in the fabric structure. The distance between the yarns was considered for computing the diameter of the ellipse, which was given by the fabric density (d

_{w}).

- -
- Electric conductivity and magnetic permeability of the metallic yarns;
- -
- Optical diameter of the metallic yarns and equivalent diameter of the electric conductor;
- -
- Distance between metallic yarns of the woven fabric, depending on float repeat and weave;
- -
- Electric conductivity and magnetic permeability of the fabric;
- -
- Fabric thickness;
- -
- Thickness of the plasma coated layer.

_{grid}and the additional EMSE

_{layer}relation, with differences between the modelled and measured values less than 5 dB, as shown in Figure 19.

_{grid}underestimates the measured values, a fact which could be explained by the two parameters with high sensitivity of the model—the electric conductivity and the equivalent diameter of the silver yarn. The electrical linear resistance of the silver yarn presented different values for different measurements, a fact explainable by its non-homogenous structure and the general terms of its specification (R

_{l}< 1.5 kΩ/m) [25]. The measured value for silver yarn conductivity introduced into the model is a potential factor of underestimated values of EMSE

_{grid}relation.

^{5}to 10

^{7}Hz, which could be explained by the low values of the EMSE

_{layer}model in case of 10

^{3}nanometer values: 1200 nm (F4) and 1750 nm (F5). On the other hand, the EMSE

_{layer}model has significant increasing values for 5600 nm (F6) and 10,000 nm (F7), which makes that EMSE

_{total}reaches the measured values for F6 and F7, as shown in Figure 20. These results show that the steady increase of the fabric conductivity upon copper coating, of 3.2 times for F6 and 3.6 times for F7 with respect to the uncoated fabric, plays an important role in the model of the EMSE

_{layer}. These facts suggest a significant role played by the conductivity of the components in the model. One has to consider that this type of composite EM shield is quite difficult to model and that the proposed relation of EMSE includes all the parameters of the electric structures of this composite shield.

## 6. Conclusions

_{grid}and EMSE

_{layer}, and the obtained values were computed to model the shielding effectiveness of the fabrics with inserted conductive yarns and conductive coatings. The approach of modelling is meant to be able to estimate the property of EMSE in the design phase of the textile shield. Although there are still differences between calculated and measured results, it is considered that the analytic model based on adding the particular contribution to EMSE of the metallic grid and of the metallic coating gives a valuable guidance when designing this type of textile shield.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**(

**a**) Macroscopic aspect and (

**b**) optical microscope image at magnification 50× for the woven cotton fabric with inserted silver yarns and copper coating of 5600 nm—F6.

**Figure 7.**SEM image of fabric with inserted silver yarns and copper coating of 5600 nm F6. (

**a**) (2000×) and (

**b**) (8000×).

**Figure 10.**Dependence of the electrical conductivity of the fabrics with inserted silver yarns on the thickness of copper layer. The dot curve is just for eye guiding for the obtained trend.

**Figure 14.**Calculated (

**red**) and measured (

**blue**) values for F2 (st. steel yarns) and 1200 nm copper coating.

**Figure 16.**Calculated (

**red**) and measured (

**blue**) values for F4 (silver yarns) and 1200 nm copper coating.

**Figure 17.**Calculated (

**red**) and measured (

**blue**) values for F6 (silver yarns) and 5600 nm copper coating.

**Figure 18.**Calculated (

**red**) and measured (

**blue**) values for F7 (silver yarns) and 10,000 nm copper coating.

**Figure 19.**Difference between measured and calculated values for fabrics with stainless steel yarns and copper coating.

**Figure 20.**Difference between measured and calculated values for fabrics with silver yarns and copper coating.

Parameters/Yarns | Raw Material | Linear Density | Linear Electric Resistance, R _{l} [Ω/m] * | Linear Electric Conductivity, σ _{y} [S/m] * | Relative Magnetic Permeability, μ _{ry} (according to [16]) | Optical Diameter, d [μm] |
---|---|---|---|---|---|---|

M1 | 100% Cotton, spun yarn | Nm 50/2 | - | 0 | 1 | 293 |

M2 | 80% Cotton, 20% stainless steel fibers, (Bekinox BK50/2) | Nm 50/2 | 2200 | 7769 | 8 | 273 |

M3 | Silver coated PA yarn, (Shieldtex 117/17 dtex) | 140 × 2 dtex | 220 | 121842 | 1 | 218 |

Properties (Standard)/Fabric Samples | Yarn Type | Float Repeat SR6431:2012 | Fabric Density [no·yarns/10 cm] EN1049-2:2000 | Distance between Conductive Yarns Warp/Weft, r [mm] | Fabric Thickness, h [mm] ISO5084:2001 | Specific Mass, [g/m ^{2}]EN12127:2003 | ||
---|---|---|---|---|---|---|---|---|

Warp | Weft | Warp, d_{wa} | Weft, d_{we} | |||||

F1 | M1, M2 | 6:2 | 5:2 | 168 | 150 | 5 | 0.532 | 129 |

F3 | M1, M3 | 6:2 | 5:2 | 168 | 150 | 5 | 0.490 | 118 |

Sample | Shape | Dimensions (a/b/h) [mm] | R_{measured} − R_{electrodes} = R_{w}[Ω] | Conductivity, σ _{m}[S/m] |
---|---|---|---|---|

F1 | Circular | 20/44/0.53 | 5.195 | 45.60 |

F2 | Circular | 20/44/0.53 | 1.835 | 129.09 |

F3 | Circular | 20/44/0.49 | 0.435 | 589.02 |

F4 | Circular | 20/44/0.49 | 0.255 | 1004.8 |

F5 | Circular | 20/44/0.49 | 0.185 | 1385.00 |

F6 | Circular | 20/44/0.50 | 0.133 | 1887.98 |

F7 | Circular | 20/44/0.51 | 0.115 | 2140.67 |

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**MDPI and ACS Style**

Radulescu, I.R.; Surdu, L.; Scarlat, R.; Constantin, C.; Mitu, B.; Morari, C.; Costea, M.
Modelling the Woven Structures with Inserted Conductive Yarns Coated with Magnetron Plasma and Testing Their Shielding Effectiveness. *Textiles* **2021**, *1*, 4-20.
https://doi.org/10.3390/textiles1010002

**AMA Style**

Radulescu IR, Surdu L, Scarlat R, Constantin C, Mitu B, Morari C, Costea M.
Modelling the Woven Structures with Inserted Conductive Yarns Coated with Magnetron Plasma and Testing Their Shielding Effectiveness. *Textiles*. 2021; 1(1):4-20.
https://doi.org/10.3390/textiles1010002

**Chicago/Turabian Style**

Radulescu, Ion Razvan, Lilioara Surdu, Razvan Scarlat, Catalin Constantin, Bogdana Mitu, Cristian Morari, and Marian Costea.
2021. "Modelling the Woven Structures with Inserted Conductive Yarns Coated with Magnetron Plasma and Testing Their Shielding Effectiveness" *Textiles* 1, no. 1: 4-20.
https://doi.org/10.3390/textiles1010002