# E-Textile Embroidered Metamaterial Transmission Line for Signal Propagation Control

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## Abstract

**:**

## 1. Introduction

## 2. Metamaterial E-Textile Design and Electrical Circuit Model

_{r}= 1.2, and loss tangent tan δ = 0.0013. The fabric structure was a non-woven structure with a 100% polyester (PES) composition. This fabric had been selected due to its durability and resistance. In fact, these textile substrates are resistant to tearing and humidity, and they offer some key advantages, including durability, chemical moisture resistance, and heat stability. The weight is 211 g/m

^{2}, and the structure is a double-sided needle punching. The ground plane had been chosen as a homogeneous uniform commercial WE-CF adhesive copper sheet layer (constant thickness t = 35 µm). Figure 1 illustrates the transmission line basic model, the embroidered e-textile (microstrip width W = 5 mm and length L = 77 mm), and the simulated and experimental S-parameters. The insertion losses (S21) and return losses (S11) were tested up to 14 GHz by means of a microwave analyzer, N9916A FieldFox (Keysight, Santa Rosa, CA, USA), operating as a vector network analyzer. At 3 GHz, the maximum frequency limit of UHF, a good matching level for practical applications was achieved, with acceptable losses (lower than 3.5 dB). Losses became higher than 10 dB at frequencies beyond 8 GHz. This effect is explained by the discontinuity of the embroidered stitches, as well as for the thread ohmic losses and the impedance of the transmission line equivalent inductance at higher frequencies. Furthermore, for UHF applications, we determined a maximum attenuation of Att = 0.45 dB/cm, and this microstrip conventional e-textile was considered a test reference. The details of the conductive thread and embroidery process are provided below.

_{1}= 25 mm, l

_{2}= 22 mm, g = 100 µm, s = 1 mm, W

_{1}= 1.6 mm (the width of SRR), and W

_{2}= 5 mm (the width of the transmission line). Again, the ground plane has been chosen as a homogeneous uniform commercial WE-CF adhesive copper sheet layer (constant thickness t = 35 µm).

## 3. Metamaterial E-Textile Theoretical Circuit Analysis

_{1}and W

_{2}, separated by a gap, g, between them. It was assumed that the mutual inductance and capacitance between the lines was the same as that between symmetrical lines of width (W

_{1}+ W

_{2})/2. By using the even- and odd-mode data of coupled symmetrical lines, the mutual inductance and mutual capacitance between the lines was computed, and it was assumed that the self-inductance and capacitance of line one in the presence of line two is the same as if line two had the same width as line one. The coupled transmission line and SRR were characterized through the even and odd characteristic impedance and electric length (Z

_{oe}, θ

_{oe}, and Z

_{oo}, θ

_{oo}, respectively). This implied the coexistence of two different modes with different phase velocities and propagation constants corresponding to the different effective relative permittivities. The even- and odd-mode characteristic impedances, Z

_{oe}and Z

_{oo}, were obtained from the expressions detailed in Reference [12]. The proposed MTM embroidered e-textile was modeled by means of the distributed equivalent circuit model shown in Figure 4a.

_{j}matrices, can be described using the following equations:

_{T}

_{1,2}is the ABCD matrix of the line of the ports,

_{C}is the ABCD matrix associated to the coupling between the host line and SRR, and

_{L}

_{1,2}is the ABCD matrix associated to the SRR line.

_{T}= 75.04 Ω, Z

_{t}= 75 Ω, Z

_{oe}= 123.72 Ω, Z

_{oo}= 29.04 Ω, θ

_{e}= 14.17, and θ

_{o}= 13.95, respectively. The result was used to calculate the network parameters of the coupled lines.

## 4. Metamaterial E-Textile Symmetrical Transmission Line Modelling

_{r1}= 6.3 pF, L

_{r1}= 1.65 nH, C

_{r2}= 4.03 pF, L

_{r2}= 4.3 nH, M = 0.57 nH, M′ = 0.09 nH.

_{r}= 1.2, and loss tangent tan δ = 0.0013.

## 5. Effects of Bending

_{21}parameters of an e-textile MTM-SRR under different bending radii were measured. It was observed that due to bending, the equivalent length of the proposed design changed and, hence, there were shifts in the resonant frequency. The more the prototype was bent, the more the resonant length was reduced, and so the resonant frequency got shifted up. This fact was evident from the experimental observations, as shown in Figure 6b. By changing the radius of bending from −90° to 90° (typical human arm radii range), the resonant frequency was shifted up 144 MHz for the felt substrate case.

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) The circuit representation of the stitched transmission line. (

**b**) Photograph of the embroidered design. (

**c**) Simulated and measured S-Parameters of stitched transmission line.

**Figure 2.**(

**a**) Layout of the e-textile transmission line loaded with one SRR. (

**b**) Lumped element circuit model that considers magnetic coupling between line and SRR.

**Figure 3.**(

**a**) Photograph of the embroidered design with satin pattern with 60 % density (top view) and ground implemented with WE-CF adhesive copper. (

**b**) S-parameter responses of the electromagnetic (EM) simulation, equivalent circuit model, and measurement of embroidered transmission line loaded with one SRR photograph of the embroidered design.

**Figure 4.**(

**a**) Schematic of proposed model of prototype with one embroidered SRR. (

**b**) S-parameter responses of the EM simulation, theoretical model, and measurement of embroidered transmission line loaded with one SRR.

**Figure 5.**(

**a**) Layout of transmission line loaded with symmetrical SRRs. (

**b**) Lumped element circuit model. (

**c**) Photograph of the embroidered design. (

**d**) S-parameter responses of the EM simulation, equivalent circuit model, and measurement of embroidered transmission line loaded with two symmetric SRRs.

**Figure 6.**(

**a**) Effect of bending with different curved angles. (

**b**) Resonant frequency of first prototype on the felt substrate.

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**MDPI and ACS Style**

Moradi, B.; Fernández-García, R.; Gil, I.
E-Textile Embroidered Metamaterial Transmission Line for Signal Propagation Control. *Materials* **2018**, *11*, 955.
https://doi.org/10.3390/ma11060955

**AMA Style**

Moradi B, Fernández-García R, Gil I.
E-Textile Embroidered Metamaterial Transmission Line for Signal Propagation Control. *Materials*. 2018; 11(6):955.
https://doi.org/10.3390/ma11060955

**Chicago/Turabian Style**

Moradi, Bahareh, Raul Fernández-García, and Ignacio Gil.
2018. "E-Textile Embroidered Metamaterial Transmission Line for Signal Propagation Control" *Materials* 11, no. 6: 955.
https://doi.org/10.3390/ma11060955