# E-Textile Metamaterials: Stop Band Pass Filter
## 2 Metamaterial E-Textile Design, Simulation, and Experimentation  
A microstrip line was designed with a 50 \(\Omega\) characteristic impedance to allow impedance matching. The substrate of the microstrip line was constructed with cotton, with a dielectric constant \(\varepsilon_{\text{r}}\) = 1.9, thickness h = 0.43 mm, and loss tangent tan \(\delta\) = 0.053. In this design, the adhesive copper sheet with constant thickness t = 35 \(\upmu\)m was chosen. Figure 2a depicts the prototype model and its dimensions, considering a microstrip width of W\({}_{2}\)= 5 mm and microstrip length of L = 77 mm. The manufactured embroidered e-textile MTM is shown in Figure 2b. Digitizer Ex software was used in order to convert the layout model to a stitch pattern. Then, for the manufacture of the prototype, a SINGER Futura XL-550 embroidery machine was used. The conductor thread that was selected for the stitches on cotton was a commercial Shieldlex 117/17 dex two-ply, for which the features were 99% pure silver-plated nylon yarn 140/17 dex with a linear resistance of less than 30 \(\Omega\)/cm [11; 12]. The prototype was sewn with two types of threads, with consideration of the mechanical limitations of the sewing machine, in which the conductive yarn was selected as bobbin thread and the sulky yarn was used as top thread. Figure 3 depicts the correspond circuit model of MTM that was loaded with four SRRs. Basically, an SRR behaves as an inductive-capacitive (LC) resonant circuit. In fact, let us consider M1 as the mutual inductance between adjacent rings and M2 as the mutual inductance between the host microstrip line and the SRRs. By considering the mathematical equations [15], the values equivalent circuit elements are calculated as follows: inductance \(L\) = 6.5 nH and capacitance C = 3 pF. In addition, \(L_{hr}\) corresponds to the intrinsic inductance of the microstrip line. The mutual inductances, \(M_{1}\) and \(M_{2}\), were calculated as 4.94 nH and 24.2 nH, respectively, by using the following equations [16]:  
\[M_{1}=\frac{\mu_{0}L_{1}}{2\pi}[0.4676+\frac{0.059w_{1}^{2}}{l_{1}^{2}}] \tag{1}\]  
\[M_{2}=\frac{\mu_{0}L_{1}}{2\pi}[0.4676+\frac{0.059(w_{1}+w_{2})^{2}}{l_{1}^{2 }}] \tag{2}\]  
Figure 2: Geometry of the SRRs coupled with the microstrip line (**a**). Photograph of the embroidered prototype (**b**). The proposed prototype was embroidered with a 60% density of satin pattern. The distance between the two needle penetrations in one side of the fabric was proportional to the stitch spacing. Scattering parameters (S11 and S21) plots of simulation and measurement are illustrated in Figure 4. If a minimum rejection level of \(-15\) dB in the stop band is assumed for this filter, the measured stop band extends from 2.7-GHz to 4.7 GHz. The simulated and experimental results present a good agreement with minor differences, due to possible mismatching in connectors and fabrication tolerances, with regard to the embroidery process. The notch bandwidth depends on the coupling of the SRRs and the main signal path implemented and between the top and ground plane. This coupling was mainly controlled by the gap between the microstrip line and SRRs and the thickness of the textile template. In order to prove the performance of the proposed stop band filter, a second filter with two SRRs was proposed, designed, and measured. Figure 5 shows the reflection coefficient response of the transmission line that was loaded with two SRRs. Figure 4: Comparative results between simulation and measurement S-parameter responses of the-transmission line loaded with four SRRs. Figure 3: Equivalent circuit model of microstrip line, loaded with four SRRs. In both cases, a deep rejection band can be observed. Figure 5 shows experimental S-parameter responses of the EM measurement of the embroidered transmission line loaded with two SRRs.